An analysis of $B \to \eta' K$ decays using a global fit in QCD factorization

Abstract.

In the framework of QCD factorization, we study $B^{ + (0)} \to \eta' K^{ + (0)}$ 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 $B \to \pi \pi$, $\pi K$, $\rho \pi$, $\rho K$, et cetera, 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 $B^{ + (0)} \to \eta' K^{ + (0)}$ 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 $\sin (2\phi_1)$ through $B^0 \to \phi K_s$, 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.