Eur. Phys. J. C (2019) 79:714 https://doi.org/10.1140/epjc/s10052-019-7216-3 Regular Article - Theoretical Physics Emerging patterns of New Physics with and without Lepton Flavour Universal contributions Marcel Algueró1,2 , Bernat Capdevila1,2,a , Andreas Crivellin3,4 , Sébastien Descotes-Genon5 , Pere Masjuan1,2 , Joaquim Matias1,2 , Javier Virto6,7 1 Grup de Física Teòrica (Departament de Física), Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain 2 Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra, Barcelona, Spain 3 Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland 4 Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland 5 Laboratoire de Physique Théorique, UMR 8627, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France 6 Physics Department T31, Technische Universität München, James Franck-Strasse 1, 85748 Garching, Germany 7 Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Av., Cambridge, MA 02139, USA Received: 27 May 2019 / Accepted: 31 July 2019 / Published online: 24 August 2019 © The Author(s) 2019 Abstract We perform a model-independent global fit to (NP). Their analyses can be efficiently and consistently per- b → s+ − observables to confirm existing New Physics formed in a model-independent effective field theory (EFT) (NP) patterns (or scenarios) and to identify new ones emerg- framework (see, for instance, [1–3]), where all short-distance ing from the inclusion of the updated LHCb and Belle mea- physics (including NP) is encoded in Wilson coefficients, surements of R K and R K ∗ , respectively. Our analysis, updat- i.e. the coefficients of higher-dimension operators. A cen- ing Refs. Capdevila et al. (J Virto JHEP 1801:093, 2018) and tral open question is then which pattern(s) in the space of Algueró et al. (J Matias Phys Rev D 99(7):075017, 2019) the Wilson coefficients is (are) preferred by b → s+ − and including these new data, suggests the presence of right- observables. More precise measurements, in particular for handed couplings encoded in the Wilson coefficients C9 μ the observables showing deviations from the Standard Model and C10 μ . It also strengthens our earlier observation that (SM) expectations (P5 [4], R K ,K ∗ ,φ , Q 5 [5]…), help us to a lepton flavour universality violating (LFUV) left-handed improve the results of this EFT analysis, which can then be lepton coupling (C9μ V = − C V ), often preferred from the used as a guideline for the construction of phenomenologi- 10μ model building point of view, accommodates the data better cally accurate NP models. if lepton-flavour universal (LFU) NP is allowed, in particular In this context we present here an update and extension of in C9U . Furthermore, this scenario with LFU NP provides a our recent works in Refs. [1,2], in the light of new measure- simple and model-independent connection to the b → cτ ν ments of key observables involved in b → s+ − anomalies. anomalies, showing a preference of ≈ 7 σ with respect to We update the experimental value of the ratio probing lepton μ+ μ− ) the SM. It may also explain why fits to the whole set of flavour universality (LFU) defined as R K = BB(B→K(B→K e+ e− ) : b → s+ − data or to the subset of LFUV data exhibit stronger preferences for different NP scenarios. Finally, moti- R [1.1,6] +0.060 +0.016 K LHCb = 0.846−0.054 −0.014 , vated by Z  models with vector-like quarks, we propose four new scenarios with LFU and LFUV NP contributions that R [1,6] +0.27 K Belle = 0.98−0.23 ± 0.06 , (1) give a very good fit to data. [q 2 >14.18] R K Belle = 1.11+0.29 −0.26 ± 0.07 , as announced recently by the LHCb collaboration [6], corre- 1 Introduction sponding to the average of Run-1 and part of Run-2 (2015- 2016) measurements, and the Belle collaboration [7], com- The flavour anomalies in b → s+ − processes are at bining the data from charged and neutral modes. The cor- present among the most promising signals of New Physics relations with the (finely binned) measurements of B(B → K μ+ μ− ) [8] are tiny and therefore neglected here. In addi- a e-mail: bcapdevila@ifae.es tion the Belle collaboration has also presented new results 123 714 Page 2 of 10 Eur. Phys. J. C (2019) 79:714 for R K ∗ , the equivalent LFU-violating (LFUV) ratio for  from the Belle collaboration [12] where the est update of P4,5 B → K ∗ , in three bins [9], again considering both charged muon and electron modes are considered separately (averag- and neutral channels: ing charged and neutral modes), superseding the previous measurement in Ref. [13] where an average over both lep- R [0.045,1.1] K∗ +0.36 = 0.52−0.26 ± 0.05, tonic modes is presented. This allows us to include an addi- tional measurement P5μ  (exhibiting a 2.6 σ discrepancy with R [1.1,6] K∗ = 0.96+0.45 −0.29 ± 0.11, respect to the SM) as well as the LFUV observable Q 5 in our R [15,19] K∗ = 1.18+0.52 −0.32 ± 0.10. (2) analysis (see Ref. [14] for another recent analysis including this update). Our treatment for the Belle observables within the global fit In addition to updating the experimental inputs, our analy- follows the same strategy as described in Ref. [1] for Q 4,5 sis explores new emerging directions in the parameter space where we introduced a nuisance parameter accounting for spanned by the effective operators driven by data within two the relative weight of each isospin component. different frameworks. First, following Ref. [1] we assume in We have also updated our average for B(Bs → μ+ μ− ) Sect. 2 that NP affects only muons and is thus purely Lepton- including the latest measurement from the ATLAS collab- Flavour Universality Violating (LFUV). In Sect. 3 we follow oration [10] and taking into account the most recent lattice the complementary approach discussed in Ref. [2], where update of f Bs for N f = 2 + 1 + 1 simulations collected in we consider the consequences of removing the frequently Ref. [11]. made hypothesis that NP is purely LFUV. We then explore A relatively small numerical impact of such updates has the implications of allowing both LFU and LFUV NP con- been found. As in Ref. [1], our analysis also includes the lat- tributions to the Wilson coefficients C9() and C10() . Table 1 Most prominent 1D patterns of NP in b → sμ+ μ− . PullSM is quoted in units of standard deviation 1D Hyp. All LFUV Best fit 1σ /2σ PullSM p-value Best fit 1 σ/ 2 σ PullSM p-value NP C9μ − 0.98 [− 1.15, − 0.81] 5.6 65.4% − 0.89 [− 1.23, − 0.59] 3.3 52.2% [− 1.31, − 0.64] [− 1.60, − 0.32] NP = − C NP C9μ − 0.46 [− 0.56, − 0.37] 5.2 55.6% − 0.40 [− 0.53, − 0.29] 4.0 74.0% 10μ [− 0.66, − 0.28] [− 0.63, − 0.18] NP = − C  C9μ − 0.99 [− 1.15, − 0.82] 5.5 62.9% − 1.61 [− 2.13, − 0.96] 3.0 42.5% 9μ [− 1.31, − 0.64] [− 2.54, − 0.41] NP C9μ = − 3C9e NP − 0.87 [− 1.03, − 0.71] 5.5 61.9% − 0.66 [− 0.90, − 0.44] 3.3 52.2% [− 1.19, − 0.55] [− 1.17, − 0.24] The p-value of the SM hypothesis is 11.0% for the fit “All” and 8.0% for the fit LFUV Table 2 Most prominent 2D patterns of NP in b → sμ+ μ− . The last five rows correspond to Hypothesis 1: (C9μ NP = − C  , C NP = C  ), 2: 9 μ 10μ 10 μ (C9μ = − C9 μ , C10μ = − C10 μ ), 3: (C9μ = − C10μ , C9 μ = C10 μ ), 4: (C9μ = − C10μ , C9 μ = − C10 μ ) and 5: (C9μ , C9 μ = − C10 μ ) NP NP NP NP NP NP NP 2D Hyp. All LFUV Best fit PullSM p-value Best fit PullSM p-value (C9μ NP , C NP ) 10μ (− 0.91, 0.18) 5.4 68.7% (− 0.16, 0.56) 3.4 76.9% NP , C  ) (C9μ 7 (− 1.00, 0.02) 5.4 67.9% (− 0.90, − 0.04) 2.9 55.1% NP , C  ) (C9μ 9μ (− 1.10, 0.55) 5.7 75.1% (− 1.79, 1.14) 3.4 76.1% NP , C  ) (C9μ 10 