The quark orbital angular momentum from Wigner distributions and light-cone wave functions
C. Lorce', B. Pasquini, X. Xiong, F. Yuan
TL;DR
The paper investigates quark orbital angular momentum in the nucleon without gauge fields, employing both Wigner distributions and light-cone wave functions. It derives a phase-space expression for OAM via Wigner distributions and provides an LCWF overlap representation across N-parton Fock sectors, with explicit treatment of the three-quark (3Q) state. A detailed partial-wave decomposition in the uds basis yields explicit contributions for l_z=0, ±1, and 2, linking LCWF amplitudes to OAM. Applying the framework to two models—the light-cone constituent quark model and the light-cone chiral quark-soliton model—produces consistent signs for up- and down-quark OAM and highlights scale evolution as essential for comparison with experimental or lattice results.
Abstract
We investigate the quark orbital angular momentum of the nucleon in the absence of gauge-field degrees of freedom, by using the concept of the Wigner distribution and the light-cone wave functions of the Fock state expansion of the nucleon. The quark orbital angular momentum is obtained from the phase-space average of the orbital angular momentum operator weighted with the Wigner distribution of unpolarized quarks in a longitudinally polarized nucleon. We also derive the light-cone wave function representation of the orbital angular momentum. In particular, we perform an expansion in the nucleon Fock state space and decompose the orbital angular momentum into the $N$-parton state contributions. Explicit expressions are presented in terms of the light-cone wave functions of the three-quark Fock state. Numerical results for the up and down quark orbital angular momenta of the proton are shown in the light-cone constituent quark model and the light-cone chiral quark-soliton model.