Hybrid Renormalization for Quasi Distribution Amplitudes of A Light Baryon

TL;DR

This paper introduces a hybrid renormalization scheme for lattice QCD calculations of light baryon distribution amplitudes, combining self-renormalization and ratio methods to improve accuracy and remove divergences.

Contribution

A novel hybrid renormalization scheme for quasi distribution amplitudes that effectively handles divergences without extra nonperturbative effects and applies it to the $$ baryon.

Findings

Successfully removed UV and linear divergences in lattice calculations.

Perturbatively calculated equal-time correlators up to next-to-leading order.

Derived hard kernels for matching quasi to lightcone distribution amplitudes.

Abstract

We develop a hybrid scheme to renormalize quasi distribution amplitudes of a light baryon on the lattice, which combines the self-renormalization and ratio scheme. By employing self-renormalization, the UV divergences and linear divergence at large spatial separations in quasi distribution amplitudes are removed without introducing extra nonperturbative effects, while making a ratio with respect to the zero-momentum matrix element can properly remove the UV divergences in small spatial separations. As a specific application, distribution amplitudes of the $\Lambda$ baryon made of $uds$ are investigated, and the requisite equal-time correlators, which define quasi distribution amplitudes in coordinate space, are perturbatively calculated up to the next-to-leading order in strong coupling constant $\alpha_s$. These perturbative equal-time correlators are used to convert lattice QCD matrix elements to the continuum space during the renormalization process. Subsequently, quasi distribution amplitudes are matched onto lightcone distribution amplitudes by integrating out hard modes and the corresponding hard kernels are derived up to next-to-leading order in $\alpha_s$ including the hybrid counterterms. These results are valuable in the lattice-based investigation of the lightcone distribution amplitudes of a light baryon from the first principles of QCD.