Rare B decays, rare tau decays, and grand unification.

Abstract

In multi-Higgs-boson extensions of the standard model, tree-level flavor-changing neutral currents exist naturally, unless suppressed by some symmetry. For a given rate, the exchanged scalar or pseudoscalar mass is very sensitive to the flavor-changing coupling between the first two generations. Since the Yukawa couplings of the first two generations are unknown and certainly very small, bounds which rely on some assumed value of this flavor-changing coupling are quite dubious. One might expect the size (and reliability) of the Yukawa couplings involving the third generation to be greater. In this paper, we consider processes involving $\ensuremath{\tau}'\mathrm{s}$ and $B'\mathrm{s}$, and determine the bounds on the flavor-changing couplings which involve third-generation fields. The strongest bound in the quark sector comes from $B\ensuremath{-}\overline{B}$ mixing and in the lepton sector, surprisingly, from $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$. It is then noted that the flavor-changing couplings in the quark sector are related to those in the lepton sector in many grand unified theories, and one can ask whether an analysis of rare $\ensuremath{\tau}$ decays or rare $B$ decays will provide the strongest constraints. We show that rare $B$ decays provide the strongest bounds, and that no useful information can be obtained from rare $\ensuremath{\tau}$ decays. It is also noted that the most promising decay modes are $B\ensuremath{\rightarrow}K\ensuremath{\mu}\ensuremath{\tau}$ and ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\tau}$, and we urge experimenters to look for rare decay modes of the $B$ in which a $\ensuremath{\tau}$ is in the final state.