Heavy quark mass dependence of the ${\Lambda }_Q$ light-cone distribution amplitude in QCD

Abstract

We study the heavy quark mass dependence of the leading-twist light-cone distribution amplitude (LCDA) of the ${\Lambda }_Q$ baryon in QCD. Starting from the factorization formula that relates the QCD LCDA to the boosted heavy-quark effective theory (bHQET) LCDA, we derive a first-order partial differential equation governing this mass dependence in the peak region. The equation is solved analytically, and the explicit factor connecting LCDAs at different heavy quark masses is presented. We further incorporate Borel-resummed perturbative corrections from a renormalon model into the factorization. The impact of these renormalon corrections on the mass dependence is studied, and a numerical analysis using a simple LCDA model is performed to illustrate the behavior and to assess the uncertainties arising from the corrections, thereby providing a numerical estimate of the associated power corrections to the mass dependence. Our results provide an essential tool for extrapolating lattice QCD calculations of heavy-baryon LCDAs from smaller simulated masses to the physical bottom quark mass.

Comments: 8 pages, 2 figures