Predictions for the azimuthal modulations in di-$J/\psi$ production for the fixed-target experiments at LHC.

Quarkonium production processes constitute rising tools for the exploration of sub-hadronic physics. Specifically, the production of a $J/\psi$-pair in a fixed-target experiment at LHC is a promising process to explore the gluon transverse momentum distributions (gTMDs), which are still very poorly known. The deep study of azimuthal modulations, arising in the cross-section of such a process from the linear polarization of gluons inside unpolarized protons, including the TMD evolution in the computation, gives improved results in this field and provides a phenomenological basis for future measurements, $e.g.$, at the LHCb experiment with the SMOG2 fixed-target apparatus. The methodology of the computation is presented along with the first results for this channel at center-of-mass energy $\sim$ 115 ${GeV}$.