Quark Wigner Distributions Using Light-Front Wave Functions

TL;DR

This paper calculates quark Wigner distributions for a simple dressed quark state using light-front wave functions, revealing insights into the quantum phase-space structure of quarks with different polarization states.

Contribution

It provides the first calculation of quark Wigner distributions for a dressed quark state with gluonic degrees of freedom using light-front wave functions, highlighting the number of independent distributions.

Findings

Only 8 of the 16 possible Wigner distributions are non-zero in the model.

Results are compared with other proton models, showing similarities and differences.

The study offers a simplified yet insightful view of quark phase-space distributions.

Abstract

The quasi-probabilistic Wigner distributions are the quantum mechanical analog of the classical phase-space distributions. We investigate quark Wigner distributions for a quark state dressed with a gluon, which can be thought of as a simple composite and relativistic spin-1/2 state with a gluonic degree of freedom. We calculate various polarization configurations, namely unpolarized, longitudinally polarized and transversely polarized quark and the target state using light-front wave functions in this model. At leading twist, one can define 16 quark Wigner distributions, however, we obtain only 8 independent non-zero Wigner distributions in our model. We compare our results with other model calculations for the proton.