Abstract
We present the first analytic mathcal{O}left({alpha}_sright) -computation at twist-1,2 of the {overline{B}}_{u,d,s} → γ form factors within the framework of sum rules on the light-cone. These form factors describe the charged decay {overline{B}}_uto gamma {mathrm{ell}}^{-}overline{v} , contribute to the flavour changing neutral currents {overline{B}}_{d,s}to gamma {mathrm{ell}}^{+}{mathrm{ell}}^{-} and serve as inputs to more complicated processes. We provide a fit in terms of a z-expansion with correlation matrix and extrapolate the form factors to the kinematic endpoint by using the gBB*γ couplings as a constraint. Analytic results are available in terms of multiple polylogarithms in the supplementary material. We give binned predictions for the {overline{B}}_uto gamma {mathrm{ell}}^{-}overline{v} branching ratio along with the associated correlation matrix. By comparing with three SCET-computations we extract the inverse moment B-meson distribution amplitude parameter λB = 360(110) MeV. The uncertainty thereof could be improved by a more dedicated analysis. In passing, we extend the photon distribution amplitude to include quark mass corrections with a prescription for the magnetic vacuum susceptibility, χq, compatible with the twist-expansion. The values χq = 3.21(15) GeV−2 and χs = 3.79(17) GeV−2 are obtained.
Highlights
In this work we provide the on-shell form factors contributing to semileptonic Bu → γ −νand flavour changing neutral decay (FCNC) Bd,s → γ + − with the method of light-cone sum rules (LCSR)
The dynamics, contrary to naive expectation, are more involved than for B → V (ρ, ω, K∗, φ) [1, 2]. This comes as the point-like photon, of leading twist-1, has no counterpart for the mesons and yet the photon is to be described by a photon distribution amplitude (DA)
Together with the fit-values given in table 4 of the previous section and the correlation matrix given in the supplementary material this constitutes the main practical results of our paper
Summary
In this work we provide the (photon) on-shell form factors contributing to semileptonic Bu → γ −νand flavour changing neutral decay (FCNC) Bd,s → γ + − with the method of light-cone sum rules (LCSR) This is the first complete next-to leading order (NLO) computation in αs including twist-1,2 and leading order (LO) twist-3 and partial twist-4. These form factors had been considered, in LCSR at LO [30], in [31] using aspects of heavy quark symmetry (with input from [32]), quark model computations [27, 33] and more recently in SCET [28] In this decay, the dipole operator mbqLσ·F b necessitates photon off-shell form factors. We provide the method-independent information on the B → γ form factors (FFs), such as the definition and the heavy quark scaling
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