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

Abstract

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].

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

“…As shown in Ref. [1], the function A cos 2ϕ (z, K 2 ⊥ ) has an extremum at z = 1/2 and K 2 ⊥ = m 2 + Q 2 /4, where m is the heavy-quark mass. This maximum value is: A cos 2ϕ (z = 1/2,…”

“…In this case, the corresponding asymmetry, containing the contributions of both f g 1 and h ⊥g 1 densities, is a function of three variables: Our analysis shows that the function A h cos 2ϕ (z, K 2 ⊥ , r) has a maximum at z = 1/2 and K 2 ⊥ = m 2 + Q 2 /4 for all values of r in the interval −1 ≤ r ≤ 1. We find [1] A h cos 2ϕ (r) ≡ A h cos 2ϕ (z = 1/2,…”

“…In particular, the gluons are completely polarized along the k T direction at r = 1, k g = ζ P + k T . The LO predictions for the azimuth-dependent cross section of the reaction (1) can be written as [1]…”

“…In Ref. [1], the leading order (LO) QCD predictions for the cos ϕ and cos 2ϕ distributions have been provided, where ϕ is the heavy quark (or anti-quark) azimuthal angle. It was shown that these azimuthal asymmetries (AAs) are expected to be large in wide kinematic ranges and very sensitive to the function h ⊥g 1 .…”

Probing the linearly polarized gluons in unpolarized proton with heavy-quark pair production

“…In Ref. [7], the cos ϕ and cos 2ϕ asymmetries in heavy flavor pair leptoproduction have been studied as probes of the linearly polarized gluons in unpolarized nucleon. Analogous analysis for the Callan-Gross ratio R = dσ L /dσ T was performed in Ref.…”