The massive Schwinger model with $SU(2)_{f}$ on the light cone

TL;DR

This paper numerically investigates the mass spectrum of the massive Schwinger model with two flavors on the light cone, revealing how the lightest particles' masses depend on coupling and fermion mass, and analyzing their bound state nature.

Contribution

It provides a numerical analysis of the mass spectrum and bound states in the two-flavor massive Schwinger model using light-front Tamm-Dancoff approximation, highlighting new behaviors in strong coupling.

Findings

The lightest isotriplet mass scales as m^{0.50} in strong coupling.

The isosinglet state is a bound state of two pions, not a valence state.

The pion decay constant is calculated as 0.3945.

Abstract

The massive Schwinger model with two flavors is studied in the strong coupling region by using light-front Tamm-Dancoff approximation. The mass spectrum of the lightest particles is obtained numerically. We find that the mass of the lightest isotriplet (``pion'') behaves as $m^{0.50}$ for the strong couplings, where $m$ is the fermion mass. We also find that the lightest isosinglet is not in the valence state (``eta'') which is much heavier in the strong coupling region, but can be interpreted as a bound state of two pions. It is 1.762 times heavier than pion at $m=1.0\times10^{-3}(e/\sqrt\pi)$, while Coleman predicted that the ratio is $\sqrt3$ in the strong coupling limit. The ``pion decay constant'' is calculated to be 0.3945.