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

TL;DR

This paper derives a factorization formula linking QCD and boosted HQET LCDAs for the $\\Lambda_Q$ baryon, simplifying the matching process and computing one-loop corrections to facilitate future lattice QCD studies.

Contribution

It introduces a simplified method for deriving the factorization formula and calculates one-loop corrections to connect QCD and HQET LCDAs for heavy baryons.

Findings

Derived a factorization formula connecting QCD and HQET LCDAs.

Applied method-of-regions to simplify perturbative calculations.

Calculated one-loop jet function as the matching kernel.

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.