Variational Mass Perturbation Theory for Light-Front Bound-State Equations

TL;DR

This paper develops a variational mass perturbation approach for light-front bound-state equations in the 't Hooft and Schwinger models, achieving high-precision meson mass calculations without bosonization, consistent with previous numerical results.

Contribution

It introduces a novel variational mass perturbation method for light-front bound states, avoiding bosonization and extending calculations to third order in fermion mass.

Findings

Accurate meson mass squared up to third order in fermion mass.

Good convergence with inclusion of higher Fock states.

Results consistent with lattice and previous numerical studies.

Abstract

We investigate the mesonic light-front bound-state equations of the 't Hooft and Schwinger model in the two-particle, i.e. valence sector, for small fermion mass. We perform a high precision determination of the mass and light-cone wave function of the lowest lying meson by combining fermion mass perturbation theory with a variational approach. All calculations are done entirely in the fermionic representation without using any bosonization scheme. In a step-by-step procedure we enlarge the space of variational parameters. For the first two steps, the results are obtained analytically. Beyond that we use computer algebraic and numerical methods. We achieve good convergence so that the calculation of the meson mass squared can be extended to third order in the fermion mass. Within the numerical treatment we include higher Fock states up to six particles. Our results are consistent with all previous numerical investigations, in particular lattice calculations. For the massive Schwinger model, we find a small discrepancy (less than 2 percent) in comparison with known bosonization results. Possible resolutions of this discrepancy are discussed.