Unified Light-Cone Treatment of Scaling and a Positivity Constraint on Short-Distance Behavior

We show that scaling in the two processes e+Π(p)-->e+X and e⁺+e^--->Π(p)+X (where Π denotes a hadron) is controlled by the behavior near the light cone of the same operator product. This is done by studying the structure of the absorptive part of the forward virtual Compton scattering amplitude. This operator product must exhibit (at least) the singularity structure of the product of two electromagnetic currents. Under the assumption that this indeed is its leading singularity, we conclude that both processes must exhibit the same scaling behavior. It is then shown that positivity leads to a restriction on the short-distance behavior of these products. Under fairly general assumptions this leads to the result that the longitudinal structure function in the process e⁺+e^--->Π(p)+X may not vanish identically. The alternatives are that either local operators contribute on the light cone or that the transverse functions satisfy the lower bound F_T>=cω as ω approaches infinity.