Work

Baryon Bethe–Salpeter equation in Minkowski-space QCD2

Year: 2026

Type: article

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.

Source: Physics Letters B

DOI: 10.1016/j.physletb.2026.141087