Factorization formula connecting the $Λ_Q$ LCDA in QCD and boosted HQET

TL;DR

This work derives a factorization formula connecting the leading-twist QCD LCDA of the Λ_Q baryon to its boosted-HQET counterpart in the peak region, enabling a lattice-based determination of the nonperturbative HQET input. By applying the method of regions within a two-step matching framework that incorporates LaMET, the authors compute the one-loop perturbative corrections to both the QCD and bHQET LCDAs and extract the jet function that serves as the matching kernel. The jet function in the Λ_Q case exhibits the same logarithmic structure as the heavy-meson jet function, a consistency that supports universality of the perturbative kernel across heavy hadrons. The resulting expressions for the jet function and the normalization ratio, together with the explicit one-loop matching formula between Φ_QCD and Φ_bHQET, establish a viable route to determine Λ_Q LCDAs nonperturbatively from lattice QCD, with direct implications for precision weak decays of heavy baryons.

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 $Λ_Q$ 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.

Figures (2)

• Figure 1: One-loop corrections to the matrix elements defined in Eq. (\ref{['eq:SCETmatrix1loop']}) and Eq. (\ref{['eq:bHQETmatrix1loop']}). The vertical single line denotes the light quark, the vertical double line represents the heavy quark, and the tilted double line corresponds to the gauge link attached to each quark fields.
• Figure 2: One-loop corrections to the matrix elements induced by local operator in Eq. (\ref{['eq:localOperMat']}), where the white crossed dot denotes the local operator.