The singlet contribution to the structure function g1( x, Q2) at small x

Abstract

The resummation of O( α s l+1 ln 2 l x) terms in the evolution of the singlet part of g 1( x, Q 2) is carried out on the basis of the renormalization group equation. The corresponding singlet anomalous dimensions are calculated explicitly referring to amplitude relations derived by Bartels et al. [J. Bartels, B.I. Ermolaev and M.G. Ryskin, DESY 96-025]. The leading small- x contribution to the three-loop splitting function matrix is determined in the MS scheme. Relations are derived for the case of N = 1 supersymmetric Yang-Mills field theory. Numerical results are presented for the polarized singlet and gluon densities, and the structure functions g 1 p ( x, Q 2) and g 1 n ( x, Q 2). They are compared for different assumptio the non-perturbative input distributions, and the stability of the results against presently unknown subleading contributions is investigated.