Hybrid renormalization with gradient flow for baryon quasidistribution amplitudes

We establish a factorization relation between baryon quasidistribution amplitudes (quasi-DAs) defined with gradient flow and their counterparts renormalized in the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mover accent="true"> <a:mi>MS</a:mi> <a:mo stretchy="true">¯</a:mo> </a:mover> </a:math> scheme. Working beyond the small flow-time limit, we perform a complete one-loop calculation that yields the full matching kernel and the associated Wilson-line linear divergence for flowed quasi-DAs. Building on this relation, we formulate a hybrid renormalization scheme that combines ratio scheme with gradient-flow matching, thereby replacing fit-dependent self-renormalization and improving theoretical control over scheme conversion. The framework enables a systematic connection between lattice QCD matrix elements and continuum baryon quasi-DAs, with reduced renormalization uncertainties and clear guidance for practical lattice analyses.