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

Considering the $B$ mesonic distribution amplitude ${\varphi }_{B2}$, 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 ${\varphi }_{B2}$ 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 ${\varphi }_{B2}$. Hence, when the nonleptonic $B$ decays are studied withe the pQCD approach, the ${\varphi }_{B2}$ should be taken into account seriously.