Bilepton Resonance in Electron-electron Scattering

Theoretical backgound for bileptonic gauge bosons is reviewed, both the SU(15) GUT model and the 3-3-1 model. Mass limits on bileptons are discussed coming from e+e− scattering, polarized muon decay and muonium-antimuonium conversion. Discovery in e−e− at a linear collider at low energy (100GeV) and high luminosity (10/cm/s) is emphasised. Introduction. It is a stunning historical fact that e−e− collisions have never been studied at a center of mass energy above 1.12 GeV as published in 1971 by Richter et al. There were plans to explore e−e− at DESY but these were abandoned when money ran out. The three large projects in HEP for the US (and internationally) for the foreseeable future are: NLC, MC and VLHC. Of these the NLC is for the first decade of the twenty-first century; the other two are for the second decade. The NLC is presently a multibillion dollar project primarily aimed at e+e−. A topic of this workshop is: should it have also e−e− capability? Why has e−e− been so neglected? Firstly e+e− is where Z ′ can be found often cited as the most conservative extension of the Standard Model (SM). By contrast e−e− is an exotic, empty channel because it has double electric charge and lepton number L = 2. Surely, e−e− would allow only checks of higher-order quantum electrodynamics. But physics is an experimental science! e−e− Resonance. Such a resonance must have L = 2 and Q = 2. It must be a boson. For spin zero a doubly-charged Higgs scalar, the coupling is a free parameter and is generically small. For a spin one gauge boson, the coupling is large and prescribed. Bilepton gauge bosons give a pronounced peak at s = M. But, as our main emphasis here, the resonance tail is detectable at much lower energy. Bilepton gauge bosons were first suggested in the context of SU(15) grand unification. First recall that in SU(5) grand unification with families each in 5+1̄0 the reason for B violation is that the second rank tensor 1̄0 has indefinite B and L quantum numbers. If SU(5) had fermions only in the 5 then B and L would necessarily be conserved perturbatively. The presence of the 1̄0 is what causes the indeterminacy of B and L and allows mediation of proton decay in the gauge sector. Since proton decay remains elusive the idea in SU(15) is to prohibit it in the gauge sector. The 15 helicity states in each family are assigned to a 15 of SU(15). Whereupon each gauge boson has definite B and L according to which pair of the fundamental fermions it couples. The first family is assigned to: 15 = (uL , u G L , u B L , d R L , d G L , d B L ; ū R L , ū G L , ū B L , d̄ R L , d̄ G L , d̄ B L ; e + L , νeL, e − L) and similarly for the second and third families. It is clear that all of the 224 gauge bosons of SU(15) have definite B and L. Anomaly cancellation is by mirror fermions disfavored aesthetically but not phenomenologically. The pattern of spontaneous symmetry breaking is: SU(15) MG −→ SU(12)q × SU(3)l MB −→ SU(6)L × SU(6)R × U(1)B × SU(3)l MA −→ SU(3)C × SU(2)L × U(1)Y In the breaking at MA color SU(3)C is embedded in SU(6)L ×SU(6)R as (3+3, 1)+ (1, 3̄ + 3̄). SU(2)L is embedded in SU(6)L × SU(3)l with 6L = 3(2)L and 3L = 2L + 1L U(1)Y is contained in SU(6)R × U(1)B × SU(3)l according to: Y = √ 3Λ + √ 2 3 B + √ 3Y with Λ, B and Y generators of SU(6)R, U(1)B and SU(3)l, respectively, normalized as SU(15) matrices with