Unpolarized and polarized quark distributions in the large-Nc limit

TL;DR

This paper computes the leading twist-2 quark distributions in the large-$N_c$ limit by describing the nucleon as a chiral soliton in an effective theory. Distributions are obtained as sums over single-particle quark levels in the background pion field, with antiquarks arising from non-occupied states, using Pauli-Villars regularization to preserve completeness and causality. The authors develop a discretized, numerically robust method (Kahana-Ripka basis) with a spherically symmetric representation and Gaussian smearing to produce smooth $x$-dependence, and they compare the results to low-scale parametrizations, finding reasonable agreement and a large antiquark content. They also discuss the implications for gluon suppression in the effective theory and outline future work on self-consistent solitons and extending to small distributions, establishing a covariant framework for nucleon structure at low normalization points.

Abstract

The isosinglet unpolarized and isovector polarized twist-2 quark distributions of the nucleon at low normalization point are calculated in the large-Nc limit. The nucleon is described as a soliton of the effective chiral theory. We derive the expressions for the distribution functions in the large-Nc limit starting from their definition as numbers of partons carrying momentum fraction x in the infinite momentum frame. We develop a numerical method for computation of the quark and antiquark distributions as sums over the quark single-particle levels in the pion field of the soliton. The contributions of the discrete bound-state level as well as the Dirac continuum are taken into account. The quark- and antiquark distributions obtained explicitly satisfy all general requirements. Results are in reasonable agreement with parametrizations of the data at low normalization point.

Figures (6)

• Figure 1: The isosinglet unpolarized quark-- and antiquark distributions. Solid line: quark distribution, $u(x) + d(x)$, total result (discrete level plus Dirac continuum); dotted line: contribution of the discrete level (after PV subtraction) to $u(x) + d(x)$. Dashed line: antiquark distribution, $\bar{u}(x) + \bar{d}(x)$, total result; dot--dashed line: contribution of the discrete level to $\bar{u}(x) + \bar{d}(x)$.
• Figure 2: The isovector polarized quark-- and antiquark distributions. Solid line: quark distribution, $\Delta u(x) - \Delta d(x)$, total result (discrete level plus Dirac continuum); dotted line: contribution of the discrete level (after PV subtraction) to $\Delta u(x) - \Delta d(x)$. Dashed line: antiquark distribution, $\Delta\bar{u}(x) - \Delta\bar{d}(x)$, total result; dot--dashed line: contribution of the discrete level to $\Delta\bar{u}(x) - \Delta\bar{d}(x)$.
• Figure 3: The isosinglet unpolarized distribution of quarks plus antiquarks, $\frac{1}{2} x [u(x) + d(x) + \bar{u} (x) + \bar{d} (x)]$. Solid line: calculated distribution (total result, cf. Fig.\ref{['fig_non']}). Points: NLO parametrization of ref.GRV95.
• Figure 4: The isosinglet unpolarized valence quark distribution, $\frac{1}{2} x [u(x) + d(x) - \bar{u} (x) - \bar{d} (x)]$. Solid line: calculated distribution (total result); dashed line: contribution of the Dirac continuum. Points: NLO parametrization of ref.GRV95.
• Figure 5: The isovector polarized distribution of quarks plus antiquarks, $\frac{1}{2} x [\Delta u(x) - \Delta d(x) + \Delta \bar{u} (x) - \Delta \bar{d} (x)]$. Solid line: calculated distribution (total result, cf. Fig.\ref{['fig_pol']}). Points: NLO parametrization of ref.GRSV96.