Chiral-odd generalized parton distributions in constituent quark models

TL;DR

The paper develops an overlap representation for chiral-odd generalized parton distributions using light-cone wave functions within a constituent quark model, focusing on the valence-quark sector with three-quark Fock states. By working in the transversity basis, it derives expressions that connect T and tilde T matrix elements to H_T, E_T, tilde H_T, and tilde E_T, and computes the four GPDs for u and d quarks at the hadronic scale, revealing characteristic SU(6) patterns and relativistic effects from Melosh rotations. In the forward limit, H_T reduces to the transversity h_1, enabling tensor-charge analysis and an angular-momentum sum-rule investigation for quarks with transverse polarization, with qualitative agreement to known models and LO QCD evolution shaping the quantitative values. The work establishes a solid framework for chiral-odd GPDs in a valence-only picture and discusses extensions to include qq̄ contributions, with implications for transverse-spin phenomena such as the Boer-Mulders and Sivers-like observables.

Abstract

We derive the overlap representation of chiral-odd generalized parton distributions using the Fock-state decomposition in the transverse-spin basis. This formalism is applied to the case of light-cone wave functions in a constituent quark model. Numerical results for the four chiral-odd generalized parton distributions at the hadronic scale are shown in different kinematics. In the forward limit we derive the transversity distribution, the tensor charge and the angular momentum sum rule for quarks with transverse polarization in an unpolarized nucleon.

Figures (7)

• Figure 1: The chiral odd generalized parton distributions calculated in the hypercentral CQM for the flavour $u$, at $\xi=0$ and different values of $t$: $t=0$ (solid curves), $t=-0.2$ (GeV)$^2$ (dashed curves), $t=-0.5$ (GeV)$^2$ (dotted curves).
• Figure 2: The same as in Fig. \ref{['fig:fig1']} but for fixed $t=-0.2$ (GeV)$^2$ and different values of $\xi$: $\xi =0$ (solid curves), $\xi=0.1$ (dashed curves), $\xi=0.2$ (dotted curves).
• Figure 3: The same as in Fig. \ref{['fig:fig1']} but for fixed $t=-0.5$ (GeV)$^2$ and different values of $\xi$: $\xi =0$ (solid curves), $\xi=0.1$ (dashed curves), $\xi=0.2$ (dotted curves).
• Figure 4: The chiral odd generalized parton distributions calculated in the hypercentral CQM for the flavour $d$, at $\xi=0$ and different values of $t$: $t=0$ (solid curves), $t=-0.2$ (GeV)$^2$ (dashed curves), $t=-0.5$ (GeV)$^2$ (dotted curves).
• Figure 5: The same as in Fig. \ref{['fig:fig4']} but for fixed $t=-0.2$ (GeV)$^2$ and different values of $\xi$: $\xi =0$ (solid curves), $\xi=0.1$ (dashed curves), $\xi=0.2$ (dotted curves).