  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.
