Constraint on the Higgs-Boson Mass from Nuclear Scattering Data

We exploit the experimental energy dependence of the neutron-lead scattering cross section to bound the mass of the Higgs boson, {ital m}{sub {ital H}}. We use the recently determined coupling constant of the Higgs particle to nucleons, {ital g}=2.1{times}10{sup {minus}3}, and find {ital m}{sub {ital H}}{approx gt}18 MeV.

The search for the Higgs boson is one of the most pressing issues in particle physics.A variety of physical processes have been used to constrain the mass of the Higgs particle.' Some of them have theoretical uncer- tainties that make them not completely reliable at present.In the light of this fact it is important to study phenomena that may lead to safe constraints on the Higgs-boson mass.
Nuclear scattering data have proven to be useful for placing constraints on the Higgs boson.Barbieri and Ericson were the first to notice that the angular depen- dence of the scattering cross section of neutrons on a nu- cleus was sensitive to the potential originated by a light- boson exchange.Here we shall show that the considera- tion of the energy dependence of the total cross section also leads to a limit on the Higgs-boson mass, which turns out to be more stringent.
In the low-energy region the energy dependence of the neutron-Pb scattering cross section then in our hard-core potential r,g is predicted to be r,ff 3 R.

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(5) The consistency of this theoretical prediction with data can be seen as follows.In the presence of the nuclear po- tential only, the value of R is obtained by using Introducing this value in Eq. ( 5) we obtain r,tr 6.3 fm. ( This has to be compared to the effective range extracted where the fit is obtained with data in the range 1.5X10 ~k ~3.1x10 fm The aim of the experiment in Ref. 4 was the deter- mination of the electric polarizability of the neutron, which is a parameter related to the linear term in k in the cross section (1).This very small effect is largely due to the nuclear charge distribution and its electric field and we will neglect it.On the contrary the values of a(0) and a2 in Eq. (2c) can be understood in terms of a simple hard-core potential and its effective range.
Indeed, the scattering amplitude for this nuclear po- tential reads which is in agreement with the prediction in Eq. (7).
A light Higgs boson would change the potential felt by a neutron when scattered off a nucleus.Indeed, a Higgs-boson exchange generates an attractive potential &0--~g 2 e mHr 4n r (9 where A is the atomic mass, mH the Higgs-boson mass, and g the coupling constant of the Higgs boson to nu- cleons.Now we need the scattering amplitude for the com- bined effect of the nuclear and the Higgs-induced poten- tial, regarding the latter contribution as a perturbation. As we will see the Higgs-boson exchange only affects the value of the parameters o(0) and a2 in Eq. ( 1).There- fore we will restrict our discussion to them.The proper treatment of our problem is the "distorted-wave Born ap- proximation." This approximation takes into account the distortion produced by the nuclear potential on the first-order scattering caused by VH, which is the weak potential.The total scattering amplitude can be written where f~i s the amplitude for the nuclear potential and is given by Eq. ( 3), and fH is the standard Born- approximation amplitude for VH only, fH(8) -2p Ag Here p is the reduced mass and 8 the scattering angle.
The term bf represents the distorting effect of the nu- clear potential and is given by 9.4B- bf -2p"VH(r) [Rp (r) jp (kr)]rdr . ( In the integrand, we have the S-wave-function solution in the presence of the nuclear potential alone, as well as the free solution jp(p) =(I/p)sinp.Explicit calculations show that bf is given by The limit on mH obviously depends on the coupling g of the Higgs boson on nucleons.Since the nucleon is a composite particle, some care is needed.The analysis of Ref. 7 leads to g ~g.5 x 10 4 nh 3 where nl, is the number of heavy quark flavors.Howev- er, recent experimental evidence for a large strange- quark sea in the nucleon increases the value in Eq. ( 19) The final amplitude in Eq. ( 10) can now be calculated by adding fH and bf given respectively by ( 11) and ( 14) to the nuclear amplitude f~g iven by (3).
Our idea is simple.It can be seen that the effect of the Higgs-boson potential is to increase the prediction for the effective range in Eq. ( 7), destroying the agree- ment we had in the limit mH , i.e. , without Higgs- boson exchange.To be conservative, we shall require that the nuclear and the Higgs-boson-induced potentials keep the agreement between theory and experiment within two standard deviations.(2i) This is our main result.
We have also calculated our limit for the coupling in Eq. ( 19).For nj, 3, we find m~~12 MeV, whereas for nq 4 we get mH ~14 MeV. (22) Finally, it is interesting to compare our results with previous work.The method of Barbieri and Ericson leads to the limit mB~10 MeV for g 2. 1x10 However, as the authors pointed out, their result holds if there are no fortuitous cancellations.Notice that our We can now find our bound as follows.We evaluate the total contribution to cr(0) and a2 keeping R and m~as free parameters.2a) and (2c) at the two-standard-deviation level.
The allowed values of R and mrs are shown in Fig. 1, for the g given by Eq. (20).We see that for high masses of the Higgs boson, R tends to the value in Eq. ( 6), as it should.Also, from Fig. 1 we can extract a lower limit on the mass of the Higgs boson,