Exclusive and diffractive $\mu^+ \mu^-$ production in $pp$ collisions at the LHC

In this paper we estimate the production of dimuons ($\mu^+ \mu^-$) in exclusive photon -- photon ($\gamma \gamma$) and diffractive Pomeron - Pomeron $(I\!P I\!P)$, Pomeron - Reggeon $(I\!P I\!R)$ and Reggeon - Reggeon $(I\!R I\!R)$ interactions in $pp$ collisions at the LHC energy. The invariant mass, rapidity and tranverse momentum distributions are calculated using the Forward Physics Monte Carlo (FPMC), which allows to obtain realistic predictions for the dimuon production with two leading intact hadrons. In particular, predictions taking into account the CMS and LHCb acceptances are presented. Moreover, the contribution of the single diffraction for the dimuon production also is estimated. Our results demonstrate that the experimental separation of these different mechanisms is feasible. In particular, the events characterized by pairs with large squared transverse momentum are dominated by diffractive interactions, which allows to investigate the underlying assumptions present in the description of these processes.