Renormalization Scale Setting for Evolution Equation of Non-Singlet Structure Functions and Their Moments

Abstract

We use the BLM procedure to eliminate the renormalization scale ambiguity in the evolution equation for the non-singlet deep-inelastic structure function $F_2^{\text{N}S}(x,Q).$ The scale of the QCD coupling in the $\overline{\text{MS}}$ scheme has the form $Q^{\ast }(x)=Q(1-x{)}^{1/2}/xf(x)$, 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 $n$th 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.

Comments: 15 pages, RevTeX