The Singlet contribution to the structure function $g_1(x, Q^2)$ at small x

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