Perturbatively stable observables in heavy-quark leptoproduction

TL;DR

This paper demonstrates that the ratios of structure functions in heavy-quark leptoproduction are perturbatively stable under QCD corrections, making them reliable for extracting heavy-quark content in the proton and useful in experimental analyses.

Contribution

It provides a detailed analysis of the stability of the Callan-Gross ratio and azimuthal asymmetry, offering analytic predictions and exploring their sensitivity to resummation effects within QCD.

Findings

Ratios $R(x,Q^2)$ and $A(x,Q^2)$ are stable under radiative corrections.

Analytic predictions are provided for low $x$ regions.

These ratios are sensitive to heavy-quark content and resummation effects.

Abstract

We study the perturbative and parametric stability of the QCD predictions for the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ and azimuthal $\cos(2\varphi)$ asymmetry, $A(x,Q^2)$, in heavy-quark leptoproduction. We review the available theoretical results for these quantities and conclude that, contrary to the production cross sections, the ratios $R(x,Q^2)$ and $A(x,Q^2)$ are stable under radiative QCD corrections in wide region of the variables $x$ and $Q^2$. This implies that large radiative contributions to the structure functions cancel each other in the ratios $R(x,Q^2)$ and $A(x,Q^2)$ with good accuracy. Then we consider some experimental and phenomenological applications of the observed perturbative stability. We provide compact analytic predictions for $R(x,Q^2)$ and azimuthal $\cos(2\varphi)$ asymmetry in the case of low $x\ll 1$. It is demonstrated that our obtained results will be useful in the extraction of the structure functions from measurements of the reduced cross sections. Finally, we analyze the properties of $R(x,Q^2)$ and $A(x,Q^2)$ within the variable-flavor-number scheme (VFNS) of QCD. We conclude that the Callan-Gross ratio and azimuthal asymmetry are perturbatively stable but sensitive to resummation of the mass logarithms of the type $\alpha_{s}\ln\left( Q^{2}/m^{2}\right)$. For this reason, the quantities $R(x,Q^2)$ and $A(x,Q^2)$ will be good probes of the heavy-quark content of the proton.