Improved vector and scalar masses in the massive Schwinger model

TL;DR

This paper improves analytical calculations of bound-state masses in the massive Schwinger model, achieving high accuracy and consistency with lattice results across various fermion masses.

Contribution

It introduces enhanced analytical methods using mass perturbation theory and a consistency condition, aligning well with numerical lattice data.

Findings

Analytical bound-state masses agree with lattice results for small and intermediate fermion masses.

Results remain within 10% of exact values at large fermion mass.

Employs both standard and renormal-ordered mass perturbation theory for improved accuracy.

Abstract

The lowest (``vector'') and next-lowest (``scalar'') bound-state masses of the massive Schwinger model have been determined recently to a very high accuracy numerically on the lattice. Therefore, improved results for these bound-state masses from analytical calculations are of some interest. Here, we provide such improved results by employing both standard and renormal-ordered (fermion) mass perturbation theory, as well as a consistency condition between the two perturbative calculations. The resulting bound-state masses are in excellent agreement with the lattice results for small and intermediate fermion mass, and remain within 10% of the exact results even in the limit of very large fermion mass.