Factorization formula connecting the $\Lambda_Q$ LCDA in QCD and boosted HQET

Abstract

Light-cone distribution amplitudes (LCDAs) are essential to precision phenomenology in heavy baryon decays. In this work, we derive a factorization formula connecting the leading-twist QCD LCDA to the boosted HQET LCDA of the $\Lambda_Q$ baryon in the peak region. We demonstrate a significant simplification of the matching procedure by applying the method-of-regions to perturbative calculations. With this simplification, we calculate the required one-loop perturbative corrections to the QCD and boosted HQET LCDAs in the $\overline{\rm MS}$ scheme, and thereby obtain the one-loop jet function that serves as the matching kernel in the factorization formula. This result provides a critical step toward lattice QCD calculation of heavy baryon LCDAs in the future.