Par-lpthe 00/12 Superheavy Majorana Neutrinos Effect in the Lepton-number Violating

In the minimal extension of the standard electroweak theory with ultra massive Majorana neutrinos, the process e− + e− → μ− + μ− could be observable, in sharp contrast with the reaction e− + e− → W−+ W− which is entirely controlled by neutrinoless double beta decay ββ0ν data. Our result provides the process background that must be confronted ”new physics” models which postulate doubly charged particles, such as the gauge bilepton Y −− in the SU(3)c ×SU(3)L ×U(1) model, the left-right SU(2)L×SU(2)R×U(1)B−L one, and its supersymmetric version with doubly charged Higgs multiplets. PACS number(s): 14.60.St 11.30.Hv 13.10.+q 12.60.-i E-mail: [email protected] LPTHE tour 16 / 1 étage, Université P. et M. Curie, BP 126, 4 place Jussieu, F-75252 PARIS CEDEX 05 (France). With nonzero neutrino mass recently reported by the Super-Kamiokande collaboration[1], it is expected that new physics beyond the Standard Model (SM) should soon show up in experiment, a typical example would be the observation of rare processes especially those which are absolutely forbidden in the SM. The amply discussed[2] electron-electron option of the future next linear collider (NLC) is an interesting area for investigating new physics. It provides the prospect for the discovery of Le, Lμ, Lτ lepton-number violation, especially the Dirac versus Majorana nature of neutrinos, their masses and mixing. While the first question – are neutrinos massless or massive?– is presumably settled[1], the second question on the neutrinos nature – are they Dirac or Majorana particles ? – remains poorly known. The purpose of this note is to point out that the e− + e− → μ− +μ− reaction could open a new window to answer the second question, in competition with ββ0ν , the ”gold-plated” neutrinoless double beta decay of nuclei (A,Z) → (A,Z + 2) + e− + e− frequently discussed in the literature. We show that the two processses ββ0ν and e− + e− → μ− + μ− are complementary, each one separately provides distinctive constraints to the Majorana nature of neutrinos, their masses and mixing. Therefore their observations could give two independent informations; both processes when considered together could further amplify our understanding in the nature and origin of neutrino masses, their Dirac or Majorana component. This e− + e− → μ− + μ− reaction is independent of ββ0ν , in sharp contrast to the e− + e− → W−+ W− process which is directly related[3] to ββ0ν . It is important to realize that while observation of ββ0ν decay cannot be directly translated to a value for the neutrino mass, it can certainly be used to infer the existence of a non-vanishing Majorana mass regardless of whatever mechanism causes ββ0ν to occur[4]. Precisely, if ββ0ν is not seen at a certain level, its absence does not imply an upper bound on Majorana neutrino mass, but if it is seen, its presence does imply a nonzero lower bound on neutrino mass[5]. As we will see, these basic facts equally apply to the reaction e− + e− → μ− + μ− that we are discussing now. In the minimal extension of the SU(2)L ×U(1)Y Standard Theory with massive Majorana neutrinos, four Feynman diagrams contribute to the e− + e− → μ− + μ− scattering in the most general renormalizable Rξ gauge. It is important to note that only massive Majorana neutrinos, but not massive Dirac neutrinos, can give rise to the e− + e− → μ− + μ− reaction. The box with two left-handed W− gauge bosons exchanged shown in Fig.1 is one graph. The three others not shown here are similar to Fig.1 in which the W− is replaced in all possible ways by the unphysical Goldstone φ− boson, the one absorbed by the W− to get mass from the Higgs mechanism. Separately each of the four diagrams is ξ-dependent, only their sum is gauge-independent. The vertices lNW and lNφ are given for instance in[6] where l stands for the electron, muon or down-type quarks and N the heavy neutrino fields or up-type quarks. The following identities are useful when dealing with Majorana neutral fermions: lγμ(1 ∓ γ5)N = −N γμ(1 ± γ5)l and l(1 ∓ γ5)N = +N c(1 ∓ γ5)l , (1) where l and N c are respectively the charge-conjugate of the l and N fermionic fields, generically denoted by ψ with ψ = Cψ t and Cγμ C = −γt μ. For Majorana field Nmaj, one has N c maj = ηNmaj where η is the phase creation factor of the field Nmaj. As an illustration, let us explicitly write down the e− + e− → μ− + μ− amplitude given by the diagram of Fig.1, neglecting the external momenta (see however the remark below) and using the Feynman-’t Hooft ξ = 1 gauge: ∫ dk (2π)4 [μγ(1− γ5) i 6k − Mi γ(1 + γ5)μ ] [eγρ(1 + γ5) i 6k − Mj γλ(1− γ5)e] (−i)2 (k2 − M2W) , (2)