Factorization of Radiative Leptonic Decays of $B^-$ and $D^-$ Mesons

TL;DR

This paper investigates the factorization of radiative leptonic decays of $B^-$ and $D^-$ mesons, emphasizing the significance of $O(rac{ ext{Lambda}_ ext{QCD}}{m_Q})$ corrections and providing explicit proofs and numerical results.

Contribution

It provides an explicit proof of factorization at order $O(rac{ ext{alpha}_s ext{Lambda}_ ext{QCD}}{m_Q})$, including the hard kernel and numerical analysis with relativistic wave functions.

Findings

$O(rac{ ext{Lambda}_ ext{QCD}}{m_Q})$ corrections are significant, especially for $D$ mesons.

Correction to $B^- o ext{gamma} e ar{ u}$ decay amplitudes is about 20-30%.

The $O(rac{ ext{Lambda}_ ext{QCD}}{m_Q})$ contributions are more important for $D$ mesons.

Abstract

In this work, we study the factorization of the radiative leptonic decays of $B^-$ and $D^-$ mesons, the contributions of the order $O(\Lambda _{\rm QCD}\left/m_Q\right.)$ are taken into account. The factorization is proved to be valid explicitly at the order $O(\alpha _s\Lambda _{\rm QCD}\left/m_Q\right.)$. The hard kernel is obtained. The numerical results are calculated using the wave-function obtained in relativistic potential model. The $O(\Lambda _{\rm QCD}\left/m_Q\right.)$ contribution is found to be very important, the correction to the decay amplitudes of $B^-\to \gamma e\bar{\nu}$ is about $20\% - 30\%$. For $D$ mesons, the $O(\Lambda _{\rm QCD}\left/m_Q\right.)$ contributions are more important.