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

Abstract

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.

Polarized DIS in 𝒩 = 4 SYM: where is spin at strong coupling?

“…Its small-x behavior has then to be studied quite independently, using the perturbative QCD evolution [31][32][33] or perhaps in the framework of Regge theory [34]. However, in strongly coupled N = 4 SYM it turns out…”

“…This is qualitatively similar to (5.4), though of course such a comparison should be taken with caution. On the other hand, predictions from perturbative QCD vary [31][32][33] depending on which terms in higher order graphs are resummed. Including the so-called double logarithmic contributions, refs.…”

Does leading $\ln x$ resummation predict the rise of $g_1$ at small $x$ ?

“…The resummation of ln x singularities for the g 1 structure function has been done in [9,10]. The result for the "parton (quark) " target with the fixed coupling constant 2 reads,…”

“…The controversial aspect between their numerical analysis and the assertion by Bartels, Ermolaev and Ryskin might be coming from the fact that the resummed part of the "coefficient function" is considered in [10] but not in [11]. Blümlein and Vogt did not include the resummed part of the coefficient function because this part turns out to fall in the next-to-leading logarithmic (NLL) corrections and depends on the factorization scheme adopted.…”

“…Recently Bartels, Ermolaev and Ryskin [10] have given the resummed expression for the g 1 structure function by using the Infra-Red Evolution Equation. They claim that the resummation effects may lead to 10 times larger results than the DGLAP ones.…”