Implications of a heavy top quark and a fourth generation on the decays B→Kl+l−,Kνν¯

We point out the importance of the Z and box diagram to the decays B→${\mathrm{Kl}}^{+}$ $l^{\mathrm{-}}$, Kνν¯. The rate for B→${\mathrm{Kl}}^{+}$ $l^{\mathrm{-}}$ grows rapidly for internal quark masses >100 GeV. With three generations and 25≲$m_t$≲200 GeV the branching ratio ranges roughly from ${10}^{\mathrm{-}6}$ to ${10}^{\mathrm{-}5}$. With four generations, this rate could go up another order of magnitude. The mode B→Kνν¯ typically has a higher branching ratio, but is harder to detect experimentally. The rare B decays combined with information from K→πνν¯ studies may provide a test of the symmetry-breaking mechanism of the standard model and/or evidence for a fourth generation.