IC/92/193
a it** •
INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS
MAJORON MODELS AND THE HIGGS SEARCH
Anjan S. Joshipura
and
INTERNATIONAL Saurabh D. Rindant ATOMIC ENERGY AGENCY
UNITED NATIONS EDUCATIONAL. SCIENTIFIC AND CULTURAL ORGANIZATION MIRAMARE'TRIESTE
IC/92/193
The I, s mechanism is a key ingredient in the description of the standard model. International Atomic Energy Agency The preii -d Higgs boson is however not yet found. The latest [1] lower limit on the and mass of 1 -tandard model (SM) Higgs coming from the data at LEP in e+e" collisions is 52 Ge\ He LEP data has been applied [2] not only to restrict the SM Higgs mass but United Nations Educational Scientific and Cultural Organization also to o rain parameters of extensions of the SM. Two popular extensions [3] studied INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS at length the minimal supersymmetric standard model (MSSM) and the general two Higgs do t models. These extensions contain more than one neutral Higgs boson which mi mong themselves. As a result of this mixing, the couplings of the neutral Higgs bo - in these models to the Z boson and fermions are different from those in the SM. I ce more freedom is available and the Higgs mass is less constrained in these MAJORON MODELS AND THE HIGGS SEARCH schemes. spite of this, the mass of any of the two neutral Higgs boson is not allowed to be les^ a about 44 GeVFl [2] in MSSM while in the general models with two Higgs doublets. could rule out a large range [2] in the values of the mixing angle as a function of the Hii mass. Anjan S. Joshipura" We w !o investigate here a possible bound on the Higgs mass in another popular extension ihe SM which is somewhat more economical and characteristically different International Centre for Theoretical Physics, Trieste, Italy from the • IT two extensions mentioned above. The class of models we consider is based on the mi ial SM extended by introducing an SU{2) x f/(l) singlet field 17, right-handed and neutrinos il a spontaneously broken global symmetry. This type of extension, with the global £/( quantum number identified with total lepton number, was first proposed [4] Saurabh D. Rindani as a novt I cans of generating neutrino mass. Since then, this type of models have been Theory Group, Physical Research Laboratory, popular i* generating neutrino masses and their decay to lighter neutrinos. The general feature of spin-zero fieldan d the massl- ! >oson can be avoided in these models [4]. The majoron thus remains invisible as far as : fermionic and the gauge couplings are concerned. This does not happen in a spontaneously broken global f/( 1) symmetry, a Higgs scalar can decay into a pair of Goldstone the Higgs lor. Despite being singlet, the rj can couple strongly to the Higgs doublet (j> bosons. This decay could dominate over the conventional decay modes into fermion-antifermion through t (uartic coupling &{
T r If no bare mass term is presentFi, < r\ > sets the scale of the right handed neutrino following coupling of H, S to the majoron J: mass matrix M- The masses of the light left-handed neutrinos are then generated in the seesaw model by the matrix Ttt£>M~1mp where mrj describes the Dirac mass term for the neutrino. Both mrj and M are arbitrary in the SU(2) x U(l) theory and the observed g. n limit on the neutrino masses cannot be used to determine the < T) >. However, if the model is embedded in some grand unified theory like the 50(10) model, then < ij > gets The above equation gives rise to the decay of H and S to two majoron states. The restricted. In some models [8], < rj > sets the scale of B — L symmetry breaking which corresponding decay width is given, for example in case of H, by is restricted from other considerations. Moreover, the neutrino mass matrices mp may get related [8] to the corresponding matrices for the charge-1 (u) quarks or the charged T{H -. JJ) = (6) 32TT ^eptons (/) in these models. If this happens then mv w 7^>- The observed limit on the neutrino masses can then be used in to set a limit on < T) >, e.g., for mo fa rnf, mUt < 1 The decay rate for H -* 66 remains essentially the same as in SM [3] except for modifica- eV implies < fj >> 250C?eV if the relevant Yukawa couplings are not much bigger than 1. tion introduced by the mixing, eq.(3}. But if one does not insist on grand unification then there are really no strong constraints on < Tj >. T(H - 66) = cos2 9. We shall therefore keep < t; > arbitrary and subject the model to the available LEP data and derive the constraints on the Higgs mass as well as on < IJ >. To do this, we The search strategy for the Higgs depends upon its mass and upon decay characteristics first discuss the parameters and the majoron couplings in the model. relevant for this mass. Accordingly [3], the Higgs with My < SOGeV can be looked for Irrespective of the nature of the neutrino masses, the Higgs sector of the majoron-type at LEPI or LEPII. Heavier Higgs can be searched at hadron colliders. If its maiis is model can be described by the following scalar potential less than twice the mass of the W, one has to rely upon its rare decays like 77, while heavier Higgs can be found through its WW and ZZ decay modes. All these searches can become difficult once the Higgs decay to majorons becomes possible. We shall mainly ) (1) concentrate on the already existing data on the search at LEPI and comment upon the other possibilities. Terms like r/2 are omitted above in view of the imposed (7(1) invariance under which we The SM Higgs is searched for [3] at LEP through the coupling HZZ". Both H and require r? to transform nontrivally and tj>t0 be trivial. Let TJ = -%• -f "**$', 4>° = 7k~^*Rj£l' S have this coupling in the majoron model due to mixing eq.