Identical particles effects on the nucleon structure functions.

Abstract

The factorization of the nucleon structure function into pointlike subprocesses and nonperturbative parton distributions is examined to determine if it can accomodate the statistical correlation effects of identical partons. In a full 3-dimensional model, we find that only partons moving in same direction will contribute to the evolution of a distribution function. The expression of the evolution equation as a convolution of the distribution function and the splitting function can only be retained when the correlation factors are turned off. Turning on the statistical factors modifies the splitting function, and the conventional convolution for the evolution equation cannot be constructed. Transition to the ordinary (unidirectional) Parton Model is achieved by suppressing the occupation of the transverse modes in the distributions. In this model, the corrections due to the statistical factors are to be expected in the order of higher twist. Their explicit calculation in the massive gluon renormalization scheme is plagued with collinear divergences which do not cancel, even when we include the parton recombination processes as suggested by the Thermal Model. The same calculation with dimensional regularization indicates the shifting of the divergent pole from D = 4 to D = 6; analytic continuation to D = 4 yields a finite result, but not the same as the finite part in the massive gluon method. We argue that this divergence must be absorbed into renormalized nonperturbative distribution functions. A renormalization procedure is then proposed, in which the absorbed factor must depend on the distribution function. We conclude that renormalized distributions extracted from deep inelastic scattering contain higher twist effects from statistical correlations of identical particles. These effects are not universal, but must be calculated separately for each process.