Theta Dependence of Meson Masses in the Small Mass Limit of the Massive Schwinger Model

TL;DR

This paper develops a continuum light-front formulation for the massive Schwinger model with a theta parameter, analyzing meson masses in the small mass and theta regime, and confirming results with bosonization.

Contribution

It introduces a novel light-front continuum approach to theta-vacua in the massive Schwinger model and computes meson masses consistent with bosonization results.

Findings

Meson mass depends on theta and fermion mass in the small limit.

Effective coupling is partially screened by vacuum polarization.

Results agree with bosonization calculations.

Abstract

We present a continuum formulation for $\theta$-vacua in the massive Schwinger model on the light-front, where $\theta$ enters as a background electric field. The effective coupling of the external field is partially screened due to vacuum polarization processes. For small fermion masses and small $\theta$ we calculate the mass of the meson and find agreement with results from bosonization.