Possible violation of sum rules for higher-twist parton distributions

Precise measurements of polarized electroproduction and Drell-Yan processes in the deep inelastic limit will soon provide the first information on the higher-twist parton distributions ${\mathit{g}}_{\mathit{T}}$(x) and ${\mathit{h}}_{\mathit{L}}$(x). Sum rules for higher-twist structure functions are only valid provided the corresponding Compton amplitudes satisfy unsubtracted dispersion relations. Subtracted dispersion relations have to be used when the (real part of the) forward scattering amplitudes do not fall off rapidly enough for ν→∞ (fixed ${\mathit{Q}}^2$). Formally, such subtractions lead to δ functions at the origin in the parton distributions, which are not accessible to experiment, and the integral over the data fails to satisfy the sum rule. The δ functions in the parton distributions can be identified with the zero modes that appear in light-front quantization. An explicit infinite momentum boost identifies these soft quark modes with low momentum contributions arising from self-energy-type interactions.