Quark Wigner distributions and spin-spin correlations

Abstract

We investigate the Wigner distributions for u and d quarks in a light front quark-diquark model of a proton to unravel the spatial and spin structure. The light-front wave functions are modeled from the soft-wall AdS/QCD prediction. We consider the contributions from both the scalar and the axial vector diquarks. The Wigner distributions for unpolarized, longitudinally polarized and transversely polarized proton are presented in transverse momentum plane as well as in transverse impact parameter plane. The Wigner distributions satisfy a Soffer bound type inequality. We also evaluate all the leading twist GTMDs and show their scale evolution. The spin-spin correlations between the quark and the proton are investigated.

Wigner Distributions Using Light-Front Wave Functions

“…In Fig. 4(a) and 4(b) we have shown the Wigner distributions ρ UU and ρ UL respectively for the u quark in a quark-diquark model for the proton, modeled using a modified form of LFWF obtained using Ads/QCD prediction [12]. Here also, we have integrated over x.…”

“…The dressed quark target represents a composite spin 1/2 state with a gluonic degree of freedom, and we have calculated the gluon Wigner distributions as well. These are expressed in terms of overlaps of LFWFs and using their analytic form we have calculated Figure 4: Plots of u-quark Wigner distributions ρ UU and ρ UL in b space in light-front quark-diquark model [12].…”

“…The analytic results for all the quark and gluon Wigner distributions for a simple composite spin 1/2 system can be found in [10,11]. The full calculation of the Wigner distributions and spin-spin correlations in quark-diquark model, where the LFWF is modeled by Ads/QCD correspondence, can be found in [12]. Here we report on some of our numerical results.…”

“…Model calculations of Wigner functions are thus important to get a qualitative idea of them. In this talk, we report on a few recent developments on model calculations of the quark and gluon Wigner distributions [10,11,12].…”

Wigner Distributions of Quarks and Gluons

“…If one integrates the Wigner distributions over transverse momentum, one obtains impact parameter dependent parton distributions, which are Fourier transform of generalized parton distributions (GPDs); integration over transverse position relates them on the other hand to transverse momentum dependent parton distributions (TMDs). Quark Wigner distributions have been investigated in several model calculations [3,6,7,8]. Most of the models do not have a gluonic degree of freedom, and thus gluon Wigner distributions are less explored apart from the small x region.…”