Hybrid renormalization for distribution amplitude of a light baryon in large momentum effective theory

TL;DR

This work implements a robust hybrid renormalization framework for baryon quasi-DAs within LaMET, addressing the challenging linear divergences of Wilson-line operators on the lattice. By combining self-renormalization at large separations with a short-distance ratio scheme, and by calibrating with MS-bar perturbation theory through zero-momentum matching, the authors obtain smooth, continuum-like coordinate-space quasi-DAs for the Λ baryon and the proton at multiple momenta and lattice spacings. The approach includes a careful extraction of the linear-divergence parameter, region-specific renormalization, and model-averaged ground-state extractions, ensuring controlled discretization effects and reliable continuum limits. The results demonstrate state-independent linear divergences and effective cancellation of UV artifacts, providing a solid foundation for precise LaMET-based determinations of light-cone baryon LCDAs.

Abstract

Lightcone distribution amplitudes for a light baryon can be extracted through the simulation of the quasi-distribution amplitudes (quasi-DAs) on the lattice. We implement the hybrid renormalization for the quasi DAs of light baryons. Lattice simulations are performed using $N_f = 2+1$ stout-smeared clover fermions and a tree-level Symanzik-improved gauge action, with three lattice spacings of ${0.105, 0.077, 0.052}$ fm. By analyzing zero-momentum matrix elements for different lattice spacings, we extract the linear divergence associated with the Wilson-line self-energy. Matching to perturbative matrix elements in the $\overline{\text{MS}}$ scheme yields the residual self-renormalization factors. Using these factors, we renormalize the quasi-DAs within the hybrid scheme, which combines self-renormalization at large separations and the ratio scheme at short distances. The renormalized results demonstrate effective cancellation of linear divergences and yield smooth, continuum-like coordinate-space distributions suitable for subsequent Fourier transformation and perturbative matching. These results establish the viability of both self and hybrid renormalization frameworks for light baryon quasi-DAs, providing a robust foundation for LaMET-based determinations of light-cone distribution amplitudes.

Figures (45)

• Figure 1: The structure of the light baryon LCDA. Three quark fields are connected with Wilson lines to a reference position. $z_3$ can be set to zero for simplification.
• Figure 2: The structure of a fast moving light baryon with valance quarks.
• Figure 3: The diagonals and regional divisions on the $z_1-z_2$ plane for quasi-DAs.
• Figure 4: A schematic diagram of renormalization regions. Distinct colors denote different region types: short-distance region (purple), long-distance region (gray), and mixing regions (blue). Separate renormalization schemes are applied to each region.
• Figure 5: Comparison of noise-to-signal ratios for the $\Lambda$ baryon two-point functions at $P^z=2.5$ GeV and F32P30 ($a=0.077$ fm) using traditional (Eq. \ref{['eq:source_zero_p']}) and modified (Eq. \ref{['eq:source_boost_p_mod']}) source interpolators.