Off-forward quark distributions of the nucleon in the large N_c limit

TL;DR

This work computes off-forward quark distributions in the nucleon within the large-Nc chiral quark-soliton framework, providing a nonperturbative, low-scale input that satisfies sum rules and positivity. A key finding is the dominant role of the Dirac continuum in shaping H(x,ξ,Δ^2), which induces sharp crossovers at |x|=ξ/2 and can amplify DVCS cross sections. Forward limits reproduce standard parton distributions and form-factor sum rules, validating the model's consistency. The results emphasize the importance of the momentum-dependent dynamical quark mass from chiral symmetry breaking and note that evolution to higher scales is essential for confronting DVCS data.

Abstract

We study the off-forward quark distributions (OFQD's) in the chiral quark-soliton model of the nucleon. This model 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 demonstrate the consistency of the approach by checking various sum rules for the OFQD's. We present numerical estimates of the isosinglet distribution H(x,ξ,Δ^2). In contrast to other approaches we find a strong qualitative dependence on the longitudinal momentum transfer, ξ. In particular, H(x,ξ,Δ^2) as a function of x exhibits fast crossovers at |x| = ξ/2. Such behaviour could lead to a considerable enhancement of the deeply-virtual Compton scattering cross section.

Figures (4)

• Figure 1: The isosinglet distribution $H(x,\xi,\Delta^2)$ 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 isosinglet distribution $H(x,\xi,\Delta^2)$ for $\Delta_T^2=0$ ($\Delta_T^2 \equiv -\Delta^2-\xi^2 M_N^2$) and $\xi=0.3$. 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: the total distribution (sum of the dashed and dashed-dotted curves). The vertical lines mark the crossover points $x=\pm \xi/2$.
• Figure 3: The isosinglet distribution $H(x,\xi,\Delta^2)$ (total result) for fixed $\Delta^2=-0.5$ GeV$^2$ and various values of $\xi$.
• Figure 4: The isosinglet distribution $H(x,\xi,\Delta^2)$ (total result) for fixed $\xi=0.3$ and various values of $\Delta^2$.