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.

Figures (7)

• Figure 1: $68\%$ probability intervals of the (partially correlated) experimental constraints on the $B_d^0\to\pi^+\pi^-$ and $B_s^0\to K^+K^-$ CP observables in the $(r_p, \theta_p)$ plane defined in \ref{['sec:su3_SR']}. The $1, 2$ and $3 \sigma$ postdictions of the global $SU(3)_\mathrm{F}$ fit are overlaid; see \ref{['sec:SU3analysis']} for details. The grey star and cross show the best-fit points from the CP asymmetries of $B_d^0\to\pi^+\pi^-$ and $B_s^0\to K^+K^-$, respectively.
• Figure 2: $68\%$ probability intervals of the experimental constraints on the $B^+\to K^+\bar{K}^0$ and $B^+\to K^0\pi^+$ branching ratios. The $1, 2$ and $3 \sigma$ postdictions of the global $SU(3)_\mathrm{F}$ fit are overlaid; see \ref{['sec:SU3analysis']} for details. The $SU(3)_\mathrm{F}$ symmetry excludes the grey region.
• Figure 3: Predicted observables within our fit models, combined with the measured values. The branching ratios and their ratios are normalised to their "Fact.-$\cancel{{SU(3)_\mathrm{F}\xspace}}$ " postdictions for readability. Grey measurements are not directly used in the fit (ratios of branching ratios are used instead).
• Figure 4: 68%, 95% and 99% cumulative contours of the $\tilde{\alpha}_1 + \tilde{\alpha}_2$ posterior distribution, assuming $\tilde{\alpha}_1 + \alpha_4^u > 0$. The "$\times$" symbol shows the analysis best-fit point. We overlay the QCDF result for $\alpha_1 + \alpha_2$ obtained in Ref. Beneke:2009ek.
• Figure 5: Corner plot of one-dimensional and two-dimensional marginalised posterior densities for the several $\alpha$ contributions. The "$\times$" symbol and the dashed black lines show the analysis best-fit point. The orange areas are the 1, 2 and $3\sigma$ contours of the posterior distribution obtained from a kernel density estimation.