Fock space distributions, structure functions, higher twists, and small x

We compute quark structure functions and the intrinsic Fock space distribution of sea quarks in a hadron wave function at small $x.\mathrm{}$ 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 ${\Lambda }_{\mathrm{QCD}}^2,$ 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 $Q^2<~M^2$ but $Q^2\gg {\mu }^2,$ the quark distribution is computed in terms of the gluon distribution function and explicit expressions are obtained. For $Q^2<~{\mu }^2$ but $Q^2\gg {\Lambda }_{\mathrm{QCD}}^2$ 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 $x.\mathrm{}$