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

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.