An Analysis of $B\to {\eta }^{\prime }K$ Decays Using a Global Fit in QCD Factorization

Abstract

In the framework of QCD factorization, we study $B^{+(0)}\to {\eta }^{\prime }{K}^{+(0)}$ 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 $B\to \pi \pi$, $\pi K$, $\rho \pi$, $\rho K$, 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 $B^{+(0)}\to {\eta }^{\prime }{K}^{+(0)}$ 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 $\sin (2{\varphi }_1)$ through $B^0\to \varphi K_s$, 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.

Comments: 23 pages, 2 figures; Some references added