Comparison of the Gottfried and Adler sum rules within the large-Nc expansion

TL;DR

This study contrasts the exact Adler sum rule with the Gottfried sum rule within the large-$N_c$ expansion, arguing that perturbative corrections to the Gottfried sum are systematically suppressed by $1/N_c^2$ and that higher-twist effects follow the same pattern. It provides an analytic two-loop result for the Gottfried sum, showing the corrections arise from a non-planar color structure and are therefore small in the large-$N_c$ limit, and develops a planar-renormalon framework to forecast suppression of higher-order and higher-twist contributions. The authors connect these perturbative insights to non-perturbative physics, attributing the observed deviation of the Gottfried sum from 1/3 to intrinsic isospin asymmetry in the nucleon sea, compatible with chiral-soliton models that survive the $N_c\to\infty$ limit. A recent addition computes the full three-loop non-singlet anomalous dimension, confirming even smaller perturbative corrections and reinforcing the view that the Gottfried-sum discrepancy is predominantly non-perturbative in origin. Overall, the work highlights a consistent large-$N_c$ picture in which perturbative radiative effects are suppressed, while non-perturbative sea flavor asymmetry remains essential to explain experimental data.

Abstract

The Adler sum rule for deep inelastic neutrino scattering measures the isospin of the nucleon and is hence exact. By contrast, the corresponding Gottfried sum rule for charged lepton scattering was based merely on a valence picture and is modified both by perturbative and non-perturbative effects. Noting that the known perturbative corrections to two-loop order are suppressed by a factor 1/N_c^2, relative to those for higher moments, we propose that this suppression persists at higher orders and also applies to higher-twist effects. Moreover, we propose that the differences between the corresponding radiative corrections to higher non-singlet moments in charged-lepton and neutrino deep inelastic scattering are suppressed by 1/N_c^2, in all orders of perturbation theory. For the first moment, in the Gottfried sum rule, the substantial discrepancy between the measured value and the valence-model expectation may be attributed to an intrinsic isospin asymmetry in the nucleon sea, as is indeed the case in a chiral-soliton model, where the discrepancy persists in the limit N_c-->infinity.