Non-planar structure of analytical QCD predictions for the Gottfried sum rule

TL;DR

This paper reveals that in large N_c-expansion calculations of QCD corrections to the Gottfried sum rule, only non-planar O(1/N_c^2) terms appear, suggesting a suppression of planar contributions and implications for light-quark flavor asymmetry.

Contribution

It demonstrates the dominance of non-planar corrections in QCD calculations of the Gottfried sum rule and proposes a suppression of planar terms, linking perturbative cancellations to quark flavor asymmetry.

Findings

Non-planar O(1/N_c^2) corrections dominate in the calculations.

Planar O(N_c^0) perturbative terms disappear in the series.

Suppression of differences in QCD corrections for charged-lepton and neutrino DIS.

Abstract

It is stressed that within large N_c-expansion {\bf analytical calculations} of the $(\alpha_s/\pi)^2$ QCD contributions to the valence part of the Gottfried sum rule for F_2 structure function of charged leptons-nucleon deep-inelastic scattering reveals the existence of the $O(1/N_c^2)$ {\bf non-planar} corrections only and the disappearance of the {\bf planar} O(N_c^0) perturbative terms. The relation between Gottfried and Adler sum rule for neutino-nucleon DIS is established and the proposal that the differebce between corresponding QCD corrections to higher non-singlet moments in charged-lepton and neutrino DIS are {\bf suppressed by 1/N_c^2} is made. The possible consequence of the cancellation of {\bf perturbative planar} graphs in the considered perturbative series, namely the existence of light-quark flavour asymmetry $\bar{u}(x)<\bar{d}(x)$, is mentioned. The effect of the similar origin, i.e. the relation of {\bf ``light-by-light-type''-type structure} in DIS characteristics at the $\alpha_s^3$-level to the generation of light quark-antiquark asymmetry, is also commented.