Order ${\alpha }_s^2$ perturbative QCD corrections to the Gottfried sum rule

Abstract

The order ${\alpha }_s^2$ perturbative QCD correction to the Gottfried sum rule is obtained. The result is based on numerical calculation of the order ${\alpha }_s^2$ contribution to the coefficient function and on the new estimate of the three-loop anomalous dimension term. The correction found is negative and rather small. Therefore it does not affect the necessity to introduce flavour-asymmetry between $\bar{u}$ and $\bar{d}$ antiquarks for the description of NMC result for the Gottfried sum rule.

LaTeX, 7 pages, the discussions of the ${\alpha }_s^2$ corrections to the anomalous dimension are modified; 1 reference added; to be published in Phys. Lett.B