Fourth generation and nucleon decay in supersymmetric theories.

Abstract

Analysis of nucleon decay in N=1 supergravity unified models including the effect of a fourth generation of matter is given. Experimental constraints from nucleon-lifetime limits on the Kobayashi-Maskawa (KM) matrix that enters nucleon decay are obtained. The decays ${K}_{L}$\ensuremath{\rightarrow}${\ensuremath{\mu}}^{+}$${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$ and ${K}^{+}$\ensuremath{\rightarrow}${\ensuremath{\pi}}^{+}$\ensuremath{\nu}\ensuremath{\nu}\ifmmode\bar\else\textasciimacron\fi{} are analyzed under these constraints, since the combination of the KM matrix that enters nucleon decay also enters these rare decays. The branching ratio ${K}^{+}$\ensuremath{\rightarrow}${\ensuremath{\pi}}^{+}$\ensuremath{\nu}\ensuremath{\nu}\ifmmode\bar\else\textasciimacron\fi{} in four generations is shown to be considerably larger than for the three-generation case except for certain narrow domains of the KM matrix for two of the four branches of solutions. Bounds on ${V}_{\mathrm{ub}}$ and ${V}_{\mathrm{ub}\mathcal{'}}$ are also obtained.