On the Possible Violation of Sum Rules for Higher-Twist Parton Distributions

Precise measurements of polarized electro-production and Drell-Yan in the deep inelastic limit will soon provide first information on the higher twist parton distributions $g_T(x)$ and $h_L(x)$. Sum rules for higher-twist structure functions are only valid provided the corresponding Compton amplitudes satisfy un-subtracted dispersion relations. Subtracted dispersion relations have to be used when the (real part of the) forward scattering amplitudes does not fall off rapidly enough for $ν\rightarrow \infty$ (fixed $Q^2$). 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 {\it infinite momentum boost} identifies these soft quark modes with low momentum contributions to the self-energy.

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