Quark Wigner distributions using light-front wave functions

Abstract

The quasiprobabilistic 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 the leading twist, one can define 16 quark Wigner distributions; however, we obtain only 8 independent nonzero Wigner distributions in our model. We compare our results with other model calculations for the proton.