Radiative Leptonic $B_c\to \gamma \ell\bar\nu$ Decay in Effective Field Theory beyond Leading Order

TL;DR

This paper analyzes the radiative leptonic decay of the $B_c$ meson using nonrelativistic QCD, incorporating higher-order QCD corrections and relativistic effects to improve decay rate predictions.

Contribution

It provides a comprehensive calculation of short-distance coefficients at NLO and relativistic corrections, enhancing the theoretical understanding of $B_c$ radiative leptonic decays.

Findings

QCD corrections significantly reduce the branching ratio

Relativistic corrections are important for accurate predictions

Results include photon, lepton, and invariant mass distributions

Abstract

We study the radiative leptonic $B_c\to \gamma\ell\bar\nu$ decays in the nonrelativistic QCD effective field theory, and consider a fast-moving photon. As a result the interactions with the heavy quarks can be integrated out, and thus we arrive at a factorization formula for the decay amplitude. We calculate not only the relevant short-distance coefficients at leading order and next-to-leading order in $\alpha_s$, but also the nonrelativistic corrections at the order $|\bold{v}|^2$ in our analysis. We find out that the QCD corrections can sizably decrease the branching ratio and thus is of great importance in extracting the long-distance operator matrix elements of $B_c$. For the phenomenological application, we present our results for the photon energy, lepton energy and lepton-neutrino invariant mass distribution.