# A factorization theorem connecting the light-cone distribution amplitudes of heavy-flavor mesons in QCD and HQET

## TL;DR

This paper establishes a new factorization theorem linking the LCDAs of heavy-flavor mesons in QCD and HQET, enabling better separation of scales and systematic resummation in B meson processes.

## Contribution

It introduces a novel factorization theorem expressing QCD LCDAs as convolutions of HQET LCDAs and calculable coefficients, clarifying scale separation in heavy-flavor meson analysis.

## Key findings

- Derivation of the factorization theorem connecting QCD and HQET LCDAs.
- Facilitation of resummation of large logarithms in B meson processes.
- Enhanced understanding of scale dependence in heavy-flavor meson amplitudes.

## Abstract

The light-cone distribution amplitude (LCDA) of a heavy-light meson defined in heavy quark effective theory (HQET), is a fundamental nonperturbative input to account for innumerable $B$ meson exclusive decay and production processes. On the other hand, the conventional heavy-flavored meson LCDA defined in QCD, also ubiquitously enters the factorization formula for hard exclusive $B$ production processes. Inspired by the observation that these two LCDAs exhibit the identical infrared behaviors, yet differ in the ultraviolet scale of order $m_b$ or greater, we propose a novel factorization theorem for the heavy-light mesons, that the LCDA defined in QCD can be further expressed as a convolution between the LCDA in HQET and a perturbatively calculable coefficient function thanks to asymptotic freedom. This refactorization program can be invoked to fully disentangle the effects from three disparate scales $Q$, $m_b$ and $\Lambda_{\rm QCD}$ for a hard exclusive $B$ production process, particularly to facilitate the resummation of logarithms of type $\ln Q/m_b$ and $\ln m_b/\Lambda_{\rm QCD}$ in a systematic fashion.