Precision calculations of the double radiative bottom-meson decays in soft-collinear effective theory

TL;DR

This paper provides a comprehensive, improved calculation of the double radiative decay amplitudes of B mesons using soft-collinear effective theory, including subleading power corrections and phenomenological implications.

Contribution

It introduces new factorization formulae for subleading power contributions and evaluates higher-twist effects up to twist-six accuracy in B-meson decays.

Findings

Enhanced theoretical predictions for B meson decay observables.

Quantified impact of subleading power corrections on decay rates.

Provided estimates of soft contributions using dispersion relations.

Abstract

Employing the systematic framework of soft-collinear effective theory (SCET) we perform an improved calculation of the leading-power contributions to the double radiative $B_{d, \, s}$-meson decay amplitudes in the heavy quark expansion. We then construct the QCD factorization formulae for the subleading power contributions arising from the energetic photon radiation off the constituent light-flavour quark of the bottom meson at tree level. Furthermore, we explore the factorization properties of the subleading power correction from the effective SCET current $J^{(A2)}$ at ${\cal O} (\alpha_s^0)$. The higher-twist contributions to the $B_{d, \, s} \to \gamma \gamma $ helicity form factors from the two-particle and three-particle bottom-meson distribution amplitudes are evaluated up to the twist-six accuracy. In addition, the subleading power weak-annihilation contributions from both the current-current and QCD penguin operators are taken into account at the one-loop accuracy. We proceed to apply the operator-production-expansion-controlled dispersion relation for estimating the power-suppressed soft contributions to the double radiative $B_{d, \, s}$-meson decay form factors. Phenomenological explorations of the radiative $B_{d, \, s} \to \gamma \, \gamma$ decay observables in the presence of the neutral-meson mixing, including the CP-averaged branching fractions, the polarization fractions and the time-dependent CP asymmetries, are carried out subsequently with an emphasis on the numerical impacts of the newly computed ingredients together with the theory uncertainties from the shape parameters of the HQET bottom-meson distribution amplitudes.