Study on the rare radiative decay $B_c \to D_s^*\gamma$ in the standard model and multiscale walking technicolor model

Applying the perturbative QCD ( PQCD ) method, we study the decay $B_c\rightarrow D_s^*\gamma$ in the standard model and multiscale walking technicolor model. In the SM, we find that the contribution of weak annihilation is more important than that of the electromagnetic penguin. The presence of Pseudo-Goldstone-Bosons in the MWTCM leads to a large enhancement in the rate of $B_c\rightarrow D_s^*\gamma$, but this model is in conflict with the branching ratio of $Z\rightarrow b\overline b$ ( $R_b$ ) and the CLEO data on the branching ratio BR ( $b\rightarrow s\gamma$ ). If topcolor is further introduced, the calculated results in the topcolor assisted MWTCM can be suppressed and be in agreement with the CLEO data for a certain range of the parameters.