Eur. Phys. J. C (2019) 79:290 https://doi.org/10.1140/epjc/s10052-019-6757-9 Regular Article - Experimental Physics Measurement √ of the top quark mass in the t t̄ → lepton+jets channel from s = 8 TeV ATLAS data and combination with previous results ATLAS Collaboration CERN, 1211 Geneva 23, Switzerland Received: 4 October 2018 / Accepted: 6 March 2019 / Published online: 29 March 2019 © CERN for the benefit of the ATLAS collaboration 2019 Abstract The top quark mass is measured using a tem- these combinations, selections of measurements from all t t¯ plate method in the t t¯ → lepton + jets channel (lepton is e decay channels are used. The latest combinations per experi- or μ) using ATLAS data recorded in 2012 at the LHC. The ment are m top = 173.16 ± 0.57 (stat) ± 0.74 (syst) GeV by data were taken at a proton–proton centre-of-mass energy CDF [12], m top = 174.95 ± 0.40 (stat) ± 0.64 (syst) GeV √ of s = 8 TeV and correspond to an integrated lumi- by D0 [13], m top = 172.84 ± 0.34 (stat) ± 0.61 (syst) GeV nosity of 20.2 fb−1 . The t t¯ → lepton + jets channel is by ATLAS [14] and m top = 172.44 ± 0.13 (stat) ± characterized by the presence of a charged lepton, a neu- 0.47 (syst) GeV by CMS [10]. trino and four jets, two of which originate from bottom In this paper, an ATLAS measurement of m top in the quarks (b). Exploiting a three-dimensional template tech- t t¯ → lepton + jets channel is presented. The result is nique, the top quark mass is determined together with a obtained from pp collision data recorded in 2012 at a centre- √ global jet energy scale factor and a relative b-to-light-jet of-mass energy of s = 8 TeV with an integrated lumi- energy scale factor. The mass of the top quark is measured nosity of about 20.2 fb−1 . The analysis exploits the decay to be m top = 172.08 ± 0.39 (stat) ± 0.82 (syst) GeV. A t t¯ → W + W − bb̄ → νq q̄  bb̄, which occurs when one W combination with previous ATLAS m top measurements gives boson decays into a charged lepton ( is e or μ including m top = 172.69 ± 0.25 (stat) ± 0.41 (syst) GeV. τ → e, μ decays) and a neutrino (ν), and the other into a pair of quarks. In the analysis presented here, m top is obtained from the combined sample of events selected in the elec- 1 Introduction tron+jets and muon+jets final states. Single-top-quark events with the same reconstructed final states contain information The mass of the top quark m top is an important parameter of about the top quark mass and are therefore included as signal the Standard Model (SM). Precise measurements of m top pro- events. vide crucial information for global fits of electroweak param- The measurement uses a template method, where simu- eters [1–3] which help to assess the internal consistency of lated distributions are constructed for a chosen quantity sen- the SM and probe its extensions. In addition, the value of sitive to the physics parameter under study using a number of m top affects the stability of the SM Higgs potential, which discrete values of that parameter. These templates are fitted has cosmological implications [4–6]. to functions that interpolate between different input values of Many measurements of m top in each t t¯ decay chan- the physics parameter while fixing all other parameters of the nel were performed by the Tevatron and LHC collabora- functions. In the final step, an unbinned likelihood fit to the tions. The most precise measurements per experiment in observed data distribution is used to obtain the value of the the t t¯ → lepton + jets channel are m top = 172.85 ± physics parameter that best describes the data. In this proce- 0.71 (stat) ± 0.84 (syst) GeV by CDF [7], m top = 174.98 ± dure, the experimental distributions are constructed such that 0.58 (stat) ± 0.49 (syst) GeV by D0 [8], m top = 172.33 ± fits to them yield unbiased estimators of the physics param- 0.75 (stat) ± 1.03 (syst) GeV by ATLAS [9] and m top = eter used as input in the signal Monte Carlo (MC) samples. 172.35 ± 0.16 (stat) ± 0.48 (syst) GeV by CMS [10]. Com- Consequently, the top quark mass determined in this way cor- binations are performed, by either the individual experi- responds to the mass definition used in the MC simulation. ments, or by several Tevatron and LHC experiments [11]. In Because of various steps in the event simulation, the mass measured in this way does not necessarily directly coincide  e-mail: atlas.publications@cern.ch with mass definitions within a given renormalization scheme, 123 290 Page 2 of 51 Eur. Phys. J. C (2019) 79:290 e.g. the top quark pole mass. Evaluating these differences is netic field, electromagnetic and hadronic calorimeters, and a topic of theoretical investigations [15–19]. a muon spectrometer. The inner tracking detector covers the The measurement exploits the three-dimensional template pseudorapidity range |η| < 2.5. It consists of silicon pixel, fit technique presented in Ref. [9]. To reduce the uncertainty silicon microstrip, and transition radiation tracking detec- in m top stemming from the uncertainties in the jet energy tors. Lead/liquid-argon (LAr) sampling calorimeters provide scale (JES) and the additional b-jet energy scale (bJES), m top electromagnetic (EM) energy measurements with high gran- is measured together with the jet energy scale factor (JSF) and ularity. A hadronic (steel/scintillator-tile) calorimeter covers the relative b-to-light-jet energy scale factor (bJSF). Given the central pseudorapidity range (|η| < 1.7). The endcap the larger data sample than used in Ref. [9], the analysis is and forward regions are instrumented with LAr calorimeters optimized to reject combinatorial background arising from for both the EM and hadronic energy measurements up to incorrect matching of the observed jets to the daughters aris- |η| = 4.9. The muon spectrometer surrounds the calorime- ing from the top quark decays, thereby achieving a better ters and is based on three large air-core toroid superconduct- balance of the statistical and systematic uncertainties and ing magnets with eight coils each. Its bending power is 2.0 to reducing the total uncertainty. Given this new measurement, 7.5 T m. It includes a system of precision tracking chambers an update of the ATLAS combination of m top measurements and fast detectors for triggering. is also presented. A three-level trigger system was used to select events. This document is organized as follows. After a short The first-level trigger is implemented in hardware and used a description of the ATLAS detector in Sect. 2, the data and subset of the detector information to reduce the accepted rate simulation samples are discussed in Sect. 3. Details of the to at most 75 kHz. This is followed by two software-based event selection are given in Sect. 4, followed by the descrip- trigger levels that together reduced the accepted event rate to tion of the reconstruction of the three observables used in 400 Hz on average depending on the data-taking conditions the template fit in Sect. 5. The optimization of the event during 2012. selection using a multivariate analysis approach is presented in Sect. 6. The template fits are introduced in Sect. 7. The evaluation of the systematic uncertainties and their statistical 3 Data and simulation samples uncertainties are discussed in Sect. 8, and the measurement of m top is given in Sect. 9. The combination of this measure- The analysis is based on pp collision data recorded by ment with previous ATLAS results is discussed in Sect. 10 the ATLAS detector in 2012 at a centre-of-mass energy of √ and compared with measurements of other experiments. The s = 8 TeV. The integrated luminosity is 20.2 fb−1 with summary and conclusions are given in Sect. 11. Additional an uncertainty of 1.9% [21]. The modelling of top quark information about the optimization of the event selection and pair (t t¯) and single-top-quark signal events, as well as most on specific uncertainties in the new measurement of m top in background processes, relies on MC simulations. For the sim- the t t¯ → lepton + jets channel are given in Appendix A, ulation of t t¯ and single-top-quark events, the Powheg- Box while Appendix B contains information about various com- v1 [22–24] program was used. Within this framework, the binations performed, together with comparisons with results simulations of the t t¯ [25] and single-top-quark production from other experiments. in the s- and t-channels [26] and the W t-channel [27] used matrix elements at next-to-leading order (NLO) in the strong coupling constant αS with the NLO CT10 [28] parton dis- 2 The ATLAS experiment tribution function (PDF) set and the h damp parameter2 set to infinity. Using m top and the top quark transverse momentum The ATLAS experiment [20] at the LHC is a multipurpose pT for the underlying leading-order Feynman diagram, the particle detector with a forward–backward symmetric cylin- dynamic  factorization and renormalization scales were set drical geometry and a near 4π coverage in the solid angle.1 to m 2top + pT2 . The Pythia (v6.425) program [29] with the It consists of an inner tracking detector surrounded by a P2011C [30] set of tuned parameters (tune) and the corre- thin superconducting solenoid providing a 2 T axial mag- sponding CTEQ6L1 PDFs [31] provided the parton shower, hadronization and underlying-event modelling. 1 ATLAS uses a right-handed coordinate system with its origin at the For m top hypothesis testing, the t t¯ and single-top-quark nominal interaction point (IP) in the centre of the detector and the z- event samples were generated with five different assumed axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle 2 The h damp parameter controls the transverse momentum pT of the around the z-axis. The pseudorapidity is defined in terms of the polar first additional emission beyond the leading-order Feynman diagram in angle θas η = − ln tan(θ/2). Angular distance is measured in units of the parton shower and therefore regulates the high- pT emission against R ≡ ( η)2 + ( φ)2 . which the t t¯ system recoils. 123 Eur. Phys. J. C (2019) 79:290 Page 3 of 51 290 values of m top in the range from 167.5 to 177.5 GeV in steps cross-section, taken to be 73 mb [21]. Finally, the simulation of 2.5 GeV. The integrated luminosity of the simulated t t¯ sample is reweighted such as to match the pile-up observed sample with m top = 172.5 GeV is about 360 fb−1 . Each of in data. these MC samples is normalized according to the best avail- A simulation [54] of the ATLAS detector response based able cross-section calculations. For m top = 172.5 GeV, the on Geant4 [55] was performed on the MC events. This sim- t t¯ cross-section is σt t¯ = 253+13 −15 pb, calculated at next-to- ulation is referred to as full simulation. The events were then next-to-leading order (NNLO) with next-to-next-to-leading processed through the same reconstruction software as the logarithmic soft gluon terms [32–36] with the Top++ 2.0 data. A number of samples used to assess systematic uncer- program [37]. The PDF- and αS -induced uncertainties in this tainties were produced bypassing the highly computing- cross-section were calculated using the PDF4LHC prescrip- intensive full Geant4 simulation of the calorimeters. They tion [38] with the MSTW2008 68% CL NNLO PDF [39,40], were produced with a faster version of the simulation [56], CT10 NNLO PDF [28,41] and NNPDF2.3 5f FFN PDF [42] which retained the full simulation of the tracking but used and were added in quadrature with the uncertainties obtained a parameterized calorimeter response based on resolution from the variation of the factorization and renormalization functions measured in full simulation samples. This simu- scales by factors of 0.5 and 2.0. The cross-sections for single- lation is referred to as fast simulation. top-quark production were calculated at NLO and are σt = 87.8 +3.4 −1.9 pb [43], σW t = 22.4 ± 1.5 pb [44] and σs = 5.6 ± 0.2 pb [45] in the t-, the W t- and the s-channels, respectively. 4 Object reconstruction, background estimation and The Alpgen (v2.13) program [46] interfaced to the event preselection Pythia6 program was used for the simulation of the pro- duction of W ± or Z bosons in association with jets. The The reconstructed objects resulting from the top quark pair CTEQ6L1 PDFs and the corresponding AUET2 tune [47] decay are electron and muon candidates, jets and missing were used for the matrix element and parton shower set- transverse momentum (E Tmiss ). In the simulated events, cor- tings. The W +jets and Z +jets events containing heavy- rections are applied to these objects based on detailed data- flavour (HF) quarks (W bb+jets, Z bb+jets, W cc+jets, to-simulation comparisons for many different processes, so Z cc+jets, and W c+jets) were generated separately using as to match their performance in data. leading-order (LO) matrix elements with massive bottom and charm quarks. Double-counting of HF quarks in the matrix 4.1 Object reconstruction element and the parton shower evolution was avoided via a HF overlap-removal procedure that used the R between Electron candidates [57] are required to have a transverse the additional heavy quarks as the criterion. If the R was energy of E T > 25 GeV and a pseudorapidity of the cor- smaller than 0.4, the parton shower prediction was taken, responding EM cluster of |ηcluster | < 2.47 with the transi- while for larger values, the matrix element prediction was tion region 1.37 < |ηcluster | < 1.52 between the barrel and used. The Z +jets sample is normalized to the inclusive the endcap calorimeters excluded. Muon candidates [58] are NNLO calculation [48]. Due to the large uncertainties in required to have transverse momentum pT > 25 GeV and the overall W +jets normalization and the flavour compo- |η| < 2.5. To reduce the contamination by leptons from HF sition, both are estimated using data-driven techniques as decays inside jets or from photon conversions, referred to described in Sect. 4.2. Diboson production processes (W W , collectively as non-prompt (NP) leptons, strict isolation cri- W Z and Z Z ) were simulated using the Alpgen program teria are applied to the amount of activity in the vicinity of with CTEQ6L1 PDFs interfaced to the Herwig (v6.520) [49] the lepton candidate [57–59]. and Jimmy (v4.31) [50] programs. The samples are normal- Jets are built from topological clusters of calorimeter ized to their predicted cross-sections at NLO [51]. cells [60] with the anti-kt jet clustering algorithm [61] using All samples were simulated taking into account the effects a radius parameter of R = 0.4. The clusters and jets are cali- of multiple soft pp interactions (pile-up) that are present in brated using the local cluster weighting (LCW) and the global the 2012 data. These interactions were modelled by overlay- sequential calibration (GSC) algorithms, respectively [62– ing simulated hits from events with exactly one inelastic colli- 64]. The subtraction of the contributions from pile-up is sion per bunch crossing with hits from minimum-bias events performed via the jet area method [65]. Jets are calibrated produced with the Pythia (v8.160) program [52] using the using an energy- and η-dependent simulation-based scheme A2 tune [53] and the MSTW2008 LO PDF. The number with in situ corrections based on data [63]. Jets originat- of additional interactions is Poisson-distributed around the ing from pile-up interactions are identified via their jet ver- mean number of inelastic pp interactions per bunch crossing tex fraction (JVF), which is the pT fraction of associated μ. For a given simulated hard-scatter event, the value of μ tracks stemming from the primary vertex. The requirement depends on the instantaneous luminosity and the inelastic pp JVF > 0.5 is applied solely to jets with pT < 50 GeV 123 290 Page 4 of 51 Eur. Phys. J. C (2019) 79:290 and |η| < 2.4 [65]. Finally, jets are required to satisfy performed in events with exactly two jets and at least one b- pT > 25 GeV and |η| < 2.5. tagged jet. Further details are given in Ref. [73]. The Z +jets Muons reconstructed within a R = 0.4 cone around and diboson background processes are normalized to their the axis of a jet with pT > 25 GeV are excluded from the predicted cross-sections as described in Sect. 3. analysis. In addition, the closest jet within a R = 0.2 cone around an electron candidate is removed, and then electrons 4.3 Event preselection within a R = 0.4 cone around any of the remaining jets are discarded. Triggering of events is based solely on the presence of a single The identification of jets containing reconstructed b- electron or muon, and no information from the hadronic final hadrons, called b-tagging, is used for event reconstruction state is used. A logical OR of two triggers is used for each and background suppression. In the following, irrespective of the t t¯ → electron + jets and t t¯ → muon + jets channels. of their origin, jets tagged by the b-tagging algorithm are The triggers with the lower thresholds of 24 GeV for electrons referred to as b-tagged jets, whereas those not tagged are or muons select isolated leptons. The triggers with the higher referred to as untagged jets. Similarly, whether they are thresholds of 60 GeV for electrons and 36 GeV for muons do tagged or not, jets containing b-hadrons in simulation are not include an isolation requirement. The further selection referred to as b-jets and those containing only lighter-flavour requirements closely follow those in Ref. [9] and are hadrons from u, d, c, s-quarks, or originating from gluons, are collectively referred to as light-jets. The working point of • Events are required to have at least one primary vertex the neural-network-based MV1 b-tagging algorithm [66] cor- with at least five associated tracks. Each track needs to responds to an average b-tagging efficiency of 70% for b-jets have a minimum pT of 0.4 GeV. For events with more in simulated t t¯ events and rejection factors of 5 for jets con- than one primary vertex, the one with the largest pT2 taining a c-hadron and 140 for jets containing only lighter- is chosen as the vertex from the hard scattering. flavour hadrons. To match the b-tagging performance in the • The event must contain exactly one reconstructed charged data, pT - and η-dependent scale factors, obtained from dijet lepton, with E T > 25 GeV for electrons and pT > and t t¯ → dilepton events, are applied to MC jets depending 25 GeV for muons, that matches the charged lepton that on their generated quark flavour, as described in Refs. [66– fired the corresponding lepton trigger. 68]. • In the t t¯ → muon + jets channel, E Tmiss > 20 GeV and The missing transverse momentum E Tmiss is the absolute E Tmiss + m TW > 60 GeV are required.3 − → value of the vector E T miss calculated from the negative vec- • In the t t¯ → electron + jets channel, more stringent torial sum of all transverse momenta. The vectorial sum takes requirements on E Tmiss and m TW are applied because of the into account all energy deposits in the calorimeters projected higher level of NP/fake-lepton background. The require- onto the transverse plane. The clusters are corrected using ments are E Tmiss > 30 GeV and m TW > 30 GeV. the calibrations that belong to the associated physics object. • The presence of at least four jets with pT > 25 GeV and Muons are included in the calculation of the E Tmiss using their |η| < 2.5 is required. momentum reconstructed in the inner tracking detectors [69]. • The presence of exactly two b-tagged jets is required. The resulting event sample is statistically independent of the 4.2 Background estimation ones used for the measurement of m top in the t t¯ → dilepton √ and t t¯ → all jets channels at s = 8 TeV [14,74]. The The contribution of events falsely reconstructed as t t¯ → observed number of events in the data after this preselection lepton + jets events due to the presence of objects misiden- and the expected numbers of signal and background events tified as leptons (fake leptons) and NP leptons originat- corresponding to the same integrated luminosity as the data ing from HF decays, is estimated from data using the are given in Table 1. For all predictions, the uncertainties are matrix-method [70]. The technique employed uses η- and estimated as the sum in quadrature of the statistical uncer- pT -dependent efficiencies for NP/fake-leptons and prompt- tainty, the uncertainty in the integrated luminosity and all leptons. They are measured in a background-enhanced con- systematic uncertainties assigned to the measurement of m top trol region with low E Tmiss and from events with dilepton listed in Sect. 8, except for the PDF and pile-up uncertain- masses around the Z boson peak [71], respectively. For the ties, which are small. The normalization uncertainties listed W +jets background, the overall normalization is estimated from data. The estimate is based on the charge-asymmetry 3Here m TW is the transverse mass of the W boson, defined as method [72], relying on the fact that at the LHC more W +    − → − → than W − bosons are produced. In addition, a data-driven 2 pT, E Tmiss 1 − cos φ(, E T miss ) , where E T miss provides an esti- estimate of the W bb̄, W cc̄, W c and W +light-jet fractions is mate of the transverse momentum of the neutrino. 