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We study the perturbative and parametric stability of the QCD predictions forthe 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 availabletheoretical results for these quantities and conclude that, contrary to theproduction cross sections, the ratios $R(x,Q^2)$ and $A(x,Q^2)$ are stableunder radiative QCD corrections in wide region of the variables $x$ and $Q^2$.This implies that large radiative contributions to the structure functionscancel 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 theobserved perturbative stability. We provide compact analytic predictions for$R(x,Q^2)$ and azimuthal $\cos(2\varphi)$ asymmetry in the case of low $x\ll1$. It is demonstrated that our obtained results will be useful in theextraction of the structure functions from measurements of the reduced crosssections. 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 theCallan-Gross ratio and azimuthal asymmetry are perturbatively stable butsensitive 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 theproton.

Perturbatively stable observables in heavy-quark leptoproduction