On the heavy Majorana neutrino and light sneutrino contribution to \bm{$e^{-}e^{-} \to \ell^{-} \ell^{-}$}, (\bm{$\ell=μ,τ)$}

Abstract

The cross section for the reaction $e^{-}e^{-} \to \ell^-\ell^-$ ($\ell=μ,τ$) is calculated in models with heavy Majorana neutrinos mediating lepton number violating amplitudes at the loop level. The contributing four-point functions are evaluated exactly (numerically) taking into account the full propagator dependence on external momenta, thereby extending %an earlier approximate low energy calculation to the energy range of interest for the next linear colliders an earlier approximate low energy calculation. The amplitude shows a non-decoupling behaviour relative to the heavy Majorana neutrino masses, but due to the stringent bounds on heavy-light mixing the signal cross section attains observable values only for the less constrained $τ$ signal. The cross section induced by lepton number violation in the $SU(2)_L$ doublet sneutrino sector of supersymmetric extensions of the standard model is constrained by the upper limits on neutrino masses and probably too tiny to be observable.