Doubly-charged Higgs boson at a future electron-proton collider

We explore the discovery prospect of the doubly-charged component of an $SU(2{)}_L$-triplet scalar at the future $e^{-}p$ collider FCC-eh, proposed to operate with an electron beam energy of 60 GeV and a proton beam energy of 50 TeV. We consider the associated production of the doubly-charged Higgs boson along with leptons and jet(s), and its subsequent prompt decay to same-sign lepton pair. This occurs for $\mathcal{O}(1)$ Yukawa coupling of the scalar triplet with charged leptons, which is expected for reasonably small vacuum expectation values of the neutral component of the triplet field that governs the neutrino mass generation in the type-II seesaw. We present our analysis for two different final states, $3l+\ge 1j$ and an inclusive $\ge 2l+\ge 1j$ channel. Considering its decay to electrons only, we find that the doubly-charged Higgs boson with a mass around a TeV could be observed at the $3\sigma$ confidence level with $\mathcal{O}(200){\mathrm{fb}}^{-1}$ of integrated luminosity, while masses up to 2 TeV could be probed within a few years of data accumulation. The signal proposed here becomes essentially background free, if it is triggered in the $\mu \mu$ mode and a $5\sigma$ discovery is achievable in this channel for a TeV-scale doubly-charged Higgs boson with an integrated luminosity as low as $\mathcal{O}(50){\mathrm{fb}}^{-1}$. We also highlight the sensitivity of FCC-eh to the Yukawa coupling responsible for the production of the doubly-charged Higgs boson as a function of its mass in both the $ee$ and $\mu \mu$ channels.

Figure 1

Feynman diagrams for the single production of doubly-charged Higgs boson at the $e^{-}p$ collider. An additional diagram exists for process I with the $t$-channel photon exchange appearing before the doubly-charged Higgs boson is radiated, which is not shown here but included in our analysis.

Figure 2

Allowed off diagonal Yukawa couplings $Y_{\mu \tau }^{\mathrm{\Delta }}$ and $Y_{e\tau }^{\mathrm{\Delta }}$ as a function of $Y_{e\mu }^{\mathrm{\Delta }}$ (shown by the color code). The diagonal couplings $Y_{ee,\mu \mu }^{\mathrm{\Delta }}$ are randomly varied between the range of 0.1 and 0.3, for a fixed $M_{H^{\pm \pm }}=1\mathrm{TeV}$. The vertical and horizontal shaded regions are excluded from the experimental constraints on the tau-LFV decay modes $\tau \to 3e$ and $\tau \to 3\mu$, respectively, for fixed $Y_{ee,\mu \mu }^{\mathrm{\Delta }}=0.3$.

Figure 3

Parton-level production cross sections (normalized to $|Y_{ee}^{\mathrm{\Delta }}{|}^2=1$) of the doubly-charged Higgs boson for process I (green, dashed) and process II (blue, dot dashed) shown in Fig. 1 at $e^{-}p$ collider with beam energies of 60 GeV (for electron) and 50 TeV (for proton). We have chosen the triplet VEV as $v_{\mathrm{\Delta }}=0.1\mathrm{eV}$.

Figure 4

The normalized distribution of $p_T$ of leading charged lepton (left) and the invariant mass ($M_{ll}$) of the same-sign lepton pair (right) for both the signal and SM background.

Figure 5

The $2\sigma$ and $3\sigma$ sensitivity reach of $Y_{ee}^{\mathrm{\Delta }}$ at FCC-eh as a function of the doubly-charged Higgs mass $M_{H^{--}}$. The left panel is for signal I and the right panel is for signal II discussed in the text. The vertical (blue) shaded region is excluded from the current lower bound on $M_{H^{\pm \pm }}$ from the $\sqrt{s}=13\mathrm{TeV}$ LHC data. The green-shaded region is excluded by the LEP constraints on the Bhabha scattering process. Here, we have considered $\mathrm{BR}(H^{\pm \pm }\to e^{\pm }{e}^{\pm })=100\%$.

Figure 6

The sensitivity reach of $Y_{ee}^{\mathrm{\Delta }}$ at FCC-eh as a function of the doubly-charged Higgs mass $M_{H^{\pm \pm }}$ for signal I with $\mathrm{BR}(H^{--}\to {\mu }^{-}{\mu }^{-})=50\%$. The vertical (blue) shaded region is excluded from the current lower bound on $M_{H^{\pm \pm }}$ from the $\sqrt{s}=13\mathrm{TeV}$ LHC data. The green-shaded region is excluded by the LEP constraints on the Bhabha scattering process.