123 Eur. Phys. J. C (2019) 79:290 Page 5 of 51 290 Table 1 The observed numbers of events in data after the event pres- m reco top is used for the BW distributions describing the semi- election and the BDT selection (see Sect. 6). In addition, the expected leptonically and hadronically decaying top quarks and is fit- numbers of signal events for m top = 172.5 GeV and background events corresponding to the same integrated luminosity as the data are given. ted event-by-event. The top quark width varies with m reco top The uncertainties in the predicted number of events take into account the according to the SM prediction [3]. The TFs are derived statistical and systematic sources explained in Sect. 4.3. Two significant from the Powheg+Pythia t t¯ signal MC simulation sam- digits are used for the uncertainties in the predicted events ple at an input mass of m top = 172.5 GeV. They represent Selection Preselection BDT selection the experimental resolutions in terms of the probability that the observed energy at reconstruction level is produced by a Data 96105 38054 given parton-level object for the leading-order decay topol- t t¯ signal 85000 ± 10000 36100 ± 5500 ogy and in the fit constrain the variations of the reconstructed Single-top-quark signal 4220 ± 360 883 ± 85 objects. NP/fake leptons (data-driven) 700 ± 700 9.2 ± 9.2 The input objects to the event likelihood are the recon- W +jets (data-driven) 2800 ± 700 300 ± 100 structed charged lepton, the missing transverse momentum Z +jets 430 ± 230 58 ± 33 and up to six jets. These are the two b-tagged jets and the four W W/W Z /Z Z 63 ± 32 7.0 ± 5.2 untagged jets with the highest pT . The x- and y-components Signal+background 93000 ± 10000 37300 ± 5500 of the missing transverse momentum are starting values for Expected background fraction 0.043 ± 0.012 0.010 ± 0.003 the neutrino transverse-momentum components, and its lon- Data/(signal+background) 1.03 ± 0.12 1.02 ± 0.15 gitudinal component pν,z is a free parameter in the kine- matic likelihood fit. Its starting value is computed from the W → ν mass constraint. If there are no real solutions for below are included for the predictions shown in this section, pν,z , a starting value of zero is used. If there are two real solu- but due to their small effect on the measured top quark mass tions, the one giving the largest likelihood value is taken. they are not included in the final measurement. Maximizing the event-by-event likelihood as a function of For the signal, the 5.7% uncertainty in the t t¯ cross-section m reco top establishes the best assignment of reconstructed jets to introduced in Sect. 3 and a 6.0% uncertainty in the single- partons from the t t¯ → lepton + jets decay. The maximiza- top-quark cross-section are used. The latter uncertainty is tion is performed by testing all possibilities for assigning obtained from the cross-section uncertainties given in Sect. 3 b-tagged jets to b-quark positions and untagged jets to light- and the fractions of the various single-top-quark produc- quark positions. With the above settings of the reconstruction tion processes after the selection requirements. The back- algorithm, compared with the settings4 used in Ref. [9], a ground uncertainties contain uncertainties of 48% in the nor- larger fraction of correct assignments of reconstructed jets to malization of the diboson and Z +jets production processes. partons from the t t¯ → lepton + jets decay is achieved. The These uncertainties are calculated using Berends–Giele scal- performance of the reconstruction algorithm is discussed in ing [75]. Assuming a top quark mass of m top = 172.5 GeV, Sect. 6. the predicted number of events is consistent within uncer- The value of m reco top obtained from the kinematic likelihood tainties with the number observed in the data. fit is used as the observable primarily sensitive to the under- lying m top . The invariant mass of the hadronically decaying 5 Reconstruction of the three observables W boson m reco W , which is sensitive to the JES, is calculated from the assigned jets of the chosen permutation. Finally, an observable called Rbq reco , designed to be sensitive to the bJES, As in Ref. [9], a full kinematic reconstruction of the event is done with a likelihood fit using the KLFitter pack- is computed as the scalar sum of the transverse momenta of age [76,77]. The KLFitter algorithm relates the mea- the two b-tagged jets divided by the scalar sum of the trans- sured kinematics of the reconstructed objects to the leading- verse momenta of the two jets associated with the hadronic order representation of the t t¯ system decay using t t¯ → W boson decay: νblep q1 q2 bhad . In this procedure, the measured jets corre- b spond to the quark decay products of the W boson, q1 and pTbhad + pTlep q2 , and to the b-quarks, blep and bhad , produced in the semi- reco Rbq = q q . pT1 + pT2 leptonic and hadronic top quark decays, respectively. The event likelihood is the product of Breit–Wigner (BW) distributions for the W bosons and top quarks and transfer 4 In Ref. [9] only four input jets were used. In addition, b-tagging functions (TFs) for the energies of the reconstructed objects efficiencies and rejection factors were used to favour permutations for which a b-tagged jet is assigned to a b-quark position and penalise those that are input to KLFitter. The W boson BW distribu- where a b-tagged jet is assigned to a light-quark position. However, the tions use the world combined values of the W boson mass latter permutations were still accepted whenever they resulted in the and decay width from Ref. [3]. A common mass parameter largest likelihood. 123 290 Page 6 of 51 Eur. Phys. J. C (2019) 79:290 The values of m reco reco W and Rbq are computed from the jet four- parts which should be better measured and therefore lead vectors as given by the jet reconstruction instead of using the to smaller uncertainties. The optimization of the selection values obtained in the kinematic likelihood fit. This ensures is based on the multivariate BDT algorithm implemented in the maximum sensitivity to the jet calibration for light-jets the TMVA package [79]. The reconstruction-level objects and b-jets. are matched to the closest parton-level object within a R of Some distributions of the observed event kinematics after 0.1 for electrons and muons and 0.3 for jets. A matched object the event preselection and for the best permutation are shown is defined as a reconstruction-level object that falls within the in Fig. 1. Given the good description of the observed number relevant R of any parton-level object of that type, and a cor- of events by the prediction shown in Sect. 4.3 and that the rect match means that this generator-level object is the one measurement of m top is mostly sensitive to the shape of the it originated from. Due to acceptance losses and reconstruc- distributions, the comparison of the data with the predictions tion inefficiencies, not all reconstruction-level objects can is based solely on the distributions normalized to the num- successfully be matched to their parton-level counterparts. ber of events observed in data. The systematic uncertainty If any object cannot be unambiguously matched, the corre- assigned to each bin is calculated from the sum in quadra- sponding event is referred to as unmatched. The efficiency ture of all systematic uncertainties discussed in Sect. 4.3. for correctly matched events cm is the fraction of correctly Within uncertainties, the predictions agree with the observed matched events among all the matched events, and the selec- distributions in Fig. 1, which shows the transverse momen- tion purity πcm is the fraction of correctly matched events tum of the lepton, the average transverse momentum of the among all selected events, regardless of whether they could jets, the transverse momentum of the hadronically decaying be matched or not. top quark pT,had , the transverse momentum of the t t¯ system, The BDT algorithm is exploited to enrich the event sample the logarithm of the event likelihood of the best permuta- in events that have correct jet-to-parton matching by reduc- tion and the distance R of the two untagged jets q1 and q2 ing the remainder, i.e. the sum of incorrectly matched and assigned to the hadronically decaying W boson. The distri- unmatched events. Using the preselection, the BDT algo- butions of transverse momenta predicted by the simulation, rithm is trained on the simulated t t¯ signal sample with e.g. the pT,had distribution shown in Fig. 1c, show a slightly m top = 172.5 GeV. Many variables were studied and only different trend than observed in data, with the data being those with a separation5 larger than 0.1% are used in the softer. This difference is fully covered by the uncertainties. training. The 13 variables chosen for the final training are This trend was also observed in Ref. [14] for the pT,b distri- given in Table 2. For all input variables to the BDT algo- bution in the t t¯ → dilepton channel and in the measurement rithm, good agreement between the MC predictions and the of the differential t t¯ cross-section in the lepton+jets chan- data is found, as shown in Fig. 1e, f for the examples of the nel [78]. likelihood of the chosen permutation and the opening angle In anticipation of the template parameterization described R of the two untagged jets associated with the W boson in Sect. 7, the following restrictions on the three observ- decay. These two variables also have the largest separation ables are applied: 125 ≤ m reco top ≤ 200 GeV, 55 ≤ m W ≤ reco for the correctly matched events and the remainder. The cor- 110 GeV, and 0.3 ≤ Rbq ≤ 3. Since in this analysis only reco responding distributions for the two event classes are shown the best permutation is considered, events that do not pass in Fig. 2a, b. These figures show a clear separation of the these requirements are rejected. This removes events in the correctly matched events and the remainder. Half the simu- tails of the three distributions, which are typically poorly lation sample is used to train the algorithm and the other half reconstructed with small likelihood values and do not contain to assess its performance. The significant difference between significant information about m top . The resulting templates the distributions of the output value rBDT of the BDT classi- have simpler shapes, which are easier to model analytically fier between the two classes of events in Fig. 2c shows their with fewer parameters. The preselection with these additional efficient separation by the BDT algorithm. In addition, rea- requirements is referred to as the standard selection to distin- sonable agreement is found for the rBDT distributions in the guish it from the boosted decision tree (BDT) optimization statistically independent test and training samples. The rBDT for the smallest total uncertainty in m top , discussed in the distributions in simulation and data in Fig. 2d agree within next section. the experimental uncertainties. The above findings justify the application of the BDT approach to the data. The full m top analysis detailed in Sect. 8 is performed, 6 Multivariate analysis and BDT event selection except for the evaluation of the small method and pile- up uncertainties described in Sect. 8, for several minimum For the measurement of m top , the event selection is refined enriching the fraction of events with correct assignments of 5The chosen definition of the separation is given in Eq. (1) of the reconstruction-level objects to their generator-level counter- TMVA manual [79]. 123 Eur. Phys. J. C (2019) 79:290 Page 7 of 51 290 18000 Events / 5 GeV Events / 5 GeV Data Z+jets 18000 Data Z+jets 16000 tt, mtop=172.5 GeV WW/WZ/ZZ tt, mtop=172.5 GeV WW/WZ/ZZ Single top NP/fake leptons 16000 Single top NP/fake leptons 14000 W+jets Uncertainty W+jets Uncertainty 14000 12000 ATLAS ATLAS 12000 10000 s=8 TeV, 20.2 fb-1 s=8 TeV, 20.2 fb-1 10000 8000 8000 6000 6000 4000 4000 2000 2000 0 0 Data/MC Data/MC 1.2 1.2 1 1 0.8 0.8 40 60 80 100 120 140 160 180 200 40 60 80 100 120 140 160 Lepton p [GeV] Average jet p [GeV] T T (a) Transverse momentum of the lepton (b) Average transverse momentum of jets Events / 5 GeV Events / 10 GeV Data Z+jets 24000 Data Z+jets 5000 tt, mtop=172.5 GeV WW/WZ/ZZ 22000 tt, mtop=172.5 GeV WW/WZ/ZZ Single top NP/fake leptons 20000 Single top NP/fake leptons W+jets Uncertainty W+jets Uncertainty 4000 18000 ATLAS 16000 ATLAS 3000 s=8 TeV, 20.2 fb-1 14000 s=8 TeV, 20.2 fb-1 12000 10000 2000 8000 6000 1000 4000 2000 0 0 Data/MC Data/MC 1.2 1.2 1 1 0.8 0.8 50 100 150 200 250 300 350 400 0 20 40 60 80 100 120 140 160 180 Hadronic Top p [GeV] p (tt) [GeV] T T (c) Transverse momentum of the hadronically decay- (d) Transverse momentum of the t t¯ system ing top quark Events / 0.22 Events Data Z+jets 14000 Data Z+jets 16000 tt, mtop=172.5 GeV WW/WZ/ZZ tt, mtop=172.5 GeV WW/WZ/ZZ 14000 Single top NP/fake leptons 12000 Single top NP/fake leptons W+jets Uncertainty W+jets Uncertainty 12000 10000 ATLAS ATLAS 10000 s=8 TeV, 20.2 fb-1 s=8 TeV, 20.2 fb-1 8000 8000 6000 6000 4000 4000 2000 2000 0 0 Data/MC Data/MC 1.2 1.2 1 1 0.8 0.8 −80 −75 −70 −65 −60 −55 −50 −45 −40 −35 −30 0 1 2 3 4 5 ln L ΔR(q,q) (e) Logarithm of the event likelihood (f) ΔR of jets from the W boson decay Fig. 1 Distributions for the events passing the preselection. The data ton, b shows the average transverse momentum of the jets, c shows the are shown together with the signal-plus-background prediction, nor- transverse momentum of the hadronically decaying top quark, d shows malized to the number of events observed in the data. The hatched area the transverse momentum of the t t¯ system, e shows the logarithm of the is the uncertainty in the prediction as described in the text. The right- event likelihood of the best permutation and f shows the distance R most bin contains all entries with values above the lower edge of this of the two untagged jets q1 and q2 from the hadronically decaying W bin, similarly the leftmost bin contains all entries with values below the boson upper edge of this bin. a shows the transverse momentum of the lep- 123 290 Page 8 of 51 Eur. Phys. J. C (2019) 79:290 Table 2 The input variables to the BDT algorithm sorted by their sep- the m top analysis (within the ranges of the template fit) in aration Fig. 4b–d. The sharp edge observed at 30 GeV in Fig. 4a Separation (%) Description originates from the different selection requirements for the W boson transverse mass in the electron+jets and muon+jets 31 Logarithm of the event likelihood of the best permutation, ln L final states. 13 R of the two untagged jets q1 and q2 from the hadronically decaying W boson, R(q, q) 5.0 pT of the hadronically decaying W boson 7 Template fit 4.3 pT of the hadronically decaying top quark 4.2 Relative event probability of the best permutation This analysis uses a three-dimensional template fit technique 2.0 pT of the reconstructed t t¯ system which determines m top together with the jet energy scale fac- 1.7 pT of the semi-leptonically decaying top quark tors JSF and bJSF. The aim of the multi-dimensional fit to 1.2 Transverse mass of the leptonically decaying W the data is to measure m top and, at the same time, to absorb boson the mean differences between the jet energy scales observed 0.3 pT of the leptonically decaying W boson in data and MC simulated events into jet energy scale fac- 0.3 Number of jets tors. By using JSF and bJSF, most of the uncertainties in 0.2 R of the reconstructed b-tagged jets m top induced by JES and bJES uncertainties are transformed 0.2 Missing transverse momentum into additional statistical components caused by the higher 0.1 pT of the lepton dimensionality of the fit. This method reduces the total uncer- tainty in m top only for sufficiently large data samples. In this case, the sum in quadrature of the additional statistical uncertainty in m top due to the JSF (or bJSF) fit and the resid- requirements on rBDT in the range of [−0.10, 0.05] in steps ual JES-induced (or bJES-induced) systematic uncertainty of 0.05 to find the point with smallest total uncertainty. The is smaller than the original JES-induced (or bJES-induced) total uncertainty in m top together with the various classes uncertainty in m top . This situation was already realized for √ of uncertainty sources as a function of rBDT evaluated in the the s = 7 TeV data analysis [9] and is even more advan- √ BDT optimization are shown in Fig. 3. The minimum require- tageous for the much larger data sample of the s = 8 TeV ment rBDT = −0.05 provides the smallest total uncertainty in data analysis. Since JSF and bJSF are global factors, they do m top . The resulting numbers of events for this BDT selection not completely absorb the JES and bJES uncertainties which are given in Table 1. Compared with the preselection, cm is have pT - and η-dependent components. increased from 0.71 to 0.82, albeit at the expense of a signif- For simultaneously determining m top , JSF and bJSF, tem- icant reduction in the number of selected events. The purity plates are constructed from the MC samples. Templates of πcm is increased from 0.28 to 0.41. In addition, the intrinsic m reco top are constructed with several input m top values used in resolution in m top of the remaining event sample is improved, the range 167.5–177.5 GeV and for the sample at m top = i.e. the statistical uncertainty in m top in Fig. 3 is almost con- 172.5 GeV also with independent input values for JSF and stant as a function of rBDT ; in particular, it does not scale with bJSF in the range 0.96–1.04 in steps of 0.02. Statistically the square root of the number of events retained. For the signal independent MC samples are used for different input values sample with m top = 172.5 GeV, the template fit functions for of m top . The templates with different values of JSF and bJSF the standard selection and the BDT selection, together with are constructed by scaling the energies of the jets appropri- their ratios, are shown in Fig. 12 in Appendix A. The shape of ately. In this procedure, JSF is applied to all jets, while bJSF the signal modelling uncertainty derives from a sum of con- is solely applied to b-jets according to the generated quark tributions with different shapes. The curves from the signal flavour. The scaling is performed after the various correction Monte Carlo generator and colour reconnection uncertain- steps of the jet calibration but before the event selection. This ties decrease, the one from the underlying event uncertainty procedure results in different events passing the BDT selec- is flat, the one from the initial- and final-state QCD radiation tion from one energy scale variation to another. However, has a valley similar to the sum of all contributions, and finally many events are in all samples, resulting in a large statisti- the one from the hadronization uncertainty rises. cal correlation of the samples with different jet scale factors. Some distributions of the observed event kinematics after Similarly, templates of m reco reco W and Rbq are constructed with the BDT selection are shown in Fig. 4. Good agreement the above listed input values of m top , JSF and bJSF. between the MC predictions and the data is found, as seen Independent signal templates are derived for the three for the preselection in Fig. 1. The examples shown are the observables for all m top -dependent samples, consisting of observed W boson transverse mass for the semi-leptonically the t t¯ signal events and single-top-quark production events. decaying top quark in Fig. 4a and the three observables of This procedure is adopted because single-top-quark produc- 123 Eur. Phys. J. C (2019) 79:290 Page 9 of 51 290 Normalized events / 1.00 0.2 Normalized events / 0.22 0.3 ATLAS Simulation s = 8 TeV ATLAS Simulation s = 8 TeV 0.18 Correctly matched Correctly matched Incorrectly + unmatched 0.16 Incorrectly + unmatched 0.25 0.14 0.2 0.12 0.1 0.15 0.08 0.1 0.06 0.04 0.05 0.02 0 0 −80 −75 −70 −65 −60 −55 −50 −45 −40 −35 −30 0 1 2 3 4 5 ln L ΔR(q,q) (a) Logarithm of the event likelihood (b) ΔR of jets from the W boson decay Events / 0.02 Normalized events / 0.02 0.1 ATLAS Simulation s = 8 TeV Data Z+jets 7000 tt, mtop=172.5 GeV WW/WZ/ZZ Test samples Single top NP/fake leptons Training samples 6000 0.08 W+jets Uncertainty Correctly matched 5000 ATLAS P(χ2,ndf) = 0.021 0.06 Incorrectly + unmatched s=8 TeV, 20.2 fb-1 4000 P(χ2,ndf) = 0.74 0.04 3000 2000 0.02 1000 0 0 −0.6 −0.4 −0.2 0 0.2 0.4 Test - Train Data/MC 2 1.2 0 σ 1 −2 0.8 −0.6 −0.4 −0.2 0 0.2 0.4 −0.6 −0.4 −0.2 0 0.2 0.4 rBDT rBDT (c) BDT test and training samples (d) Data-to-simulation comparison for rBDT Fig. 2 Input and results of the BDT training on t t¯ signal events for the butions peaking at around rBDT = 0.1 are for the correctly matched preselection. a shows the logarithm of the event likelihood of the best events, the ones to the left are for incorrectly or unmatched events. The permutation (ln L) for the correctly matched events and the remainder. ratio figure shows the difference between the number of events in the Similarly, b shows the distribution of the R between the two untagged training and test samples divided by the statistical uncertainty in this jets assigned to the W boson decay. c shows the distribution of the BDT difference. Finally, d shows the comparison of the rBDT distributions output (rBDT ) for the two classes of events for both the training (his- observed in data and MC simulation. The hatched area includes the tograms) and test samples (points with statistical uncertainties). The uncertainties as detailed in the text. The uncertainty bars correspond to compatibility in terms of the χ 2 probability is also listed. The distri- the statistical uncertainties in the data tion carries information about the top quark mass, and in this function, while both the m reco reco W and the Rbq distributions are way, m top -independent background templates can be used. fitted to the sum of two Gaussian functions. The signal templates are simultaneously fitted to the sum of In Fig. 5a–c, the sensitivity of m reco top to the fit parameters a Gaussian and two Landau functions for m reco top , to the sum of m top , JSF and bJSF is shown by the superposition of the two Gaussian functions for m reco W and to the sum of two Gaus- signal templates and their fits for three input values per varied sian and one Landau function for Rbq reco . This set of functions parameter. In a similar way, the sensitivity of m reco W to JSF leads to an unbiased estimate of m top , but is not unique. For is shown in Fig. 5d. The dependences of m reco W on the input the background, the m reco top distribution is fitted to a Landau values of m top and bJSF are negligible and are not shown. 