Probing the gluon Transverse Momentum-Dependent distributions inside the proton through quarkonium-pair production at the LHC

Transverse momentum-dependent factorisation is used to describe hadronic collisions while taking into account the intrinsic transverse momentum of partons inside hadrons. This requires Transverse Momentum-Dependent Parton Distribution Functions (TMDPDFs or simply TMDs) which need to be extracted from experimental data. Gluon TMDs in particular remain poorly known.We propose to use quarkonium-pair production to study the two gluon TMDs accessible through unpolarised proton collisions at the Large Hadron Collider (LHC). Quarkonia are bound states of a heavy flavour quark-antiquark pair. J/psi mesons, made of a charm-anticharm pair, are produced in large amounts at the LHC. J/psi pairs originate from gluon fusion in vast majority, which is important to study gluon TMDs.We first use a simple model of Gaussian-based TMDs to compute observables in J/psi-pair production that are sensitive to the TMDs. These are the transverse-momentum spectrum of the pair and azimuthal asymmetries. We see that J/psi-pair production is an ideal process to probe the linearly-polarised gluon TMD through azimuthal asymmetries. We also use the LHCb data on the J/psi-pair transverse momentum to fit the average gluon transverse momentum.We then improve our predictions by including TMD evolution in our calculations. Indeed some contributions to the gluon TMDs can be evaluated perturbatively to improve the fit procedure. We observe that the asymmetries are suppressed but remain sizeable and could be detected at the LHC. We also provide predictions for Upsilon-pair production.We finally discuss the helicity structure of the quarkonium-pair production amplitude which explains how it maximises some azimuthal asymmetries. Moreover, it shows that the amplitude zero for longitudinally polarised pairs predicted at leading order in the collinear regime could be detected for intermediate masses as hard gluon emissions are suppressed in the TMD regime