Mass Perturbation Theory in the 2-Flavor Schwinger Model with Opposite Masses

TL;DR

This paper investigates how small fermion masses affect the conformal sector of the 2-flavor Schwinger model, showing that the unparticle behavior persists and providing detailed perturbative calculations of correlators.

Contribution

It demonstrates that small fermion masses do not break conformal symmetry in the model and offers a detailed perturbative framework for analyzing unparticle correlators.

Findings

Mass gap remains zero for small fermion masses.

Conformal symmetry is preserved at long distances.

Explicit calculations of scalar correlators support unparticle behavior.

Abstract

I discuss the 2-flavor Schwinger model with $\theta=0$ and small equal and opposite fermion masses (or $\theta=\pi$ with equal masses). The massless model has an unparticle sector with unbroken conformal symmetry. I argue that this special mass term modifies the conformal sector without breaking the conformal symmetry. I show in detail how mass-perturbation-theory works for correlators of flavor-diagonal fermion scalar bilinears. The result provides quantitative evidence that the theory has no mass gap for small non-zero fermion masses. The massive fermions are bound into conformally invariant unparticle stuff. I show how the long-distance conformal symmetry is maintained when small fermion masses are turned on and calculate the relevant scaling dimensions for small mass. I calculate the corrections to the 2- and 4-point functions of the fermion-bilinear scalars to leading order in perturbation theory in the fermion mass and describe a straightforward procedure to extend the calculation to all higher scalar correlators. I hope that this model as a useful and non-trivial example of unparticle physics, a sector with unbroken conformal symmetry coupled to interacting massive particles, in which we can analyze the particle physics in a consistent approximation.