Conjecture on the approach to scaling in deep-inelastic electron scattering and some comments on electromagnetic mass differences

We conjecture that if the equal-time commutator of the electromagnetic current with its third time derivative exists as defined by Bjorken's asymptotic expansion, then the approach to scaling in deep-inelastic electron scattering is like $\frac{1}{q^2}$, where q² is the square of the mass of the virtual photon. We show that in the scaling region one can expect the structure functions for charged pions to be the same as those for neutral pions. If the longitudinal structure functions vanish in the nonscaling as well as in the scaling region, then the pion mass difference, as calculated via the Cottingham formalism, converges. For nucleons, on the other hand, a similar assumption for an "almost" longitudinal structure function does not guarantee convergence. The condition that does, however, may be consistent with experiment.