Abstract
The high energy Operator Product Expansion for the product of two electromagnetic currents is extended to the sub-eikonal level in a rigorous way. I calculate the impact factors for polarized and unpolarized structure functions, define new distribution functions, and derive the evolution equations for unpolarized and polarized structure functions in the flavor singlet and non-singlet case.
Highlights
If we try to calculate one loop correction either to the coefficient function or to the matrix element of the Wilson-line operators, we will find divergences which are identified by rapidity divergences as a remnant of the fact that the parameter we use to discriminate between background field from the quantum field is the rapidity
In the appendix C we have identified further distribution functions that, will not contribute to g1 structure functions
We found that the polarized and unpolarized quark distribution functions as well as the polarized gluon distributions are energy suppressed with respect to the unpolarized gluon ones
Summary
In view of future collider experiments, in which hadronic matter will be probed at unprecedented kinematic regimes, there has been, in recent years, an ever growth of interest in understanding the fundamental properties of hadrons, spin and mass, from their constituents, quarks, and gluons [1,2,3,4,5,6, 9,10,11,12,13]. The plan is to bring the knowledge of the unpolarized and polarized small-x structure function at the same level To this end, first we need to extend the high-energy OPE of the T -product of two-electromagnetic currents to include terms that are not symmetric in the exchange of the two Lorentz indexes of the DIS hadronic tensor. We will derive the leading order (LO) impact factor and the associated Wilson-line operators together with their evolution equations This will serve as a smooth transition to the OPE at sub-eikonal level in section 3 where we will give a new expression [46]) of the quark propagator with sub-eikonal corrections in the background of gluon fields, and will identify the relevant sub-eikonal corrections which will be used, in section 4, to calculate the impact factors for polarized and unpolarized structure functions. We will argue that the result we obtained agree in some limiting case, they differ from the ones calculated in refs. [5, 7, 8] because of the way the quark and gluon operators are treated under one loop evolution
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