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An Analysis of $B \to η' K$ Decays Using a Global Fit in QCD Factorization

In the framework of QCD factorization, we study $B^{+(0)} \to η' K^{+(0)}$ decays. In order to more reliably determine the phenomenological parameters $X_H$ and $X_A$ arising from end-point divergences in the hard spectator scattering and weak annihilation contributions, we use the global analysis for twelve $B \to PP$ and $VP$ decay modes, such as $B \to ππ$, $πK$, $ρπ$, $ρK$, etc, but excluding the modes whose (dominant) internal quark-level process is $b \to s \bar s s$. Based on the global analysis, we critically investigate possible magnitudes of $X_{H,A}$ and find that both large and small $X_{H,A}$ terms are allowed by the global fit. In the case of the large $X_{H,A}$ effects, the standard model (SM) prediction of the branching ratios (BRs) for $B^{+(0)} \to η' K^{+(0)}$ is large and well consistent with the experimental results. In contrast, in the case of the small $X_{H,A}$ effects, the SM prediction for these BRs is smaller than the experimental data. Motivated by the recent Belle measurement of $\sin (2ϕ_1)$ through $B^0 \to ϕK_s$, if we take into account possible new physics effects on the quark-level process $b \to s \bar s s$, we can explicitly show that these large BRs can be understood even in the small $X_{H,A}$ case. Specifically, we present two new physics scenarios: R-parity violating SUSY and R-parity conserving SUSY.