Parton degrees of freedom from the path-integral formalism

Abstract

We formulate the hadronic tensor ${W}_{\ensuremath{\mu}\ensuremath{\nu}}$ of deep inelastic scattering in the path-integral formalism. It is shown that there are 3 gauge invariant and topologically distinct contributions. In addition to the valence contribution, there are two sources for the sea---one in the connected insertion and the other in the disconnected insertion. The operator product expansion is carried out in this formalism. The operator rescaling and mixing reveal that the connected sea partons evolve the same way as the valence; i.e., their evolution is decoupled from the disconnected sea and the gluon distribution functions. We explore the phenomenological consequences of this classification in terms of the small x behavior, Gottfried sum rule violation, and flavor dependence. In particular, we point out that in the nucleon $\ifmmode \bar{u}\else \={u}\fi{}$ and $\overline{d}$ partons have both connected and disconnected sea contributions, whereas the $\overline{s}$ parton has only the disconnected sea contribution. This difference between $\ifmmode \bar{u}\else \={u}\fi{}+\overline{d}$ and $\overline{s},$ as far as we know, has not been taken into account in the fitting of parton distribution functions to experiments.