Sum rules for higher-twist parton distributions

In deep-inelastic scattering experiments, there is a general connection between subtractions in dispersion relations, violations of sum-rules and $\delta$-functions in parton distribution functions. It is explained why one might expect a small violation in sum rules for the twist-3 distribution functions $g_T(x)$ and $h_L(x)$ when the sum-rules are applied to $x\neq 0$ data only. The non-perturbative predictions are studied in the context of a one-loop model.