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 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. 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.

Small x Asymptotics of the Quark and Gluon Helicity Distributions

“…In [1], we derived the polarized small-x evolution equations for the TMD quark helicity distribution [6], …”

“…As is well-known, the TMD (3) contains a process-dependent gauge link U[0, r]. For specificity, in [1] we considered semi-inclusive deep inelastic scattering (SIDIS), although the resulting small-x evolution equations also apply to the collinear quark helicity distribution, which is process independent.…”

“…The polarized dipole scattering amplitude G 10 (zs) was defined as the polarized generalization of the forward dipole S-matrix in terms of Wilson lines [1]:…”

“…To obtain a closed system of equations one has to invoke either the large-N c or the large-N c &N f limits (the latter would also require the quark exchange contribution added to the polarized Wilson lines). In the large-N c limit, with DLA accuracy, the polarized evolution equations are [1,3] …”

“…Below we will review our determination of the small-x asymptotics of the quark helicity, and then present the determination of the small-x asymptotics for the gluon helicity distributions. This talk and these proceedings are based on [1][2][3][4][5].…”