# Contributions from ${\Phi}_{B2}$ to the $B$ ${\to}$ $PP$ decays within the QCD factorization

## TL;DR

This paper investigates the role of the ${\

## Contribution

It introduces the ${\

## Key findings

- ${\Phi}_{B2}$ affects nonfactorizable annihilation amplitudes.
- ${\Phi}_{B2}$ contributions are small but may improve decay predictions.
- Potential impact on pure annihilation $B$ decays.

## Abstract

With the potential for the improvements of measurement precision,the refinement of theoretical calculation on hadronic $B$ weak decays is necessary. In this paper, we study the contributions of $B$ mesonic distribution amplitude ${\Phi}_{B2}$ within the QCD factorization approach, and find that ${\Phi}_{B2}$ contributes to only the nonfactorizable annihilation amplitudes for the $B$ ${\to}$ $PP$ decays ($P$ denotes the ground $SU(3)$ pseudoscalar mesons). Although small, the ${\Phi}_{B2}$ contributions might be helpful for improving the performance of the QCD factorization approach, especially for the pure annihilation $B_{d}$ ${\to}$ $K^{+}K^{-}$ and $B_{s}$ ${\to}$ ${\pi}^{+}{\pi}^{-}$ decays.