Detailed $SU(3)$ Flavour Symmetry Analysis of Charmless Two-Body $B$-Meson Decays Including Factorizable Corrections

Abstract: We study the decays of $B_{(s)}$ mesons into light pseudoscalar mesons under the $SU(3)$ flavour symmetry. Assuming exact $SU(3)$ symmetry at the level of the amplitudes leads to a simple parameterization. Using the available experimental data and, for the first time, mixing effects in the $B_s^0$ decays, we find that the data cannot be described with this assumption. We improve this parametrization by including {\it factorizable} $SU(3)_\mathrm{F}$-breaking effects. This new approach allows for an excellent description of the data, with a fit $p$ value of $32.3\%$. We provide posterior predictions for all observables and identify several decay channels that would significantly impact our analysis. Finally, we briefly compare our results with the predictions of QCD factorization, paving the way to a more detailed analysis which could provide insights into QCD effects at low energy scales.