123 290 Page 10 of 51 Eur. Phys. J. C (2019) 79:290 Uncertainty [GeV] Total Total exp. Stat. with Total syst. Signal model. Ptop (m reco,i top | m top , JSF, bJSF, f bkg ) 1 sig = (1 − f bkg ) · Ptop (m reco,i top | m top , JSF, bJSF) bkg + f bkg · Ptop (m reco,i top | JSF, bJSF), 0.5 PW (m reco,i W | JSF, f bkg ) sig ATLAS = (1 − f bkg ) · PW (m reco,i W | JSF) s=8 TeV, 20.2 fb -1 bkg 0 + f bkg · PW (m reco,i W | JSF), and Standard -0.10 -0.05 0.00 0.05 reco,i rBDT PRbq (Rbq | m top , JSF, bJSF, f bkg ) sig reco,i Fig. 3 Various classes of m top uncertainties as a function of the mini- = (1 − f bkg ) · PRbq (Rbq | m top , JSF, bJSF) mum requirement on the BDT output rBDT and for the standard selec- bkg reco,i tion. The total uncertainty (solid line) is the sum in quadrature of the sta- + f bkg · PRbq (Rbq | bJSF) tistical (dotted line) and total systematic uncertainty (short dash-dotted line). The total systematic uncertainty consists of the total experimental where the fraction of background events is denoted by f bkg . (dashed line) and total signal-modelling uncertainty (long dash-dotted The parameters determined by the fit are m top , JSF and bJSF, line). The uncertainties in the background estimate are included in the total experimental uncertainty. The minimum requirement on rBDT while f bkg is fixed to its expectation shown in Table 1. It defining the BDT selection is indicated by the vertical black dashed was verified that the correlations between m reco reco top , m W and line. All uncertainties are included except for the method and the pile- Rbq of ρ(m top , m W ) = 0.05, ρ(m top , Rbq ) = 0.18, reco reco reco reco reco up uncertainties W , Rbq ) = −0.13, are small enough that formu- and ρ(m reco reco lating the likelihood in Eq. (1) as a product of three one- Consequently, to increase the size of the simulation sample, dimensional likelihoods does not bias the result. the fit is performed on the sum of the m reco Pseudo-experiments are used to verify the internal con- W distributions of the samples with different input top quark masses. Finally, sistency of the fitting procedure and to obtain the expected reco to the input values of m the sensitivity of Rbq top and bJSF statistical uncertainty for the data. For each set of parameter is shown in Fig. 5e, f. The dependence of Rbq reco on JSF (not values, 500 pseudo-experiments are performed, each corre- shown) is much weaker than the dependence on bJSF. sponding to the integrated luminosity of the data. To retain the For the signal, the parameters of the fitting functions for correlation of the three observables for the three-dimensional m reco top depend linearly on m top , JSF and bJSF. The param- fit, individual events are used. Because this exceeds the num- eters of the fitting functions for m reco ber of available MC events, results are corrected for oversam- W depend linearly on JSF. Finally, the parameters of the fitting functions for Rbqreco pling [80]. The results of pseudo-experiments for different depend linearly on m top , JSF and bJSF. For the background, input values of m top are obtained from statistically indepen- the dependences of the parameters of the fitting functions dent samples, while the results for different JSF and bJSF are are identical to those for the signal, except that they do not obtained from statistically correlated samples as explained depend on m top and that those for Rbq reco do not depend on above. For each fitted quantity and each variation of input JSF. parameters, the residual, i.e. the difference between the input sig value and the value obtained by the fit, is compatible with Signal and background probability density functions Ptop bkg zero. The three expected statistical uncertainties are and Ptop for the m reco reco reco top , m W and Rbq distributions are used in an unbinned likelihood fit to the data for all events, i = σstat (m top ) = 0.389 ± 0.004 GeV, 1, . . . N . The likelihood function maximized is σstat (JSF) = 0.00115 ± 0.00001, and +jets L shape (m top , JSF, bJSF, f bkg ) σstat (bJSF) = 0.0046 ± 0.0001,  N = Ptop (m reco,i where the values quoted are the mean and RMS of the distri- top | m top , JSF, bJSF, f bkg ) i=1 bution of the statistical uncertainties in the fitted quantities from pseudo-experiments. The widths of the pull distribu- × PW (m reco,i W | JSF, f bkg ) tions are below unity for m top and the two jet scale factors, reco,i × PRbq (Rbq | m top , JSF, bJSF, f bkg ), (1) which results in an overestimation of the uncertainty in m top of up to 7%. Since this leads to a conservative estimate of the uncertainty in m top , no attempts to mitigate this feature are made. 123 Eur. Phys. J. C (2019) 79:290 Page 11 of 51 290 Events / 5 GeV Events / GeV 5000 Data Z+jets 1600 Data Z+jets tt, mtop=172.5 GeV WW/WZ/ZZ tt, mtop=172.5 GeV WW/WZ/ZZ Single top NP/fake leptons 1400 Single top NP/fake leptons 4000 W+jets Uncertainty W+jets Uncertainty 1200 ATLAS ATLAS 3000 1000 s=8 TeV, 20.2 fb-1 s=8 TeV, 20.2 fb-1 800 2000 600 400 1000 200 0 0 Data/MC Data/MC 1.2 1.2 1 1 0.8 0.8 0 20 40 60 80 100 120 140 160 180 200 130 140 150 160 170 180 190 200 mW T [GeV] mreco top [GeV] (a) W boson transverse mass (b) Reconstructed top quark mass 2400 Events / 0.1 Events / GeV Data Z+jets 4500 Data Z+jets 2200 tt, mtop=172.5 GeV WW/WZ/ZZ tt, mtop=172.5 GeV WW/WZ/ZZ 2000 Single top NP/fake leptons 4000 Single top NP/fake leptons 1800 W+jets Uncertainty W+jets Uncertainty 3500 1600 ATLAS ATLAS 3000 1400 s=8 TeV, 20.2 fb-1 s=8 TeV, 20.2 fb-1 1200 2500 1000 2000 800 1500 600 1000 400 200 500 0 0 Data/MC Data/MC 1.2 1.2 1 1 0.8 0.8 60 70 80 90 100 110 0.5 1 1.5 2 2.5 3 mreco W [GeV] Rreco bq (c) Reconstructed W boson mass (d) Reconstructed ratio of jet transverse momenta Fig. 4 Distributions for the events passing the BDT selection. The data semi-leptonic top quark decay. The remaining figures show the three are shown, together with the signal-plus-background prediction normal- observables used for the determination of m top , where b shows the ized to the number of events observed in the data. The hatched area is reconstructed top quark mass m reco top , c shows the reconstructed invariant the uncertainty in the prediction described in the text. The rightmost mass of the W boson m reco W and d shows the reconstructed ratio of jet bin contains all entries with values above the lower edge of this bin, transverse momenta Rbqreco . The three distributions are shown within the similarly the leftmost bin contains all entries with values below the ranges of the template fit upper edge of this bin. a shows the W boson transverse mass for the 8 Uncertainties affecting the mtop determination nal MC sample with 500 pseudo-experiments each, drawn from the full MC sample. In the absence of a ±1σ varia- This section focuses on the treatment of uncertainty sources tion, e.g. for the evaluation of the uncertainty induced by the of a systematic nature. The same systematic uncertainty choice of signal MC generator, the full observed difference is sources as in Ref. [9] are investigated. If possible, the cor- assigned as a symmetric systematic uncertainty and further responding uncertainty in m top is evaluated by varying the treated as a variation equivalent to a ±1σ variation. Wher- respective quantities by ±1σ from their default values, con- ever a ±1σ variation can be performed, half the observed structing the corresponding event sample and measuring the difference between the +1σ and −1σ variation in m top is average m top change relative to the result from the nomi- assigned as an uncertainty if the m top values obtained from 123 290 Page 12 of 51 Eur. Phys. J. C (2019) 79:290 Normalized events / GeV Normalized events / GeV 0.035 ATLAS Simulation m top = 167.5 GeV ATLAS Simulation JSF = 0.96 s= 8 TeV 0.03 s= 8 TeV 0.03 m top = 172.5 GeV JSF = 1.00 m top = 177.5 GeV 0.025 JSF = 1.04 0.025 0.02 0.02 0.015 0.015 0.01 0.01 0.005 0.005 0 0 2 2 Ratio Ratio 1.5 1.5 1 1 0.5 0.5 0 130 140 150 160 170 180 190 200 0 130 140 150 160 170 180 190 200 mreco top [GeV] mreco top [GeV] reco with three input m (a) mtop reco with three input JSF (b) mtop top Normalized events / GeV Normalized events / GeV ATLAS Simulation bJSF = 0.96 JSF = 0.96 ATLAS Simulation s= 8 TeV 0.05 0.03 s= 8 TeV bJSF = 1.00 JSF = 1.00 bJSF = 1.04 JSF = 1.04 0.025 0.04 0.02 0.03 0.015 0.02 0.01 0.01 0.005 0 0 2 2 Ratio Ratio 1.5 1.5 1 1 0.5 0.5 0 130 140 150 160 170 180 190 200 0 60 70 80 90 100 110 mreco top [GeV] mreco W [GeV] reco with three input bJSF (c) mtop reco with three input JSF (d) mW Normalized events / 0.1 Normalized events / 0.1 ATLAS Simulation m top = 167.5 GeV ATLAS Simulation bJSF = 0.96 0.045 0.045 s= 8 TeV s= 8 TeV m top = 172.5 GeV bJSF = 1.00 0.04 0.04 m top = 177.5 GeV bJSF = 1.04 0.035 0.035 0.03 0.03 0.025 0.025 0.02 0.02 0.015 0.015 0.01 0.01 0.005 0.005 0 0 Ratio Ratio 1.4 1.4 1.2 1.2 1 1 0.8 0.8 0.6 0.6 0.5 1 1.5 2 2.5 3 0.5 1 1.5 2 2.5 3 Rreco bq Rreco bq reco with three input m (e) Rbq reco with three input bJSF (f) Rbq top Fig. 5 Template parameterizations for signal events, composed of t t¯ overlaid with the corresponding probability density function from the and single-top-quark production events. a–c show the sensitivity of combined fit to all templates described in the text. The ratios shown m reco reco top to m top , JSF and bJSF, d shows the sensitivity of m W to JSF are calculated relative to the probability density function of the central reco to m and e, f show the sensitivity of Rbq top and bJSF. Each template is sample with m top = 172.5 GeV, JSF = 1 and bJSF = 1 123 Eur. Phys. J. C (2019) 79:290 Page 13 of 51 290 Table 3 Systematic √ √ Event selection s = 7 TeV s = 8 TeV uncertainties in m top . The measured values of m top are Standard Standard BDT given together with the statistical and systematic m top result [GeV] 172.33 171.90 172.08 uncertainties in GeV for the Statistics 0.75 0.38 0.39 standard and the BDT event – Stat. comp. (m top ) 0.23 0.12 0.11 selections. For comparison, the result in the√t t¯ → lepton + jets – Stat. comp. (JSF) 0.25 0.11 0.11 channel at s = 7 TeV from – Stat. comp. (bJSF) 0.67 0.34 0.35 Ref. [9] is also listed. For each Method 0.11 ± 0.10 0.04 ± 0.11 0.13 ± 0.11 systematic uncertainty listed, the Signal Monte Carlo generator 0.22 ± 0.21 0.50 ± 0.17 0.16 ± 0.17 first value corresponds to the uncertainty in m top , and the Hadronization 0.18 ± 0.12 0.05 ± 0.10 0.15 ± 0.10 second to the statistical Initial- and final-state QCD radiation 0.32 ± 0.06 0.28 ± 0.11 0.08 ± 0.11 precision in this uncertainty. An Underlying event 0.15 ± 0.07 0.08 ± 0.15 0.08 ± 0.15 integer value of zero means that the corresponding uncertainty is Colour reconnection 0.11 ± 0.07 0.37 ± 0.15 0.19 ± 0.15 negligible and therefore not Parton distribution function 0.25 ± 0.00 0.08 ± 0.00 0.09 ± 0.00 evaluated. Statistical Background normalization 0.10 ± 0.00 0.04 ± 0.00 0.08 ± 0.00 uncertainties quoted as 0.00 are smaller than 0.005. The W +jets shape 0.29 ± 0.00 0.05 ± 0.00 0.11 ± 0.00 statistical uncertainty in the total Fake leptons shape 0.05 ± 0.00 0 0 systematic uncertainty is Jet energy scale 0.58 ± 0.11 0.63 ± 0.02 0.54 ± 0.02 calculated from uncertainty Relative b-to-light-jet energy scale 0.06 ± 0.03 0.05 ± 0.01 0.03 ± 0.01 propagation. The last line refers to the sum in quadrature of the Jet energy resolution 0.22 ± 0.11 0.23 ± 0.03 0.20 ± 0.04 statistical and systematic Jet reconstruction efficiency 0.12 ± 0.00 0.04 ± 0.01 0.02 ± 0.01 uncertainties Jet vertex fraction 0.01 ± 0.00 0.13 ± 0.01 0.09 ± 0.01 b-tagging 0.50 ± 0.00 0.37 ± 0.00 0.38 ± 0.00 Leptons 0.04 ± 0.00 0.16 ± 0.01 0.16 ± 0.01 Missing transverse momentum 0.15 ± 0.04 0.08 ± 0.01 0.05 ± 0.01 Pile-up 0.02 ± 0.01 0.14 ± 0.01 0.15 ± 0.01 Total systematic uncertainty 1.04 ± 0.08 1.07 ± 0.10 0.82 ± 0.06 Total 1.28 ± 0.08 1.13 ± 0.10 0.91 ± 0.06 the variations lie on opposite sides of the nominal result. If thus the total uncertainty is taken as the sum in quadrature of they lie on the same side, the maximum observed difference uncertainties from all sources. The individual uncertainties is taken as a symmetric systematic uncertainty. Since the are compared in Table 3 for three cases: the standard selec- √ systematic uncertainties are derived from simulation or data tion for the s = 7 TeV [9] and 8 TeV data and the BDT √ samples with limited numbers of events, all systematic uncer- selection for s = 8 TeV data. Many uncertainties in m top tainties have a corresponding statistical uncertainty, which is obtained with the standard selection at the two centre-of-mass calculated taking into account the statistical correlation of the energies agree within their statistical uncertainties such that considered samples, as explained in Sect. 8.5. The statistical the resulting total systematic uncertainties are almost iden- √ uncertainty in the total systematic uncertainty is dominated tical. Consequently, repeating the s = 7 TeV analysis on √ by the limited sizes of the simulation samples. The resulting s = 8 TeV data would have only improved the statistical systematic uncertainties are given in Table 3 independent of precision. The picture changes when comparing the uncer- √ their statistical significance. Further information is given in tainties in s = 8 TeV data for the standard selection and Tables 8, 9, 10, 11 and 12 in Appendix A. This approach the BDT selection. In general, the experimental uncertainties follows the suggestion in Ref. [81] and relies on the fact change only slightly, with the largest reduction observed for that, given a large enough number of considered uncertainty the JES uncertainty. In contrast, a large improvement comes sources, statistical fluctuations average out.6 The uncertainty from the reduced uncertainties in the modelling of the t t¯ sig- sources are designed to be uncorrelated with each other, and nal processes as shown in Table 3. This, together with the improved intrinsic resolution in m top , more than compen- 6 In the limit of many small systematic uncertainties with large statis- sates for the small loss in precision caused by the increased tical uncertainties, this procedure on average leads to an overestimate statistical uncertainty. The individual sources of systematic of the total systematic uncertainty. 123 290 Page 14 of 51 Eur. Phys. J. C (2019) 79:290 uncertainties and the evaluation of their effect on m top are Thanks to the restrictive event-selection requirements, the described in the following. contribution of non-t t¯ processes, comprising the single-top- quark process and the various background processes, is very low. The systematic uncertainty in m top from the uncertainty 8.1 Statistics and method calibration in the single-top-quark normalization is estimated from the corresponding uncertainty in the theoretical cross-section Uncertainties related to statistical effects and the method cal- given in Sect. 3. The resulting systematic uncertainty is small ibration are discussed here. compared with the systematic uncertainty in the t t¯ production Statistical: The quoted statistical uncertainty consists of and is consequently neglected. For the modelling of the sig- three parts: a purely statistical component in m top and the con- nal processes, the consequence of including single-top-quark tributions stemming from the simultaneous determination of variations in the uncertainty evaluation was investigated JSF and bJSF. The purely statistical component in m top is for various uncertainty sources and found to be negligible. obtained from a one-dimensional template method exploit- Therefore, the single-top-quark variations are not included ing only the m reco top observable, while fixing the values of JSF in the determination of the signal event uncertainties. and bJSF to the results of the three-dimensional analysis. The Signal Monte Carlo generator: The full observed differ- contribution to the statistical uncertainty in the fitted param- ence in fitted m top between the event samples produced eters due to the simultaneous fit of m top and JSF is estimated with the Powheg- Box and MC@NLO [82,83] programs as the difference in quadrature between the statistical uncer- is quoted as a systematic uncertainty. For the renormaliza- tainty in a two-dimensional fit to m reco reco top and m W while fix- tion and factorization scales the Powheg- Box sample uses ing the value of bJSF and the one-dimensional fit to the data the function given  in Sect. 3, while the MC@NLO sample described above. Analogously, the contribution of the statis- tical uncertainty due to the simultaneous fit of m top together uses μR,F = m 2top + 0.5( pT,t 2 + p 2 ). Both samples are T,t¯ with JSF and bJSF is defined as the difference in quadrature generated with a top quark mass of m top = 172.5 GeV with between the statistical uncertainties obtained in the three- the CT10 PDFs in the matrix-element calculation and use dimensional and the two-dimensional fits to the data. This the Herwig and Jimmy programs with the ATLAS AUET2 separation allows a comparison of the statistical sensitivities tune [47]. of the m top estimator used in this analysis, to those of anal- Hadronization: To cover the choice of parton shower and yses exploiting a different number of observables in the fit. hadronization models, samples produced with the Powheg- In addition, the sensitivity of the estimators to the global jet Box program are showered with either the Pythia6 pro- energy scale factors can be compared directly. These uncer- gram using the P2011C tune or the Herwig and Jimmy pro- tainties are treated as uncorrelated uncertainties in m top com- grams using the ATLAS AUET2 tune. This includes different binations. Together with the systematic uncertainty in the approaches in shower modelling, such as using a pT -ordered residual jet energy scale uncertainties discussed below, they parton showering in the Pythia program or angular-ordered directly replace the uncertainty in m top from the jet energy parton showering in the Herwig program, the different par- scale variations present without the in situ determination. ton shower matching scales, as well as fragmentation func- Method: The residual difference between fitted and gen- tions and hadronization models, such as choosing the Lund erated m top when analysing a template from a MC sample string model [84,85] implemented in the Pythia program reflects the potential bias of the method. Consequently, the or the cluster fragmentation model [86] used in the Herwig largest observed fitted m top residual and the largest observed program. The full observed difference between the samples statistical uncertainty in this quantity, in any of the five signal is quoted as a systematic uncertainty. samples with different assumed values of m top , is assigned As shown in Fig. 1, the distributions of transverse as the method calibration uncertainty and its corresponding momenta in data are slightly softer than those in the statistical uncertainty, respectively. This also covers effects Powheg+Pythia MC simulation samples. Similarly to from limited numbers of simulated events in the templates what was observed in the t t¯ → dilepton channel for the and potential deficiencies in the template parameterizations. pT,b distribution, in the t t¯ → lepton + jets channel the Powheg+Herwig sample is much closer to the data for sev- eral distributions of transverse momenta. The pT,had distri- 8.2 Modelling of signal processes bution is much better described by the Powheg+Herwig sample as was also observed in Ref. [78]. In addition, but The modelling of t t¯ → lepton + jets events incorporates to a lesser extent, the MC@NLO sample used to assess the a number of processes that have to be accurately described, signal Monte Carlo generator uncertainty and the samples to resulting in systematic effects, ranging from the t t¯ production assess the initial- and final-state QCD radiation uncertainty to the hadronization of the showered objects. 