QCD corrections to B→πB→π form factors from light-cone sum rules

We compute perturbative corrections to B→πB→π form factors from QCD light-cone sum rules with B-meson distribution amplitudes. Applying the method of regions we demonstrate factorization of the vacuum-to-B  -meson correlation function defined with an interpolating current for pion, at one-loop level, explicitly in the heavy quark limit. The short-distance functions in the factorization formulae of the correlation function involves both hard and hard-collinear scales; and these functions can be further factorized into hard coefficients by integrating out the hard fluctuations and jet functions encoding the hard-collinear information. Resummation of large logarithms in the short-distance functions is then achieved via the standard renormalization-group approach. We further show that structures of the factorization formulae for fBπ+(q2) and fBπ0(q2) at large hadronic recoil from QCD light-cone sum rules match that derived in QCD factorization. In particular, we perform an exploratory phenomenological analysis of B→πB→π form factors, paying attention to various sources of perturbative and systematic uncertainties, and extract |Vub|=(3.05−0.38+0.54|th.±0.09|exp.)×10−3 with the inverse moment of the B  -meson distribution amplitude ϕB+(ω) determined by reproducing fBπ+(q2=0) obtained from the light-cone sum rules with π   distribution amplitudes. Furthermore, we present the invariant-mass distributions of the lepton pair for B→πℓνℓB→πℓνℓ (ℓ=μ,τ) in the whole kinematic region. Finally, we discuss non-valence Fock state contributions to the B→πB→π form factors fBπ+(q2) and fBπ0(q2) in brief.