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

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.