How to measure the linear polarization of gluons in unpolarized proton using the heavy-quark pair production

In recent papers [1,2], two new ways have been proposed to probe the linear polarization of gluons in unpolarized proton: using the azimuthal asymmetries and Callan-Gross ratio in heavy-quark pair leptoproduction, $lN\rightarrow l^{\prime}Q\bar{Q}X$. In this talk, we discuss in details the sensitivity of the QCD predictions for the azimuthal $\cos \varphi$ and $\cos 2\varphi$ asymmetries to the contribution of linearly polarized gluons inside unpolarized proton, where the azimuth $\varphi$ is the angle between the lepton scattering plane $(l,l^{\prime})$ and the heavy quark production plane $(N,Q)$. Our analysis shows that the azimuthal distributions under consideration vary from 0 to 1 depending on the transverse-momentum dependent gluonic counterpart of the Boer-Mulders function, $h_{1}^{\perp g}$. We conclude that the $\cos \varphi$ and $\cos 2\varphi$ asymmetries in heavy-quark pair production in DIS processes are predicted to be large in wide kinematic ranges and sensitive to the contribution of linearly polarized gluons.