123 Eur. Phys. J. C (2019) 79:290 Page 15 of 51 290 discussed next also lead to a softer distribution in simulation. the P2012 tune and the P2012 loCR tune [30] for parton Given this, the observed difference in the pT,had distribution showering and hadronization. The full observed difference is covered by a combination of the signal-modelling uncer- is assigned as a systematic uncertainty. tainties given in Table 3. Parton distribution function (PDF): The PDF systematic Despite the fact that the JES and bJES are estimated uncertainty is the sum in quadrature of three contributions. independently using dijet and other non-t t¯ samples [63], These are the sum in quadrature of the differences in fit- some double-counting of hadronization-uncertainty-induced ted m top for the 26 eigenvector variations of the CT10 PDF uncertainties in the JES and m top cannot be excluded. This and two differences in m top obtained from reweighting the was investigated closely for the ATLAS top quark mass mea- √ central CT10 PDF set to the MSTW2008 PDF [39] and the surement in the t t¯ → lepton + jets channel at s = 7 TeV. NNPDF2.3 PDF [42]. The results in Ref. [87] revealed that the amount of double- counting of JES and hadronization effects for the t t¯ → 8.3 Modelling of background processes lepton + jets channel is small. Initial- and final-state QCDradiation (ISR/FSR): ISR/FSR Uncertainties in the modelling of the background processes leads to a higher jet multiplicity and different jet energies than are taken into account by variations of the corresponding the hard process, which affects the distributions of the three normalizations and shapes of the distributions. observables. The uncertainties due to ISR/FSR modelling are estimated with samples generated with the Powheg- Box Background normalization: The normalizations are varied program interfaced to the Pythia6 program for which the for the data-driven background estimates according to their parameters of the generation are varied to span the ranges uncertainties. For the negligible contribution from diboson compatible with the results of measurements of t t¯ produc- production, no normalization uncertainty is evaluated. tion in association with jets [88–90]. This uncertainty is eval- Background shape: For the W +jets background, the shape uated by comparing two dedicated samples that differ in uncertainty is evaluated from the variation of the heavy- several parameters, namely the QCD scale QCD , the trans- flavour fractions. The corresponding uncertainty is small. verse momentum scale for space-like parton-shower evolu- Given the very small contribution from Z +jets, diboson and tion Q 2max , the h damp parameter [91] and the P2012 RadLo NP/fake-lepton backgrounds, no shape uncertainty is evalu- and RadHi tunes [30]. In Ref. [90], it was shown that a num- ated for these background sources. ber of final-state distributions are better accounted for by the Powheg+Pythia samples with h damp = m top . Therefore, 8.4 Detector modelling these samples are used for evaluating this uncertainty, tak- ing half the observed difference between the up variation and The level of understanding of the detector response and of the down variation sample. Because the parameterizations for the particle interactions therein is reflected in numerous sys- the template fit to data are obtained from Powheg+Pythia tematic uncertainties. samples using h damp = ∞, it was verified that, consider- ing the method uncertainty quoted in Table 3, applying the Jet energy scale (JES): The JES is measured with a relative same functions to the h damp = m top samples leads to a result precision of about 1% to 4%, typically falling with increas- compatible with the input top quark mass. ing jet pT and rising with increasing jet |η| [93,94]. The total JES uncertainty consists of more than 60 subcompo- Underlying event: To reduce statistical fluctuations in the nents originating from the various steps in the jet calibration. evaluation of this systematic uncertainty, the difference in The number of these nuisance parameters is reduced with underlying-event modelling is assessed by comparing a pair a matrix diagonalization of the full JES covariance matrix of Powheg- Box samples based on the same partonic events including all nuisance parameters for a given category of the generated with the CT10 PDFs. A sample with the P2012 tune JES uncertainty components. is compared with a sample with the P2012 mpiHi tune [30], √ √ The analyses of s = 7 TeV and s = 8 TeV data with both tunes using the same CTEQ6L1 PDFs [92] for par- make use of the EM+JES and LCW+GSC [93] jet calibra- ton showering and hadronization. The Perugia 2012 mpiHi tions, respectively. The two calibrations feature different sets tune provides more semi-hard multiple parton interactions of nuisance parameters, and the LCW+GSC calibration gen- and is used for this comparison with identical colour recon- erally has smaller uncertainties than the EM+JES calibra- nection parameters in both tunes. The full observed differ- tion. While the pile-up correction for the jet calibration for ence is assigned as a systematic uncertainty. √ s = 7 TeV data only depends on the number of primary Colour reconnection: This systematic uncertainty is esti- vertices (n vtx ) and the mean number of interactions per bunch mated using a pair of samples with the same partonic events crossing (μ), a pile-up subtraction method based on jet area √ as for the underlying-event uncertainty evaluation but with is introduced for the s = 8 TeV data. Terms to account 123 290 Page 16 of 51 Eur. Phys. J. C (2019) 79:290 for uncertainties in the pile-up estimation are added. They Similarly to the JES uncertainties, the b-tagging uncertain- depend on the jet pT and the local transverse momentum ties are estimated by using an eigenvector approach, based on density. In addition, the punch-through uncertainty, i.e. an the b-tagging calibration analysis [66–68]. They include the uncertainty for jets that penetrate through to the muon spec- uncertainties in the b-tagging, c/τ -tagging and mistagging trometer, is added. The final reduced number of nuisance scale factors. This uncertainty in m top is derived by vary- √ parameters for the s = 8 TeV analysis is 25. The JES- ing the scale factors within their uncertainties and adding uncertainty-induced uncertainty in m top is the dominant sys- the resulting fitted differences in quadrature. In this proce- tematic uncertainty for all results shown in Table 3. When dure, uncertainties that are considered both in the b-tagging only a one-dimensional fit to m reco top or a two-dimensional fit calibration and as separate sources in the m top analysis are to m reco top and m reco is done, this uncertainty is 0.99 GeV or W taken into account simultaneously by applying the corre- 0.74 GeV, respectively. sponding varied b-tagging scale factors together with the varied sample when assessing the corresponding uncertainty Relative b-to-light-jet energy scale (bJES): The bJES in m top . The final uncertainty is the sum in quadrature of uncertainty is an additional uncertainty for the remaining these independent components. Compared with the result differences between b-jets and light-jets after the global JES √ from s = 7 TeV data, this uncertainty is reduced by about is applied, and therefore the corresponding uncertainty is one third for both the standard and BDT event selections in uncorrelated with the JES uncertainty. An additional uncer- accordance with the improvements made in the calibrations tainty of 0.2% to 1.2% is assigned to b-jets, with the low- of the b-tagging algorithm [66,67]. est uncertainty for b-jets with high transverse momenta [63]. Due to the determination of bJSF, the bJES uncertainty leads Leptons: The lepton uncertainties are related to the elec- to a very small contribution to the uncertainty in m top in tron energy or muon momentum scale and resolution, as well Table 3. However, performing only a two-dimensional fit to as trigger, isolation and identification efficiencies. These are m reco reco top and m W would result in an uncertainty of 0.47 GeV measured very precisely in high-purity J/ψ → + − and from this source. Z → + − data [57,58,95]. For each component, the corre- sponding uncertainty is propagated to the analysis by varia- Jet energy resolution (JER): The JER uncertainty is deter- tion of the respective quantity. The changes are propagated mined following an eigenvector decomposition strategy sim- to the E Tmiss as well. ilar to the JES systematic uncertainties [93,94]. The 11 com- ponents take into account various effects evaluated from Missing transverse momentum: The remaining contribu- simulation-to-data comparisons including calorimeter noise tion to the missing-transverse-momentum uncertainty stems terms in the forward region. The corresponding uncertainty from the uncertainties in calorimeter-cell energies associ- in m top is the sum in quadrature of the components of the ated with low- pT jets (7 GeV < pT < 20 GeV) without any eigenvector decomposition. corresponding reconstructed physics object or from pile-up interactions. They are accounted for as described in Ref. [69]. Jet reconstruction efficiency (JRE): This uncertainty is The corresponding uncertainty in m top is small. evaluated by randomly removing 0.23% of the jets with pT < 30 GeV from the simulated events prior to the event Pile-up: Besides the component treated in the JES uncer- selection to reflect the precision with which the data-to- tainty, the residual dependence of the fitted m top on the simulation JRE ratio is known [62]. The fitted m top differ- amount of pile-up activity and a possible mismodelling of ence between the varied sample and the nominal sample is pile-up in MC simulation is determined. For this, the m top taken as a systematic uncertainty. dependence in bins of n vtx and μ is determined for data and MC simulated events. Within the statistical uncertainties, the Jet vertex fraction (JVF): When summing the scalar pT of slopes of the linear dependences of m top observed in data and all tracks in a jet, the JVF is the fraction contributed by tracks predicted by the MC simulation are compatible. The same is originating at the primary vertex. The uncertainty in m top is true for JSF and bJSF. The final effect on the measurement is evaluated by varying the requirement on the JVF within its assessed by a convolution of the linear dependence with the uncertainty [65]. respective n vtx and μ distributions observed for data and MC b-tagging: Mismodelling of the b-tagging efficiency and simulated events. The maximum of the n vtx and μ effects is mistag rate is accounted for by the application of jet-specific assigned as an uncertainty due to pile-up. The pile-up con- √ scale factors to simulated events [66]. These scale factors ditions differ between the s = 7 and 8 TeV data. For the √ depend on jet pT , jet η and the underlying quark flavour. The BDT selection of s = 8 TeV data used here, the average ones used in this analysis are derived from dijet and t t¯ → of the mean number of inelastic pp interactions per bunch dilepton [66] events. They are the same as those used for crossing is μ = 20.3 and the average number of recon- the measurement of m top in the t t¯ → dilepton channel [14]. structed primary vertices is about n vtx = 9.4, to be compared 123 Eur. Phys. J. C (2019) 79:290 Page 17 of 51 290 √ with μ = 8.8 and n vtx = 7.0 for s = 7 TeV data [65]. The upper matrix corresponds to the correlations for statisti- The corresponding uncertainty is somewhat larger than for cal uncertainties only, while the lower matrix is obtained by √ s = 7 TeV data but still small. additionally taking into account all systematic uncertainties. Figure 6 shows the m reco reco reco top , m W and Rbq distributions in 8.5 Statistical precision of systematic uncertainties the data with statistical uncertainties together with the cor- responding fitted probability density functions for the back- The systematic uncertainties quoted in Table 3 carry statisti- ground alone and for the sum of signal and background. The cal uncertainties themselves. In view of a combination with uncertainty band attached to the fit to data is obtained in the other measurements, the statistical precision σ from a com- following way. At each point in m reco reco reco top , m W and Rbq , the parison of two samples (1 and 2) is determined for each uncer- band contains 68% of all fit function values obtained by ran- tainty source based on the statistical correlation ρ12 of the domly varying m top , JSF and bJSF within their total uncer- underlying samples using σ 2 = σ12 +σ22 −2ρ12 σ1 σ2 . The sta- tainties and taking into account their correlations. The waist tistical correlation is expressed as a function of the fraction of in the uncertainty band is caused by the usage of normalized √ shared√events of both samples ρ12 = N12 /N1 · N12 /N2 = probability density functions. The band visualises the vari- N12 / N1 · N2 , with N1 and N2 being the unweighted ations of the three template fit functions caused by all the numbers of events in the two samples and N12 being the uncertainties in m top listed in Table 3. The total uncertainty unweighted number of events present in both samples. The in all three fitted parameters is dominated by their systematic size of the MC sample at m top = 172.5 GeV results in a uncertainty. Therefore, the band shown is much wider than statistical precision in m top of about 0.1 GeV. Most estima- the band that would be obtained by fitting to the distributions tions are based on the same sample with only a change in a with statistical uncertainties only. single parameter, such as lepton energy scale uncertainties. The measured value of m top in the t t¯ → lepton + jets √ This leads to a high correlation of the central m top values and channel at s = 8 TeV is a correspondingly low statistical uncertainty in their differ- ence. Others, which do not share the same generated events m top = 172.08 ± 0.39 (stat) ± 0.82 (syst) GeV or exhibit other significant differences, have a lower correla- tion, and the corresponding statistical uncertainty is higher, with a total uncertainty of 0.91 GeV. The statistical precision such as in the case of the signal-modelling uncertainty. The of the systematic uncertainty is 0.06 GeV. This result corre- statistical uncertainty in the total systematic uncertainty is sponds to a 19% improvement on the result obtained using calculated from the individual statistical uncertainties by the the standard selection on the same data. Compared with the √ propagation of uncertainties. result in the t t¯ → lepton + jets channel at s = 7 TeV, the improvement is 29%. On top of the smaller statistical uncer- tainty, the increased precision is mainly driven by smaller 9 Results theory modelling uncertainties achieved by the BDT selec- √ tion. The larger number of events in the s = 8 TeV dataset is For the BDT selection, the likelihood fit to the data results in effectively traded for lower systematic uncertainties, result- ing in a significant gain in total precision. The new ATLAS m top = 172.08 ± 0.39 (stat) GeV, result in the t t¯ → lepton + jets channel is more precise than JSF = 1.005 ± 0.001 (stat), and the result from the CDF experiment, but less precise than the CMS and D0 results, measured in the same channel, as bJSF = 1.008 ± 0.005 (stat). shown in Fig. 14b in Appendix B. The statistical uncertainties are taken from the parabolic approximation of the likelihood profiles. The expected statis- tical uncertainties, calculated in Sect. 7, are compatible with 10 Combination with previous ATLAS results those. The correlation matrices of the three variables with i = 0, 1 and 2 corresponding to m top , JSF and bJSF are This section presents the combination of the six m top results of the ATLAS analyses in the t t¯ → dilepton, t t¯ → ⎛ ⎞ lepton + jets and t t¯ → all jets channels at centre-of-mass 1 −0.27 −0.92 √ ρstat = ⎝ −0.27 1 −0.02 ⎠ and energies of s = 7 and 8 TeV. The treatment of the results −0.92 −0.02 1 that are input to the combinations are described, followed by ⎛ ⎞ a detailed explanation of the evaluation of the estimator cor- 1 −0.30 −0.39 relations for the various sources of systematic uncertainty. ρtot = ⎝ −0.30 1 −0.42 ⎠ . The compatibilities of the measured m top values are inves- −0.39 −0.42 1 tigated using a pairwise χ 2 for all pairs of measurements 123 290 Page 18 of 51 Eur. Phys. J. C (2019) 79:290 Events / GeV Events / GeV ATLAS data, l+jets ATLAS data, l+jets 1800 1200 s=8 TeV, 20.2 fb-1 Best fit background s=8 TeV, 20.2 fb-1 Best fit background Best fit 1600 Best fit 1000 Uncertainty 1400 Uncertainty 1200 800 1000 600 800 400 600 400 200 200 0 0 130 140 150 160 170 180 190 200 60 70 80 90 100 110 mreco top [GeV] mreco W [GeV] (a) Reconstructed top quark mass (b) ReconstructedW boson mass Events / 0.05 ATLAS data, l+jets 1800 s=8 TeV, 20.2 fb-1 Best fit background 1600 Best fit Uncertainty 1400 1200 1000 800 600 400 200 0 0.5 1 1.5 2 2.5 3 reco Rbq (c) Reconstructed ratio of jet transverse momenta Fig. 6 Results of the likelihood fit to the data. The figures show the standard deviation total uncertainty in the fit function. It is based on the data distributions of the three observables with statistical uncertainties total uncertainty in the three fitted parameters as explained in the text. together with the fitted probability density function for the background a shows the distribution of the reconstructed top quark mass m reco top , b alone (barely visible at the bottom of the figure) and for the sum of shows the distribution of the reconstructed W boson mass m reco W and c signal and background. The uncertainty band corresponds to the one shows the reconstructed ratio of jet transverse momenta Rbq reco and by evaluating the compatibility of selected combinations. For the combinations to follow, the combined uncertain- Finally, the six results are combined, displaying the effect of ties for the previous results, namely t t¯ → dilepton and t t¯ → √ individual results on the combined result. lepton + jets at s = 7 TeV from Ref. [9], t t¯ → all jets √ √ at s = 7 TeV from Ref. [96], t t¯ → dilepton at s = 8 TeV √ 10.1 Inputs to the combination and categorization of from Ref. [14] and t t¯ → all jets at s = 8 TeV from uncertainties Ref. [74], were all re-evaluated. In all cases, the numbers agree to within 0.01 GeV with the original publications, The measured values of the individual analyses and their which in any case is the rounding precision due to the preci- statistical and systematic uncertainties are given in Table 4. sion of some of the