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

D.J Broadhurst,A.L Kataev,C.J Maxwell

doi:10.1016/j.physletb.2004.03.059

D.J Broadhurst, A.L Kataev + Show 1 more

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https://doi.org/10.1016/j.physletb.2004.03.059

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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 by non-perturbative effects. Noting that the known perturbative corrections to two-loop order are suppressed by a factor 1/Nc2, 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/Nc2, 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 Nc→∞.

Highlights

Alone among the various sum rules of deep inelastic scattering (DIS) the isospin Adler sum rule [1] has the special feature that its quark-parton model expression IA ≡ 1 dx 0xF2νp(x, Q2) − F2νn(x, Q2) (1)= 2 dx u(x) − d(x) − u(x) + d(x) = 4I3 = 2 coincides with its QCD extension and receives neither perturbative nor non-perturbative corrections
In this paper we examine the QCD corrections to the moments of parton-model densities, for non-singlet neutrino and charged-lepton DIS, with the N = 1 moments corresponding to the Adler and Gottfried sum rules, and comment upon a striking feature which they exhibit in the large-Nc limit [11] at the two-loop level
First we present an analytical result for the two-loop radiative correction that was evaluated numerically in Ref.[7] and comment on its structure as Nc → ∞

Summary

Introduction

Alone among the various sum rules of deep inelastic scattering (DIS) the isospin Adler sum rule [1] has the special feature that its quark-parton model expression. = 2 dx u(x) − d(x) − u(x) + d(x) = 4I3 = 2 coincides with its QCD extension and receives neither perturbative nor non-perturbative corrections (for a discussion, see Ref.[2]) This sum rule is supported by the existing neutrino–nucleon DIS data, which show no significant Q2 variation in the range 2 GeV2 ≤ Q2 ≤ 30 GeV2 and give [3]. In contrast to the Adler sum rule, the original quark-parton model expression for the Gottfried sum rule is modified by perturbative QCD contributions, analyzed numerically at the αs2-level in Ref.[7] These corrections turn out to be small and cannot be responsible for the significant discrepancy between and the naive expectation of.

Analytical two-loop correction to the Gottfried sum rule

The nucleon sea at large Nc

Findings

Conclusions