Double Prompt J/ψ Hadroproduction in the Parton Reggeization Approach with High-Energy Resummation

We study double prompt $J/\ensuremath{\psi}$ hadroproduction within the nonrelativistic-QCD factorization formalism adopting the parton Reggeization approach to treat initial-state radiation in a gauge invariant and infrared-safe way. We present first predictions for the cross section distributions in the transverse momenta of the subleading $J/\ensuremath{\psi}$ meson and the $J/\ensuremath{\psi}$ pair. Already at leading order in ${\ensuremath{\alpha}}_{s}$, these predictions as well as those for the total cross section and its distributions in the invariant mass ${m}_{\ensuremath{\psi}\ensuremath{\psi}}$ and the rapidity separation $|Y|$ of the $J/\ensuremath{\psi}$ pair nicely agree with recent ATLAS and CMS Collaboration measurements, except for the large-${m}_{\ensuremath{\psi}\ensuremath{\psi}}$ and $\mathrm{large}\text{\ensuremath{-}}|Y|$ regions, where the predictions substantially undershoot the data. In the latter regions, Balitsky-Fadin-Kuraev-Lipatov resummation is shown to enhance the cross sections by up to a factor of 2 and so to improve the description of the data.