Helicity Evolution at Small-x

Yuri V. Kovchegov; Daniel Pitonyak; Matthew D. Sievert

Paper

Helicity Evolution at Small-x

Abstract

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the

structure function. These evolution equations resum powers of

in the polarization-dependent evolution along with the powers of

in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-

and large-

limits. As a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for

structure function derived previously by Bartels, Ermolaev and Ryskin.