New Application of the large-Nc expansion : comparison of the Gottfried and Adler sum rules

Abstract

The Adler sum rule for deep inelastic neutrino scattering measures the isospin of the nucleus, and is hence exact. In contrast the Gottfried sum rule for charged lepton scattering does receive perturbative and non-perturbative corrections. We show that at two-loop level the Gottfried sum rule is suppressed by a factor 1/Nc^2 relative to higher moments, and we conjecture that this suppression holds to all-orders, and also for higher-twist effects. It is further noted that differences between radiative corrections for higher moments of neutrino and charged lepton deep inelastic scattering, are 1/Nc^2 suppressed at two-loops, and this is also conjectured to hold to all-orders. The 1/Nc^2 suppression of corrections to the Gottfried sum rule makes it plausible that the deviations from the parton model value are dominated by a light quark flavour asymmetry in the nucleon sea. This asymmetry indeed persists as Nc-->infinity as predicted in a chiral soliton model.