Experimental constraints on coefficients of $\alpha_S$-expansion of Gottfried sum rule

The $x$- and $Q^2$-dependences of the Gottfried sum rule $S_G(x,Q^2)$ based on the experimental data on proton and deuteron structure functions are studied. The dependence of $S_G(x,Q^2)$ on $Q^2$ for low $x$ points to flavour asymmetry of sea quark distributions. For the first time, the coefficients $c_1, c_2$ of the expansion of $S_G(x,Q^2)$ in $\alpha_S/\pi$ up to second order are evaluated through the phenomenological analysis of NMC and H1 data. It is found that $c_1$ is negative while $c_2$ is positive. The obtained result is in disagreement with QCD predictions for these coefficients. We suggest measuring the low $x$-dependence of the $F_2^D$ deuteron structure function at HERA in order to study the $Q^2$-dependence of the Gottfried sum rule.