Covariant boost and structure functions of baryons in Gross-Neveu models

TL;DR

This paper studies baryons in two-dimensional Gross-Neveu models, demonstrating covariant energy-momentum relations and exact momentum distributions across frames, revealing effects of the Dirac sea on structure functions, especially at infinite momentum.

Contribution

It introduces a covariant boost approach for baryons in Gross-Neveu models and computes exact momentum distributions in arbitrary frames, linking them to structure functions.

Findings

Covariant energy-momentum relations are confirmed for boosted baryons.

Exact momentum distributions interpolate between rest and infinite momentum frames.

Dirac sea effects cause divergences in structure functions at x=0 for kink baryons.

Abstract

Baryons in the large N limit of two-dimensional Gross-Neveu models are reconsidered. The time-dependent Dirac-Hartree-Fock approach is used to boost a baryon to any inertial frame and shown to yield the covariant energy-momentum relation. Momentum distributions are computed exactly in arbitrary frames and used to interpolate between the rest frame and the infinite momentum frame, where they are related to structure functions. Effects from the Dirac sea depend sensitively on the occupation fraction of the valence level and the bare fermion mass and do not vanish at infinite momentum. In the case of the kink baryon, they even lead to divergent quark and antiquark structure functions at x=0.