On the perturbative stability of the QCD predictions for the ratio R=F L /F T in heavy-quark leptoproduction

Abstract

We analyze the perturbative and parametric stability of the QCD predictions for the Callan–Gross ratio, R(x,Q 2)=F L /F T , in heavy-quark leptoproduction. We consider the radiative corrections to the dominant photon–gluon fusion mechanism. In various kinematic regions, the following contributions are investigated: exact NLO results at low and moderate Q 2≲m 2, asymptotic NLO predictions at high Q 2≫m 2, and both NLO and NNLO soft-gluon (or threshold) corrections at large Bjorken variable x. Our analysis shows that large radiative corrections to the structure functions F T (x,Q 2) and F L (x,Q 2) cancel each other in their ratio R(x,Q 2) with good accuracy. As a result, the NLO contributions to the Callan–Gross ratio are less than 10% in a wide region of the variables x and Q 2. We provide compact LO predictions for R(x,Q 2) in the case of low x ≪1. A simple formula connecting the high-energy behavior of the Callan–Gross ratio and low-x asymptotics of the gluon density is derived. It is shown that the obtained hadron-level predictions for R(x→0,Q 2) are stable under the DGLAP evolution of the gluon distribution function. Our analytic results simplify the extraction of the structure functions F 2 (x,Q 2) and F 2 (x,Q 2) from measurements of the corresponding reduced cross sections, in particular at DESY HERA.