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

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 $|\mathbf{v}{|}^2$ 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.

Comments: 24 pages, 5 figures, and 2 tables;new references and a new table added and typos corrected