CERN Accelerating science

Leading decay branching fractions of $H(A)$ (left panel) and $H^\pm$ (right panel) as a function of $\tan\beta$ in four Types of 2HDMs for $m_\Phi=2$ TeV and $\cos(\beta-\alpha)=0$. In the right panel, red curve (Type-I) overlaps with the blue curve (Type-F).

Representative Feynman diagram for the EW scalar pair production in $\mm$ annihilation $\mm\to \phi_1 \phi_2 $.

Cross sections versus the c.m.~energy $\sqrt{s}$. For the left panel: $\mu^+\mu^-\to H^+H^- $ (red), and $HA$ (green) through $\mu^+\mu^-$ annihilation; and for the right panel: in addition, $H^\pm H/H^\pm A$ (blue), $HH/AA$ (purple), through VBF in the alignment limit $\cos(\beta-\alpha)=0$. Solid, dashed and dotted lines for degenerate Higgs masses $m_\Phi=1$ TeV, 2 TeV and 5 TeV, respectively. The vertical axis on the right shows the corresponding event yields for a 10 ab$^{-1}$ integrated luminosity.

Vector boson parton luminosities $d\mathcal{L}_{ij}/{d\tau}$ versus $\tau =\hat{s}/s$ at $Q=\sqrt{\hat{s}}/2$ and $\sqrt s= 14$ TeV.

Representative Feynman diagrams for the VBF process $V_1 V_2\to \phi_1 \phi_2$.

Cross sections versus the c.m.~energy $\sqrt s$ for individual contributions from different VBF sub-processes to the production of $H^+H^-$ (left panel) and $HH$ (right panel), with a degenerate Higgs mass of $m_\Phi=1$~TeV.

Normalized invariant mass $m_{H^+H^-}$ distribution for $\mu^+\mu^-\to H^+H^- $ at $\sqrt{s}=14$ TeV for charged Higgs boson mass $m_{H^\pm}=1$ TeV (red) and 2 TeV (blue). Solid (dashed) lines are for annihilation (VBF) contribution.

95\% C.L. exclusion contour at muon collider with center of mass energy $\sqrt{s}=14$ (dash curves), 30 (dotted curves) TeV for different types of 2HDM from pair production channels with annihilation contribution only. For the Type-II 2HDM, the 95\% C.L. exclusion limits from the HL-LHC with 3 ab$^{-1}$ as well as the 100 TeV $pp$ collider with 30 ab$^{-1}$ are also shown (taken from Ref.~\cite{Craig:2016ygr}).

Representative Feynman diagram for the annihilation process: $\mm\to f\bar{f}^\prime \phi$.

Cross sections versus the c.m.~energy $\sqrt{s}$ for a single heavy Higgs production associated with a pair of fermions, left panel for $\mu^+\mu^-$ annihilation, and right panel for VBF. Acceptance cuts of $p_{T}^f>50$ GeV and $10^\circ<\theta_f<170^\circ$ are imposed on all outgoing fermions. A veto cut of $0.8m_\Phi

Representative Feynman diagrams for the VBF process $V_1V_2 \rightarrow f\bar{f}^\prime \phi$.

Cross sections versus the c.m.~energy $\sqrt s$ for individual contributions from different VBF sub-processes, for $\tan\beta=1$ and $m_\Phi=2$ TeV. Acceptance and veto cuts are the same as described in the caption of~\autoref{fig:com_ffH}.

Representative Feynman diagrams of the fermion associated production $tbH^\pm$ and $t\bar{t} H^\pm$ through VBF.

Normalized invariant mass distributions for $\mu^+\mu^-\to t\bar t H$ at $\sqrt{s}=14$ TeV, left panel for $m_{t\bar t}$ and right panel for $m_{t\bar t H}$, for $\mu^+\mu^-$-annihilation channels (solid) and VBF channels (dashed), respectively. Red and blue curves are for $m_H=1$ and 2 TeV, respectively.

Event distributions of the annihilation process for the $\mm \to tbH^\pm(\to tb)$ signal (two left panels) and the $\mm \to t\bar t b\bar b$ background (two right panels) in the planes of $\Delta R(tb)$-$\Delta R(t'b')$ (top panels) and $\Delta R(tt)$-$\Delta R(bb)$ (bottom panels), with $m_\Phi=2$ TeV and $\sqrt{s}=14$ TeV. The invariant mass cut $m_{tb}>0.9m_{H^\pm}$ is imposed to the background.

Event distributions of the annihilation process for the $\mm \to tbH^\pm(\to tb)$ signal (two left panels) and the $\mm \to t\bar t b\bar b$ background (two right panels) in the planes of $\Delta R(tb)$-$\Delta R(t'b')$ (top panels) and $\Delta R(tt)$-$\Delta R(bb)$ (bottom panels), with $m_\Phi=2$ TeV and $\sqrt{s}=14$ TeV. The invariant mass cut $m_{tb}>0.9m_{H^\pm}$ is imposed to the background.

Event distributions of the annihilation process for the $\mm \to tbH^\pm(\to tb)$ signal (two left panels) and the $\mm \to t\bar t b\bar b$ background (two right panels) in the planes of $\Delta R(tb)$-$\Delta R(t'b')$ (top panels) and $\Delta R(tt)$-$\Delta R(bb)$ (bottom panels), with $m_\Phi=2$ TeV and $\sqrt{s}=14$ TeV. The invariant mass cut $m_{tb}>0.9m_{H^\pm}$ is imposed to the background.

Event distributions of the annihilation process for the $\mm \to tbH^\pm(\to tb)$ signal (two left panels) and the $\mm \to t\bar t b\bar b$ background (two right panels) in the planes of $\Delta R(tb)$-$\Delta R(t'b')$ (top panels) and $\Delta R(tt)$-$\Delta R(bb)$ (bottom panels), with $m_\Phi=2$ TeV and $\sqrt{s}=14$ TeV. The invariant mass cut $m_{tb}>0.9m_{H^\pm}$ is imposed to the background.

The $\tan\beta$ dependence of the leading Higgs production cross sections in association with a pair of heavy fermions at $\sqrt{s}=14$ TeV, $m_\Phi=2$ TeV and $\cos(\beta-\alpha)=0$. The left panels show the annihilation production and the right panels show the VBF production.

Illustrative diagram for the radiative return to resonant production of a heavy Higgs boson with ISR.

Cross sections of single heavy Higgs $H$ production through the radiative return. Left panel is for $m_H=1$, 2 and 15 TeV and $\tan\beta=1$ versus the c.m.~energy $\sqrt s$, with the solid curves for the convoluted ISR spectrum and the dashed curves for single photon radiation $\mu^+\mu^- \rightarrow H \gamma$ with $10^\circ<\theta_\gamma<170^\circ$. Right panel is for the $\tan\beta$ dependence of the cross section for $\sqrt{s}=14$ TeV and $m_H=12$ TeV. The vertical axis on the right shows the corresponding event yields for a 10 ab$^{-1}$ integrated luminosity.