Exclusive Rare Decays of B and B _c Mesons in a Relativistic Quark Model

Abstract

In these lectures we give, first, the model-independent analysis of the exclusive rare decays $B\to K \bar l l$ and $B_c\to D(D^\ast)\bar l l$ with special emphasis on the cascade decay $B_c\to D^\ast(\to D\pi)\bar l l$. We derive a four-fold angular decay distribution for this process in terms of helicity amplitudes including lepton mass effects. The four-fold angular decay distribution allows to define a number of physical observables which are amenable to measurement. Second, we calculate the relevant form factors within a relativistic constituent quark model, for the first time without employing the impulse approximation. The calculated form factors are used to evaluate differential decay rates and polarization observables. We present results on a set of observables with and without long-distance contributions. and compare them with the results of other studies.