μ (− 1.14, − 0.35) 5.9 78.6% (− 1.88, − 0.62) 3.8 91.3% NP , C NP ) (C9μ 9e (− 1.05, − 0.23) 5.3 66.2% (− 0.73, 0.16) 2.8 52.3% Hyp. 1 (− 1.06, 0.26) 5.7 75.7% (− 1.62, 0.29) 3.4 77.6% Hyp. 2 (− 0.97, 0.09) 5.3 65.2% (− 1.95, 0.25) 3.2 66.6% Hyp. 3 (− 0.47, 0.06) 4.8 55.7% (− 0.39, − 0.13) 3.4 76.2% Hyp. 4 (− 0.49, 0.12) 5.0 59.3% (− 0.48, 0.17) 3.6 84.3% Hyp. 5 (− 1.14, 0.24) 5.9 78.7% (− 2.07, 0.52) 3.9 92.5% 123 Eur. Phys. J. C (2019) 79:714 Page 3 of 10 714 Motivated by the new emerging directions in the LFUV 2 Global fits in presence of LFUV NP case we also extend our analysis of NP scenarios to allow for the presence of LFU NP right handed-currents (RHC). In We start by considering the fits for NP scenarios which affect Sect. 4, we focus on a particular scenario (scenario 8) which muon modes only. Tables 1, 2 and 3 and Fig. 1 update the can, within an EFT framework, link the flavour anomalies in corresponding tables and figures of Ref. [1] based on fits to b → s+ − and b → cν processes. Furthermore, we con- the full set of data (“All”) or restricted to quantities assessing sider new patterns, motivated by Z  models with vector-like LFUV. While we do not observe any significant difference in quarks, which naturally predict LFU effects in C10() com- the 1D scenarios with “All” data compared to Ref. [1], some plemented by LFUV ones. Finally, we sum up our results of the Pulls (with respect to the SM) for the LFUV 1D fits get in Sect. 5. An appendix is devoted to the description of the reduced by half a standard deviation. A few other comments correlations obtained for the various Wilson coefficients in are in order: the most relevant scenarios considered in this article. Table 3 1 and 2 σ confidence intervals for the NP contributions to Wilson coefficients in the 6D hypothesis allowing for NP in b → sμ+ μ− operators dominant in the SM and their chirally-flipped counterparts, for the fit “All” C7NP NP C9μ NP C10μ C7 C9 μ C10 μ Best fit + 0.01 − 1.10 + 0.15 + 0.02 + 0.36 − 0.16 1σ [− 0.01, +0.05] [− 1.28, − 0.90] [− 0.00, +0.36] [− 0.00, +0.05] [− 0.14, +0.87] [− 0.39, +0.13] 2σ [− 0.03, +0.06] [− 1.44, − 0.68] [− 0.12, +0.56] [− 0.02, +0.06] [− 0.49, +1.23] [− 0.58, +0.33] The PullSM is 5.1 σ and the p-value is 81.6% Fig. 1 From left to right: allowed regions in the (C9μ NP , C NP ), (C NP , C  ) and (C NP , C NP ) planes for the corresponding 2D hypotheses, using all 10μ 9μ 9μ 9μ 9e available data (fit “All”) upper row or LFUV fit lower row 123 714 Page 4 of 10 Eur. Phys. J. C (2019) 79:714 Table 4 Coefficients for the polynomial parameterisation of the numerator and denominator of R [1.1,6] K in the vicinity of the SM point α0μ α1μ α2μ α3μ α4μ α5μ α6μ α7μ α8μ α9μ α10μ 4.00 0.92 0.12 0.92 0.12 0.24 − 1.06 0.12 − 1.06 0.12 0.25 α0e α1e α2e α3e α4e α5e α6e α7e α8e α9e α10e 3.99 0.92 0.12 0.92 0.12 0.24 − 1.05 0.12 − 1.05 0.12 0.24 1. The scenario C9μ NP = − C  , which favours a SM-like 9μ With the updated data, little change is observed among the value of R [1.1,6] [2,15], has an increased significance in preferred 2D NP models. Nevertheless, with an R [1.1,6] K value K the “All” fit compared to our earlier analysis. closer to one, scenarios with right-handed currents (RHC), 2. The scenario C9μ NP has the largest p-value in the “All” namely (C9μ NP , C  ) and (C NP , C  ), seem to emerge. The 9μ 9μ 10 μ NP = − C NP has the largest p-value in the fit while C9μ first scenario is naturally generated in a Z  model with oppo- 10μ LFUV fit, a difference which can be solved through the site couplings to right-handed and left-handed quarks and introduction of LFU NP (see Ref. [2] and next section). was proposed in Ref. [17] within the context of a gauged 3. The best-fit point for the scenario C9μ NP