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

We examine the large branching ratio for the process $B\to η^{\prime} K$ from the standpoint of R parity violating supersymmetry. We have given all possible $R_p$ violating contributions to $B\to η^{\prime} K$ amplitudes. We find that only two pairs of $λ^{\prime}$-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.}, $B^\pm \to π^{\pm}K^0$, $B^{\pm,0} \to K^{*\pm,0} η^{(\prime)}$, $B^{\pm} \toϕK^{\pm}$ etc., and predict their branching ratios. Further, one of these two pairs of couplings is found to lower the branching ratio of $B^{\pm}\toϕK^\pm$, thereby allowing larger $ξ\equiv{1\over N_c}$. This allows us to fit $B^{\pm}\to ωK^{\pm}$ and $B^{\pm}\to ωπ^{\pm}$, which could not be done in the SM framework.