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.
Highlights
It is well known that many breakthrough discoveries have come from precise experiments
Considering the B mesonic distribution amplitude φB2, we reinvestigated the B → PP decays with the perturbative QCD approach based on the kT factorization for three scenarios
Various B meson decay modes with branching ratio larger than 10−6 have been extensively studied by the BABAR and Belle Collaborations with 0.56 ab−1 and 1.02 ab−1 data samples in the past years [1,2]
Summary
Mπ0 1⁄4 134.98 MeV, mK0 1⁄4 497.61 MeV, mBu 1⁄4 5279.34ð12Þ MeV, mb 1⁄4 4.78ð6Þ GeV, Decay constants [1]. ΤBÆ 1⁄4 1.638ð4Þ ps, Gegenbauer moments at the scale of μ 1⁄4 1 GeV [16] aπ1 1⁄4 0, aK1 1⁄4 0.06ð3Þ, λ 1⁄4 0.22650ð48Þ, η 1⁄4 0.357ð11Þ, mπÆ 1⁄4 139.57 MeV, mKÆ 1⁄4 493.68 MeV, mBd 1⁄4 5279.65ð12Þ MeV, ms 1⁄4 130.0ð1.8Þ MeV [15], f3π 1⁄4 0.45ð15Þ × 10−2 GeV2 [16], f3K 1⁄4 0.45ð15Þ × 10−2 GeV2 [16], τBÆ 1⁄4 1.519ð4Þ ps, aπ2 1⁄4 0.25ð15Þ, aK2 1⁄4 0.25ð15Þ. Perturbatively calculable at the scale of OðmWÞ and evolved to the b quark decay scale OðmbÞ with the RG equation [14]. GF, CKM factors and Ci could be regarded as the universal and effective couplings of the operators Oi. The tree operators O1;2, QCD penguin operators O3∼6 and electromagnetic penguin operators O7∼10 are local four-quark interactions and expressed as follows
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