References - Bogoliubov Laboratory of Theoretical Physics - JINR

INFRARED PROPERTIES OF THE SPIN STRUCTURE FUNCTION G1
B.I. Ermoalev 1 † ,M.Greco 2 and S.I. Troyan 3
(1) Ioffe Physico-Technical Institute, 194021 St.Petersburg, Russia
(2) Department of Physics and INFN, University Rome III, Rome, Italy
(3) St.Petersburg Institute of Nuclear Physics, 188300 Gatchina, Russia
† E-mail: ermolaev@mail.cern.ch
Abstract
We present analysis of the infrared dependence of the perturbative contributions
to the spin structure function g1.
1 Introduction
Factorization [1] of the long and short -distance strong interactions is introduced to guarantee
applicability of Perturbative QCD for calculating the DIS structure functions. According
to this concept, the perturbative calculations involve dealing with virtual partons
(quarks and gluons) of the virtualities � μ 2 while contributions of the partons with small
virtualities � μ 2 are collected into the initial parton densities. Therefore, parameter μ
plays the role of a border between the perturbative and non-perturbative QCD. Being
artificial parameter, μ should vanish when both perturbative and non-perturbative QCD
contributions are taken into account, i.e. in convolutions of the perturbative expressions
for g1 with initial parton distributions. For example, the non-singlet component of g1 can
be written as
g NS
1
NS pert
Naturally, the perturbative part, g1 the Standard Approach and beyond it.
NS pert
= g1 ⊗ δq. (1)
depends on μ. This dependence is different in
2 The μ -dependence of g1 in Standard Approach
Standard Approach describes g1 at large x. It is based on the DGLAP evolution equations
[2]. It is believed that the μ dependence in this approach appears in the first-loop
integration over k⊥ while calculations in higher loops do not depend on μ because of the
well-known DGLAP- ordering
μ 2