Consistent Resolution of Possible Anomalies inB0→ϕKSandB+→η′K+Decays

In the framework of $R$-parity violating (${\mathrm{R̸}}_p$) supersymmetry, we try to find a consistent explanation for both recently measured $CP$ asymmetry in $B^0\to \varphi K_S$ decay and the large branching ratio of $B^{\pm }\to {\eta }^{\prime }{K}^{\pm }$ decay, which are inconsistent with the standard model (SM) prediction. We also investigate other charmless hadronic $B\to PP$ and $B\to VP$ decay modes whose experimental data favor the SM: for instance, recently measured $CP$ asymmetries in $B^0\to {\eta }^{\prime }{K}_S$ and $B^0\to J/\Psi K_S$. We find that all the observed data can be accommodated for certain values of ${\mathrm{R̸}}_p$ couplings.