On the perturbative stability of the QCD predictions for the ratio R = FL/FT in heavy-quark leptoproduction

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) less than or similar to 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(c) (x, Q(2)) and F-2(b) (x, Q(2)) from measurements of the corresponding reduced cross sections, in particular at DESY HERA.