(3). A priori, both of them where we have set < JJ >= ^ and < ^° >= -75. The above potential then leads to a could be lighter than Z and could be copiously produced in e+e~ collisions at the Z physical massless Goldstone boson namely the majoron J and two massive neutral scalars resonance. For simplicity of analysis, we shall assume that only one of them is lighter denoted by H and S respectively. These are given in terms of the original fields as follows than the Z and investigate the consequences of such an assumption. For definiteness, we take H to be lighter than Z. The complementary case of the lighter S can be obtained H = cos 6(J>R - sin from above by the replacement 9 —* 6 + ff/2. S = s (2) For a Higgs whose mass lies above the threshold for 66 production, the standard signal is two jets accompanied by missing energy or charged lepton pairs coming from the decay J = 1 of the virtual Z. It is possible to search for this signat in the SM since, for MH > lOGcV, where the mixing angle 6 and masses Mf, s of Higgs scalars are related to the parameters the most prominent decay js into bit pairs. By contrast, in the present case, H -* JJ of the potential in the following way: can dominate over H -* bb if tan^ and sin# are not unusually small. There exists a large range in these parameters for which H —» JJ dominates over H —t bb and the LEP 2foto = (Ml-(j Mji) sin 29 observations cannot exclude the Higgs for parameters in this range, since majorons escape 2 2W = MlJ--2M coswj.i^2 v6 1+ j-Jcsi Mi sin : P (3) detection. We determine this range below. M H cos $ + 2 2 2 2 Neglecting the smail decay rates of H -» l l~,qq(q = u, c, d,), the branching ratio B 2A2iw M| cos 9 +M sin 0, H for H ~> bb is given from eqs. (6,7) by 26vw tan 20 = -- (4) B = 1+r' (8)
The Higgs masses MgH, the mixing angle 9, and the ratio of two vacuum expectation where values tan /J = ^ can be taken as independent parameters in terms of which all couplings can be fixed. There are no physical charged Higgs. The potential in eq.(l) generates the The production cross section for the Higgs is also modified compared to the SM value by If for some reason, the scale < tj > coincides with the weak scale, the mixing IT the cos5 9. Taking this into account, the number Nj of the expected events with H —+ 66 and model would get strongly restricted. We display in Fig 2 limits on MH and cos 8 following Z* —v vT7, t+l~ is given by in this case corresponding to tan /3 = 1. r With increase in the mass of the Higgs, the branching ratio for H —> bb goes down Nj = S.u -g±, (10) and the Higgs search for example at LEP2 would be more difficult in the type of model + where N$M is the corresponding number of the events expected in the SM. These num- considered here. This is true not only for the searches at e e~ machines but also at hadron bers depend upon the theoretical rates and experimental cuts imposed to reduce the colliders. Unlike the. former, the latter search cannot depend upon the H —* bb signal due to an overwhelmingly large background coming from the quark-antiquark or gluon-gluon background. Various groups [1, 2, 9] have presented their values of NSM as a function of Higgs mass obtained after a detailed Monte Carlo simulation. We shall use here the fusion. The search for a Higgs of intermediate mass (Mz < MH < 2Mw) therefore relies numbers quoted by the ALEPH group [2]. They do not observe any event corresponding on the rare decay of Higgs like H —* 77. The presence of the invisible decay mode could to H —* bb and Zm ~» vV,l+l~. Monte Carlo simulation predicts the expected number reduce the already small branching ratio making the Higgs search difficult. The details of events for Higgs with mass < 48 GeV to be > 3.05 ruling out such a Higgs at the depend upon the mass parameters Mn,s in addition to on tan/? and 9. As an illustration 95% confidence level. The parameters in the present model are restricted by demanding of what is expected, consider a situation with MH < Ms < 2MH- In this case both, the that Nj be less than 3.05. The minimum allowed value of tan 0 as a function of the Ms and MH mainly decay to bb and 13 channels. They can be produced as in the SM Higgs maaa M// is displayed in figure 1 for two values of 6. The suppression in N$M is through gluon-gluon fusion, but the rate is reduced by appropriate mixing factors. The brought about due to the Higgs decay into a majoron pair and also due to reduction in expected number of events with 2*/ final state at the collider is given by the production cross section itself. The latter by itself is sufficient to suppress the Higgs rsm29 signal in the said experiment if cos* < 0.2. Thus any value of MH and tan/? are allowed JVj(27) = L (14) if 90° > 9 > 78°. The situation here should be contrasted with the general two-doublet 1+r models or supersymmetric models. In these models [3], when the mixing angle is small where L is luminosity and
