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)LxU(N)R invariant, it admits a larger U(2N) invariance. However, when the axial anomaly is accounted for in the effective theory by a close-quote t Hooft interaction, only SU(N)LxSU(N)RxU(1)B contained-in U(2N) survives. There is, however, a residual discrete symmetry that is not a symmetry of the QCD lagrangian. This S2 subgroup of U(2N) has many interesting properties. For instance, when explicit chiral symmetry breaking effects are present, S2 is broken unless bar θ=0 or π. 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 S2. In particular, S2 implies that forward pion endash hadron scattering becomes purely elastic at high energies, in good agreement with experiment. copyright 1998 Academic Press, Inc