Top-Quark Mass and Bottom-Quark Decay

Abstract

The possibility of a long $B$-meson lifetime is explored, in which case the weak mixing angles ${\ensuremath{\theta}}_{2}$ and ${\ensuremath{\theta}}_{3}$ are quite small. This allows the derivation of a lower bound on the top-quark mass as a function of the $B$-meson lifetime, by comparison of the short-distance prediction for the $\mathrm{CP}$-nonconservation parameter $\ensuremath{\epsilon}$ with its experimental value. The bound is significant for ${\ensuremath{\tau}}_{B}>4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ s.