1 < 2 2 (11) try to soive the strong CP problem by imposing the Peccei-Quinn [12] symmetry. But MHcos 6 + M\ sin 6' unlike in the present case, the Higgs doublet also has to be non-trivial under the (7(1) 2v2 symmetry in these models. This constrains the < rj > strongly in such models. Thus for tan2 0 < (12) M% sin2 6 + Ml cos2 8' example, from the considerations of the energy loss in the red giant stars, [13] one infers 7 4v4 that < ri >> Id GeV. With such a large value for < r\ >, the coupling of majorons to H tan2 0 < (13) (Ml-M2 y sin2 26' becomes very small for natural values of the parameters A1>2 and 6. Thus one does not H expect significant departures from the standard model constraints on Higgs mass. The where we have also used the limit AfJ > Ml for consistency". Of these, the bound same is also true if < 7 > is identified with some grand unification scale. coming by requiring Ai < 1 and S < 1 do not impose significant restrictions while the We have tried to illustrate in this paper how the data at LEP can be used to derive one arising from A2 does constrain the parameters somewhat as displayed in fig 1. It important constraints on parameters in the majoron model. The analysis is by no means follows that combination of the LEP data with the requirement of small quartic coupling exhaustive. For our purpose we have mainly concentrated on the existing analysis of one + do restrict MH if 9 is small, e.g. for 6 < 10° one gets MH > 36GeV. of the collaborations for the process Z —> Z'H with H —> bb and Z —* vv, l l~. It should
r be possible to derive further constraints on the model by a judicious use of the data on Z* —• vv, H —> bb since the signal for this is similar to Z' —> qq, H —t JJ. References It is also possible to analyse existing LEP data which rules out the Higgs masses [1] The L3 collaboration, B. Aveda et al,CERN-PPE/92-40. beSow the bb threshold, right up to MH = 0, in the majoron model. The analysis is slightly more complicated because of a larger number of decay channels present, but [2] The ALEPH collaboration, D. Decamp et al CERN-PPE-91-149 (1991). straightforward in principle. There are large ranges of parameters where the JJ decay [3] J. Gunion et al The Higgs Hunters Guide, Addison Wesley, (Melno Park, 1991). mode of H would be dominant. The parameters would be somewhat more constrained in the case of MH < 2m,,, since the negative search for a long-lived standard Higgs which [4] Y. Chikashige, R. N. Mohapatra and R. D. Peccei, Phys. Lett. 98B (1980) 265. escapes detection would also be applicable to the unobservable two-majoron decay mode. For simplicity, we restricted ourselves to the case of one of the Higgs being lighter than [5] R.E. Schrock and M. Suzuki, Phys. Lett. 1OB(J982) 250; E.D. Carlson and L.B. the Z and neglected the virtual effects of the other. In general both of them could be Hall, Phys. Rev. D40 (1985) 3187. light and could contribute appreciably. While more detailed analysis could include these effects, the considerations of this paper do illustrate how a trivial modification of the SM [6] G. Jungman and M.A. Luty Nucl. Phys. B361 (1991) 24. can nontrivally influence the Higgs search strategies. [7] A. S. Joshipura and S. D. Rindani, Physical Research Lab. Report, PRL-TH/92-10, Phys. Rev. D (in press) [8] P. Langacker, Phys. Rep. C72 (1981) 185.
Acknowledgement: [9] DELPHI collaboration, PP. Abreu et al, Z. Phys. C51(1991)25; OPAL collaboration, The authors would like 10 ihank D.P. Roy for his interest in ihc work and for helpful M. Akrawy ef al, CERN-PPE/91-116 (1991). discussions. Thanks are also due to S. Banerjee, D. Choudhury and S.N. Ganguli for [10] S. Dawson, Brookheven National Lab. report, BNL-45781 (1991). comments and discussions. A.S.J. would like 10 lhank Professor Abdus Salam, the International Atomic Energy Agency and UNESCO for hospitality at (he Internaiional [11] M. Dine, W. FischSer and M. Srednicki, Phys. Lett.lO4B (1982) 199. Centre for Theoretical Physics, Trieste. [12] R. D. Peccei and H. Quinn, Phys. Rev. Lett. 38(1977) 1440 [13] D. Discus et al Phys. Rev. D18 (1978)1879; M. Fukugita et al, Phys. Rev. Lett. 48 (198'2) 1522.
Footnotes
Fl. This Simit ignores the radiative corrections in the Higgs mass matrix that can arise in the MSSM. The improved limits which include these effects are also presented by the ALEPH group [2]. F2. If t/(l) is identified with the total lepton number then a bare mass term is forbidden by the symmetry. If U(l) involves a combination of the family lepton numbers then it is possible to write both the bare mass term and couplings to the singlet. An example is presented in [7], F3. For Ms > Mz, the limits presented in fig.l improve. If Ms < Mz then the present analysis should be modified to include the production and decay of the real S as well. 0.8
0.6
0.4
0.2
_L 30 10 20 30 40 50 MH {GeV) MH (GeV)
Fig. 2. Allowed values of cos20 and M following from the LEP data (ref. (2)) if tan/?=l. F«g 1. The allowed region in the tan/3-MH plane implied by a) the LEP data of ref.(2) b) H the requirement of the validity of perturbation theory for 0 = 10° (dotted ) and 8 = 40° The region above the curve is excluded. (solid). The region below (above) curves a(b) is excluded.
10 '**»* V