Mass corrections in deep-inelastic scattering

The moment sum rules for deep-inelastic lepton scattering are expected for asymptotically free field theories to display a characteristic pattern of logarithmic departures from scaling at large enough $Q^2$. In the large-$Q^2$ limit these patterns do not depend on hadron or quark masses $m$. For modest values of $Q^2$ one expects corrections at the level of powers of $\frac{m^2}{Q^2}$. We discuss the question whether these mass effects are accessible in perturbation theory, as applied to the twist-2 Wilson coefficients and more generally. Our conclusion is that some part of the mass effects must arise from a nonperturbative origin. We also discuss the corrections which arise from higher orders in perturbation theory for very large $Q^2$, where mass effects can perhaps be ignored. The emphasis here is on a characterization of the $Q^2$, $x$ domain where higher-order corrections are likely to be unimportant.