inputs. On top of this, the results listed in For each result, the evaluated systematic uncertainties are Table 4 differ in some aspects from the original publications shown together with their statistical uncertainties. The sta- as explained below. tistical uncertainties in the total systematic uncertainties and The combination follows the approach developed for the √ the total uncertainties are obtained from the propagation of combination of s = 7 TeV analyses in Ref. [9], including uncertainties.7 the evaluation of the correlations given in Sect. 10.2 below. The treatment of uncertainty categories for the t t¯ → dilepton √ 7 For the previous results in the t t¯ → dilepton and t t¯ → lepton + jets and t t¯ → lepton + jets measurements at s = 7 TeV channels, the values quoted for the statistical uncertainties in the total exactly follows Ref. [9]. The uncertainty categorizations for √ systematic uncertainties differ from the ones in the original publications, the t t¯ → all jets measurements at s = 7 and 8 TeV where just the sum in quadrature of the statistical uncertainties in the from Refs. [74,96] closely follow this categorization but have individual systematic uncertainties was used. 123 Table 4 The six measured values of m top (i = 0, . . . , 5) and their statistical and systematic uncertainty sources k, numbered as given in the first column. For the individual measurements, the systematic uncertainty in m top and its associated statistical uncertainty are given for each source of uncertainty. The last line refers to the sum in quadrature of the statistical and systematic uncertainties. The statistical uncertainties in the total systematic uncertainties and in the total uncertainties are calculated from the propagation of uncertainties. Systematic uncertainties listed as 0 are not evaluated, while an empty cell indicates an uncertainty not applicable to the corresponding measurement. Statistical uncertainties quoted as 0.00 are smaller than 0.005 √ √ s = 7 TeV s = 8 TeV dilepton +jets all jets dilepton +jets all jets m top [GeV] m top [GeV] m top [GeV] m top [GeV] m top [GeV] m top [GeV] Eur. Phys. J. C (2019) 79:290 k Results (i = 0 . . . , 5) 173.79 172.33 175.06 172.99 172.08 173.72 0 Statistics 0.54 0.75 1.35 0.41 0.39 0.55 – Stat. comp. (m top ) 0.23 0.11 – Stat. comp. (JSF) 0.25 0.11 – Stat. comp. (bJSF) 0.67 0.35 1 Method 0.09 ± 0.07 0.11 ± 0.10 0.42 ± 0.01 0.05 ± 0.07 0.13 ± 0.11 0.11 2 Signal Monte Carlo generator 0.26 ± 0.16 0.22 ± 0.21 0.30 ± 0.30 0.09 ± 0.15 0.16 ± 0.17 0.18 ± 0.21 3 Hadronization 0.53 ± 0.09 0.18 ± 0.12 0.50 ± 0.15 0.22 ± 0.09 0.15 ± 0.10 0.64 ± 0.15 4 Initial- and final-state QCD radiation 0.47 ± 0.05 0.32 ± 0.06 0.22 ± 0.11 0.23 ± 0.07 0.08 ± 0.11 0.10 ± 0.28 5 Underlying event 0.05 ± 0.05 0.15 ± 0.07 0.08 ± 0.10 0.10 ± 0.14 0.08 ± 0.15 0.12 ± 0.16 6 Colour reconnection 0.14 ± 0.05 0.11 ± 0.07 0.22 ± 0.10 0.03 ± 0.14 0.19 ± 0.15 0.12 ± 0.16 7 Parton distribution function 0.10 ± 0.00 0.25 ± 0.00 0.09 ± 0.00 0.05 ± 0.00 0.09 ± 0.00 0.09 ± 0.00 8 Background normalization 0.04 ± 0.00 0.10 ± 0.00 0.03 ± 0.00 0.08 ± 0.00 9 W/Z +jets shape 0.00 ± 0.00 0.29 ± 0.00 0 0.11 ± 0.00 10 Fake leptons shape 0.01 ± 0.00 0.05 ± 0.00 0.07 ± 0.00 0 11 Data-driven all-jets background 0.35 ± 0.21 0.17 12 Jet energy scale 0.76 ± 0.09 0.58 ± 0.11 0.50 ± 0.05 0.54 ± 0.04 0.54 ± 0.02 0.60 ± 0.03 13 Relative b-to-light-jet energy scale 0.68 ± 0.02 0.06 ± 0.03 0.62 ± 0.05 0.30 ± 0.01 0.03 ± 0.01 0.34 ± 0.02 14 Jet energy resolution 0.19 ± 0.04 0.22 ± 0.11 0.01 ± 0.08 0.09 ± 0.05 0.20 ± 0.04 0.10 ± 0.04 15 Jet reconstruction efficiency 0.07 ± 0.00 0.12 ± 0.00 0.01 ± 0.01 0.01 ± 0.00 0.02 ± 0.01 0 16 Jet vertex fraction 0.00 ± 0.00 0.01 ± 0.00 0.01 ± 0.01 0.02 ± 0.00 0.09 ± 0.01 0.03 ± 0.01 17 b-tagging 0.07 ± 0.00 0.50 ± 0.00 0.16 ± 0.00 0.04 ± 0.02 0.38 ± 0.00 0.10 ± 0.00 18 Leptons 0.13 ± 0.00 0.04 ± 0.00 0 0.14 ± 0.01 0.16 ± 0.01 0.01 ± 0.00 19 Missing transverse momentum 0.04 ± 0.03 0.15 ± 0.04 0.02 ± 0.05 0.01 ± 0.01 0.05 ± 0.01 0.01 ± 0.01 20 Pile-up 0.01 ± 0.00 0.02 ± 0.01 0.02 ± 0.00 0.05 ± 0.01 0.15 ± 0.01 0.01 ± 0.00 21 All-jets trigger 0.01 ± 0.01 0.08 ± 0.01 22 Fast vs. full simulation 0.24 ± 0.18 Total systematic uncertainty 1.31 ± 0.07 1.04 ± 0.08 1.21 ± 0.13 0.74 ± 0.05 0.82 ± 0.06 1.02 ± 0.11 Total 1.42 ± 0.07 1.28 ± 0.08 1.82 ± 0.13 0.85 ± 0.05 0.91 ± 0.06 1.16 ± 0.11 123 Page 19 of 51 290 290 Page 20 of 51 Eur. Phys. J. C (2019) 79:290 some extra, analysis-specific sources of uncertainty, as shown 10.2 Mathematical framework and evaluation of estimator √ in Table 4. In addition, the t t¯ → all jets result at s = 8 TeV correlations from Ref. [74] is based on a different treatment of the PDF- uncertainty-induced uncertainty in m top . To allow the evalu- All combinations are performed using the best linear unbi- ation of the estimator correlations also for this uncertainty in ased estimate (BLUE) method [97,98] in a C++ implementa- m top , for this combination, the respective uncertainty is newly tion described in Ref. [99]. The BLUE method uses a linear evaluated according to the prescription given in Sect. 8. combination of the inputs to combine measurements. The √ For the t t¯ → all jets result at s = 7 TeV the statistical coefficients (BLUE weights) are determined via the mini- precisions in the systematic uncertainties were not evaluated mization of the variance of the combined result. They can in Ref. [9] but were calculated for this combination. For the be used to construct measures for the importance of a given √ t t¯ → all jets result at s = 8 TeV in Ref. [74], for some single measurement in the combination [98]. For any combi- of the sources, the statistical uncertainty in the systematic nation, the measured values xi , the list of uncertainties σik and uncertainty was not evaluated, such that the quoted statistical the correlations ρi jk of the estimators (i, j) for each source uncertainty in the total systematic uncertainty is a lower limit. of uncertainty (k) have to be provided. For all uncertain- For the mapping of uncertainty categories for data taken ties, a Gaussian probability distribution function is assumed. at different centre-of-mass energies, the choice of Ref. [14] For the uncertainties in m top for which the measurements are is employed. The most complex cases are the uncertainties correlated, when using ±1σ variations of a systematic effect, involving eigenvector decompositions, such as the JES and e.g. when changing the bJES by ±1σ , there are two possibili- b-tagging scale factor uncertainties, and the uncertainty cate- ties. When simultaneously applying a variation for a system- gories that do not apply to all input measurements. The JES- atic uncertainty, e.g. +1σ for the bJES, to a pair (i, j) of mea- uncertainty-induced uncertainty in m top is obtained from a surements, e.g. the t t¯ → lepton + jets and t t¯ → dilepton √ number of JES subcomponents. Some JES subcomponents measurements at s = 8 TeV, both analyses can result in have an equivalent at the other centre-of-mass energy and oth- a larger or smaller m top value than the one obtained for the ers do not. As in Ref. [14], the JES subcomponents without nominal case (full correlation, ρi jk = +1), or one analysis an equivalent at the other centre-of-mass energy are treated can result in a larger and the other in a smaller value (full as independent, resulting in vanishing estimator correlations anti-correlation, ρi jk = −1). Consequently, an uncertainty for that part of the covariance matrix. For the remaining sub- from a source only consisting of a single variation, such as components, the estimator correlations are partly positive and the bJES-uncertainty-induced uncertainty or the uncertainty partly negative. As an example, for the flavour part of the related to the choice of MC generator for signal events, results JES-uncertainty-induced uncertainty in m top , the two most in a correlation of ρi jk = ±1. The estimator correlations precise results, the t t¯ → dilepton and t t¯ → lepton + jets for composite uncertainties are evaluated by calculating the √ measurements at s = 8 TeV, are negatively correlated. correlation from the subcomponents. As an example, for the √ Consequently, for this pair, the resulting estimator correla- t t¯ → lepton + jets result at s = 8 TeV, the subcomponents tion for the total JES-induced uncertainty in m top is also neg- of the JES uncertainty are shown in Table 10 in Appendix A. ative. At the quoted precision, the two assumptions about the For any pair of measurements (i, j), this evaluation is done equivalence of the JES subcomponents between the datasets by adding the covariance terms of the subcomponents k with at the two centre-of-mass energies, i.e. the weak and strong ρi jk = ±1 and dividing by the total uncertainties for that correlation scenarios described in Table 10 in Appendix A, source. The resulting estimator correlation is leave the combined value and uncertainty unchanged. √  Ncomp Following Ref. [14], the s = 7 and 8 TeV measurements k=1 ρi jk σik σ jk are treated as uncorrelated for the nuisance parameters of the ρi j = . σi σ j b-tagging, c/τ -tagging, mistagging and JER uncertainties. In Ref. [14] it was shown that a correlated treatment of the  Ncomp 2 The quantity σi2 = k=1 σik is the sum of the single sub- flavour-tagging nuisance parameters results in an insignifi- component variances in analysis i. This procedure is applied cant change in the combination. For the statistical, method √ to all uncertainty sources that consist of more than one sub- calibration, MC-based background shape at s = 7 and component to reduce the large list of uncertainty subcompo- 8 TeV, and the pile-up uncertainties in m top , the measure- nents per estimator of O(100) to a suitable number of uncer- ments are assumed to be uncorrelated. Details of the evalu- tainty sources, i.e. to those given in Table 4. Since the full ation of the correlations for all remaining systematic uncer- tainties are discussed below. 123 Eur. Phys. J. C (2019) 79:290 Page 21 of 51 290 Δ mtop (8TeV) [GeV] Δ mtop (8TeV) [GeV] 0.8 0.8 ATLAS ATLAS 0.6 0.6 0.4 0.4 l+jets all jets 0.2 0.2 0 0 −0.2 −0.2 −0.4 −0.4 −0.6 ρ = +1 −0.6 ρ = +1 ρ = -1 ρ = -1 −0.8 −0.8 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 dilepton dilepton Δ mtop (8TeV) [GeV] Δ mtop (8TeV) [GeV] (a) t t¯ → dilepton (8 TeV) and t t¯ → lepton + jets (8 TeV) (b) t t¯ → dilepton (8 TeV) and t t¯ → all jets (8 TeV) Δ mtop (8TeV) [GeV] Δ mtop (7TeV) [GeV] 0.8 0.8 ATLAS ATLAS 0.6 0.6 0.4 0.4 all jets 0.2 l+jets 0.2 0 0 −0.2 −0.2 −0.4 −0.4 −0.6 ρ = +1 −0.6 ρ = +1 ρ = -1 ρ = -1 −0.8 −0.8 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 l+jets l+jets Δ mtop (8TeV) [GeV] Δ mtop (8TeV) [GeV] (c) t t¯ → lepton + jets (8 TeV) and t t¯ → all jets (8 TeV) (d) t t¯ → lepton + jets (8 TeV) and t t¯ → lepton + jets (7 TeV) √ Fig. 7 The pairwise shifts in m top when simultaneously varying a pair measurement with the t t¯ → all jets measurement at s = 8 TeV, of measurements for a systematic uncertainty or a subcomponent of a while d shows the correlations of the√present measurement with the systematic uncertainty. √ a, b show the correlations of the t t¯ → dilepton t t¯ → lepton + jets measurement at s = 7 TeV. The crosses indi- measurement at s = 8 TeV with the two other measurements at the cate the statistical uncertainty in the systematic uncertainties. The solid same centre-of-mass energy for all sources of uncertainty for which points indicate the fully correlated cases, and the open points indicate the estimators are correlated. c shows the correlations of the present the anti-correlated ones covariance matrix is independent of how the subsets are cho- the two results. The solid points indicate the fully correlated sen, this does not affect the combination. cases, and the open points indicate the anti-correlated ones.8 For the three analyses, the evaluated shifts in m top per For many significant sources of uncertainty in Fig. 7a, uncertainty subcomponent are referred to as m top dilepton , the t t¯ → lepton + jets and t t¯ → dilepton measurements +jets all jets are anti-correlated. As shown in Ref. [9], this is caused by m top and m top . They are shown in Fig. 7 for the the in situ determination of the JSF and bJSF in the three- various uncertainty subcomponents in selected pairs of anal- √ dimensional t t¯ → lepton + jets analysis. In contrast, for yses. The pairs using the results from s = 8 TeV data most sources of uncertainty, a positive estimator correlation are shown in Fig. 7a–c, while Fig. 7d is for the two anal- is observed for the t t¯ → dilepton and t t¯ → all jets measure- yses in the t t¯ → lepton + jets channel at the two centre- √ ments at s = 8 TeV, shown in Fig. 7b. The prominent of-mass energies. Each point represents the observed shifts for a systematic uncertainty or a subcomponent of a system- 8 In the course of including more results into the combination of atic uncertainty together with a cross, indicating the corre- Ref. [14], the definitions of the variations were homogenized while sponding statistical precision in the systematic uncertainty in leaving the estimator correlations unchanged. As a consequence, for the corresponding figures some of the points now are located √in the respec- tive other quadrant, e.g. for the t t¯ → dilepton result at s = 8 TeV. 123 290 Page 22 of 51 Eur. Phys. J. C (2019) 79:290 √ Table 5 The pairwise correlations ρi jk of the six measurements for t t¯ → all jets at s = 8 TeV. The correspondence of the indices i, j = 0, . . . , 5 of m top for each source of systematic uncertainty k = 0, . . . , 22 and the sources of systematic uncertainty are given in k = 0, . . . , 22, along with the total estimator correlations and the com- Table 4. Correlations that are assigned, or cannot be evaluated because patibility of the measurements using χi2j from Eq. (2). The indices i and one uncertainty in the covariance term is zero at the quoted precision, √ ¯ 7 TeV, 1 for t t¯ → lepton + jets √ 0 for t t → dilepton at s = √ j are are given as integer values, while evaluated correlations are shown as at √s = 7 TeV, 2 for t t¯ → all jets at s = 7 TeV, ¯ √3 for t t → dilepton real values at s = 8 TeV, 4 for t t¯ → lepton + jets at s = 8 TeV, and 5 dilepton +jets all jets dilepton +jets k m top 7 TeV m top 7 TeV m top 7 TeV m top 8 TeV m top 8 TeV i =0 i =1 i =2 i =3 i =4 ρ01 ρ02 ρ03 ρ04 ρ05 ρ12 ρ13 ρ14 ρ15 ρ23 ρ24 ρ25 ρ34 ρ35 ρ45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1.00 −1.00 1.00 1.00 1.00 −1.00 1.00 1.00 1.00 −1.00 −1.00 −1.00 1.00 1.00 1.00 3 1.00 1.00 1.00 −1.00 −1.00 1.00 1.00 −1.00 −1.00 1.00 −1.00 −1.00 −1.00 −1.00 1.00 4 −1.00 1.00 1.00 1.00 1.00 −1.00 −1.00 −1.00 −1.00 1.00 1.00 1.00 1.00 1.00 1.00 5 −1.00 1.00 1.00 1.00 −1.00 −1.00 −1.00 −1.00 1.00 1.00 1.00 −1.00 1.00 −1.00 −1.00 6 −1.00 1.00 1.00 −1.00 −1.00 −1.00 −1.00 1.00 1.00 1.00 −1.00 −1.00 −1.00 −1.00 1.00 7 0.53 0.22 −0.02 0.72 −0.61 −0.36 −0.32 0.72 −0.81 0.41 −0.05 0.27 −0.48 0.40 −0.76 8 1.00 0 0.31 −0.77 0 0 0.31 −0.74 0 0 0 0 −0.06 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0.20 0 0 0 0 0 0.27 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 12 −0.24 0.86 0.36 0.18 0.36 0.10 0.04 −0.29 0.13 0.41 0.09 0.42 −0.54 0.98 −0.57 13 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 14 −1.00 1.00 0 0 0 −1.00 0 0 0 0 0 0 0.22 −0.07 −0.17 15 1.00 1.00 1.00 1.00 0 1.00 1.00 1.00 0 1.00 1.00 0 1.00 0 0 16 −1.00 1.00 −1.00 −1.00 −1.00 −1.00 1.00 1.00 1.00 −1.00 −1.00 −1.00 1.00 1.00 1.00 17 −0.80 −0.03 0 0 0 0 0 0 0 0 0 0 −0.23 1 1 18 −0.35 0 0.93 −0.08 0.42 0 −0.51 −0.17 0.02 0 0 0 0.11 0.28 −0.36 19 0.00 −0.26 −0.26 −0.12 0.04 0.84 0.26 0.22 0.16 0 0 0 0.97 0.86 0.96 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 0 0 0 0 0 0 0 0 0 0 0 1.00 0 0 0 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total −0.07 0.42 0.52 0.06 0.08 −0.01 −0.00 −0.07 −0.02 0.29 −0.06 −0.01 −0.19 0.32 0.00 χi2j 0.55 0.51 0.44 1.09 0.00 1.50 0.18 0.02 0.64 1.37 2.06 0.39 0.45 0.37 1.25 exception is the hadronization-uncertainty-induced uncer- example. Using the choices of assigned correlations from tainty in m top , i.e. the single largest uncertainty in the Ref. [11] for the ATLAS results in the t t¯ → dilepton √ √ t t¯ → all jets measurement at s = 8 TeV, for which and t t¯ → lepton + jets channels at s = 7 TeV listed the two measurements are anti-correlated. On the contrary, in Table 4 gives a combined value of m top = 172.91 ± the t t¯ → lepton + jets and t t¯ → all jets measurements at 0.50 (stat) ± 1.05 (syst) GeV compared with m top = √ s = 8 TeV, shown in Fig. 7c, are positively correlated for 172.99 ± 0.48 (stat) ± 0.78 (syst) GeV. The significant this uncertainty. Finally, the t t¯ → lepton + jets measure- improvement in the precision of the combination demon- ments at the two centre-of-mass energies in Fig. 7d show a strates the particular importance of evaluating the correla- rather low correlation. The correlations per source of uncer- tions. tainty and the total estimator correlations are summarized in For the combinations presented in this paper, most esti- Table 5. mator correlations could be evaluated. The most prominent The improvement in the combination obtained by the exception is for the b-tagging uncertainty, where the t t¯ → √ use of evaluated correlations compared with using estima- all jets measurement at s = 8 TeV is based on a different tor correlations assigned solely by physics assessments (here b-tagging algorithm and calibration than the t t¯ → dilepton √ referred to as assigned correlations) is quantified using an and t t¯ → lepton + jets measurements at s = 8 TeV. It 123 Eur. Phys. J. C (2019) 79:290 Page 23 of 51 290 √ was verified that assignments of the estimator correlations of is 39% smaller than the one obtained from the results at s = ρi5k ∈ [−1, 1], with i = 3, 4 and k = 17, yield insignificant 7 TeV (m 7TeV top ). As shown in Fig. 13a, b in Appendix B, for differences in the full combination. Estimator correlations of both centre-of-mass energies, the combination is dominated ρi5 = 1 are assigned for this case, as this choice gives the by the results in the t t¯ → dilepton and t t¯ → lepton + jets largest uncertainty in the combination. A similar situation channels. arises for the data-driven all-jets background uncertainty in To investigate whether the measured m top depends on the the two t t¯ → all jets measurements, where the method used t t¯ decay mode, a combination of the six results is performed for the background estimate is similar but not identical for in which the results in the three t t¯ decay channels are treated dilepton the two measurements. Consequently, the conservative ad as determining potentially different masses, namely m top , hoc assignment of ρ25k = 1 was also made for this source +jets all jets m top and m top . In such a combination, results obtained k = 11. in one decay channel influence the combined result in another decay channel by means of their estimator correlation. There- 10.3 Compatibility of the inputs and selected combinations dilepton fore, for each observable, e.g. m top , by construction the sum of weights of the results in the corresponding decay Before any combination is performed, the compatibility of channel equals unity, while for each of the other decay chan- the input results is verified. For each pair of results, their nels the sum of weights of the results equals zero [100]. The compatibility is expressed by the ratio of the squared differ- combination yields compatible results for the three masses ence between the pair of measured values and the uncertainty listed in Table 6. Consequently, the data do not show any sign in this difference [98] as of a decay-channel-dependent m top . The correlation matrix dilepton (xi − x j )2 of the three observables 0, 1 and 2 corresponding to m top , χi2j = . (2) +jets all jets σi2 + σ j2 − 2ρi j σi σ j m top and m top is ⎛ ⎞ The corresponding values are given in Table 5. Analysing the 1 −0.14 0.43 χi2j values reveals good χ 2 probabilities, with the smallest ρm top = ⎝ −0.14 1 −0.05 ⎠ , χ 2 probability being P(χ 2 , 1) = 15%. The largest sum of 0.43 −0.05 1 χ 2 values by far is observed for the t t¯ → all jets result at √i j and the smallest χ 2 probability of any pair of combined s = 7 TeV. The dependences of the combined values and their uncer- results for determining the same m top is P(χ 2 , 1) = 11%. As shown in Fig. 13c–e in Appendix B, for the combination tainties on the total correlation for pairwise combinations of √ results are analysed. The dependences for pairs of the three of the three observables, the results based on s = 7 TeV √ data lead to significant improvements