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Exclusive production of heavy charged Higgs boson pairs in the $p p \to p p H^+ H^-$ reaction at the LHC and a future circular collider

We calculate differential cross sections for exclusive production of heavy charged scalar, weakly interacting particles (charged Higgs bosons, charged technipions, etc.) via photon-photon exchanges in the $p p \to p p H^+ H^-$ reaction with exact $2 \to 4$ kinematics. We present distributions in rapidities, transverse momenta, and correlations in azimuthal angles between the protons and between the charged Higgs bosons. As an example, the integrated cross section for $\sqrt{s}$ = 14~TeV (LHC) is about 0.1~fb and about 0.9~fb at the Future Circular Collider (FCC) for $\sqrt{s}$ = 100~TeV when assuming $m_{H^{\pm}} = 150$~GeV. The results are compared with results obtained within standard equivalent-photon approximation known from the literature. We discuss the role of the Dirac and Pauli electromagnetic form factors of the proton. We have also performed first calculations of cross sections for the exclusive diffractive Khoze-Martin-Ryskin mechanism. We have estimated limits on the $g_{h H^+ H^-}$ coupling constant within two-Higgs dublet model based on recent experimental data from the LHC. The diffractive contribution is, however, much smaller than the $γγ$ one. The $Z γ$, $γZ$, and $ZZ$ exchanges give even smaller contributions. Absorption corrections are calculated for the first time differentially for various distributions. In general, they lead to a damping of the cross section. The damping depends on the $M_{H^{+}H^{-}}$ invariant mass and on $t$ four-momentum transfers squared. In contrast to diffractive processes, the larger the collision energy, the smaller the effect of absorption. We discuss a possibility to measure the exclusive production of two charged Higgs bosons with the help of so-called "forward proton detectors" at the LHC experiments.