Fock Space Distributions, Structure Functions, Higher Twists and Small x

Abstract

We compute quark structure functions and the intrinsic Fock space distribution of sea quarks in a hadron wavefunction at small x. The computation is performed in an effective theory at small x where the gluon field is treated classically. At $Q^2$ large compared to an intrinsic scale associated with the density of gluons ${\mu }^2$, large compared to the QCD scale ${\Lambda }_{QCD}^2$, and large compared to the quark mass squared $M^2$, the Fock space distribution of quarks is identical to the distribution function measured in deep inelastic scattering. For $Q^2\le M^2$ but $Q^2>>{\mu }^2$, the quark distribution is computed in terms of the gluon distribution function and explicit expressions are obtained. For $Q^2\le {\mu }^2$ but $Q^2>>{\Lambda }_{QCD}^2$ we obtain formal expressions for the quark distribution functions in terms of the glue. An evaluation of these requires a renormalization group analysis of the gluon distribution function in the regime of high parton density. For light quarks at high $Q^2$, the DGLAP flavor singlet evolution equations for the parton distributions are recovered. Explicit expressions are given for heavy quark structure functions at small x.

52 pages Latex, Revised with minor typos corrected

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