Charged and neutral $$ {\overline{B}}_{u,d,s} $$ → γ form factors from light cone sum rules at NLO

Abstract

A bstract We present the first analytic $$ \mathcal{O}\left({\alpha}_s\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:mfenced> </mml:math> -computation at twist-1,2 of the $$ {\overline{B}}_{u,d,s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:math> → γ form factors within the framework of sum rules on the light-cone. These form factors describe the charged decay $$ {\overline{B}}_u\to \gamma {\mathrm{\ell}}^{-}\overline{v} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>u</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>γ</mml:mi> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , contribute to the flavour changing neutral currents $$ {\overline{B}}_{d,s}\to \gamma {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>γ</mml:mi> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:math> 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 BB*γ couplings as a constraint. Analytic results are available in terms of multiple polylogarithms in the supplementary material. We give binned predictions for the $$ {\overline{B}}_u\to \gamma {\mathrm{\ell}}^{-}\overline{v} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>u</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>γ</mml:mi> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> branching ratio along with the associated correlation matrix. By comparing with three SCET-computations we extract the inverse moment B -meson distribution amplitude parameter λ B = 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, χ q , compatible with the twist-expansion. The values χ q = 3 . 21(15) GeV − 2 and χ s = 3 . 79(17) GeV − 2 are obtained.

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