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We include $p p \to p \Delta^{+} \mu^{+} \mu^{-}$ and $p p \to \Delta^{+}\Delta^{+} \mu^{+} \mu^{-}$ processes in addition to the standard $p p \to p p\mu^{+} \mu^{-}$ process both in equivalent-photon approximation (EPA) and inexact $2 \to 4$ calculations. For comparison we calculate also the continuumproton dissociation in a recently developed $k_{t}$-factorization approach to$\gamma \gamma$-involved processes with parametrizations of $F_{2}$ structurefunction known from the literature. The calculated cross section including allthe processes is considerably larger than the one measured recently by theATLAS collaboration. We calculate absorption effects for $p p \to p p \mu^{+}\mu^{-}$ process in the momentum space. The final cross section with absorptioneffects is by 10\% larger than the one measured by the ATLAS collaborationwhich is difficult to explain. Several differential distributions with theATLAS experimental cuts are presented. It is shown that the processes withelectromagnetic $p \to \Delta(1232)$ and $p \to N(1440)$ transitions, that havesimilar characteristics as the $p p \to p p \mu^+ \mu^-$ process, increase thecross section for $\mu^+ \mu^-$ production and thus can affect its theoreticalinterpretation when the leading baryons are not detected as is the case for theCMS and ATLAS measurements. The mechanism of dissociation into hadroniccontinuum is not under full control as the corresponding absorption effects arenot fully understood. We present first predictions for future ATLAS experimentwith the ALFA sub-detectors and discuss observables relevant for thismeasurement.

physical review. d/physical review. d.

Exclusive and semiexclusive production of $\mu^+ \mu^-$ pairs with  $\Delta$ isobars and other resonances in the final state and the size of  absorption effects