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.

No abstract

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.

Explicit expressions for the singlet g1 at small x and small Q 2 are obtained with the total resummation of the leading logarithmic contributions. It is shown that g1 practically does not depend on x in this kinematic region. In contrast, it would be interesting to investigate its dependence on the invariant energy 2pq because, being g1 positive at small 2pq, it can turn negative at greater values of this variable. The position of the turning point is sensitive to the ratio between the initial quark and gluon densities, so its experimental detection would enable to estimate this ratio.

The treatment of the running QCD coupling in evolution equations is discussed. It is shown that the use of the virtuality of ladder (vertical) partons as the scale for QCD coupling in every rung of ladder graphs is an approximation that holds for DIS at large x only. On the contrary, in the small x region the coupling depends on the virtuality of s -channel (horizontal) gluons. This observation leads to different results for the Regge-like processes and DIS structure functions at small x.

The running of the QCD coupling is incorporated into the infrared evolution equations for the flavour structure function g1. The explicit expressions for g1 including the total resummation of the double-logarithmic contributions and accounting for the running coupling are obtained. We predict that asymptotically g1 ∼ x −∆ S , with the intercept ∆S = 0.86, which is more than twice larger than the non-singlet intercept ∆NS = 0.4. The impact of the initial quark (δq) and gluon (δg) densities on the sign of g1 at x ≪ 1 is discussed and explicit expressions relating δq and δg are obtained.