Heavy Higgs bosons in 2HDM at a muon collider

We study the discovery potential of the non-Standard Model (SM) heavy Higgs bosons in the Two-Higgs-Doublet Models (2HDMs) at a multi-TeV muon collider and explore the discrimination power among different types of 2HDMs. We find that the pair production of the non-SM Higgs bosons via the universal gauge interactions is the dominant mechanism once above the kinematic threshold. Single Higgs boson production associated with a pair of heavy fermions could be important in the parameter region with enhanced Yukawa couplings. For both signal final states, ${\mu }^{+}{\mu }^{-}$ annihilation channels dominate over the vector boson fusion (VBF) processes, except at high center of mass energies where the VBF processes receive large logarithmic enhancement with the increase of energies. Single Higgs boson $s$-channel production in ${\mu }^{+}{\mu }^{-}$-annihilation via the radiative return can also be important for the Type-L 2HDM in the very large $\tan \beta$ region, extending the kinematic reach of the heavy Higgs boson mass to the collider energy. Considering both the production and decay of non-SM Higgs bosons, signals can be identified over the Standard Model backgrounds. With the pair production channels via annihilation, 95% C.L. exclusion reaches in the Higgs mass up to the production mass threshold of $\sqrt{s}/2$ are possible when channels with different final states are combined. Including single production modes can extended the reach further. Different types of 2HDMs can be distinguishable for moderate and large values of $\tan \beta$.

Figure 1

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 $m_{\mathrm{\Phi }}=2\mathrm{TeV}$ and $\cos (\beta -\alpha )=0$. In the right panel, red curve (Type-I) overlaps with the blue curve (Type-F).

Figure 2

Representative Feynman diagram for the EW scalar pair production in ${\mu }^{+}{\mu }^{-}$ annihilation ${\mu }^{+}{\mu }^{-}\to {\varphi }_1{\varphi }_2$.

Figure 3

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 $m_{\mathrm{\Phi }}=1\mathrm{TeV}$, 2 TeV and 5 TeV, respectively. The vertical axis on the right shows the corresponding event yields for a $10{\mathrm{ab}}^{-1}$ integrated luminosity.

Figure 4

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

Figure 5

Representative Feynman diagrams for the VBF process $V_1{V}_2\to {\varphi }_1{\varphi }_2$.

Figure 6

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

Figure 7

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

Figure 8

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 $3{\mathrm{ab}}^{-1}$ as well as the 100 TeV $pp$ collider with $30{\mathrm{ab}}^{-1}$ are also shown (taken from Ref. [5]).

Figure 9

Representative Feynman diagram for the annihilation process: ${\mu }^{+}{\mu }^{-}\to f{\overline{f}}^{\prime }\varphi$.

Figure 10

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 $p_T^f>50\mathrm{GeV}$ and $10°<{\theta }_f<170°$ are imposed on all outgoing fermions. A veto cut of $0.8m_{\mathrm{\Phi }}<m_{f{f}^{\prime }}<1.2m_{\mathrm{\Phi }}$ is applied to the associated fermions to remove contributions from resonant Higgs decays. The vertical axis on the right shows the corresponding event yields for a $10{\mathrm{ab}}^{-1}$ integrated luminosity.

Figure 11

Representative Feynman diagrams for the VBF process $V_1{V}_2\to f{\overline{f}}^{\prime }\varphi$.

Figure 12

Cross sections versus the c.m. energy $\sqrt{s}$ for individual contributions from different VBF subprocesses, for $\tan \beta =1$ and $m_{\mathrm{\Phi }}=2\mathrm{TeV}$. Acceptance and veto cuts are the same as described in the caption of Fig. 10.

Figure 13

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

Figure 14

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

Figure 15

Event distributions of the annihilation process for the ${\mu }^{+}{\mu }^{-}\to tb{H}^{\pm }(\to tb)$ signal (two left panels) and the ${\mu }^{+}{\mu }^{-}\to t\overline{t}b\overline{b}$ background (two right panels) in the planes of $\mathrm{\Delta }R(tb)-\mathrm{\Delta }R(t^{\prime }{b}^{\prime })$ (top panels) and $\mathrm{\Delta }R(tt)-\mathrm{\Delta }R(bb)$ (bottom panels), with $m_{\mathrm{\Phi }}=2\mathrm{TeV}$ and $\sqrt{s}=14\mathrm{TeV}$. The invariant mass cut $m_{tb}>0.9m_{H^{\pm }}$ is imposed to the background.

Figure 16

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

Figure 17

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

Figure 18

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 ${\mu }^{+}{\mu }^{-}\to H\gamma$ with $10°<{\theta }_{\gamma }<170°$. Right panel is for the $\tan \beta$ dependence of the cross section for $\sqrt{s}=14\mathrm{TeV}$ and $m_H=12\mathrm{TeV}$. The vertical axis on the right shows the corresponding event yields for a $10{\mathrm{ab}}^{-1}$ integrated luminosity.