# $W$ radiative decay to heavy-light mesons in HQET factorization through ${\cal O}(\alpha_s)$

## TL;DR

This paper applies HQET factorization to the rare decay process W to heavy-light mesons plus a photon, verifying the factorization at NLO in alpha_s and showing reduced scale dependence, with future work suggested on resumming large logarithms.

## Contribution

It introduces the use of HQET factorization for W to heavy-light meson decays and confirms its validity at NLO in alpha_s, expanding the applicability of HQET methods.

## Key findings

- Decay form factors factorize into hard kernel and LCDA.
- NLO corrections reduce scale dependence.
- Potential for resumming large logarithms.

## Abstract

Analogous to NRQCD factorization for heavy quarkonium exclusive production, in this work we propose to employ the heavy-quark-effective-theory (HQET) factorization, which has been predominantly applied to account for exclusive $B$ decays, to study the exclusive production of the heavy-flavored mesons. We take $W\to B(D_s)+\gamma$ as a prototype process. The validity of the HQET factorization rests upon the presumed scale hierarchy: $m_W\sim m_b\gg \Lambda_{\rm QCD}$. Through an explicit analysis at next-to-leading order in $\alpha_s$ yet at leading order in $1/m_b$, we verify that the decay form factors can indeed be expressed as the convolution between perturbatively calculable hard-scattering kernel and the $B$ meson light-cone distribution amplitude (LCDA) defined in HQET. It is observed that the factorization scale dependence becomes reduced after incorporating the NLO perturbative correction. An interesting future investigation is to identify and resum large collinear logarithms of $m_W/m_b$ that arise ubiquitously in the fixed-order expressions of the hard-scattering kernel in HQET factorization.