Helicity Evolution at Small x: Summary of Recent Developments

Abstract

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. We construct a numerical solution of the helicity evolution equations in the large-$N_c$ limit. Employing the extracted intercept, we are able to predict directly from theory the behavior of the quark helicity PDFs at small $x$, which should have important phenomenological consequences. We also give an estimate of how much of the proton's spin may be at small $x$ and what impact this has on the so-called "spin crisis." Based on JHEP 1601 (2016) 072 (arXiv:1511.06737), arXiv:1610.06197 and arXiv:1610.06188.

Comments: 8 pages, 6 figures; combined proceedings of "QCD Evolution 2016" workshop, Amsterdam, Netherlands, May 30 - June 3, 2016 and the 22nd International Spin Symposium (SPIN 2016), Champaign, IL, USA, September 26 - 30, 2016. Based on JHEP 1601 (2016) 072 (arXiv:1511.06737), arXiv:1610.06197 and arXiv:1610.06188