Six-dimensional light-front Wigner distributions of the proton

Abstract We investigate six-dimensional quark Wigner distributions of the proton in a light-front quark spectator-diquark model. Benefiting from the light-front boost-invariant longitudinal variable $$\tilde{z}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>z</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> , these light-front Wigner distributions provide complete information of parton distribution in the phase space and the correlation with spins. At the leading twist, one can define 16 independent distribution functions in according to different combinations of quark and proton polarizations. Numerical results of all these Wigner distributions are presented, unraveling rich structures of the proton, which may potentially provide new observables to be explored at future experiments.