Origin of the Q 2-dependence of the DIS structure functions

Abstract

We consider in detail the Q 2 -dependence of the DIS structure functions, with Q being the virtual photon momentum. Very often this dependence is claimed to be originated by the Q 2 -dependence of the QCD coupling. This leads to the small-x asymptotics of the structure functions with Q 2 -dependent intercepts. We demonstrate that the DGLAP parametrization αs = αs(Q 2 ) is an approximation valid in the region of large x (where 2pq can be approximated by Q 2 ) only, providing the factorization scale is also large. Outside this region, the DGLAP parametrization fails, so αs should be replaced by an effective coupling which is independent of Q 2 at small x. As a consequence, intercepts of the structure functions are independent of Q 2 . Nevertheless, the small-x asymptotics of the structure functions explicitly depend on Q 2 , even when the coupling does not depend on it. We also consider the structure functions at small Q 2 and give a comment on power-Q 2 corrections to the structure functions at large and small Q 2 .