Abstract
We consider transverse momentum dependent gluon distributions inside both unpolarized and transversely polarized protons and show how they can be probed by looking at azimuthal modulations in $e \, p \to e \, J/\psi \, \mathrm{jet} \, X$. We find that the contribution due to quark induced subprocesses is always suppressed in the considered kinematic regions, accessible in principle at a future Electron-Ion Collider. Our model-independent estimates of the maximal values of these asymmetries allowed by positivity bounds suggest the feasibility of their measurement. In addition, by adopting the McLerran-Venugopalan model for the unpolarized and linearly polarized gluon densities, we study the behavior of the $\cos2\phi$ asymmetries in the small-$x$ limit.
Highlights
Transverse momentum dependent distribution functions (TMDs) of gluons inside unpolarized and polarized protons have been defined in terms of QCD operators for the first time in Refs. [1,2]
This in principle allows us to cross-check the results obtained at the Electron-Ion Collider (EIC) and Large Hadron Collider (LHC) for unpolarized protons, and, in case a polarized fixed target experiment will be achieved at the LHC [34,35,36], for transversely polarized protons as well
We compute the ratio of the collinear quark- over total unpolarized cross section in nonrelativistic QCD (NRQCD), using for the parton distribution functions (PDFs) the MSTW2008LO set [47]
Summary
Transverse momentum dependent distribution functions (TMDs) of gluons inside unpolarized and polarized protons have been defined in terms of QCD operators for the first time in Refs. [1,2]. We point out that the gluon TMDs probed in ep → eJ=ψ jet X and in ep → eJ=ψX can be directly related, pending factorization theorems, to the ones characterized by past-pointing gauge links which are of the WW type, appearing for example in Higgs or heavy scalar quarkonium production in proton-proton collisions This in principle allows us to cross-check the results obtained at the EIC and Large Hadron Collider (LHC) for unpolarized protons, and, in case a polarized fixed target experiment will be achieved at the LHC [34,35,36], for transversely polarized protons as well.
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