coincides now in L μ − L τ symmetry with vector-like quarks. The latter (of the “All” and LFUV fits. masses m D and m Q ) are charged under L μ − L τ and have 4. The scenario with only C10μ NP has a significance in the the same SM quantum numbers as right-handed down quarks “All” fit of only 4.0σ level and 3.9σ for the LFUV fit, and left-handed quark doublets, respectively. The vector-like which explains its absence from Table 1 as happens in quarks couple to the SM ones and to a scalar φ which breaks Ref. [1]. the L μ − L τ symmetry with couplings Y D,Q . We show the update of Fig. 2 of Ref. [17] assuming Y D,Q = 1 in Fig. 2. Since the current fit allows for C9 μ = 0 at the two sigma Concerning the 2D scenarios collected in Table 2, the same level, the SU (2) singlet vector-like quark can still be decou- picture arises as in Ref. [1], except that C9e NP is now basically pled [18]. zero and small contributions to RHC seem slightly favoured (C9 μ > 0, C10 μ < 0).1 Indeed, these RHC contributions tend to increase the value of R [1.1,6] K while C9μNP < 0 tend to decrease it as can be seen from the explicit expression of R [1.1,6] K = Aμ /Ae where the numerator and the denominator can be given by an approximate polynomial parameterisation near the SM point  2 A = α0 + α1 C9 NP + α2 C9 NP + α3 C9   2 +α4 C9  + α5 C9 NP C9   2 +α6 C10 NP + α7 C10NP  2 +α8 C10  + α9 C10  + α10 C10 NP C10  (3) with the coefficients provided in Table 4 (for linearised expressions, see Refs. [2,16]). We introduce a new Hyp. 5 in Table 2. The comparison between Hyps. 4 and 5 shows that the scenario C9 μ = − C10 μ (left-handed lepton coupling for right-handed quarks) prefers to be associated with C9μ NP (vector lepton coupling for left-handed quarks) rather than NP = − C NP (left-handed lepton coupling for left-handed C9μ 10μ quarks). Finally, no significant changes are observed in the 6D fit, except for the slight increase in the PullSM , see Table 3. Fig. 2 Preferred regions (at the 1, 2 and 3 σ level) for the L μ − L τ 1 Interestingly, these small contributions also reduce slightly the mild model of Ref. [17] from b → s+ − data (green) in the (m Q , m D ) tension between P5 at large and low recoils pointed out in Ref. [15] plane with Y D,Q = 1. The contour lines denote the predicted values compared to the scenario with only C9μ NP . for R [1.1,6] K (red, dashed) and R [1.1,6] K∗ (blue, solid) 123 Eur. Phys. J. C (2019) 79:714 Page 5 of 10 714 3 Global fits in presence of LFUV and LFU NP shown by the scenarios 6, 8 in Table 5 with p-values larger than 70%. We turn to scenarios that allow also for the presence of LFU We observe a very slight decrease in significance for the NP [2,15] (in addition to LFUV contributions to muons only), scenarios 5–7, with the exception of scenario 8 which exhibits leading to the value of the Wilson coefficients one of the most significant pulls with respect to the SM. Scenario 8 of Ref. [2] can actually be realized via off-shell Cie = CiU , Ciμ = CiU + CiV . (4) photon penguins [19] in a leptoquark model explaining also (with i = 9, 10) for b → se+ e− and b → sμ+ μ− transitions b → cτ ν data (we will return to this point in the following respectively. section). We update some of the scenarios considered in Ref. [2] Updated plots of the 2D LFU-LFUV scenarios discussed in Table 5. Concerning new directions in parameter space in Ref. [2] are shown in Fig. 3. we allow for RHC, motivated by the results of the previous The new scenarios 9–13 are characterized by a C10( U  ) con- section, and focus on scenarios that could be fairly easily tribution. This arises naturally in models with modified Z obtained in simple NP models. couplings (to a good approximation C9( U can be neglected). ) With the