Estimating QCD-factorization amplitudes through $SU(3)$ symmetry in $B\rightarrow P P$ decays

TL;DR

This paper estimates the size of weak annihilation amplitudes in B meson decays using $SU(3)$ symmetry and experimental data, finding they are generally small but can be larger due to uncertainties.

Contribution

It establishes a novel connection between QCD factorization and $SU(3)$-invariant descriptions for B decays, enabling model-independent amplitude estimates.

Findings

Weak annihilation amplitudes are below 4% in constrained cases.

Large experimental uncertainties allow amplitudes up to 30%.

Global fit approach reduces theoretical bias.

Abstract

We estimate the potential size of the weak annihilation amplitudes in QCD factorization as allowed by experimental data. To achieve this goal, we establish a connection between the amplitudes in the QCD factorization and the so-called topological and $SU(3)$-invariant descriptions. Our approach is based purely on the analysis of the tensor structure of the decay amplitudes. By focusing on the processes $B\rightarrow P P$ and considering data from CP asymmetries and branching fractions, we perform a global fit to the $SU(3)$-irreducible quantities assuming minimal theoretical bias. Subsequently we translate the outcome to the QCD factorization decomposition, and find that the most constrained weak annihilation amplitudes are below $4\%$. However, in view of the large uncertainties in several of the experimental input parameters, values up to $30\%$ are allowed in certain cases.