Nonsinglet parton distribution functions from the precise next-to-next-to-next-to leading order QCD fit

Abstract

We present the results of our QCD analysis for non-singlet unpolarized quark distributions and structure function $F_2(x,Q^2)$ up to N$^3$LO. In this regards 4-loop anomalous dimension can be obtain from the Pad\'e approximations. The analysis is based on the Jacobi polynomials expansion of the structure function. New parameterizations are derived for the non-singlet quark distributions for the kinematic wide range of $x$ and $Q^2$. Our calculations for non-singlet unpolarized quark distribution functions up to N$^3$LO are in good agreement with available theoretical models. The higher twist contributions of $F_2^{p,d}(x,Q^2)$ are extracted in the large $x$ region in N$^3$LO analysis. The values of $\Lambda_{QCD}$ and $\alpha_s(M_z^2)$ are determined.