Baryon Bethe-Salpeter Equation in Minkowski-Space QCD$_2$

TL;DR

This paper develops a Minkowski-space QCD$_2$ framework for baryons, deriving a three-quark Bethe-Salpeter equation, solving it numerically, and analyzing the spectrum and structure functions, providing insights into confinement and hadron structure.

Contribution

It introduces a three-quark Bethe-Salpeter equation in Minkowski space, connecting it to known meson equations, and computes baryon properties including spectrum and structure functions.

Findings

Ground-state baryon mass agrees with previous light-cone results.

The excited spectrum follows a Regge trajectory similar to experimental data.

Computed structure functions and densities offer insights into baryon internal structure.

Abstract

We study the three-quark ladder Bethe--Salpeter equation in Minkowski-space QCD$_2$ in the light-cone gauge. Using the quasi-potential expansion, we project the baryon equation onto the light front and show that, at leading order in the valence truncation, the resulting mass-squared eigenvalue equation is equivalent to the Bars--Durgut equation. We also derive the endpoint power-law behavior of the valence wave function in terms of the quark mass and coupling, closely paralleling the original 't Hooft analysis for mesons. The resulting three-quark equation is solved numerically for $N_c=3$, and the ground-state baryon mass is found to be in reasonable agreement with previous light-cone quantization results in QCD$_2$, suggesting that the valence sector provides the dominant contribution to the ground state. The excited-state spectrum further yields a Regge trajectory that captures the overall trend of the experimental nucleon spectrum, and we compute selected structure observables, including parton distribution functions, double distribution amplitudes, and coordinate-space densities. This framework provides a useful confining test bed for Minkowski-space bound-state methods and for future developments toward confining formulations in 3+1 dimensions beyond the valence truncation.