QCD-factorization amplitudes from flavour symmetries: beyond the $SU(3)$ symmetric case

Abstract

Using experimental information on branching ratios as well as direct and mixing-induced CP asymmetries, we perform a data-driven analysis of charmless non-leptonic $B \to PP$ decays, where $P$ is any of the light pseudoscalar mesons. Implementing flavour-$SU(3)$ breaking at the level of transition form factors, decay constants and phase space factors, we find a good fit to the current experimental data. Our best-fit point materializes in QCD-factorization amplitudes whose central values resemble many features of the dynamical predictions obtained within the QCD factorization framework. Moreover, we do not find any strong indications that the size of annihilation amplitudes is numerically enhanced beyond the na\"ive $\Lambda_{\textrm{QCD}}/m_b$ scaling. Subsequently, we address a number of phenomenological applications, among which are various flavour puzzles that have been persisting in non-leptonic $B$ decays for quite some time.