Wigner distributions and orbital angular momentum of a proton

TL;DR

Addresses the three-dimensional partonic structure and angular momentum decomposition of the proton by computing Wigner distributions in a light-front scalar diquark AdS/QCD framework. The study connects Wigner distributions to GTMDs, TMDs, and GPDs, and derives quark orbital angular momentum (canonical and kinetic) and spin-orbit correlations. Results show circularly symmetric unpolarized densities, flavor-dependent dipole distortions for spin-polarized cases, and negative quark-spin–OAM correlations for both u and d, with canonical OAM positive and kinetic OAM negative. Limitations include using a single scalar diquark and a low hadronic scale; future work should include axial-vector diquarks and transverse polarization to test robustness and compare with other models.

Abstract

The Wigner distributions for u and d quarks in a proton are calculated using the light front wave functions (LFWFs) of the scalar quark-diquark model for nucleon constructed from the soft-wall AdS/QCD correspondence. We present a detail study of the quark orbital angular momentum(OAM) and its correlation with quark spin and proton spin. The quark density distributions, considering the different polarizations of quarks and proton, in transverse momentum plane as well as in transverse impact parameter plane are presented for both u and d quarks.

Figures (12)

• Figure 1: The variation of canonical OAM $\ell^q_z(x)$ and kinetic OAM $L^q_z(x)$ with longitudinal momentum fraction $x$, for (a) $u$ quark and (b) $d$ quark.
• Figure 2: The Wigner distributions of unpolarized quarks in an unpolarized proton in the transverse momentum plane(a,b) with ${\bf b}_{\perp}=0.4\hat{y}~ fm$ and in the transverse impact parameter plane(c,d) with ${\bf p}_{\perp}=0.3\hat{y}~ GeV$ for $u$ quarks(left column) and $d$ quarks(right column).
• Figure 3: $\tilde{\rho}^q_{UU}(b_x,p_y)$ in mixed transverse plane for $u$ quark(a) and $d$ quark(b).
• Figure 4: The dipolar behavior of $\rho^q_{UL}$ in the transverse momentum plane(a,b) with ${\bf b}_{\perp}=0.4\hat{y}~ fm$ and in the transverse impact parameter plane(c,d) with ${\bf p}_{\perp}=0.3\hat{y}~ GeV$ for $u$ quarks(left column) and $d$ quarks(right column).
• Figure 5: $\tilde{\rho}^q_{UL}(b_x, p_y)$ in mixed transverse plane corresponding to $u$ quark(a) and $d$ quark(b).