Abstract
Quarkonium production offers good possibilities to study gluon TMDs. In this proceedings contribution this topic is explored for the linearly polarized gluons inside unpolarized hadrons and unpolarized gluons inside transversely polarized hadrons. It is argued that chi _{b0/2} and eta _b production at LHC are best to study the effects of linearly polarized gluons in hadronic collisions, by means of angular independent ratios of ratios of cross sections. This can be directly compared to cos 2phi asymmetries in heavy quark pair and dijet production in DIS at a future high-energy Electron-Ion Collider (EIC), which probe the same TMDs. In the small-x limit this corresponds to the Weizsäcker–Williams (WW) gluon distributions, which should show a change in behavior for transverse momenta around the saturation scale. Together with investigations of the dipole (DP) gluon distributions, this can provide valuable information about the polarization of the Color Glass Condensate if sufficiently small x-values are reached. Quarkonia can also be useful in the study of single transverse spin asymmetries. For transversely polarized hadrons the gluon distribution can be asymmetric, which is referred to as the Sivers effect. It leads to single spin asymmetries in for instance J{/}psi (pair) production at AFTER@LHC, which probe the WW or f-type gluon Sivers TMD. It allows for a test of a sign-change relation w.r.t. the gluon Sivers TMD probed at an EIC in open heavy quark pair production. Single spin asymmetries in backward inclusive C-odd quarkonium production, such as J{/}psi production, may offer probes of the DP or d-type gluon Sivers TMD at small x-values in the polarized proton, which in that limit corresponds to a correlator of a single Wilson loop, describing the spin-dependent odderon.
Highlights
Inclusive quarkonium production processes offer good possibilities to probe gluons inside protons
This article belongs to the Topical Collection “New Observables in Quarkonium Production”
A priori it is not clear that this path dependence will affect observables, but it turns out that it does. This became clear from the study of single spin asymmetries [27,28,32,33] arising from the Sivers effect. It is well-known that in semi-inclusive DIS the quark TMD correlator contains a future pointing staple-like Wilson line arising from final state interactions (FSI)
Summary
Inclusive quarkonium production processes offer good possibilities to probe gluons inside protons. Because of the additional dependence on the transverse momentum vector, there are more gluon TMDs than collinear gluon densities: at leading twist there are eight gluon TMDs, compared to only two collinear gluon densities (g(x) and g(x)) This means that six gluon TMD structures average to zero, when integrated over all transverse momenta. One of these describes the gluon Sivers effect [1], which is odd in the transverse momentum. Another describes the distribution of linearly polarized gluons, that is even in the transverse momentum, but corresponds to a cos 2φ dependence that averages away too. This article belongs to the Topical Collection “New Observables in Quarkonium Production”
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