Exclusive production of double $J/\psi$ mesons in hadronic collisions

We present the first calculation of exclusive double $J/\psi$ production in hadronic collisions. We analyse in detail the form of the Born-level $gg \to J/\psi J/\psi$ amplitudes within the non-relativistic quarkonium approximation and discuss the implications of this for the central exclusive production channel, within the `Durham' perturbative model. In addition we show that this direct single parton scattering contribution is expected to be strongly dominant in the exclusive case. We present predictions for the LHC and show that the expected cross sections are in reasonable agreement with the LHCb Run-I measurement of exclusive double $J/\psi$ production, with the measured invariant mass distribution described well by the theory. Motivated by this encouraging result we present predictions for observables that may be measured in LHC Run-II, and estimate the size of the expected cross sections in the $\psi(2S)$ and $\chi_{c}$ cases.