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.

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

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Cited by in corpus (15)

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• Relativistic corrections to the form factors of $B_c$ into $S$-wave Charmonium
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• Relativistic corrections to the form factors of $B_c$ into $P$-wave orbitally excited charmonium
• Relativistic corrections to light-cone distribution amplitudes of S-wave $B_c$ mesons and heavy quarkonia
• The Exclusive Decay of Upsilon into $h_c$, the $X(3940)$ and $X(4160)$
• Scrutinizing New Physics in Semi-leptonic $B_c\to J/\psi \tau \nu$ Decay
• Weak decays of $B_c$ into two hadrons under flavor SU(3) symmetry
• Decay constant of $B_c^{\ast }$ accurate up to $\mathcal{O}({\alpha }_s^3)$
• Factorization for radiative heavy quarkonium decays into scalar Glueball
• Analyzing the semileptonic and nonleptonic $B_c\to J/\psi ,{\eta }_c$ decays
• $B_c$ to $A$ Transition Form Factors and Semileptonic Decays in Self-consistent Covariant Light-front Approach
• Exclusive production of $B_c$ mesons in $e^{+}{e}^{-}$ colliders
• Form factors for semileptonic $B_c$ decays into ${\eta }^{{(}^{\prime })}$ and Glueball