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 $μ^2$, large compared to the QCD scale $Λ^2_{QCD}$, 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 $Q^2 >> μ^2$, the quark distribution is computed in terms of the gluon distribution function and explicit expressions are obtained. For $Q^2 \le μ^2$ but $Q^2 >> Λ_{QCD}^2$ 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.