Sivers Mechanism for Gluons
Matthias Burkardt
TL;DR
The paper addresses T-odd, gauge-invariant unintegrated gluon densities and the Sivers mechanism in QCD, framing the problem via gauge links and light-cone gauge. It defines future-pointing Wilson-line augmented gluon densities and derives the x-integrated average transverse momentum associated with the gluon Sivers effect. The central result proves that the sum of Sivers-induced transverse momenta from gluons and all quark flavors cancels, due to color conservation and pure-gauge boundary conditions, providing a nontrivial constraint on gluon Sivers distributions. This constraint links gluon and quark Sivers effects across processes and serves as a practical check for phenomenological parameterizations.
Abstract
We study T-odd gauge invariantly defined T-odd unintegrated gluon densities in QCD. The average $\perp$ momentum of the gluons in a $\perp$ polarized nucleon can be nonzero due to the Sivers mechanism. However, we find that the sum of the transverse momenta due to the Sivers mechanism from gluons and all quark flavors combined vanishes, i.e. $<{\bf k_{\perp,g}}> + \sum_q < {\bf k_{\perp,q}}> =0$.