on their more precise results from s = 8 TeV data are shown in Fig. 8. The largest √ information gain is achieved by combining the t t¯ → dilepton counterparts obtained from s = 8 TeV data, apart from the √ t t¯ → dilepton channel. and t t¯ → lepton + jets results at s = 8 TeV, shown in Fig. 8a, b, which are anti-correlated, i.e. ρ = −0.19. Given that no dependence of m top on the centre-of-mass Based on Tables 4 and 5, selected combinations are energy or the t t¯ decay channel is expected, the above exam- analysed, yielding the results given in Table 6 and shown ples of combinations are merely additional investigations of in Fig. 9. The BLUE weights and the pulls9 of the results are the compatibility of the input results. The compatibility com- given in Table 7. binations are summarized in Fig. 9 and listed in Table 6. For To investigate the difference in precision of combined all combinations, the values quoted in Fig. 9 are the combined √ value, the statistical uncertainty, the systematic uncertainty, results obtained from s = 7 and 8 TeV results, two inde- pendent combinations of the three results per centre-of-mass the total uncertainty and the statistical uncertainty in the total energy are performed. For each decay channel, the results uncertainty. √ at s = 8 TeV are significantly more precise than those √ 10.4 The combined result of m top at s = 7 TeV. In addition, the two most precise results per centre-of-mass energy are significantly less correlated at √ √ The use of the statistical uncertainties in the systematic uncer- s = 8 TeV than at s = 7 TeV. Consequently, the size of √ tainties has two main advantages. Firstly, it allows a deter- the uncertainty of the combined result at s = 8 TeV (m 8TeV top ) mination of the uncertainties in the evaluation of the total 9 Using the individual results xi ± σi and the combined result x ± σx , correlations of the estimators, avoiding the need to perform  the pull of result i is calculated as (xi − x)/ σi2 − σx2 and should ad hoc variations. Secondly, it enables the monitoring of the be Gaussian distributed with mean zero and width unity. The pull is a evolution of the combined result in relation to the precision measure of the likeliness of the xi measured in data. in its uncertainty while including results, thereby evaluating 123 290 Page 24 of 51 Eur. Phys. J. C (2019) 79:290 1.8 σ(mtop)[GeV] mtop[GeV] 175 ATLAS dilepton ATLAS dilepton mtop (8TeV) = 172.99 GeV σ(mtop (8TeV)) = 0.85 GeV l+jets mtop (8TeV) = 172.08 GeV 1.6 σ(m l+jets (8TeV)) = 0.91 GeV top σ(m 174 mtop = 172.56 GeV 1.4 top ) = 0.56 GeV mtop vs. ρ σ(m ) vs. ρ top 1.2 173 1 0.8 172 0.6 171 0.4 0.2 170 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 ρ ρ (a) t t¯ → dilepton (8 TeV) and t t¯ → lepton + jets (8 TeV) (b) t t¯ → dilepton (8 TeV) and t t¯ → lepton + jets (8 TeV) 175.5 σ(mtop)[GeV] mtop[GeV] ATLAS dilepton 2.2 ATLAS dilepton mtop (8TeV) = 172.99 GeV σ(mtop (8TeV)) = 0.85 GeV 175 all jets 2 all jets mtop (8TeV) = 173.72 GeV σ(m (8TeV)) = 1.16 GeV top 174.5 mtop = 173.20 GeV 1.8 σ(m top ) = 0.78 GeV mtop vs. ρ σ(mtop) vs. ρ 1.6 174 1.4 173.5 1.2 173 1 172.5 0.8 0.6 172 0.4 171.5 0.2 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 ρ ρ (c) t t¯ → dilepton (8 TeV) and t t¯ → all jets (8 TeV) (d) t t¯ → dilepton (8 TeV) and t t¯ → all jets (8 TeV) σ(mtop)[GeV] mtop[GeV] ATLAS 2.2 ATLAS 177 l+jets mtop (8TeV) = 172.08 GeV l+jets σ(mtop (8TeV)) = 0.91 GeV all jets mtop (8TeV) = 173.72 GeV 2 σ(mtop all jets (8TeV)) = 1.16 GeV 176 mtop = 172.71 GeV 1.8 σ(mtop) = 0.72 GeV 175 mtop vs. ρ 1.6 σ(mtop) vs. ρ 174 1.4 173 1.2 172 1 0.8 171 0.6 170 0.4 169 0.2 168 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 ρ ρ (e) t t¯ → lepton + jets (8 TeV) and t t¯ → all jets (8 TeV) (f) t t¯ → lepton + jets (8 TeV) and t t¯ → all jets (8 TeV) Fig. 8 The combined values (left) and uncertainties √ (right) of the com- t t¯ → all jets results. Finally, the combination of the t t¯ → lepton + jets bination of pairs of individual results at s = 8 TeV, shown as func- and t t¯ → all jets results is shown in the bottom row. For comparison, tions of the total correlation ρ (solid lines). The combination of the the corresponding values for the input results are also shown (dashed t t¯ → dilepton and t t¯ → lepton + jets results is shown in the top lines) row. The middle row is for the combination of the t t¯ → dilepton and 123 √ √ Table 6 The results for selected combinations based on the six results at s = 7 and 8 TeV. The left two columns of results show the combination of the three results at s = 7 TeV (m 7TeV top ) √ or at s = 8 TeV (m 8TeV top ), both combinations neglecting the results at the respective other centre-of-mass energy. The middle three columns show the combination of the six results as if pairs dilepton +jets all jets of measurements would determine a decay-specific top quark mass, namely m top , m top and m top . Finally, shown on the right is the combination of the three most important results in the (3) combination denoted by m top and the combination of all results, i.e. the ATLAS result for m top shown in Fig. 10. For each combination, the uncertainty is given for each source of uncertainty. Uncertainties quoted as 0.00 are smaller than 0.005, while empty cells indicate uncertainties that do not apply to the respective combination. Finally, the total systematic uncertainty and the sum in quadrature of the statistical and systematic uncertainties are given. Both are quoted including the precision at which the respective uncertainty is known Eur. Phys. J. C (2019) 79:290 dilepton +jets all jets m 7TeV top [GeV] m 8TeV top [GeV] m top [GeV] m top [GeV] m top [GeV] m (3) top [GeV] m top [GeV] Results 173.20 172.68 172.98 172.13 174.08 172.13 174.08 Statistics 0.46 0.26 0.39 0.37 0.56 0.27 0.25 Method 0.08 0.06 0.05 0.10 0.14 0.06 0.06 Signal Monte Carlo generator 0.17 0.13 0.12 0.15 0.03 0.14 0.12 Hadronization 0.35 0.04 0.18 0.03 0.32 0.07 0.00 Initial- and final-state QCD radiation 0.03 0.15 0.26 0.07 0.13 0.07 0.07 Underlying event 0.05 0.07 0.10 0.01 0.06 0.05 0.03 Colour reconnection 0.02 0.08 0.02 0.16 0.02 0.08 0.08 Parton distribution function 0.15 0.03 0.05 0.13 0.08 0.07 0.05 Background normalization 0.07 0.04 0.03 0.04 0.00 0.03 0.02 W/Z +jets shape 0.15 0.05 0.01 0.12 0.00 0.07 0.06 Fake leptons shape 0.03 0.03 0.07 0.02 0.00 0.03 0.03 Data-driven all-jets background 0.04 0.02 0.01 0.01 0.22 0.03 Jet energy scale 0.40 0.27 0.53 0.34 0.51 0.21 0.22 Relative b-to-light-jet energy scale 0.35 0.19 0.32 0.01 0.41 0.15 0.17 Jet energy resolution 0.04 0.10 0.09 0.16 0.07 0.10 0.09 Jet reconstruction efficiency 0.09 0.01 0.01 0.05 0.00 0.03 0.03 Jet vertex fraction 0.00 0.05 0.02 0.07 0.02 0.05 0.05 b-tagging 0.24 0.18 0.05 0.30 0.09 0.17 0.17 Leptons 0.04 0.10 0.14 0.11 0.01 0.09 0.08 Missing transverse momentum 0.08 0.03 0.01 0.07 0.01 0.04 0.04 Pile-up 0.01 0.07 0.05 0.10 0.01 0.06 0.06 All-jets trigger 0.00 0.01 0.00 0.00 0.06 0.01 Fast vs. full simulation 0.03 0.01 0.01 0.07 0.01 Total systematic uncertainty 0.76 ± 0.04 0.48 ± 0.04 0.74 ± 0.04 0.61 ± 0.04 0.80 ± 0.05 0.42 ± 0.04 0.41 ± 0.03 Total 0.89 ± 0.04 0.54 ± 0.04 0.84 ± 0.04 0.71 ± 0.04 0.98 ± 0.05 0.50 ± 0.04 0.48 ± 0.03 123 Page 25 of 51 290 290 Page 26 of 51 Eur. Phys. J. C (2019) 79:290 Compatibility evaluations ATLAS the added estimate. The last line in Fig. 10b shows the new mtop ± stat. ± syst. (total) ATLAS combined value of m top . √ m7topTeV 173.20 ± 0.46 ± 0.76 (0.89 ± 0.04) The inclusion of the t t¯ → lepton + jets result at s = m8topTeV 172.68 ± 0.26 ± 0.48 (0.54 ± 0.04) 8 TeV leads to the result quoted in the second line, which improves the combined uncertainty by much more than the dilepton mtop 172.98 ± 0.39 ± 0.74 (0.84 ± 0.04) statistical precision in the uncertainty of the most precise result. The same is found when adding the t t¯ → lepton + jets l+jets mtop 172.13 ± 0.37 ± 0.61 (0.71 ± 0.04) √ result at s = 7 TeV and comparing with the statistical all jets mtop 174.08 ± 0.56 ± 0.80 (0.98 ± 0.05) uncertainty in the previous combination, albeit at a much ATLAS (2018) 172.69 ± 0.25 ± 0.41 (0.48 ± 0.03) reduced significance. The corresponding result obtained from these three results, denoted by m (3) top , is also listed in ATLAS Combination stat. uncertainty stat. uncertainty Table 6. total uncertainty total uncertainty The improvement in the combination by applying the BDT √ 165 170 175 180 185 selection to the t t¯ → lepton + jets analysis at s = 8 TeV mtop [GeV] is sizeable. This is seen from repeating the combination of (3) m top but using the result from the standard selection from Fig. 9 The compatibility combinations performed for the six ATLAS √ Table 3. With this, the correlation of the s = 8 TeV t t¯ → results of m top . The figure shows the combined results listed in Table 6, √ which are obtained from data taken at different centre-of-mass energies lepton + jets result with the s = 8 TeV t t¯ → dilepton and for the three decay channels, in comparison to the new ATLAS result changes from −0.19 to −0.02. The resulting uncer- result. The values quoted are the combined value, the statistical uncer- tainty in the combination is 0.59 ± 0.05 GeV, i.e. the com- tainty, the systematic uncertainty, the total uncertainty and the uncer- (3) bination is 18% less precise than m top obtained using the tainty in the total uncertainty. The results are compared with the new ATLAS combination listed in the last line and shown as the grey vertical result from the BDT selection. Adding the remaining results bands reduces the quoted combined uncertainty by 0.02 GeV, which is smaller than the statistical precision in the uncertainty of their influence on the combination. The significance of the the previously achieved result of m (3)top . individual results in the combination is shown in Fig. 10. The The changes in statistical uncertainties in the combined individual results are shown in Fig. 10a. Their combination value and its uncertainty due to variations of the input sys- is displayed in Fig. 10b where, following Ref. [98], starting tematic uncertainties within their uncertainties are evaluated (3) from the most precise result, i.e. the t t¯ → dilepton measure- for two cases, namely for m top and for the combination of √ ment at s = 8 TeV, results are added to the combination all results. Following Ref. [14], the distributions of the com- one at a time according to their importance, and the combined bined values and uncertainties are calculated from 500 com- result is reported. Each following line of this figure shows the binations, where for each combination, the sizes of the uncer- combined result when adding the result listed to the input of tainties as well as the correlations are newly evaluated. Due to the combination, indicated by the ‘+’ in front of the name of the re-evaluation of the correlation, the resulting distributions Table 7 The BLUE weights √ √ s = 7 TeV s = 8 TeV and the pulls of the results for dilepton +jets all jets dilepton +jets all jets the combinations reported in m top m top m top m top m top m top Table 6. The upper part refers to the independent combinations of m 7TeV top Weight 0.36 0.51 0.13 the three results per Pull 0.54 −0.95 1.18 centre-of-mass energy resulting in uncorrelated results m 7TeV m 8TeV top Weight 0.45 0.44 0.12 top and m 8TeV top . The middle part is Pull 0.48 −0.82 1.02 for the combination of the three dilepton m top Weight 0.08 −0.04 −0.04 0.92 0.04 0.04 observables from pairs of results +jets per t t¯ decay channel, resulting m top Weight −0.09 0.33 0.03 0.09 0.67 −0.03 dilepton in correlated results m top , all jets m top Weight −0.04 −0.01 0.30 0.04 0.01 0.71 +jets all jets m top and m top . The lower Pull 0.71 0.18 0.64 0.05 −0.09 −0.58 part refers to the combination of (3) the three most important results m top Weight 0.17 0.43 0.40 m (3) top and of all results m top Pull −0.16 0.70 −0.57 m top Weight −0.03 0.16 0.04 0.35 0.37 0.10 Pull 0.83 −0.30 1.36 0.43 −0.79 0.98 123 Eur. Phys. J. C (2019) 79:290 Page 27 of 51 290 Inputs to the combination ATLAS Comb. according to importance ATLAS mtop ± stat. ± syst. (total) mtop ± stat. ± syst. (total) dilepton dilepton mtop (8 TeV) 172.99 ± 0.41 ± 0.74 (0.85 ± 0.05) mtop (8 TeV) 172.99 ± 0.41 ± 0.74 (0.85 ± 0.04) l+jets l+jets mtop (8 TeV) 172.08 ± 0.39 ± 0.82 (0.91 ± 0.06) + mtop (8 TeV) 172.56 ± 0.28 ± 0.48 (0.56 ± 0.04) l+jets l+jets mtop (7 TeV) 172.33 ± 0.75 ± 1.04 (1.28 ± 0.08) + mtop (7 TeV) 172.51 ± 0.27 ± 0.42 (0.50 ± 0.04) all jets all jets mtop (8 TeV) 173.72 ± 0.55 ± 1.02 (1.16 ± 0.11) + mtop (8 TeV) 172.61 ± 0.25 ± 0.42 (0.49 ± 0.03) all jets all jets mtop (7 TeV) 175.06 ± 1.35 ± 1.21 (1.82 ± 0.13) + mtop (7 TeV) 172.70 ± 0.24 ± 0.42 (0.48 ± 0.03) dilepton dilepton mtop (7 TeV) 173.79 ± 0.54 ± 1.31 (1.42 ± 0.07) + mtop (7 TeV) 172.69 ± 0.25 ± 0.41 (0.48 ± 0.03) Combination Combination stat. uncertainty stat. uncertainty stat. uncertainty stat. uncertainty total uncertainty total uncertainty total uncertainty total uncertainty 165 170 175 180 185 170 175 180 mtop [GeV] mtop [GeV] (a) Inputs to the combination (b) Combination according to importance Fig. 10 The combination of the six ATLAS results of m top accord- the uncertainty in the total uncertainty. In this figure, each line shows ing to importance Ref. [98]. a shows the inputs to the combination. b the combined result when adding the result listed to the combination shows results of the combination when successively adding results to indicated by a ‘+’. The new ATLAS combination is given in the last the most precise one. The values quoted are the combined value, the sta- line, and shown in both figures as the vertical grey bands tistical uncertainty, the systematic uncertainty, the total uncertainty and mW [GeV] are not Gaussian and are also not exactly centred around the ATLAS mW = 80.370 ± 0.019 GeV combined value and the combined uncertainty. For m (3)top , the 80.5 mtop = 172.69 ± 0.48 GeV root mean square of the distribution of the combined value mH = 125.1 ± 0.2 GeV 80.45 68/95% CL of mW and mtop is 0.03 GeV, and that of the distribution of its uncertainty is 0.04 GeV. The corresponding values for the new ATLAS combination are 0.07 GeV and 0.03 GeV, respectively. 80.4 The full breakdown of uncertainties for the new com- bined ATLAS result for m top is reported in the last column 80.35 of Table 6. The combined result is 68/95% CL of Electroweak 80.3 Fit w/o mW and mtop m top = 172.69 ± 0.25 (stat) ± 0.41 (syst) GeV (Eur. Phys. J. C 78 (2018) 675) 80.25 165 170 175 180 185 with a total uncertainty of 0.48±0.03 GeV, where the quoted mtop [GeV] uncertainty in this uncertainty is statistical. This means that Fig. 11 Comparison of indirect determinations and direct measure- the uncertainty in this combined result is only known to this ments of the top quark and W boson masses. The direct ATLAS mea- precision, which, given its size, is fully adequate. surements of m W and m top are shown as the horizontal and vertical The χ 2 probability of m (3) top is 78%. Driven by the larger bands, respectively. Their 68% and 95% confidence-level (CL) contours pulls of the remaining three results listed in Table 7, the χ 2 are compared with the corresponding results from the electroweak fit probability of 64% for the new ATLAS combination of m top surements of the two masses. The top quark mass used in is lower but still good. The new ATLAS combined result of this figure was obtained above, while the W boson mass is m top provides a 44% improvement relative to the most pre- taken from Ref. [101]. The electroweak fit uses as input the cise single input result, which is the t t¯ → dilepton analysis at √ LHC combined result of the Higgs boson mass of m H = s = 8 TeV. With a relative precision of 0.28%, it improves 125.09 ± 0.24 GeV from Ref. [102]. There is good agree- on the previous combination in Ref. [14] by 31% and super- ment between the direct ATLAS mass measurements and sedes it. As shown in Appendix B, the new ATLAS combined their indirect determinations by the electroweak fit. result of m top is more precise than the results from the CDF and D0 experiments, and has a precision similar to the CMS 11 Conclusion combined result. In Fig. 11, the 68% and 95% confidence-level contours of The top quark mass is measured via a three-dimensional tem- the indirect determination of m W and m top from the global plate method in the t t¯ → lepton + jets channel and com- electroweak fit in Ref. [2] are compared with the correspond- bined with previous ATLAS m top measurements at the LHC. ing confidence-level contours of the direct ATLAS mea- 123 290 Page 28 of 51 Eur. Phys. J. C (2019) 79:290 √ For the t t¯ → lepton + jets analysis from s = 8 TeV bined result is mostly limited by the uncertainties in the cal- proton–proton collision data with an integrated luminosity ibration of the jet energy scales, b-tagging and in the Monte of about 20.2 fb−1 , the event selection of the corresponding Carlo modelling of signal events. √ s = 7 TeV analysis is refined. An optimization employing a BDT selection to efficiently suppress less-well-reconstructed Acknowledgements We thank CERN for the very successful oper- ation of the LHC, as well as the support staff from our insti- events results in a significant reduction in total uncertainty, tutions without whom ATLAS could not be operated efficiently. driven by a significant decrease in theory-modelling-induced We acknowledge the support of ANPCyT, Argentina; YerPhI, Arme- uncertainties. With this approach, the measured value of m top nia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbai- is jan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC m top = 172.08 ± 0.39 (stat) ± 0.82 (syst) GeV CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, and MPG, with a total uncertainty of 0.91±0.06 GeV, where the quoted Germany; GSRT, Greece; RGC, Hong Kong SAR, China; ISF and uncertainty in the total uncertainty is statistical. The precision Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, is limited by systematic uncertainties, mostly by uncertainties Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC in the calibration of the jet energy scale, b-tagging and the KI, Russian Federation; JINR; MESTD, Serbia; MSSR, Slovakia; Monte Carlo modelling of signal events. This result is more ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; precise than the result from the CDF experiment, but less SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; precise than the CMS and D0 results, measured in the same STFC, United Kingdom; DOE and NSF, United States of America. In channel. addition, individual groups and members have received support from The correlations of six measurements of m top , performed BCKDF, CANARIE, CRC and Compute Canada, Canada; COST, ERC, √ in the three t t¯ decay channels from s = 7 and 8 TeV ATLAS ERDF, Horizon 2020, and Marie Skłodowska-Curie Actions, European Union; Investissements d’ Avenir Labex and Idex, ANR, France; DFG data, are evaluated for all sources of the systematic uncer- and AvH Foundation, Germany; Herakleitos, Thales and Aristeia pro- tainty. Using a dedicated mapping of uncertainty categories, grammes co-financed by EU-ESF and the Greek NSRF, Greece; BSF- combinations are performed, where measurements are added NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya, one at a time according to their importance. Treating the pairs Spain; The Royal Society and Leverhulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowl- of measurements in the three t t¯ decay channels as determin- edged gratefully, in particular from CERN, the ATLAS Tier-1 facili- dilepton +jets ing potentially different masses, namely m top , m top and ties at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC- all jets IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL- m top , yields consistent values within uncertainties, i.e. the T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL data do not show any sign of a decay-channel-dependent (USA), the Tier-2 facilities worldwide and large non-WLCG resource m top . providers. Major contributors of computing resources are listed in The combined result of m top from the six measurements Ref. [103]. is Data Availability Statement This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All ATLAS sci- m top = 172.69 ± 0.25 (stat) ± 0.41 (syst) GeV entific output is published in journals, and preliminary results are made available in Conference Notes. All are openly available, without restric- tion on use by external parties beyond copyright law and the standard with a total uncertainty of 0.48±0.03 GeV, where the quoted conditions agreed by CERN. Data associated with journal publications uncertainty in the total uncertainty is statistical. This combi- are also made available: tables and data from plots (e.g. cross section nation is dominated by three input measurements: the mea- values, likelihood profiles, selection efficiencies, cross section limits, √ surement in the t t¯ → dilepton channel from s = 8 TeV …) are stored in appropriate repositories such as HEPDATA (http:// hepdata.cedar.ac.uk/). ATLAS also strives to make additional material data and the two measurements in the t t¯ → lepton + jets √ related to the paper available that allows a reinterpretation of the data channel from s = 8 and 7 TeV data. With a relative preci- in the context of new theoretical models. For example, an extended sion of 0.28%, this new ATLAS combination of m top is more encapsulation of the analysis is often provided for measurements in the precise than the result from the CDF and D0 experiments framework of RIVET (http://rivet.hepforge.org/).” This information is taken from the ATLAS Data Access Policy, which is a public docu- and has a precision similar to the CMS combined result. This ment that can be downloaded from http://opendata.cern.ch/record/413 result supersedes the previous combined ATLAS result. [opendata.cern.ch].] With this precision in m top achieved, precise knowledge of the relation between the mass definition of the experimental Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecomm analysis and the pole mass is becoming relevant. The com- ons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Funded by SCOAP3 . 