$J/\psi$ polarization in semi-inclusive DIS at low and high transverse momentum

TL;DR

This paper investigates $J/$ polarization in semi-inclusive deep-inelastic scattering, proposing a theoretical framework linking angular distributions to gluon distributions, and suggests an experiment at the Electron-Ion Collider to probe linearly polarized gluons.

Contribution

It introduces a factorized expression for $J/$ decay angular distributions incorporating transverse momentum dependent gluon distributions and shape functions, connecting low and high transverse momentum regimes.

Findings

Derived perturbative tails of shape functions independent of polarization

Identified the $\u03c6$ azimuthal asymmetry as a probe of linearly polarized gluons

Proposed a novel experimental method at the Electron-Ion Collider

Abstract

We study the polar and azimuthal decay angular distributions of $J/\psi$ 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 $v^4$ 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 $J/\psi$ 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 $J/\psi$ polarization. In particular, we focus on the $\cos 2\phi$ 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.