Abstract:The singlet contribution to the g 1 (x, Q 2 ) structure function is calculated in the double-logarithmic approximation of perturbative QCD in the region x ≪ 1. Double logarithmic contributions of the type (α s ln 2 (1/x)) k which are not included in the GLAP evolution equations are shown to give a power-like rise at small-x which is much stronger than the extrapolation of the GLAP expressions. The dominant contribution is due to the gluons which, in contrast to the unpolarized case, mix with the fermions also in the region x ≪ 1. The two main reasons why the small-x behavior of the double logarithmic approximation is so much stronger than the usual GLAP evolution are: the larger kinematical region of integration (in particular, no ordering in transverse momentum) and the contributions from non-ladder diagrams.

The singlet contribution to the g 1 (x, Q 2 ) structure function is calculated in the double-logarithmic approximation of perturbative QCD in the region x ≪ 1. Double logarithmic contributions of the type (α s ln 2 (1/x)) k which are not included in the GLAP evolution equations are shown to give a power-like rise at small-x which is much stronger than the extrapolation of the GLAP expressions. The dominant contribution is due to the gluons which, in contrast to the unpolarized case, mix with the fermions also in the region x ≪ 1. The two main reasons why the small-x behavior of the double logarithmic approximation is so much stronger than the usual GLAP evolution are: the larger kinematical region of integration (in particular, no ordering in transverse momentum) and the contributions from non-ladder diagrams.

On the relation between collinear and three dimensional rate constants associated with vibrational energy transfer in diatom-diatom collisions J. Chem. Phys. 72, 1945 10.1063/1.439340 Relations between the deuteron form factors and the wave functions AIP Conf. Proc. 41, 555 (1978); 10.1063/1.31247On the relation between collinear and three dimensional collision rates with applications to vibrational energy transfer Abstract. Collinear and k T -factorizations were introduced from different theoretical considerations and for different perturbative methods. We demonstrate that they both can be obtained from a more general factorization. We prove that they can be related to each other with imposing a simple assumption for the unintegrated parton distributions.

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Infrared evolution equations for small-x behaviour of the non-singlet structure functions f NS 1 and g NS 1 are obtained and solved in the next-to-leading approximation, to all orders in α s , and including running α s effects. The intercepts of these structure functions, i.e. the exponents of the power-like small-x behaviour, are calculated. A detailed comparison with the leading logarithmic approximation (LLA) and DGLAP is made. We explain why the LLA predictions for the small-x dependence of the structure functions may be more reliable than the prediction for the Q 2 dependence in the range of Q 2 explored at HERA.