123 Eur. Phys. J. C (2019) 79:290 Page 29 of 51 290 Appendix A: Results from the BDT optimization and In Fig. 12, the template fit functions of the three observ- individual sources of systematic uncertainty ables are compared for the standard and the BDT event selec- tion. The distributions of m reco reco top and m W are narrower for the This appendix has additional details of the measurement of BDT event selection, which means the resolution in the two √ m top in the t t¯ → lepton + jets channel from s = 8 TeV masses is improved compared with what is observed for the data discussed in the main text. standard selection. The Rbqreco distribution is slightly shifted to lower values for the BDT event selection, but the difference is small. Normalized pdf Normalized pdf 0.03 ATLAS Simulation ATLAS Simulation s=8 TeV Standard 0.04 s=8 TeV Standard 0.025 BDT 0.035 BDT 0.02 0.03 0.025 0.015 0.02 0.01 0.015 0.01 0.005 0.005 0 0 Ratio Ratio 1.8 1.4 1.6 1.4 1.2 1.2 1 1 130 140 150 160 170 180 190 200 60 70 80 90 100 110 mreco top [GeV] mreco W [GeV] (a) Reconstructed top quark mass (b) Reconstructed W boson mass Normalized pdf ATLAS Simulation 0.08 s=8 TeV Standard 0.07 BDT 0.06 0.05 0.04 0.03 0.02 0.01 0 Ratio 1.05 1 0.95 0.9 0.5 1 1.5 2 2.5 3 Rreco bq (c) Reconstructed ratio of jet transverse momenta Fig. 12 Comparison of the template fit functions of the three observ- tions are also shown. a shows the reconstructed top quark mass m reco top , ables for the standard event selection (solid line) and the BDT event b shows the reconstructed W boson mass m reco W and c shows the recon- selection (dashed line). The ratios (standard/BDT) of the pairs of func- reco structed jet- pT ratio Rbq 123 290 Page 30 of 51 Eur. Phys. J. C (2019) 79:290 Table 8 The individual up Uncertainty m top [GeV] m dw top [GeV] m top [GeV] components of the uncertainty sources considered for the Signal Monte Carlo generator 0.16 ± 0.17 t√t¯ → lepton + jets analysis at s = 8 TeV for the sources of Powheg- Box - MC@NLO (Herwig) −0.161 ± 0.168 uncertainty not documented in Hadronization 0.15 ± 0.10 Tables 9, 10, 11 and 12. The Powheg+Pythia - Powheg+Herwig +0.146 ± 0.098 uncertainties together with their statistical precisions are listed in Initial- and final-state QCD radiation 0.08 ± 0.11 boldface and given with Less I/FSR - more I/FSR +0.086 −0.075 +0.080 ± 0.111 0.01 GeV precision. The Underlying event 0.08 ± 0.15 uncertainty per source is calculated as the sum in P2012 - P2012 mpiHi −0.080 ± 0.153 quadrature of the Colour reconnection 0.19 ± 0.15 subcomponents. Uncertainties P2012 - P2012 loCR +0.191 ± 0.154 quoted as 0.00 (0.000) are Background normalization 0.08 ± 0.00 smaller than 0.005 (0.0005) Z +jets norm. +0.007 −0.015 +0.011 ± 0.000 W +jets norm. −0.017 −0.061 −0.061 ± 0.000 Fake lepton norm. +0.046 ± 0.000 W/Z+jets shape 0.11 ± 0.00 W +jets HF0 −0.001 −0.070 −0.070 ± 0.000 W +jets HF1 −0.005 −0.087 −0.087 ± 0.000 Jet reconstruction efficiency 0.02 ± 0.01 Nominal - 0.23% drop +0.022 ± 0.013 Jet vertex fraction 0.09 ± 0.01 +0.077 −0.112 0.095 ± 0.009 Leptons 0.16 ± 0.01 Electron energy scale +0.025 −0.006 +0.016 ± 0.006 Electron energy resolution −0.152 −0.145 −0.152 ± 0.013 Muon resolution (muon spectrometer) +0.027 ± 0.000 Muon resolution (inner detector) +0.023 ± 0.000 Muon scale −0.013 +0.015 −0.014 ± 0.000 Lepton trigger SF −0.005 −0.003 −0.005 ± 0.001 Lepton identification SF +0.005 −0.011 +0.008 ± 0.001 Lepton reconstruction SF +0.003 −0.008 +0.005 ± 0.000 Missing transverse momentum(E Tmiss ) 0.05 ± 0.01 E Tmiss (resolution soft term) +0.003 +0.012 +0.012 ± 0.018 E Tmiss (scale soft term) +0.054 −0.039 +0.047 ± 0.009 For the BDT selection, a number of systematic uncertain- rounded by the values from the two variations. In this case up ties listed in Table 3 are calculated by performing pseudo- | m top | is 0.5·| m top − m dw top |, otherwise it is the maximum up experiments for more than one systematic variation. The indi- of | m top | and | m dwtop |. In both cases, the sign of m top is vidual components are given in Tables 8, 9, 10, 11 and 12 up the one from m top . below. Whenever the uncertainty is obtained from just a pair of samples, the shift m top is listed together with the defini- tion of the difference evaluated indicating the direction of the Appendix B: Additional information about the various shift. For the other cases, the shift in m top is quoted relative combinations to the value measured in the central sample for the upward up variation ( m top ), the downward variation ( m dw top ) and the This appendix gives additional information about the various final shift assigned to this uncertainty component ( m top ). combinations discussed in the main text. For all combina- up For most of the cases the signs of m top and m dw top are tions the values quoted are the combined value, the statistical different, indicating that m top from the central sample is sur- uncertainty, the systematic uncertainty, the total uncertainty 123 Eur. Phys. J. C (2019) 79:290 Page 31 of 51 290 Table 9 The individual components of the√PDF uncertainty consid- and the uncertainty in the total uncertainty, which is statisti- ered for the t t¯ → lepton + jets analysis at s = 8 TeV, the resulting cal. PDF-uncertainty-induced shifts in m top and the final uncertainty in m top . The components [31,39,42] together with their statistical precisions are Figure 13a, b shows the independent combinations per listed in boldface. The total uncertainty in the CT10 variations is calcu- centre-of-mass energy. For both centre-of-mass energies, lated as the sum in quadrature of the CT10 subcomponents. The total the combination is dominated by the results in the t t¯ → uncertainty is given with 0.01 GeV precision. Uncertainties quoted as dilepton and t t¯ → lepton + jets channels. Using only those 0.00 (0.000) are smaller than 0.005 (0.0005). The term nuisance param- eter is denoted by NuP. The last line refers to the sum in quadrature of in the combinations yields combined results of m 7TeV top = 172.99 ± 0.48 (stat) ± 0.78 (syst) GeV with an uncer- the PDF subcomponents √ tainty of 0.91 ± 0.05 GeV at s = 7 TeV and m 8TeV top = PDF uncertainty components m top [GeV] 172.56 ± 0.28 (stat) ± 0.48 (syst) GeV with an uncertainty √ CT10 variations 0.09 ± 0.00 of 0.56 ± 0.04 GeV at s = 8 TeV. At both centre-of-mass CT10 NuP2 - NuP1 −0.001 ± 0.000 energies, the difference between the combined uncertainties CT10 NuP4 - NuP3 +0.000 ± 0.000 of the partial and full combination is much smaller than the CT10 NuP6 - NuP5 +0.015 ± 0.000 respective statistical precision in the total systematic uncer- CT10 NuP8 - NuP7 +0.005 ± 0.003 tainties. This statistical precision is obtained from varying CT10 NuP10 - NuP9 +0.004 ± 0.000 each systematic uncertainty within its statistical precision CT10 NuP12 - NuP11 +0.002 ± 0.000 and repeating the combination, as explained in the main text. CT10 NuP14 - NuP13 −0.026 ± 0.001 Figure 13c–e shows the dependent combinations per t t¯ dilepton −0.004 ± 0.000 decay channel. The combined result of m top based only on CT10 NuP16 - NuP15 √ CT10 NuP18 - NuP17 −0.015 ± 0.001 ¯ the t t → dilepton measurement from s = 8 TeV data and dilepton CT10 NuP20 - NuP19 +0.013 ± 0.001 the measurements in the other decay channels is m top = CT10 NuP22 - NuP21 +0.006 ± 0.001 172.94 ± 0.41 (stat) ± 0.73 (syst) GeV with an uncertainty CT10 NuP24 - NuP23 +0.063 ± 0.001 of 0.84 ± 0.05 GeV. As a consequence of the influence of the CT10 NuP26 - NuP25 +0.000 ± 0.001 measurements in the other decay channels discussed in the main text, this result does not coincide with the t t¯ → dilepton CT10 NuP28 - NuP27 +0.009 ± 0.000 √ CT10 NuP30 - NuP29 −0.004 ± 0.000 result at s = 8 TeV. CT10 NuP32 - NuP31 +0.007 ± 0.001 In Fig. 14, the most precise ATLAS results of m top per decay channel and the new ATLAS combined value of m top CT10 NuP34 - NuP33 +0.019 ± 0.002 are compared with the respective results from the CDF, D0 CT10 NuP36 - NuP35 −0.011 ± 0.001 and CMS experiments. CT10 NuP38 - NuP37 −0.001 ± 0.000 CT10 NuP40 - NuP39 −0.001 ± 0.001 CT10 NuP42 - NuP41 −0.005 ± 0.001 CT10 NuP44 - NuP43 −0.003 ± 0.000 CT10 NuP46 - NuP45 −0.002 ± 0.000 CT10 NuP48 - NuP47 +0.027 ± 0.000 CT10 NuP50 - NuP49 +0.002 ± 0.000 CT10 NuP52 - NuP51 −0.003 ± 0.001 NNPDF - CT10 −0.034 ± 0.001 MSTW - CT10 −0.024 ± 0.002 Total 0.09 ± 0.00 123 290 Page 32 of 51 Eur. Phys. J. C (2019) 79:290 √ Table 10 The individual components of √the JES uncertainty considered used for s = 7 TeV data is given for the weak and the strong corre- for the t t¯ → lepton + jets analysis at s = 8 TeV, the resulting JES- lation scenarios. The ‘+’ sign indicates corresponding components at and bJES-uncertainty-induced shifts in m top and the final uncertainty the two centre-of-mass energies for the weak and strong scenario, while in m top . The components [63] together with their statistical precisions the ‘(+)’ sign indicates components that only correspond for the strong are listed in boldface and, wherever applicable, calculated as the sum in scenario. Finally, mentioning √ a name indicates that the mapped sources quadrature of the respective subcomponents. A shift listed as ‘0’ means carry different names at s = 7 and 8 TeV. The uncertainty compo- that the corresponding variation resulted in an unchanged event sample. nents and the total uncertainty are given with 0.01 GeV precision. The Uncertainties quoted as 0.00 (0.000) are smaller than 0.005 (0.0005). term nuisance parameter is denoted by NuP. The last line refers to the In the rightmost column, the mapping to the uncertainty components sum in quadrature of the JES components up √ JES uncertainty components m top [GeV] dw m top [GeV] m top [GeV] Map to s = 7 TeV Statistical (total) 0.17 ± 0.01 Statistical NuP1 −0.159 +0.151 −0.155 ± 0.013 Statistical NuP2 −0.008 +0.048 −0.028 ± 0.006 Statistical NuP3 +0.063 −0.035 +0.049 ± 0.009 Statistical NuP4 +0.020 +0.022 +0.022 ± 0.018 η inter-calibration (stat.) −0.062 +0.020 −0.041 ± 0.011 Modelling (total) 0.38 ± 0.02 Modelling NuP1 −0.372 +0.389 −0.380 ± 0.020 (+) Modelling NuP2 +0.029 −0.000 +0.014 ± 0.006 (+) Modelling NuP3 +0.010 +0.005 +0.010 ± 0.018 (+) Modelling NuP4 +0.034 −0.026 +0.030 ± 0.006 (+) η inter-calibration (model) +0.056 −0.038 +0.047 ± 0.013 + Detector (total) 0.11 ± 0.01 Detector NuP1 +0.116 −0.103 +0.110 ± 0.011 + Detector NuP2 −0.015 +0.017 −0.016 ± 0.009 Detector NuP3 +0.015 −0.014 +0.015 ± 0.006 (+) Detector NuP2 Mixed (total) 0.09 ± 0.01 Mixed NuP1 −0.004 −0.029 −0.029 ± 0.022 (+) Mixed NuP2 +0.053 −0.054 +0.054 ± 0.009 Mixed NuP3 −0.044 +0.061 −0.052 ± 0.009 Mixed NuP4 +0.039 −0.016 +0.028 ± 0.006 (+) Mixed NuP2 Single particle high-pT 0.01 ± 0.00 Single particle high-pT 0 +0.005 +0.005 ± 0.000 Pile-up (total) 0.18 ± 0.02 Pile-up: offset (μ) +0.041 −0.040 +0.041 ± 0.011 + Pile-up: offset (n vtx ) +0.065 −0.083 +0.074 ± 0.017 + Pile-up: pT +0.042 +0.040 +0.042 ± 0.018 Pile-up: ρ −0.173 +0.141 −0.157 ± 0.017 Punch-through 0.02 ± 0.01 Punch-through +0.013 +0.017 +0.017 ± 0.013 Flavour (total) 0.24 ± 0.02 Flavour composition +0.079 −0.119 +0.099 ± 0.000 + Flavour response +0.220 −0.211 +0.215 ± 0.018 + bJES 0.03 ± 0.01 + bJES +0.006 −0.047 +0.026 ± 0.013 + Total (without bJES) 0.54 ± 0.02 123 Eur. Phys. J. C (2019) 79:290 Page 33 of 51 290 Table 11 The individual components of the √ JER uncertainty consid- nents are quoted as the difference from the nominal sample. The total ered for the t t¯ → lepton + jets analysis at s = 8 TeV, the resulting uncertainty is calculated as the sum in quadrature of the subcompo- JER-uncertainty-induced shifts in m top and the final uncertainty in m top . nents and given with 0.01 GeV precision. The term nuisance parameter The data versus simulation difference and noise forward region compo- is denoted by NuP up JER uncertainty components m top [GeV] m dw top [GeV] m top [GeV] JER data versus simulation difference −0.034 ± 0.018 JER noise forward region +0.032 ± 0.013 JER NuP1 (only down var.) −0.111 ± 0.052 JER NuP2 −0.034 +0.055 −0.044 ± 0.018 JER NuP3 +0.025 −0.084 +0.054 ± 0.024 JER NuP4 −0.074 +0.090 −0.082 ± 0.021 JER NuP5 +0.078 +0.016 +0.078 ± 0.037 JER NuP6 −0.041 +0.017 −0.029 ± 0.019 JER NuP7 −0.039 +0.076 −0.057 ± 0.016 JER NuP8 −0.053 −0.013 −0.053 ± 0.029 JER NuP9 (only up var.) +0.036 ± 0.018 Total 0.20 ± 0.04 Table 12 The individual up Flavour-tagging uncertainty components m top [GeV] m dw top [GeV] m top [GeV] components of the flavour-tagging uncertainty b-tagging scale factor variations 0.31 ± 0.00 considered for the t√t¯ → lepton + jets analysis at b-tagging NuP1 +0.051 −0.062 +0.057 ± 0.000 s = 8 TeV, the resulting shifts b-tagging NuP2 −0.230 +0.143 −0.187 ± 0.000 in m top and the final b-tagging NuP3 −0.090 +0.005 −0.047 ± 0.001 b-tagging-uncertainty-induced uncertainty in m top . The b-tagging NuP4 +0.090 −0.175 +0.132 ± 0.000 uncertainty components b-tagging NuP5 −0.230 +0.148 −0.189 ± 0.000 together with their statistical b-tagging NuP6 +0.023 −0.105 +0.064 ± 0.001 precisions are listed in boldface and calculated as the sum in c/τ -tagging scale factor variations 0.15 ± 0.00 quadrature of the respective c/τ -tagging NuP1 +0.098 −0.102 +0.100 ± 0.000 subcomponents. The uncertainty c/τ -tagging NuP2 −0.057 −0.026 −0.057 ± 0.000 components and the total c/τ -tagging NuP3 +0.046 −0.125 +0.085 ± 0.000 uncertainty are given with 0.01 GeV precision. c/τ -tagging NuP4 −0.057 −0.023 −0.057 ± 0.000 Uncertainties quoted as Mistagging scale factor variations 0.16 ± 0.00 0.00 (0.000) are smaller than Mistagging NuP1 −0.005 +0.003 −0.004 ± 0.000 0.005 (0.0005). The term nuisance parameter is denoted Mistagging NuP2 −0.042 −0.039 −0.042 ± 0.000 by NuP. The last line refers to Mistagging NuP3 −0.038 −0.036 −0.038 ± 0.000 the sum in quadrature of the Mistagging NuP4 −0.032 −0.040 −0.040 ± 0.000 components Mistagging NuP5 −0.037 −0.044 −0.044 ± 0.000 Mistagging NuP6 −0.036 −0.045 −0.045 ± 0.000 Mistagging NuP7 −0.034 −0.040 −0.040 ± 0.000 Mistagging NuP8 −0.041 −0.040 −0.041 ± 0.000 Mistagging NuP9 −0.029 −0.045 −0.045 ± 0.000 Mistagging NuP10 −0.073 −0.001 −0.073 ± 0.000 Mistagging NuP11 −0.026 −0.055 −0.055 ± 0.000 Mistagging NuP12 +0.007 −0.095 +0.051 ± 0.000 Total 0.38 ± 0.00 123 290 Page 34 of 51 Eur. Phys. J. C (2019) 79:290 Results from 7 TeV data ATLAS Results from 8 TeV data ATLAS mtop ± stat. ± syst. (total) mtop ± stat. ± syst. (total) l+jets dilepton mtop (7 TeV) 172.33 ± 0.75 ± 1.04 (1.28 ± 0.05) mtop (8 TeV) 172.99 ± 0.41 ± 0.74 (0.85 ± 0.05) dilepton l+jets + mtop (7 TeV) 172.99 ± 0.48 ± 0.78 (0.91 ± 0.05) + mtop (8 TeV) 172.56 ± 0.28 ± 0.48 (0.56 ± 0.04) all jets all jets + mtop (7 TeV) 173.20 ± 0.46 ± 0.76 (0.89 ± 0.04) + mtop (8 TeV) 172.68 ± 0.26 ± 0.48 (0.54 ± 0.04) Combination Combination stat. uncertainty stat. uncertainty stat. uncertainty stat. uncertainty total uncertainty total uncertainty total uncertainty total uncertainty 170 175 180 170 175 180 mtop [GeV] mtop [GeV] (a) (b) Results in dilepton channel ATLAS Results in l+jets channel ATLAS mtop ± stat. ± syst. (total) mtop ± stat. ± syst. (total) dilepton l+jets mtop (8 TeV) 172.94 ± 0.41 ± 0.73 (0.84 ± 0.05) mtop (8 TeV) 172.01 ± 0.42 ± 0.78 (0.89 ± 0.06) dilepton l+jets + mtop (7 TeV) 172.98 ± 0.39 ± 0.74 (0.84 ± 0.04) + mtop (7 TeV) 172.13 ± 0.37 ± 0.61 (0.71 ± 0.04) Combination Combination stat. uncertainty stat. uncertainty stat. uncertainty stat. uncertainty total uncertainty total uncertainty total uncertainty total uncertainty 170 175 180 168 170 172 174 176 178 mtop [GeV] mtop [GeV] (c) t t¯ → dilepton channel (d) t t¯ → lepton + jets channel Results in all jets channel ATLAS mtop ± stat. ± syst. (total) all jets mtop (8 TeV) 173.84 ± 0.56 ± 1.00 (1.15 ± 0.10) all jets + mtop (7 TeV) 174.08 ± 0.56 ± 0.80 (0.98 ± 0.05) Combination stat. uncertainty stat. uncertainty total uncertainty total uncertainty 170 175 180 mtop [GeV] (e) t t¯ → all jets channel Fig. 13 Selected combinations of the six ATLAS measurements of tainty, the total uncertainty and the uncertainty in the total uncertainty, m top according to importance. The figures show the combined result which is statistical. a and b refer to the independent combinations of when successively adding results to the most precise one of a given cat- the three measurements per centre-of-mass energy resulting in uncor- egory. Each line of this figure shows the combined result when adding related results m 7TeV 8TeV top and m top . c–e refer to the combination of the the result listed to the combination, indicated by a ‘+’. The values quoted three correlated observables from pairs of measurements per t t¯ decay are the combined value, the statistical uncertainty, the systematic uncer- dilepton +jets all jets channel, resulting in m top , m top and m top 123 Eur. Phys. J. C (2019) 79:290 Page 35 of 51 290 Dilepton channel ATLAS L+jets channel ATLAS mtop ± stat. ± syst. (total) mtop ± stat. ± syst. (total) CDF 171.46 ± 1.91 ± 2.51 (3.16) CDF 174.85 ± 0.71 ± 0.85 (1.11) D0 173.32 ± 1.36 ± 0.85 (1.60) D0 174.98 ± 0.58 ± 0.49 (0.76) ATLAS 172.99 ± 0.41 ± 0.74 (0.85 ± 0.05) ATLAS 172.08 ± 0.39 ± 0.82 (0.91 ± 0.06) CMS 172.82 ± 0.19 ± 1.22 (1.24) CMS 172.35 ± 0.16 ± 0.48 (0.51) ATLAS (2018) 172.69 ± 0.25 ± 0.41 (0.48 ± 0.03) ATLAS (2018) 172.69 ± 0.25 ± 0.41 (0.48 ± 0.03) ATLAS Combination ATLAS Combination stat. uncertainty stat. uncertainty stat. uncertainty stat. uncertainty total uncertainty total uncertainty total uncertainty total uncertainty 165 170 175 180 185 165 170 175 180 185 mtop [GeV] mtop [GeV] (a) t t¯ → dilepton channel (b) t t¯ → lepton + jets channel All jets channel ATLAS Combinations per experiment ATLAS mtop ± stat. ± syst. (total) mtop ± stat. ± syst. (total) CDF 175.07 ± 1.19 ± 1.56 (1.96) CDF (2014) 173.16 ± 0.57 ± 0.74 (0.93) ATLAS 173.72 ± 0.55 ± 1.02 (1.16 ± 0.11) D0 (2016) 174.95 ± 0.40 ± 0.64 (0.75) CMS 172.32 ± 0.25 ± 0.59 (0.64) CMS (2016) 172.44 ± 0.13 ± 0.47 (0.48) ATLAS (2018) 172.69 ± 0.25 ± 0.41 (0.48 ± 0.03) ATLAS (2018) 172.69 ± 0.25 ± 0.41 (0.48 ± 0.03) ATLAS Combination ATLAS Combination stat. uncertainty stat. uncertainty stat. uncertainty stat. uncertainty total uncertainty total uncertainty total uncertainty total uncertainty 165 170 175 180 185 190 165 170 175 180 185 mtop [GeV] mtop [GeV] (c) t t¯ → all jets channel (d) Combinations Fig. 14 The most precise result of m top per experiment in the dif- systematic uncertainty, the total uncertainty and for ATLAS results also ferent t t¯ decay channels and m top from the latest combinations per- the uncertainty in the total uncertainty, which is statistical. 