Exclusive production of heavy charged Higgs boson pairs in the $pp\to pp{H}^{+}{H}^{-}$ 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 $pp\to pp{H}^{+}{H}^{-}$ 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 $\sqrt{s}=14\mathrm{TeV}$ (LHC) is about 0.1 fb and about 0.9 fb at the Future Circular Collider (FCC) for $\sqrt{s}=100\mathrm{TeV}$ when assuming $m_{H^{\pm }}=150\mathrm{GeV}$. 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 the two-Higgs doublet model based on recent experimental data from the LHC. The diffractive contribution is, however, much smaller than the $\gamma \gamma$ one. The $Z\gamma$, $\gamma Z$, 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.

Figure 1

Born diagrams for exclusive production of pairs of charged scalar particles via photon-photon exchanges.

Figure 2

Distribution in the auxiliary variables ${\xi }_1$ or ${\xi }_2$ at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and 100 TeV (right panel). The online red solid lines represent the calculation of exact amplitude (including spinors of protons). The black upper and lower long-dashed lines correspond to calculations in the high-energy approximation (2.15) without and with the absorption corrections, respectively.

Figure 3

Rapidity distribution of charged (Higgs) bosons at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and 100 TeV (right panel). The meaning of the lines is the same as in Fig. 2. The short-dashed (online green) lines represent results of EPA.

Figure 4

DiHiggs boson invariant mass distributions at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and 100 TeV (right panel). The meaning of the lines is the same as in Fig. 2. The short-dashed (online green) lines represent results of EPA.

Figure 5

DiHiggs boson invariant mass (left panel) and Higgs boson rapidity (right panel) distributions for $\sqrt{s}=14\mathrm{TeV}$ in the Born approximation and for the amplitudes given by Eq. (2.15). The double spin-conserving contribution (cc) is show by the long-dashed line, the double spin-flipping contribution (ff) by the dotted line, and the mixed contributions (cf) and (fc) by the dashed lines. The solid line represents the sum of all the contributions and corresponds to the upper long-dashed lines in Figs. 3 and 4 (left panels).

Figure 6

The dependence of the gap survival factor due to $pp$ interactions on $M_{H^{+}{H}^{-}}$ for exact $2\to 4$ kinematics at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and 100 TeV (right panel). This is quantified by the ratio of full (including absorption) and Born differential cross sections $⟨S^2(M_{H^{+}{H}^{-}})⟩$ (3.1).

Figure 7

Ratio of the cross section when all ($F_1$, $F_2$) terms are included to that with $F_1$ terms only for exact $2\to 4$ kinematics (black long-dashed lines) and EPA (online green short-dashed lines) calculations at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and $\sqrt{s}=100\mathrm{TeV}$ (right panel). The lowest long-dashed lines represent results with the absorption corrections.

Figure 8

The relative corrections in percent as a function of $M_{H^{+}{H}^{-}}$ for exact Born amplitude including spinors of protons (online red solid lines) and for EPA (online green short-dashed lines) calculations at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and 100 TeV (right panel).

Figure 9

The distributions in the Higgs boson transverse momentum at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and 100 TeV (right panel). The meaning of the lines is the same as in Fig. 2. The online green short-dashed lines represent results of EPA.

Figure 10

Distribution in momentum transfer(s) squared ($t_1$ or $t_2$) at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and 100 TeV (right panel). The meaning of the lines is the same as in Fig. 2.

Figure 11

Distributions in momentum transfer squared $t_1$ (left panel) and $t_2$ (right panel) at $\sqrt{s}=14\mathrm{TeV}$ in the Born approximation and for the amplitudes given by Eq. (2.15). The double spin-conserving contribution (cc) is show by the long-dashed line, the double spin-flipping contribution (ff) by the dotted line, and the mixed contributions (cf) and (fc) by the dashed and dot-dashed line, respectively. The solid line represents the sum of all the contributions and corresponds to the upper long-dashed line in Fig. 10.

Figure 12

Distribution in relative azimuthal angle between outgoing protons at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and 100 TeV (right panel). The meaning of the lines is the same as in Fig. 2.

Figure 13

Distribution in relative azimuthal angle between outgoing charged (Higgs) bosons at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and 100 TeV (right panel). The meaning of the lines is the same as in Fig. 2.

Figure 14

The diffractive mechanism of the exclusive charged Higgs boson production through the intermediate $CP$-even neutral recently discovered Higgs boson. The absorption corrections due to $pp$ interactions (indicated by the blob) are relevant at high energies.

Figure 15

The triple-Higgs coupling constant $|g_{h{H}^{+}{H}^{-}}|$ in the ($\tan \beta$, $(\beta -\alpha )$) plane for the MSSM (left panel) and the type-II 2HDM with $m_{H^{\pm }}=m_A=300\mathrm{GeV}$ (right panel). Here we consider the type-II 2HDM in which the scalar potential parameters are $\mathrm{Re}({\lambda }_5)$ (explicit $Z_2$ symmetry) and ${\lambda }_6={\lambda }_7=0$.

Figure 16

$|g_{h{H}^{+}{H}^{-}}|$ for the 2HDM as a function of $m_{H^{\pm }}$ and $m_A$ for the alignment limit $\beta -\alpha =\pi /2$.

Figure 17

DiHiggs boson invariant mass distributions at $\sqrt{s}=14\mathrm{TeV}$ (left panel) and 100 TeV (right panel). The upper lines represent the $\gamma \gamma$ contribution. We also show contribution of the diffractive mechanism (the shaded area) for the MSTW08 NLO collinear gluon distribution [104] and $g_{h{H}^{+}{H}^{-}}=100$ (1000) GeV for the lower (upper) limit.