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 wave function 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 ${\ensuremath{\mu}}^{2},$ large compared to the QCD scale ${\ensuremath{\Lambda}}_{\mathrm{QCD}}^{2},$ 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 ${Q}^{2}\ensuremath{\gg}{\ensuremath{\mu}}^{2},$ the quark distribution is computed in terms of the gluon distribution function and explicit expressions are obtained. For ${Q}^{2}<~{\ensuremath{\mu}}^{2}$ but ${Q}^{2}\ensuremath{\gg}{\ensuremath{\Lambda}}_{\mathrm{QCD}}^{2}$ 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 $x.$