KL→μe in SU(2)L×U(1) and SU(2)L×SU(2)R×U(1) models with large neutrino masses

Abstract

The expectations for B($K_L$→μe) generated by massive neutrinos are studied in detail for the SU(2${)}_{\mathrm{L}}$×U(1) and SU(2${)}_{\mathrm{L}}$×SU(2${)}_{\mathrm{R}}$×U(1) models. The effects of Dirac and Majorana masses for the ordinary as well as for fourth-family and SU(2${)}_{\mathrm{L}}$-singlet (right-handed) neutrinos are considered, taking into account all existing laboratory and cosmological constraints on the neutrino masses and mixings, as well as plausible (i.e., not requiring extreme fine-tuning) expectations for mixing between light and heavy neutrinos. We consider general SU(2${)}_{\mathrm{L}}$×SU(2${)}_{\mathrm{R}}$×U(1) models, in which the right-handed quark mixing matrix $U^R$ is arbitrary, as well as the special case of manifest or pseudomanifest left-right symmetry ($U^R$=$U^L$ or $U^{L\mathrm{*}}$), and incorporate existing limits on the mass and mixing of the $W_R$ and on $U^R$. It is found that all plausible versions of the SU(2${)}_{\mathrm{L}}$×U(1) model lead to immeasurably small branching ratios. Branching ratios as large as 2×${10}^{\mathrm{-}13}$ are allowed in the SU(2${)}_{\mathrm{L}}$×SU(2${)}_{\mathrm{R}}$×U(1) model, but only for tiny corners of parameter space. For most parameter values (including manifest and pseudomanifest left-right symmetry) one has B($K_L$→μe)≤${10}^{\mathrm{-}15}$. .AE