Factorization Theorem Connecting the Light-Cone Distribution Amplitudes of Heavy-Flavor Mesons in QCD and Heavy-Quark Effective Theory

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 ${\mathrm{\Lambda }}_{\mathrm{QCD}}$ for a hard exclusive $B$ production process, particularly to facilitate the resummation of logarithms of type $\ln Q/m_b$ and $\ln m_b/{\mathrm{\Lambda }}_{\mathrm{QCD}}$ in a systematic fashion.