Flavor singlet contribution to the structure functiong 1 at small-x

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.

Spin structure function g1 at low x: status and plans

“…by those terms of the perturbative expansion which correspond to the powers of ln 2 (1/x) at each order of the expansion [12]. The ln 2 (1/x) effects go beyond the standard (i.e.…”

Transverse single spin asymmetries at smallxand the anomalous magnetic moment

“…From Eq. [16] and Eq. [17], one finds that this ratio scales as k ⊥ at low transverse momentum, while it scales as 1/k 3 ⊥ at high transverse momentum.…”

“…The early work includes the study of small x evolution of spin dependent structure function g 1 [16]. It was pointed out that the spin asymmetries could also be generated by the pomeronodderon interference effect [17].…”

The evolution of the small x gluon TMD

“…We anticipate that two different type large logarithms also show up at the same time for these polarization dependent gluon TMDs in the small x limit. However, we would like to emphasize that the small x evolution of the gluon helicity distribution has to be treated in a complete different way [17,18,47]. Third, by extracting the large logarithm terms from the complete two loop order results for TMDs [60,61] one should be able to reproduce the same result presented in this paper.…”