# QCD calculations of *B* → *π*, *K* form factors with higher-twist corrections

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## Abstract

We update QCD calculations of *B* → *π*, *K* form factors at large hadronic recoil by including the subleading-power corrections from the higher-twist *B*-meson light-cone distribution amplitudes (LCDAs) up to the twist-six accuracy and the strange-quark mass effects at leading-power in Λ/*m*_{b} from the twist-two *B*-meson LCDA *ϕ* _{ B} ^{+} (*ω*, *μ*). The higher-twist corrections from both the two-particle and three-particle *B*-meson LCDAs are computed from the light-cone QCD sum rules (LCSR) at tree level. In particular, we construct the local duality model for the twist-five and -six *B*-meson LCDAs, in agreement with the corresponding asymptotic behaviours at small quark and gluon momenta, employing the method of QCD sum rules in heavy quark effective theory at leading order in *α*_{s}. The strange quark mass effects in semileptonic *B* → *K* form factors yield the leading-power contribution in the heavy quark expansion, consistent with the power-counting analysis in soft-collinear effective theory, and they are also computed from the LCSR approach due to the appearance of the rapidity singularities. We demonstrate explicitly that the SU(3)-flavour symmetry breaking effects between *B* → *π* and *B* → *K* form factors, free of the power suppression in Λ/*m*_{b}, are suppressed by a factor of \( {\alpha}_s\left(\sqrt{m_b\Lambda}\right) \) in perturbative expansion, and they also respect the large-recoil symmetry relations of the heavy-to-light form factors at least at one-loop accuracy. An exploratory analysis of the obtained sum rules for *B* → *π*, *K* form factors with two distinct models for the *B*-meson LCDAs indicates that the dominant higher-twist corrections are from the Wandzura-Wilczek part of the two-particle LCDA of twist five *g* _{ B} ^{−} (*ω*, *μ*) instead of the three-particle *B*-meson LCDAs. The resulting SU(3)-flavour symmetry violation effects of *B* → *π*, *K* form factors turn out to be insensitive to the non-perturbative models of *B*-meson LCDAs. We further explore the phenomenological aspects of the semileptonic *B* → *πℓν* decays and the rare exclusive processes *B* → *Kνν*, including the determination of the CKM matrix element |*V*_{ub}|, the normalized differential *q*^{2} distributions and precision observables defined by the ratios of branching fractions for the above-mentioned two channels in the same intervals of *q*^{2}.

## Keywords

NLO Computations QCD Phenomenology## Notes

### **Open Access**

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