Helicity skewed quark distributions of the nucleon and chiral symmetry

TL;DR

This work computes helicity skewed quark distributions $\widetilde{H}$ and $\widetilde{E}$ in the chiral quark-soliton model, highlighting the role of spontaneously broken chiral symmetry and the large-$N_c$ limit. It shows that a pion-pole contribution to $\widetilde{E}^{(3)}$ is required by chiral Ward identities and dominates in many kinematic regions, while the Dirac continuum is essential for $\widetilde{H}^{(3)}$, especially for antiquark channels. The study demonstrates non-factorizable $\Delta^2$-dependence and maintains polynomiality of Mellin moments, offering insights for DVCS and hard exclusive meson production observables such as azimuthal spin asymmetries. Comparisons with other models underscore the importance of chiral dynamics and the continuum in shaping skewed helicity distributions. These results provide a theoretically consistent framework for interpreting spin-dependent exclusive processes in terms of familiar nucleon structure functions.

Abstract

We compute the helicity skewed quark distributions $\widetilde{H}$ and $\widetilde{E}$ in the chiral quark-soliton model of the nucleon. This model emphasizes correctly the role of spontaneously broken chiral symmetry in structure of nucleon. It is based on the large-N_c picture of the nucleon as a soliton of the effective chiral lagrangian and allows to calculate the leading twist quark- and antiquark distributions at a low normalization point. We discuss the role of chiral symmetry in the helicity skewed quark distributions $\widetilde{H}$ and $\widetilde{E}$. We show that generalization of soft pion theorems, based on chiral Ward identities, leads in the region of -ξ< x < ξto the pion pole contribution to $\widetilde{E}$ which dominates at small momentum transfer.

Figures (5)

• Figure 1: The isovector distribution $\widetilde{H}(x,\xi,\Delta^2)$ in the forward limit, $\Delta=0$. Dashed line: contribution from the discrete level. Dashed-dotted line: contribution from the Dirac continuum according to the interpolation formula, eq. (\ref{['H-1-sym-res-mp']}). Solid line: total distribution (sum of the dashed and dashed-dotted curves).
• Figure 2: The same as Fig. 1 but for no-forward case $\Delta^2=-0.5$ GeV$^2$ and $\xi=0.2$.
• Figure 3: Calculated isovector SPD $\widetilde{H}$ at various values of $\Delta^2$ and $\xi$.
• Figure 4: Comparison of pion pole contribution and non-pole part of isovector $\widetilde{E}$ at various values of $\Delta^2$ and $\xi$. The positive curves correspond to pion pole contributions.
• Figure 5: Total result (pole+non-pole) for isovector $\widetilde{E}$ at $\xi=0.2$ and various values of $\Delta^2$.