Theory of Rare B Decays

We discuss some selected topics in rare B decays in the context of the standard model and compare theoretical estimates with available data. Salient features of the perturbative-QCD and power corrections in the decay rate for $B \to X_s + \gamma$ are reviewed and this framework is used to determine the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $\mathrm{\mid }{V}_{ts}\mathrm{\mid }$. We review estimates of the ratio $R_{K^} \equiv \Gamma(B \to K^ + \gamma)/\Gamma(B \to X_s + \gamma)$ in a number of theoretical models, which give a consistent account of this quantity. Issues bearing on the photon energy spectrum in $B \to X_s + \gamma$arealsodiscussed\mathrm{.}TheCKM-suppresseddecays$B \to X_d + \gamma$,$B^\pm \to \rho^\pm + \gamma$,and$B^{0} \to (\rho^{0}, \omega) + \gamma$ are reviewed with particular emphasis on the long-distance contributions in the exclusive decays. The impending interest in these decays in determining the parameters of the CKM matrix is emphasized. Finally, the semileptonic decays $B\to X_s{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ are also discussed in the context of the SM.