A global $SU(3)/U(3)$ flavor symmetry analysis for $B\to PP$ with $\eta-\eta'$ Mixing

TL;DR

This paper performs a global analysis of B meson decays into two pseudoscalar mesons using SU(3)/U(3) flavor symmetry, fitting new experimental data to determine decay amplitudes and eta-eta' mixing parameters.

Contribution

It introduces a comprehensive SU(3)/U(3) flavor symmetry framework to analyze B to PP decays, incorporating recent experimental data and predicting unmeasured decay modes.

Findings

SU(3) flavor symmetry explains the data well

Small annihilation amplitudes are consistent with observations

Predicted decay modes accessible at LHCb

Abstract

A large number of new experimental data on $B$ decay into two light pesudoscalar ($P$) mesons have been collected by the LHCb collaboration. Besides confirming information on $B_{u,d} \to PP$ decays obtained earlier by B-factories at KEK and SLAC, new information on $B_s\to PP$ and also more decay modes with $P$ being $\eta$ or $\eta'$ have been obtained. Using these new data, we perform a global fit for $B \to PP$ to determine decay amplitudes in the framework of $SU(3)/U(3)$ flavor symmetry. We find that $SU(3)$ flavor symmetry can explain data well. The annihilation amplitudes are found to be small as expected. Several CP violating relations predicted by $SU(3)$ flavor symmetry are in good agreement with data. Current available data can give constraints on the amplitudes which induce $P = \eta,\;\eta'$ decays in the framework of $U(3)$ flavor symmetry, and can also determine the $\eta-\eta'$ mixing angle $\theta$ with $\theta = (-18.4\pm1.2)^\circ$. Several $B \to PP$ decay modes which have not been measured are predicted with branching ratios accessible at the LHCb. These decays can provide further tests for the framework of $SU(3)/U(3)$ flavor symmetry for $B$ decays.