Perturbative stability of the QCD predictions for the ratio R=F_L/F_T and azimuthal asymmetry 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 and azimuthal cos(2φ) asymmetry in heavy-quark leptoproduction. Our analysis shows that large radiative corrections to the structure functions cancel each other in their ratio R(x, Q 2) and azimuthal asymmetry with good accuracy. As a result, the NLO contributions to the Callan-Gross ratio and cos(2φ) asymmetry are less than 10% in a wide region of the variables x and Q 2. We provide compact analytic predictions for R(x, Q 2) and asymmetry in the case of low x ≪ 1. Simple formulae connecting the high-energy behavior of the Callan-Gross ratio and azimuthal asymmetry with the low-x asymptotics of the gluon density in the target are derived. It is shown that the obtained hadron-level predictions for R(x, Q 2) and azimuthal asymmetry are stable at x ≪ 1 under the DGLAP evolution of the gluon distribution function. Concerning the experimental aspects, we propose to exploit the observed perturbative stability of the Callan-Gross ratio and cos(2φ) asymmetry in the extraction of the structure functions from the corresponding reduced cross sections. In particular, our obtained analytic expressions simplify essentially the determination of F c 2 (x, Q 2) and F b 2 (x, Q 2) from available data of the H1 Collaboration. Our results will also be useful in extraction of the azimuthal asymmetries from the incoming and future data on heavy-quark leptoproduction.