Abstract
We investigate the gluon Wigner distributions for unpolarized, longitudinally polarized and transversely polarized target state. Instead of a nucleon, we take the target state to be a quark dressed with a gluon at one loop and investigate the gluon Wigner distributions at leading twist. Better numerical convergence is obtained compared to an earlier study, that removes the regulator dependence of the results. We present a first calculation of the Wigner distribution for the transversely polarized target and linearly polarized gluon. We study the spin densities in momentum and impact parameter space. We also investigate the quark and gluon helicity and orbital angular momentum distributions at small-x.
Highlights
Wigner distributions are not always positive definite
Most of the models have no gluonic degrees of freedom, and so gluon generalized transverse- momentum-dependent distributions (GTMDs) and gluon Wigner distributions cannot be investigated in such models
We have investigated the gluon Wigner distributions for unpolarized, longitudinally polarized and transversely polarized target state, taking into account all possible polarization combinations of the gluon at leading twist
Summary
Wigner distributions are not always positive definite. So far the Wigner distributions of quarks and gluon have only been studied through model calculations, for example in constituent quark model and chiral quark soliton model [6], spectator model [17] and holographic model [18,19]. Recent interest in quark and gluon Wigner distributions and GTMDs is related to the fact that these can provide important information about the so far unknown quark and gluon orbital angular momentum (OAM) in the nucleon [35,36,37,38]. It was shown in [25] that both the WW type and dipole type gluon GTMDs give the same gluon OAM distribution.
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