Chasing Long-Lived Doubly Charged Scalars at Future Lepton Colliders

We come up with a novel search strategy for long-lived doubly charged scalars at future proposed lepton colliders. The doubly charged scalar studied in this work belongs to an $SU(2)_L$ complex scalar triplet that accounts for tiny neutrino masses via the Type-II Seesaw mechanism. For scalar masses $\lesssim 200 $ GeV and appropriate values of the triplet vacuum expectation value, this state can be long-lived and decay predominantly into like-sign muon pairs (e.g. $μ^+μ^+ $ or $μ^-μ^-$), producing distinctive displaced-vertex signals. We investigate the pair production of these scalars at the International Linear Collider (ILC) and a prospective muon collider, considering their planned center-of-mass energies. Incorporating theoretical and experimental constraints, we study the resulting signature of four leptons accompanied by missing transverse energy. Displaced vertices offer direct evidence of the scalar’s long lifetime, while we further show that the invariant mass distribution of same-sign dilepton pairs serves as a powerful complementary probe for discovering doubly charged Higgs bosons at both the ILC and muon collider.

💡 Research Summary

The paper proposes a novel search strategy for long‑lived doubly‑charged scalars (H^{±±}) that arise in the Type‑II seesaw model, where an SU(2)_L complex triplet Δ is added to the Standard Model. In this framework the triplet acquires a tiny vacuum expectation value (v_t) and generates Majorana neutrino masses through the Yukawa coupling Y_Δ. For v_t in the range 10^{-4}–10^{-3} GeV and scalar masses between 100 GeV and 200 GeV, the doubly‑charged component becomes long‑lived: its total width can be as small as 10^{-14} GeV, corresponding to proper decay lengths cτ of order 0.1 mm to several centimeters. In this regime the dominant decay mode is into same‑sign muon pairs (μ^+μ^+ or μ^-μ^-), providing a clean experimental signature.

The authors first review the model, detailing the scalar potential, mass spectrum, and the relation between v_t, Y_Δ and neutrino masses. They then compile all relevant theoretical and experimental constraints: vacuum stability, perturbative unitarity, electroweak precision observables (especially the ρ‑parameter and the T‑parameter), Higgs diphoton signal strength, and existing LHC/LEP limits on singly‑ and doubly‑charged scalars. Because most LHC searches assume prompt decays, a region of parameter space remains viable: m_{H^{±±}}≈89–200 GeV with v_t≈10^{-4}–10^{-3} GeV.

Three benchmark points (BP1: m=100 GeV, v_t=9×10^{-4} GeV, Br(H^{±±}→μμ)=19.5 %, cτ≈26 mm; BP2: m=120 GeV, v_t=5×10^{-4} GeV, Br≈17 %, cτ≈8.6 mm; BP3: m=180 GeV, v_t=1.6×10^{-4} GeV, Br≈6 %, cτ≈0.14 mm) illustrate how the decay length shrinks as the mass grows and the W^±W^± channel opens.

The collider analysis focuses on two future lepton machines: the International Linear Collider (ILC) operating at √s=500 GeV with 4 ab⁻¹, and a prospective muon collider at √s=10 TeV with 10 ab⁻¹. At the ILC, the dominant production mechanism is Drell–Yan pair production via s‑channel γ/Z exchange (e⁺e⁻→H^{++}H^{–}), which yields cross sections of order 10 fb for the considered masses. At the muon collider, the Drell–Yan rate is suppressed at high energy, while vector‑boson fusion (VBF) processes (μ⁺μ⁻→ν_μ \barν_μ W⁺W⁻→H^{++}H^{–}) become dominant. Both machines lead to a final state with four same‑sign muons (four‑lepton signature) plus missing transverse energy from neutrinos in the VBF case.

Signal and background events are generated with MadGraph5_aMC@NLO and showered with Pythia 8. Basic acceptance cuts (|η|<2.5, p_T>10 GeV, ΔR>0.4) are applied. The analysis exploits two complementary observables:

1. Displaced vertices: for BP1 and BP2 the proper decay length translates into measurable transverse displacements (>1 mm) in the tracking detectors, providing a background‑free LLP signature.
2. Invariant mass of same‑sign dileptons: the μ^±μ^± pair from each H^{±±} decay reconstructs a sharp peak at m_{H^{±±}}. Even when the decay is prompt (BP3), this mass peak remains a powerful discriminant against SM backgrounds such as ZZ or WW production.

The study shows that with a few hundred fb⁻¹ of data the ILC can discover H^{±±} up to ~180 GeV via displaced‑vertex searches, while the muon collider can extend the reach to higher masses using VBF production and the invariant‑mass technique. The combination of LLP identification and mass reconstruction dramatically improves sensitivity compared to conventional prompt‑decay searches.

In conclusion, the paper demonstrates that future lepton colliders, thanks to their clean environment and excellent vertexing capabilities, are ideally suited to probe the long‑lived doubly‑charged scalars predicted by the Type‑II seesaw. This opens a discovery window for scalar masses well below current LHC limits, especially in the region where the scalar decays predominantly to muon pairs with macroscopic lifetimes. The authors suggest that extending the analysis to other decay channels (e.g., H^{±±}→W^{±}W^{±}) and incorporating more sophisticated detector simulations would further strengthen the case for dedicated LLP searches at upcoming lepton facilities.