updated experimental inputs, we confirm our ear- The pattern of scenario 9 occurs in Two-Higgs-Doublet mod- lier result [2] that a LFUV left-handed lepton coupling struc- els where this flavour universal effect can be supplemented ture (corresponding to C9V = − C10 V and preferred from a by a C9V = − C10V effect [20]. model-building point of view) yields a better description of In case of scenarios 11–13, one can invoke models with data with the addition of LFU-NP in the coefficients C9,10 , as vector-like quarks where modified Z couplings are even Table 5 Most prominent patterns for LFU and LFUV NP contributions from Fit “All” Scenario Best-fit point 1σ 2σ PullSM p-value Scenario 5 V C9μ − 0.36 [− 0.86, +0.10] [− 1.41, +0.52] 5.2 71.2% V C10μ + 0.67 [+0.24, +1.03] [− 1.73, +1.36] C9U = U C10 − 0.59 [− 0.90, − 0.12] [− 1.13, +0.68] Scenario 6 V = − CV C9μ − 0.50 [− 0.61, − 0.38] [− 0.72, − 0.28] 5.5 71.0% 10μ C9U = U C10 − 0.38 [− 0.52, − 0.22] [− 0.64, − 0.06] Scenario 7 V C9μ − 0.78 [− 1.11, − 0.47] [− 1.45, − 0.18] 5.3 66.2% C9U − 0.20 [− 0.57, +0.18] [− 0.92, +0.55] Scenario 8 V = − CV C9μ − 0.30 [− 0.42, − 0.20] [− 0.53, − 0.10] 5.7 75.2% 10μ C9U − 0.74 [− 0.96, − 0.51] [− 1.15, − 0.25] Scenario 9 V = − CV C9μ − 0.57 [− 0.73, − 0.41] [− 0.87, − 0.28] 5.0 60.2 % 10μ U C10 − 0.34 [− 0.60, − 0.07] [− 0.84, +0.18] Scenario 10 V C9μ − 0.95 [− 1.13, − 0.76] [− 1.30, − 0.57] 5.5 69.5 % U C10 + 0.27 [0.08, 0.47] [− 0.09, 0.66] Scenario 11 V C9μ − 1.03 [− 1.22, − 0.84] [− 1.38, − 0.65] 5.6 73.6 % U C10  − 0.29 [− 0.47, − 0.12] [− 0.63, 0.05] Scenario 12 C9V μ − 0.03 [− 0.22, 0.15] [− 0.40, 0.32] 1.6 15.7% U C10 +0.41 [0.21, 0.63] [0.02, 0.83] Scenario 13 V C9μ − 1.11 [− 1.28, − 0.91] [− 1.41, − 0.71] 5.4 78.7% C9V μ +0.53 [0.24, 0.83] [− 0.10, 1.11] U C10 +0.24 [0.01, 0.48] [− 0.21, 0.69] U C10  − 0.04 [− 0.28, 0.20] [− 0.48, 0.42] Scenarios 5–8 were introduced in Ref. [2]. Scenarios 9 (motivated by 2HDMs [20]) and 10–13 (motivated by Z  models with vector-like quarks [21]) are new 123 714 Page 6 of 10 Eur. Phys. J. C (2019) 79:714 Fig. 3 Updated plots of Ref. [2] corresponding to scenarios 6, 7, 8 and the new scenario 9 induced at tree level. The LFU effect in C10( U  ) can be accom- not be swapped for its chirally-flipped counterpart without V  panied by a C9,10( ) effect from Z exchange [21]. Vector- consequences. Finally, the allowed regions for the new LFU like quarks with the quantum numbers of right-handed down scenarios are displayed in Fig. 4. quarks (left-handed quarks doublets) generate effect in C10 U V U V  and C9 (C10( ) and C9 ) for a Z boson with vector couplings 4 Model-independent connection to b → cν to muons [21]. The comparison of scenarios 10 and 12 illustrates that In complement with the above EFT analysis, we focus now C9μ V plays an important role in LFU NP scenarios and can- on the NP interpretation of scenario 8. Indeed, this sce- Fig. 4 Updated plots of Ref. [2] corresponding to the new scenarios 10, 11, 12 123 Eur. Phys. J. C (2019) 79:714 Page 7 of 10 714 Fig. 5 Left: preferred regions at the 1, 2 and 3 σ level (green) in the predicted values for these ratios. Right: Impact of favoured NP scenar- V = − C V , C U ) plane from b → s+ − data. The red contour (C9μ 10μ 9 ios on the observable P5 . Only central values for the NP scenarios are lines show the corresponding regions once R D (∗) is included in the fit displayed. The most interesting scenarios cluster together while tradi- (for  = 2 TeV). The horizontal blue (vertical yellow) band is con- tional scenarios like C9μ = − C10μ or the scenario C10μ considered in sistent with R D (∗) (R K ) at the 2 σ level and the contour lines show the Ref. [28] fail to explain this anomaly nario allows for a model-independent connection between models [31,32]), we neglect it here, leading to the left plot the anomalies in b → s+ − and those in b → cτ ν, which in Fig. 5, where we include the recent update of Ref. [33] to are now at the 3.1σ level [22]. draw the band for R D(∗) . Note that this scenario has a pull Such a correlation arises in the SMEFT scenario where of 7.0 σ due to the inclusion of R D (∗) , which increases χ 2 C (1) = C (3) expressed in terms of gauge-invariant dimension- by ∼ 20. 