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

• Published in: arXiv.org 2019-05
• Main Authors: Saadi Ishaq, Yu, Jia, Xiong, Xiaonu, De-Shan, Yang
• Format: Article
• Language: English
• Subjects: Amplitudes; Convolution; Factorization; Flavor (particle physics); Logarithms; Mesons; Quarks; Theorems
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1905.06930

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.