On the equivalence of Flavor SU(3) analyses of $B\to PP$ decays

TL;DR

This paper demonstrates the equivalence of different SU(3) analysis methods for B to two pseudoscalar meson decays, establishing a consistent framework for analyzing heavy meson decay data.

Contribution

It shows that the RME, IRA, and TDA approaches are equivalent and derives relations between their amplitudes, providing a unified basis for SU(3) analyses.

Findings

Complete basis of ten RMEs for B to PP decays identified.

Relations between RME, IRA, and TDA amplitudes established.

Electroweak penguin contributions are negligible in the Standard Model.

Abstract

We conduct an SU(3) analysis of $B\to PP$ decays based on reduced matrix elements (RMEs), with $P$ being a light pseudoscalar meson excluding $\eta^{(\prime)}$. We show that a complete basis for the $B\to PP$ decays consists of ten RMEs, where the three RMEs arise from the electroweak penguin operators $O_{7,8}$. In the Standard Model, the relevant Wilson coefficients are small and thus can be neglected. We further demonstrate the equivalence of the RME approach with the irreducible representation amplitude (IRA) and topological diagram amplitude (TDA) methods, and derive relations between the ten RME amplitudes and corresponding IRA/TDA amplitudes. These relations lay a foundation for consistent SU(3) analyses of heavy meson decays.