6 operators [23,24]. This scenario stems naturally from mod- els with an SU (2) singlet vector leptoquark [25–27]. The operator involving-third generation leptons explains R D (∗) 5 Conclusions and the one involving the second generation gives a LFUV effect in b → sμ+ μ− processes. The constraint from b → In summary, including recent updates (R K , R K ∗ and B(Bs → cτ ν and SU (2) L invariance leads generally to large con- μ+ μ− )) our global model-independent analysis yields a very tributions to the operator s̄γ μ PL bτ̄ γμ PL τ , which enhances similar picture to the one previously found in Refs. [1,2] for b → sτ + τ − processes [24], but also mixes into O9 and gen- the various NP scenarios of interest with some important erates C9U at μ = m b [19]. Note that not all models addressing peculiarities. In presence of LFUV NP contributions only, the charged and neutral current anomalies simultaneously the 1D fits to “All” observables remain basically unchanged have an anarchic flavour structure. In fact, in the case of showing the preference for C9μ NP scenario over C NP = − C NP . 9μ 10μ alignment in the down-sector [29,30] one does not find large If only LFUV observables are considered the situation is effects in b → sτ + τ − or C9U . reversed, as already found in Ref. [1], but now with an Therefore, scenario 8 is reproduced in this setup with an increased gap between the significances. This difference additional correlation between C9U and R D (∗) . Assuming a between the preferred hypotheses, depending on the data set generic flavour structure so that small CKM elements can be used, can be solved introducing LFU NP contributions [2]. neglected [19,24], we get The main differences arise for the 2D scenarios: the cases NP , C  ), (C NP , C  ) or (C NP , C     including RHC, (C9μ 10 μ 9μ 9μ 9μ 9μ = R D (∗) log(2 /(1TeV2 )) − C10 μ ), can accommodate better the recent updates, which C9 ≈ 7.5 1 − U 1+ . (5) R D (∗) SM 10.5 enhances the significance of these scenarios compared to Ref. [1], pointing to new patterns including RHC. A more pre- Realizations of this scenario in specific NP models yield cise experimental measurement of the observable P1 [34,35] also an effect in C7 generally [19]. However, since this effect would be very useful to confirm or not the presence of RHC is model dependent (and in fact small in some UV complete NP encoded in C9 μ and C10 μ . 123 714 Page 8 of 10 Eur. Phys. J. C (2019) 79:714 We also observe interesting changes in the 2D fits in ment brought by RHC has been observed in Refs. [14,36], the presence of LFU NP, where new scenarios (not con- whereas the interest of LFU NP contributions is also identi- sidered in Ref. [2]) give a good fit to data with C10 U () and fied in Refs. [14,28,38]. Most of the analyses observe that additional LFUV contributions. For example scenario 11 the slight deviation from B(Bs → μ+ μ− ) plays no specific V , C  ) can accommodate b → s+ − data very well, at (C9μ role in the global fit [36,37], apart from Ref. [28]. In the 10 μ the same level as scenario 8. Scenarios including LFU NP in latter analysis, the significance of a scenario with only C10μ NP left-handed currents (discussed in Ref. [2]) stay practically is much more important than in our case, and the