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Wengler35 , S. Wenig35 , N. Wermes24 , M. D. Werner76 , P. Werner35 , M. Wessels59a , T. D. Weston20 , K. Whalen127 , N. L. Whallon145 , A. M. Wharton87 , A. S. White103 , A. White8 , M. J. White1 , R. White144b , D. Whiteson168 , B. W. Whitmore87 , F. J. Wickens141 , W. Wiedenmann178 , M. Wielers141 , C. Wiglesworth39 , L. A. M. Wiik-Fuchs50 , F. Wilk98 , H. G. Wilkens35 , L. J. Wilkins91 , H. H. Williams133 , S. Williams31 , C. Willis104 , S. Willocq100 , J. A. Wilson21 , I. Wingerter-Seez5 , E. Winkels153 , F. Winklmeier127 , O. J. Winston153 , B. T. Winter50 , M. Wittgen150 , M. Wobisch93 , A. Wolf97 , T. M. H. Wolf118 , R. Wolff99 , M. W. Wolter82 , H. Wolters136a,136c , V. W. S. Wong172 , N. L. Woods143 , S. D. Worm21 , B. K. Wosiek82 , K. W. Woźniak82 , K. Wraight55 , M. Wu36 , S. L. Wu178 , X. Wu52 , Y. Wu58a , T. R. Wyatt98 , B. M. Wynne48 , S. Xella39 , Z. Xi103 , L. Xia175 , D. Xu15a , H. Xu58a,e , L. Xu29 , T. Xu142 , W. Xu103 , B. Yabsley154 , S. Yacoob32a , K. Yajima129 , D. P. Yallup92 , D. Yamaguchi162 , Y. Yamaguchi162 , A. Yamamoto79 , T. Yamanaka160 , F. Yamane80 , M. Yamatani160 , T. Yamazaki160 , Y. Yamazaki80 , Z. Yan25 , H. J. Yang58c,58d , H. T. Yang18 , S. Yang75 , Y. Yang160 , Z. Yang17 , W-M. Yao18 , Y. C. Yap44 , Y. Yasu79 , E. Yatsenko58c,58d , J. Ye41 , S. Ye29 , I. Yeletskikh77 , E. Yigitbasi25 , E. Yildirim97 , K. Yorita176 , K. Yoshihara133 , C. J. S. Young35 , C. Young150 , J. Yu8 , J. Yu76 , X. Yue59a , S. P. Y. Yuen24 , B. Zabinski82 , G. Zacharis10 , E. Zaffaroni52 , R. Zaidan14 , A. M. Zaitsev140,al , T. Zakareishvili156b , N. Zakharchuk33 , J. Zalieckas17 , S. Zambito57 , D. Zanzi35 , D. R. Zaripovas55 , S. V. Zeißner45 , C. Zeitnitz179 , G. Zemaityte131 , J. C. Zeng170 , Q. Zeng150 , O. Zenin140 , D. Zerwas128 , M. Zgubič131 , D. F. Zhang58b , D. Zhang103 , F. Zhang178 , G. Zhang58a , G. Zhang15b , H. Zhang15c , J. Zhang6 , L. Zhang15c , L. Zhang58a , M. Zhang170 , P. Zhang15c , R. Zhang58a , R. Zhang24 , X. Zhang58b , Y. Zhang15d , Z. Zhang128 , P. Zhao47 , Y. Zhao58b,128,ah , Z. Zhao58a , A. Zhemchugov77 , Z. Zheng103 , D. Zhong170 , B. Zhou103 , C. Zhou178 , L. Zhou41 , M. S. Zhou15d , M. Zhou152 , N. Zhou58c , Y. Zhou7 , C. G. Zhu58b , H. L. Zhu58a , H. Zhu15a , J. Zhu103 , Y. Zhu58a , X. Zhuang15a , K. Zhukov108 , V. Zhulanov120a,120b , A. Zibell174 , D. Zieminska63 , N. I. Zimine77 , S. Zimmermann50 , Z. Zinonos113 , M. Zinser97 , M. Ziolkowski148 , G. Zobernig178 , A. Zoccoli23a,23b , K. Zoch51 , T. G. Zorbas146 , R. Zou36 , M. Zur Nedden19 , L. Zwalinski35 1 Department of Physics, University of Adelaide, Adelaide, Australia 2 Physics Department, SUNY Albany, Albany, NY, USA 3 Department of Physics, University of Alberta, Edmonton, AB, Canada 123 290 Page 46 of 51 Eur. Phys. J. C (2019) 79:290 4 (a) Department of Physics, Ankara University, Ankara, Turkey; (b) Istanbul Aydin University, Istanbul, Turkey; (c) Division of Physics, TOBB University of Economics and Technology, Ankara, Turkey 5 LAPP, Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France 6 High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA 7 Department of Physics, University of Arizona, Tucson, AZ, USA 8 Department of Physics, University of Texas at Arlington, Arlington, TX, USA 9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece 10 Physics Department, National Technical University of Athens, Zografou, Greece 11 Department of Physics, University of Texas at Austin, Austin, TX, USA 12 (a) Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey; (b) Faculty of Engineering and Natural Sciences, Istanbul Bilgi University, Istanbul, Turkey; (c) Department of Physics, Bogazici University, Istanbul, Turkey; (d) Department of Physics Engineering, Gaziantep University, Gaziantep, Turkey 13 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan 14 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain 15 (a) Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China; (b) Physics Department, Tsinghua University, Beijing, China; (c) Department of Physics, Nanjing University, Nanjing, China; (d) University of Chinese Academy of Science (UCAS), Beijing, China 16 Institute of Physics, University of Belgrade, Belgrade, Serbia 17 Department for Physics and Technology, University of Bergen, Bergen, Norway 18 Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley, CA, USA 19 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany 20 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 21 School of Physics and Astronomy, University of Birmingham, Birmingham, UK 22 Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia 23 (a) Dipartimento di Fisica e Astronomia, Università di Bologna, Bologna, Italy; (b) INFN Sezione di Bologna, Bologna, Italy 24 Physikalisches Institut, Universität Bonn, Bonn, Germany 25 Department of Physics, Boston University, Boston, MA, USA 26 Department of Physics, Brandeis University, Waltham, MA, USA 27 (a) Transilvania University of Brasov, Brasov, Romania; (b) Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania; (c) Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania; (d) Physics Department, National Institute for Research and Development of Isotopic and Molecular Technologies, Cluj-Napoca, Romania; (e) University Politehnica Bucharest, Bucharest, Romania; (f) West University in Timisoara, Timisoara, Romania 28 (a) Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia; (b) Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 29 Physics Department, Brookhaven National Laboratory, Upton, NY, USA 30 Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina 31 Cavendish Laboratory, University of Cambridge, Cambridge, UK 32 (a) Department of Physics, University of Cape Town, Cape Town, South Africa; (b) Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa; (c) School of Physics, University of the Witwatersrand, Johannesburg, South Africa 33 Department of Physics, Carleton University, Ottawa, ON, Canada 34 (a) Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies-Université Hassan II, Casablanca, Morocco; (b) Centre National de l’Energie des Sciences Techniques Nucleaires (CNESTEN), Rabat, Morocco; (c) Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Marrakech, Morocco; (d) Faculté des Sciences, Université Mohamed Premier and LPTPM, Oujda, Morocco; (e) Faculté des sciences, Université Mohammed V, Rabat, Morocco 35 CERN, Geneva, Switzerland 36 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA 37 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France 38 Nevis Laboratory, Columbia University, Irvington, NY, USA 123 Eur. Phys. J. C (2019) 79:290 Page 47 of 51 290 39 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 40 (a) Dipartimento di Fisica, Università della Calabria, Rende, Italy; (b) INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Frascati, Italy 41 Physics Department, Southern Methodist University, Dallas, TX, USA 42 Physics Department, University of Texas at Dallas, Richardson, TX, USA 43 (a) Department of Physics, Stockholm University, Stockholm, Sweden; (b) Oskar Klein Centre, Stockholm, Sweden 44 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany 45 Lehrstuhl für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund, Germany 46 Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany 47 Department of Physics, Duke University, Durham, NC, USA 48 SUPA-School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK 49 INFN e Laboratori Nazionali di Frascati, Frascati, Italy 50 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany 51 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 52 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland 53 (a) Dipartimento di Fisica, Università di Genova, Genoa, Italy; (b) INFN Sezione di Genova, Genoa, Italy 54 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 55 SUPA-School of Physics and Astronomy, University of Glasgow, Glasgow, UK 56 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France 57 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA 58 (a) Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China; (b) Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China; (c) School of Physics and Astronomy, Shanghai Jiao Tong University, KLPPAC-MoE, SKLPPC, Shanghai, China; (d) Tsung-Dao Lee Institute, Shanghai, China 59 (a) Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (b) Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 60 Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan 61 (a) Department of Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong; (b) Department of Physics, University of Hong Kong, Hong Kong, China; (c) Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 62 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 63 Department of Physics, Indiana University, Bloomington, IN, USA 64 (a) INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy; (b) ICTP, Trieste, Italy; (c) Dipartimento di Chimica, Fisica e Ambiente, Università di Udine, Udine, Italy 65 (a) INFN Sezione di Lecce, Lecce, Italy; (b) Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy 66 (a) INFN Sezione di Milano, Milan, Italy; (b) Dipartimento di Fisica, Università di Milano, Milan, Italy 67 (a) INFN Sezione di Napoli, Naples, Italy; (b) Dipartimento di Fisica, Università di Napoli, Naples, Italy 68 (a) INFN Sezione di Pavia, Pavia, Italy; (b) Dipartimento di Fisica, Università di Pavia, Pavia, Italy 69 (a) INFN Sezione di Pisa, Pisa, Italy; (b) Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy 70 (a) INFN Sezione di Roma, Rome, Italy; (b) Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy 71 (a) INFN Sezione di Roma Tor Vergata, Rome, Italy; (b) Dipartimento di Fisica, Università di Roma Tor Vergata, Rome, Italy 72 (a) INFN Sezione di Roma Tre, Rome, Italy; (b) Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy 73 (a) INFN-TIFPA, Povo, Italy; (b) Università degli Studi di Trento, Trento, Italy 74 Institut für Astro- und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria 75 University of Iowa, Iowa City, IA, USA 76 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA 77 Joint Institute for Nuclear Research, Dubna, Russia 78 (a) Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil; (b) Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil; (c) Universidade Federal de São João del Rei (UFSJ), São João del Rei, Brazil; (d) Instituto de Física, Universidade de São Paulo, São Paulo, Brazil 79 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 123 290 Page 48 of 51 Eur. Phys. J. C (2019) 79:290 80 Graduate School of Science, Kobe University, Kobe, Japan 81 (a) Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Kraków, Poland; (b) Marian Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland 82 Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland 83 Faculty of Science, Kyoto University, Kyoto, Japan 84 Kyoto University of Education, Kyoto, Japan 85 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan 86 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 87 Physics Department, Lancaster University, Lancaster, UK 88 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK 89 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 90 School of Physics and Astronomy, Queen Mary University of London, London, UK 91 Department of Physics, Royal Holloway University of London, Egham, UK 92 Department of Physics and Astronomy, University College London, London, UK 93 Louisiana Tech University, Ruston, LA, USA 94 Fysiska institutionen, Lunds universitet, Lund, Sweden 95 Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules (IN2P3), Villeurbanne, France 96 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain 97 Institut für Physik, Universität Mainz, Mainz, Germany 98 School of Physics and Astronomy, University of Manchester, Manchester, UK 99 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 100 Department of Physics, University of Massachusetts, Amherst, MA, USA 101 Department of Physics, McGill University, Montreal, QC, Canada 102 School of Physics, University of Melbourne, Melbourne, VIC, Australia 103 Department of Physics, University of Michigan, Ann Arbor, MI, USA 104 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA 105 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus 106 Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Belarus 107 Group of Particle Physics, University of Montreal, Montreal, QC, Canada 108 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 109 Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia 110 National Research Nuclear University MEPhI, Moscow, Russia 111 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 112 Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany 113 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany 114 Nagasaki Institute of Applied Science, Nagasaki, Japan 115 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 116 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA 117 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, The Netherlands 118 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands 119 Department of Physics, Northern Illinois University, De Kalb, IL, USA 120 (a) Budker Institute of Nuclear Physics, SB RAS, Novosibirsk, Russia; (b) Novosibirsk State University, Novosibirsk, Russia 121 Department of Physics, New York University, New York, NY, USA 122 Ohio State University, Columbus, OH, USA 123 Faculty of Science, Okayama University, Okayama, Japan 124 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA 125 Department of Physics, Oklahoma State University, Stillwater, OK, USA 126 Palacký University, RCPTM, Joint Laboratory of Optics, Olomouc, Czech Republic 127 Center for High Energy Physics, University of Oregon, Eugene, OR, USA 123 Eur. Phys. J. C (2019) 79:290 Page 49 of 51 290 128 LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France 129 Graduate School of Science, Osaka University, Osaka, Japan 130 Department of Physics, University of Oslo, Oslo, Norway 131 Department of Physics, Oxford University, Oxford, UK 132 LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France 133 Department of Physics, University of Pennsylvania, Philadelphia, PA, USA 134 Konstantinov Nuclear Physics Institute of National Research Centre “Kurchatov Institute”, PNPI, St. Petersburg, Russia 135 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA 136 (a) Laboratório de Instrumentação e Física Experimental de Partículas-LIP, Lisbon, Portugal; (b) Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal; (c) Departamento de Física, Universidade de Coimbra, Coimbra, Portugal; (d) Centro de Física Nuclear da Universidade de Lisboa, Lisbon, Portugal; (e) Departamento de Física, Universidade do Minho, Braga, Portugal; (f) Departamento de Física Teorica y del Cosmos, Universidad de Granada, Granada, Spain; (g) Dep Física and CEFITEC of Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal 137 Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 138 Czech Technical University in Prague, Prague, Czech Republic 139 Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic 140 State Research Center Institute for High Energy Physics, NRC KI, Protvino, Russia 141 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK 142 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France 143 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA 144 (a) Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile; (b) Departamento de Física, Universidad Técnica Federico Santa María, Valparaiso, Chile 145 Department of Physics, University of Washington, Seattle, WA, USA 146 Department of Physics and Astronomy, University of Sheffield, Sheffield, UK 147 Department of Physics, Shinshu University, Nagano, Japan 148 Department Physik, Universität Siegen, Siegen, Germany 149 Department of Physics, Simon Fraser University, Burnaby, BC, Canada 150 SLAC National Accelerator Laboratory, Stanford, CA, USA 151 Physics Department, Royal Institute of Technology, Stockholm, Sweden 152 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA 153 Department of Physics and Astronomy, University of Sussex, Brighton, UK 154 School of Physics, University of Sydney, Sydney, Australia 155 Institute of Physics, Academia Sinica, Taipei, Taiwan 156 (a) E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b) High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 157 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel 158 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 159 Department of Physics, Aristotle University of Thessaloniki, Thessaloníki, Greece 160 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan 161 Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan 162 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 163 Tomsk State University, Tomsk, Russia 164 Department of Physics, University of Toronto, Toronto, ON, Canada 165 (a) TRIUMF, Vancouver, BC, Canada; (b) Department of Physics and Astronomy, York University, Toronto, ON, Canada 166 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 167 Department of Physics and Astronomy, Tufts University, Medford, MA, USA 168 Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA 169 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 170 Department of Physics, University of Illinois, Urbana, IL, USA 171 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain 172 Department of Physics, University of British Columbia, Vancouver, BC, Canada 123 290 Page 50 of 51 Eur. Phys. J. C (2019) 79:290 173 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada 174 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany 175 Department of Physics, University of Warwick, Coventry, UK 176 Waseda University, Tokyo, Japan 177 Department of Particle Physics, Weizmann Institute of Science, Rehovot, Israel 178 Department of Physics, University of Wisconsin, Madison, WI, USA 179 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 180 Department of Physics, Yale University, New Haven, CT, USA 181 Yerevan Physics Institute, Yerevan, Armenia a Also at Borough of Manhattan Community College, City University of New York, NY, USA b Also at California State University, East Bay, USA c Also at Centre for High Performance Computing, CSIR Campus, Rosebank, Cape Town, South Africa d Also at CERN, Geneva, Switzerland e Also at CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France f Also at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève, Switzerland g Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain h Also at Departamento de Física Teorica y del Cosmos, Universidad de Granada, Granada, Spain i Also at Department of Applied Physics and Astronomy, University of Sharjah, Sharjah, United Arab Emirates j Also at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece k Also at Department of Physics and Astronomy, University of Louisville, Louisville, KY, USA l Also at Department of Physics and Astronomy, University of Sheffield, Sheffield, UK m Also at Department of Physics, California State University, Fresno, CA, USA n Also at Department of Physics, California State University, Sacramento, CA, USA o Also at Department of Physics, King’s College London, London, UK p Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia q Also at Department of Physics, Stanford University, Stanford, USA r Also at Department of Physics, University of Fribourg, Fribourg, Switzerland s Also at Department of Physics, University of Michigan, Ann Arbor, MI, USA t Also at Giresun University, Faculty of Engineering, Giresun, Turkey u Also at Graduate School of Science, Osaka University, Osaka, Japan v Also at Hellenic Open University, Patras, Greece w Also at Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania x Also at II Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany y Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain z Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany aa Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, The Netherlands ab Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary ac Also at Institute of Particle Physics (IPP), Canada ad Also at Institute of Physics, Academia Sinica, Taipei, Taiwan ae Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan af Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia ag Also at Istanbul University, Dept. of Physics, Istanbul; Turkey ah Also at LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France ai Also at Louisiana Tech University, Ruston, LA, USA aj Also at LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France ak Also at Manhattan College, New York, NY, USA al Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia am Also at National Research Nuclear University MEPhI, Moscow, Russia an Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany ao Also at School of Physics, Sun Yat-sen University, Guangzhou, China 123 Eur. Phys. J. C (2019) 79:290 Page 51 of 51 290 ap Also at The City College of New York, New York, NY, USA aq Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China ar Also at Tomsk State University, Tomsk, and Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia as Also at TRIUMF, Vancouver, BC, Canada at Also at Universita di Napoli Parthenope, Naples, Italy ∗ Deceased 123