On the Perturbative Stability of the QCD Predictions for the Ratio $R=F_L/F_T$ in Heavy-Quark Leptoproduction

TL;DR

This paper investigates the stability of QCD predictions for the ratio of structure functions in heavy-quark leptoproduction, demonstrating that radiative corrections largely cancel in the ratio, leading to stable and accurate predictions across various kinematic regions.

Contribution

The study provides a detailed analysis of the perturbative stability of the Callan-Gross ratio, including exact NLO, asymptotic NLO, and NNLO soft-gluon corrections, with simplified formulas for practical use.

Findings

Radiative corrections cancel in the ratio R, ensuring stability.

NLO contributions to R are less than 10% across a wide kinematic range.

Derived simple formulas connect high-energy behavior of R with low-x gluon density asymptotics.

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 $Q^2\lesssim m^2$, asymptotic NLO predictions at high $Q^2\gg m^2$, and both NLO and NNLO soft-gluon (or threshold) corrections at large Bjorken $x$. 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 $x\ll 1$. 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 $R(x\to 0,Q^2)$ 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.