hierar- unchanged but with some preference for scenarios 6 and 8, chies between the significances of 2D scenarios is different. which have a (V − A) structure for the LFUV-NP and a V After discussion with the authors of Ref. [28], this differ- or (V + A) structure for the LFU-NP. Furthermore, we have ence comes from their inclusion of Bs - B̄s mixing and the included additional scenarios 9 and 10 that exhibit a signifi- assumption that F = 2 observables are purely governed cance of 5.0σ and 5.5σ respectively. by the SM, which helps them sharpening the prediction for We note that the amount of LFU NP is sensitive to the B(Bs → μ+ μ− ) and increase the weight of this observable structure of the LFUV component. For instance, in scenario in the fit. Our present analysis does not rely on this strong V and C U ) the LFU component is negligible at its best 7 (C9μ hypothesis, which should be contrasted with the fact that most 9 fit point. On the contrary, if the LFUV-NP has a (V − A) models invoked to explain b → s+ − anomalies typically structure, the LFU-NP component (C9U ) is large, as illus- affect also F = 2 observables. trated by scenarios 6, 8 and 9. Scenarios with NP in RHC (either LFU or LFUV) prefer such contributions at the 2σ Acknowledgements This work received financial support from Euro- pean Regional Development Funds under the Spanish Ministry of level (see scenarios 11 and 13) with the exception of sce- Science, Innovation and Universities (Projects FPA2014-55613-P and nario 12 with negligible C9V μ . The new values of R K and FPA2017-86989-P) and from the Agency for Management of Univer- R K ∗ seem thus to open a window for RHC contributions sity and Research Grants of the Government of Catalonia (project SGR while the new B(Bs → μμ) update (theory and experiment) 1069) [MA, BC, PM, JM] and from European Commission (Grant Agreements 690575, 674896 and 69219) [SDG]. The work of PM is helps only marginally scenarios with C10μ NP . supported by the Beatriu de Pinos postdoctoral program co-funded by Finally, we showed that scenario 8, which allows for the Agency for Management of University and Research Grants of a model-independent connection between the b → cτ ν the Government of Catalonia and by the COFUND program of the anomalies and the ones in b → s+ − , can explain all data Marie Sklodowska-Curie actions under the framework program Hori- zon 2020 of the European Commission. JM gratefully acknowledges the consistently and is preferred over the SM by 7 σ . financial support by ICREA under the ICREA Academia programme. Figure 5 illustrates the impact on the largest anomaly (P5 ) JV acknowledges funding from the European Union’s Horizon 2020 of some of the most significant scenarios. Interestingly, sev- research and innovation programme under the Marie Sklodowska-Curie eral of the scenarios currently favoured cluster around the Grant agreement no 700525, ‘NIOBE’ and support from SEJI/2018/033 (Generalitat Valenciana). The work of AC is supported by a Professor- same values for the bins showing deviations with respect to ship Grant (PP00P2_176884) of the Swiss National Science Founda- the SM. tion. We have thus identified a number of NP scenarios with similarly good p-values and pulls with respect to the SM, Data Availability Statement This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The experimental which are able to reproduce the b → s+ − data very well. data used in the analysis presented in this paper has already been pub- Hierarchies among these scenarios can be identified, but addi- lished by the different experiments cited in the text. Any further data tional data and reduced uncertainties are required to come to related to the specifics of our analysis can be reproduced by