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We present the QCD predictions for the azimuthal $\cos 2\varphi$ asymmetry incharm leptoproduction for the kinematics of the COMPASS experiment at CERN. Theasymmetry is predicted to be large, about 15%. The radiative corrections to theQCD predictions for the $\cos 2\varphi$ distribution are estimated to be small,less than 10%. Our calculations show that the azimuthal asymmetry in charmproduction is well defined in pQCD: it is stable both perturbatively andparametrically, and practically insensitive to theoretical uncertainties in theinput parameters. We analyze the nonperturbative contributions to the $\cos2\varphi$ distribution due to the gluon transverse motion in the target and the$c$-quark fragmentation. Because of the $c$-quark low mass, the nonperturbativecontributions are expected to be sizable, about (30--40)%. We conclude thatextraction of the azimuthal asymmetries from available COMPASS data willprovide valuable information about the transverse momentum dependentdistribution of the gluon in the proton and the $c$-quark hadronizationmechanism. Finally, we discuss the $\cos 2\varphi$ asymmetry as a probe of thegluonic analogue of the Boer-Mulders function, $h_{1}^{\perp g}$, describingthe linear polarization of gluons inside unpolarized proton.

QCD predictions for the azimuthal asymmetry in charm leptoproduction for the COMPASS kinematics