What does the CCFR measurement of the Gross--Llewelyn Smith sum rule tell us?

Abstract

Recently the CCFR Collaboration reported the measurement of the Gross--Llewellyn Smith sum rule %at $Q^2=3\; \mr{GeV}^2$: $\int^{1}_{0}\mr{d}F_{3}^{νp+\bareνp}(x,Q^2=3\;\mr{GeV}^2)= 2.50\pm 0.018(\mr{stat})$. Subsequently Kataev and Sidorov analyzed the $Q^2$--dependence of this sum rule and pointed out a discrepancy between the results obtained via integration of the NLO fits to $xF_{3}(x,Q^2)$ and the purely perturbative prediction. We suggest an explanation of this disagreement and show that the result of the CCFR measurement of the GLS sum rule integral can be determined from the knowledge of the value of $Λ_{\bbare{MS}}$ only.