Helicity evolution at small x

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 alpha(s) ln(2)(1/x) in the polarization-dependent evolution along with the powers of alpha(s) ln(1/x) 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-N-c and large-N-c & N-f limits. 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 [1].