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

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.

Comments: 20 pages, 0 figures - extensively revised with a new section on higher correlators (confusing statement after eq (21) clarified in the last revision - no other changes)-typos corrected in eqs (44) and (66) - reference [12] added in revision before publication - extensive revision of sections 1-3 to make the paper easier to read