Renormalization scale setting for evolution equation of non-singlet structure functions and their moments

We use the BLM procedure to eliminate the renormalization scale ambiguity in the evolution equation for the non-singlet deep-inelastic structure function F_2^{\text NS}(x,Q). The scale of the QCD coupling in the \overline{\text{MS}} scheme has the form Q^*(x) = Q (1-x)^{1/2} / x~f(x) , where x is the Bjorken variable and f(x) is a smoothly varying function bounded between 0.30 to 0.45. Equivalently, the evolution of the nth moment of the structure function should contain an effective \Lambda_{\text{QCD}} pattern, with \Lambda_n \sim n^{1/2}. This variation of \Lambda_n agrees with experimental data