Top-Quark Mass and Bottom-Quark Decay

The possibility of a long $B$-meson lifetime is explored, in which case the weak mixing angles ${\theta }_2$ and ${\theta }_3$ 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 $\epsilon$ with its experimental value. The bound is significant for ${\tau }_B>4\mathrm{}\times {10}^{-13\mathrm{}}$ s.