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Flavor Doubling and the Nature of Asymptopia

We consider the possibility that QCD with N flavors has a useful low-energy description with 2N flavors. Specifically, we investigate a free theory of 2N quarks. Although the free theory is U(N)_L X U(N)_R invariant, it admits a larger U(2N) invariance. However, when the axial anomaly is accounted for in the effective theory by a 't Hooft interaction, only SU(N)_L X SU(N)_R X U(1)_B \subset U(2N) survives. There is however a residual discrete symmetry that is not a symmetry of the QCD lagrangian. This S_2 subgroup of U(2N) has many interesting properties. For instance, when explicit chiral symmetry breaking effects are present, S_2 is broken unless \barθ=0 or pi. By expressing the free theory on the light-front, we show that flavor doubling implies several superconvergence relations in pion-hadron scattering. Implicit in the 2N-flavor effective theory is a Regge trajectory with vacuum quantum numbers and unit intercept whose behavior is constrained by S_2. In particular, S_2 implies that forward pion-hadron scattering becomes purely elastic at high-energies, in good agreement with experiment.