follow- a final conclusion. The full exploitation of LHC run-2 data ing the procedures detailed in the article and predecessors, that we cite whenever it is appropriate.] by the LHCb experiment (as well as by ATLAS and CMS) and the forthcoming results from the Belle and Belle II col- Open Access This article is distributed under the terms of the Creative laborations are expected to improve the situation very sig- Commons Attribution 4.0 International License (http://creativecomm nificantly in the forthcoming years, helping us to pin down ons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit the actual NP pattern hinted at by the b → s+ − anomalies to the original author(s) and the source, provide a link to the Creative currently observed and to build accurate phenomenological Commons license, and indicate if changes were made. models to be confirmed through other experimental probes Funded by SCOAP3 . such as direct production experiments. Note added After the completion of this work, several global analyses have been performed to assess NP scenar- Appendix A Correlations among fit parameters ios affecting b → s+ − processes [14,28,36,37]. They agree well with our findings, with small differences stem- In addition to the confidence regions provided for the vari- ming mainly from slightly different theoretical approaches ous scenarios in this article, we display here the correlation as well as theoretical and experimental inputs. The improve- matrices for the most interesting NP scenarios. 123 Eur. Phys. J. C (2019) 79:714 Page 9 of 10 714 1 Correlation matrices of fits to LFUV NP Below one can find the correlation matrices of scenarios 5– 11, in that order. First, we present the correlations between fit parameters of ⎛ ⎞ the NP scenarios defined in Tables 2 and 3. These are all NP 1.00 −0.93 0.91 solutions whose parameters assess LFUV NP. Corr(C9μV , C9U = C10 U , C10μ V ) = ⎝−0.93 1.00 −0.94⎠ By order of appearance in Table 2, the correlations 0.91 −0.94 1.00 between the coefficients of all 2D scenarios with PullSM  1.00 0.17 V Corr(C9μ = −C10μ V , C9U = C10 U )= 5.3σ are, 0.17 1.00 1.00 0.30 1.00 −0.85 , C10μ ) = NP NP Corr(C9μ V Corr(C9μ , C9U ) = 0.30 1.00 −0.85 1.00 1.00 −0.39 1.00 −0.44 NP Corr(C9μ , C9 μ ) = V Corr(C9μ = −C10μ V , C9U ) = −0.39 1.00 −0.44 1.00 1.00 0.33 1.00 0.69 NP Corr(C9μ , C10 μ ) = V Corr(C9μ = −C10μ V , C10 U )= 0.33 1.00 0.69 1.00 1.00 0.51 1.00 0.05 , C9e ) = NP NP Corr(C9μ V Corr(C9μ , C10 U )= 0.51 1.00 0.05 1.00 1.00 −0.17 1.00 0.20 NP Corr(C9μ = −C9 μ , C10μ NP = C10 μ ) = V Corr(C9μ , C10 U ) = −0.17 1.00 0.20 1.00 1.00 −0.34 No significant changes can be observed when comparing NP Corr(C9μ , C9 μ = −C10 μ ) = −0.34 1.00 with the results in App. 2 of Ref. [2]. As expected, C9μ V and The last two matrices correspond to Hyp. 1 and Hyp. 5 as C9U are highly anti-correlated, with its nominal value some- defined in Table 2. Despite the high PullSM of the 2D scenario what smaller than in [2]. Fit estimates of the parameters in NP , C  } (5.4σ ), its correlation matrix is not collected here {C9μ scenario {C9μ V = −C V , C U = C U } are now slightly corre- 10μ 9 10 7 due to the value of C7 being negligible, with tiny errors. lated, while before their correlation was negligible. Interest- Regarding the 6D fit of Table 3, ingly, however, we find the parameters of the new scenario V , C U } statistically independent up to a large extent. {C9μ ⎛ ⎞ 10 1.00 −0.34 −0.07 0.06 0.02 −0.03 ⎜−0.34 1.00 0.24 −0.06 0.04 0.24 ⎟ ⎜ ⎟ ⎜−0.07 0.24 1.00 −0.13 0.61 0.59 ⎟ Corr6D = ⎜ ⎜ ⎟ References ⎟ ⎜ 0.06 −0.06 −0.13 1.00 −0.13 −0.08⎟ ⎝ 0.02 0.04 0.61 −0.13 1.00 0.85 ⎠ 1. B. Capdevila, A. Crivellin, S. Descotes-Genon, J. Matias, J. 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