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We analyze the azimuthal dependence of the heavy-quark-initiated contributions to the leptonnucleon deep inelastic scattering (DIS). First we derive the relations between the parton level semiinclusive structure functions and the helicity γ * Q cross sections in the case of arbitrary values of the heavy quark mass. Then the azimuth-dependent O(αs) lepton-quark DIS is calculated in the helicity basis. Finally, we investigate numerically the properties of the cos ϕ and cos 2ϕ distributions caused by the photon-quark scattering (QS) contribution. It turns out that, contrary to the basic photongluon fusion (GF) component, the QS mechanism is practically cos 2ϕ-independent. This fact implies that measurements of the azimuthal distributions in charm leptoproduction could directly probe the charm density in the proton.

We study the azimuthal cos ϕ and cos 2ϕ asymmetries in heavy-quark pair leptoproduction, lN → l ′ QQX, as probes of linearly polarized gluons inside unpolarized proton, where the azimuth ϕ is the angle between the lepton scattering plane (l, l ′ ) and the heavy quark production plane (N, Q). First, we determine the maximal values for the cos ϕ and cos 2ϕ asymmetries allowed by the photon-gluon fusion with unpolarized gluons; these predictions are large, ( √ 3 − 1)/2 and 1/3, respectively. Then we calculate the contribution of the transverse-momentum dependent gluonic counterpart of the Boer-Mulders function, h ⊥g 1 , describing the linear polarization of gluons inside unpolarized proton. Our analysis shows that the maximum values of the azimuthal distributions depend strongly on the gluon polarization; they vary from 0 to 1 depending on h ⊥g 1 . We conclude that the azimuthal cos ϕ and cos 2ϕ asymmetries in heavy-quark pair leptoproduction are predicted to be large and very sensitive to the contribution of linearly polarized gluons. For this reason, future measurements of the azimuthal distributions in charm and bottom production at the proposed EIC and LHeC colliders seem to be very promising for determination of the linear polarization of gluons inside unpolarized proton. .ru (A.V. Efremov), nikiv@yerphi.am (N.Ya. Ivanov), teryaev@theor.jinr.ru (O.V. Teryaev) 1 Concerning the opportunities to measure the function h ⊥g 1 in unpolarized hadron-hadron collisions, see review [6].

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