Reinvestigating the $B$ ${\to}$ $PP$ decays by including the contributions from ${\phi}_{B2}$

TL;DR

This paper revisits $B o PP$ decays using pQCD, highlighting the significant role of the ${}_{B2}$ distribution amplitude in accurately predicting form factors and branching ratios.

Contribution

It demonstrates that including ${}_{B2}$ contributions is crucial for precise calculations of $B$ decay observables within the pQCD framework.

Findings

${}_{B2}$ contributions are comparable to NLO corrections.

${}_{B2}$ improves the explanation of $B o K ext{π}$ decays.

Nonleptonic $B$ decays require ${}_{B2}$ consideration for accuracy.

Abstract

Considering the $B$ mesonic distribution amplitude ${\phi}_{B2}$, we reinvestigated the $B$ ${\to}$ $PP$ (where $P$ $=$ ${\pi}$ and $K$) decays with the perturbative QCD (pQCD) approach based on the $k_{T}$ factorization for three scenarios. It is found that the contributions of ${\phi}_{B2}$ to formfactors $F_{0}^{B{\to}P}(0)$ and branching ratios are comparable with those from the NLO corrections. The $B$ ${\to}$ $K{\pi}$ decays could be well explained by considering the ${\phi}_{B2}$. Hence, when the nonleptonic $B$ decays are studied withe the pQCD approach, the ${\phi}_{B2}$ should be taken into account seriously.