Q 2 evolution of xF 3(x,Q 2) structure function and Gross–Llewellyn Smith sum rule up to next-next-to-leading order at low x and low Q 2 using a Q 2-dependent Regge ansatz

Abstract

A Q 2-dependent Regge ansatz for $$xF_3 (x,Q^2 )$$ structure function as the initial input is utilized to solve analytically the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi evolution equation in leading order, next-to-leading order and next-next-to-leading order. The solutions of the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi equations are also used to predict the Q 2 behavior of Gross–Llewellyn Smith sum rule. Dokshitzer–Gribov–Lipatov–Altarelli–Parisi evolved results for $$xF_3 (x,Q^2)$$ structure functions as well as obtained sum rule results are analyzed phenomenologically in comparison with other results taken from Chicago–Columbia–Fermilab–Rochester, Neutrino experiment at the Fermlab Tevatron, CERN Hybrid Oscillation Research Apparatus and CERN–Dortmund–Heidelberg–Saclay–Warsaw collaborations, and a very good agreement is observed in this regard.