Double prompt $J/\psi$ hadroproduction in the parton Reggeization approach with high-energy resummation

We study double prompt $J/\psi$ 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 $J/\psi$ meson and the $J/\psi$ pair. Already at leading order in $\alpha_s$, these predictions as well as those for the total cross section and its distributions in the invariant mass $m_{\psi\psi}$ and the rapidity separation $|Y|$ of the $J/\psi$ pair nicely agree with recent ATLAS and CMS measurements, except for the large-$m_{\psi\psi}$ and large-$|Y|$ regions, where the predictions substantially undershoot the data. In the latter regions, BFKL resummation is shown to enhance the cross sections by up to a factor of two and so to improve the description of the data.