A supersymmetric resolution of the anomaly in charmless nonleptonic $B$-decays

Abstract

We examine the large branching ratio for the process $B\to {\eta }^{\prime }K$ from the standpoint of R parity violating supersymmetry. We have given all possible $R_p$ violating contributions to $B\to {\eta }^{\prime }K$ amplitudes. We find that only two pairs of ${\lambda }^{\prime }$-type $R_p$ violating couplings can solve this problem after satisfying all other experimental bounds. We also analyze those modes where these couplings can appear, {\em e.g.}, $B^{\pm }\to {\pi }^{\pm }{K}^0$, $B^{\pm ,0}\to K^{\ast \pm ,0}{\eta }^{(\prime )}$, $B^{\pm }\to \varphi K^{\pm }$ etc., and predict their branching ratios. Further, one of these two pairs of couplings is found to lower the branching ratio of $B^{\pm }\to \varphi K^{\pm }$, thereby allowing larger $\xi \equiv \frac{1}{N_c}$. This allows us to fit $B^{\pm }\to \omega K^{\pm }$ and $B^{\pm }\to \omega {\pi }^{\pm }$, which could not be done in the SM framework.

Comments: 12 pages, 5 figures