The puzzle of the non-planar structure of the QCD contributions to the Gottfried sum rule

Abstract

The recent finding, that in QCD at the $O({\alpha }_s^2)$-level only non-planar diagrams, which are suppressed by a factor $1/N_c^2$ relative to planar ones, are contributing to the valence part of the Gottfried sum rule, is described. To our knowledge, this intriguing unique feature did not manifest itself previously in any perturbative expansion of any gauge quantum field model. We hope that this discovery may have some theoretical explanation.

Comments: 8 pages, Based on the invited talks presented at the Workshop "Hadron Structure in QCD: from Low to High Energies", St.Peterburg, Repino, Russia, 18-22 May 2004 and at the Bogolyubov Conference "Problems of Theoretical and Mathematical Physics", September 2-6, Dubna, Russia; some misprints are eliminated