J/ψ polarization in semi-inclusive DIS at low and high transverse momentum

Abstract

We study the polar and azimuthal decay angular distributions of J/ψ mesons produced in semi-inclusive, deep-inelastic electron-proton scattering. For the description of the quarkonium formation mechanism, we adopt the framework of nonrelativistic QCD, with the inclusion of the intermediate color-octet channels that are suppressed at most by a factor v4 in the velocity parameter v relative to the leading color-singlet channel. We put forward factorized expressions for the helicity structure functions in terms of transverse momentum dependent gluon distributions and shape functions, which are valid when the J/ψ transverse momentum is small with respect to the hard scale of the process. By requiring that such expressions correctly match with the collinear factorization results at high transverse momentum, we determine the perturbative tails of the shape functions and find them to be independent of the J/ψ polarization. In particular, we focus on the cos 2ϕ azimuthal decay asymmetry, which originates from the distribution of linearly polarized gluons inside an unpolarized proton. We therefore suggest a novel experiment for the extraction of this so-far unknown parton density that could be performed, in principle, at the future Electron-Ion Collider.

$J/ψ$ polarization in large-$P_T$ semi-inclusive deep-inelastic scattering at the EIC

“…For more details and the complete formalism we refer the reader to Ref. [25]. We consider the SIDIS process e(k) + p(P ) → e (k ) + J/ψ(P ψ ) + X(P X ) ,…”

“…(2.35) of Ref. [25] to ensure the normalization when integrated over the solid angle, see Eq. ( 8) below.…”

Inclusive production of a $J/ψ$ or a $Υ$ from single-parton fragmentation plus a jet in hybrid factorization

“…Recent phenomenological analyses of gluon TMDs through observables sensitive to quarkonium production in electron-proton and proton-proton collisions were can be found in Refs. [81][82][83][84][85] and [86][87][88][89], respectively 1 . Studies on TMD factorization for heavyquarkonium emissions were recently conducted in a Soft and Collinear Effective Theory (SCET) [91,92], and then extended to di-jet and heavy-meson pair emissions in lepton-proton scatterings [93].…”

Azimuthal asymmetries in $J/ψ$-photon production at the EIC

“…However, TMD factorization has not been proven for all processes [19]. Many proposals have been put forward in order to probe the gluon TMDs both in the lepton-proton and proton-proton collisions processes [16,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37], however, experimentally, they are harder to be extracted as compared with the quark TMDs. Most of the proposals are based on analyzing the transverse momentum dependent azimuthal asymmetries in the heavy quark-antiquark pair productions or the bound state quarkonia productions because they are sensitive to the gluon content of hadrons, specially in the small longitudinal momentum fraction, x, domain [33].…”