Helicity evolution at small x

Abstract

Here, we construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g 1 structure function. These evolution equations resum powers of α s ln 2 (1/x) in the polarization-dependent evolution along with the powers of α s ln(1/x) in the unpolarized evolution which includes saturation effects. Moreover, 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-N c and large-N c & N f limits. Finally, as a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for the g 1 structure function derived previously by Bartels, Ermolaev and Ryskin.