Isovector unpolarized quark distribution in the nucleon in the large-N_c limit

TL;DR

This work computes the isovector unpolarized quark/antiquark distributions at a low normalization point in the large-$N_c$ limit by modeling the nucleon as a chiral soliton and performing a $1/N_c$ expansion. The isovector distribution first appears at next-to-leading order and receives contributions from both bound-state and Dirac continuum quark levels, with ultraviolet regularization via Pauli–Villars subtractions to preserve sum rules. The results yield a flavor-asymmetric antiquark sea and a Gottfried-sum deviation in line with experimental observations, and the derived distributions exhibit reasonable agreement with the GRV95 parametrization after accounting for the low scale. The approach demonstrates how non-perturbative chiral dynamics in a soliton picture can furnish input for low-scale parton distributions and clarifies the connections between sum rules and the underlying spectrum, while outlining sensitivity to ultraviolet details in the small-$x$ region.

Abstract

We calculate the isovector (flavor-nonsinglet) unpolarized quark- and antiquark distributions in the nucleon at a low normalization point in the large-N_c limit. The nucleon is described as a soliton of the effective chiral theory. The isovector distribution appears in the next-to-leading order of the 1/N_c-expansion. Numerical results for the quark- and antiquark distributions compare well with the parametrizations of the data at a low normalization point. This large-N_c approach gives a flavor asymmetry of the antiquark distribution (violation of the Gottfried sum rule) in good agreement with the measurements.

Figures (4)

• Figure 1: The contribution of the Dirac continuum to the isovector distribution function $u(x) - d(x)$, for $M = 350\,{\rm MeV}$. At negative $x$ the function shown describes minus the antiquark distribution. Solid line: Total result, as obtained from the expansion in angular velocity, given by the sum of Eq.(\ref{['isovec_combined_1']}) and Eq.(\ref{['isovec_combined_2']}). Dashed line: Result obtained dropping the contribution Eq.(\ref{['isovec_combined_2']}), corresponding to the prescription of Ref.WK97.
• Figure 2: Contributions to the isovector unpolarized distribution function, $u(x) - d(x)$, for $M = 350\,{\rm MeV}$. At negative $x$ the function shown describes minus the antiquark distribution. Dashed line: Contribution of the discrete level. Dot--dashed line: Contribution of the negative Dirac continuum. Solid line: Total result.
• Figure 3: The isovector unpolarized distribution function, $u(x) - d(x)$, for constituent quark masses $M = 350\,{\rm MeV}$ ( solid line) and $M = 420\,{\rm MeV}$ ( dashed line). At negative $x$ the function shown describes minus the antiquark distribution.
• Figure 4: Solid lines: The calculated isovector unpolarized quark-- and antiquark distributions, $x[u(x) - d(x)]$ and $x[\bar{u}(x) - \bar{d}(x)]$, for $M = 350\,{\rm MeV}$. Shown is the total result, corresponding to the solid line in Fig.\ref{['fig_fig2']}. Dotted lines: The GRV NLO parametrizations GRV95.