Abstract
We compute perturbative corrections to B→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→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→πℓνℓ (ℓ=μ,τ) in the whole kinematic region. Finally, we discuss non-valence Fock state contributions to the B→π form factors fBπ+(q2) and fBπ0(q2) in brief.
Highlights
Making every endeavor to achieve precision determinations of heavy-to-light transition form factors is of utmost importance to, on the one hand, test the CKM sector of the Standard Model, and on the other side to sharpen our knowledge towards diverse facets of the theory of strong interaction (QCD)
To demonstrate the stability of the LCSR predictions we show the dependencies of fB+π (q2) on the “internal” sum rule parameters M2 and s0 in Fig. 6 where the two plots on the top are obtained from NLL resummation improved sum rules (78) with fπ extracted from the experimental data as explained before; while the two-point QCD sum rules of fπ are substituted in the LCSR to produce the two plots on the bottom
For the first time, perturbative corrections to B → π form factors from the QCD LCSR with B-meson distribution amplitudes (DAs) proposed in [1,2] where the sum rules for heavy-to-light form factors were established at tree level including contributions from both two-particle and three-particle DAs
Summary
Making every endeavor to achieve precision determinations of heavy-to-light transition form factors is of utmost importance to, on the one hand, test the CKM sector of the Standard Model, and on the other side to sharpen our knowledge towards diverse facets of the theory of strong interaction (QCD). Computations of B → π form factors with TMD factorization approach have been pushed to O(αs) for twist-2 [24,25] and twist-3 [26] contributions of pion DAs. one needs to be aware of the fact that TMD factorization of hard exclusive processes becomes extraordinarily delicate due to complex infrared subtractions beyond the leading order in αs [27] and a complete understanding of TMD factorization for exclusive processes with large momentum transfer has not been achieved to date on the conceptual side. We generalize factorization proof of the correction function to the one-loop order in Section 3 by showing a complete cancellation of soft contributions to the one-loop QCD diagrams and infrared subtractions determined by convolutions of the one-loop partonic DAs of the B-meson and the tree-level hard-scattering kernel, at leading power in /mb. Spectral representations of the convolution integrals for constructing the LCSR with B-meson DAs and two-point QCD sum rules for the decay constants of the B-meson and the pion are collected in Appendices B and C
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