Charged and Neutral ${\bar{B}}_{u,d,s}\to \gamma$ Form Factors from Light Cone Sum Rules at NLO

Abstract

We present the first analytic $\mathcal{O}({\alpha }_s)$-computation at twist-$1$,$2$ of the ${\bar{B}}_{u,d,s}\to \gamma$ form factors within the framework of sum rules on the light-cone. These form factors describe the charged decay ${\bar{B}}_u\to \gamma {\ell }^{-}\bar{\nu }$, contribute to the flavour changing neutral currents ${\bar{B}}_{d,s}\to \gamma {\ell }^{+}{\ell }^{-}$ 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 $g_{B{B}^{\ast }\gamma }$ couplings as a constraint. Analytic results are available in terms of multiple polylogarithms as ancillary files. We give binned predictions for the ${\bar{B}}_u\to \gamma {\ell }^{-}\bar{\nu }$ branching ratio along with the associated correlation matrix. By comparing with three SCET-computations we extract the inverse moment $B$-meson distribution amplitude parameter ${\lambda }_B=360(110)\text{MeV}$. 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, ${\chi }_q$, compatible with the twist-expansion. The values ${\chi }_q=3.21(15){\text{GeV}}^{-2}$ and ${\chi }_s=3.79(17){\text{GeV}}^{-2}$ are obtained.

54 pp (plus refs), 13 figs, 9 tables and 4 ancillary files (z-expansion fit etc) - version accepted in JHEP results unchanged

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Cited by in corpus (1)

• Radiative Decays of Heavy-light Mesons and the $f_{H,H^{\ast },H_1}^{(T)}$ Decay Constants