Probing the pair production of first-generation vector-like leptons at future $e^+e^-$ colliders

This work explores the discovery potential of the first-generation weak isosinglet Vector-Like Leptons (VLLs), denoted by $E^\pm$, via pair production at future electron-positron colliders. Our analysis adopts a comprehensive framework that incorporates beam polarization configurations and leverages detailed detector simulations. We focus on two distinct multilepton signatures: the $2\ell + 2j + \slashed{E}_T$ and $3\ell + 2j + \slashed{E}T$ final states ($\ell = e, μ$). Both signatures arise from the decay $E^{\pm} \to Z e^{\pm} / W^{\pm} ν\ell$ and are distinguished by the decay patterns of the associated gauge bosons. By applying optimized selection criteria to both signal and background events, we establish exclusion sensitivities and discovery prospects across the VLL mass spectrum. Our findings demonstrate that, for integrated luminosities of $\SI{25}{fb^{-1}}$, $\SI{90}{fb^{-1}}$ and $\SI{1000}{fb^{-1}}$ at corresponding center-of-mass (c.m.) energies of $\SI{1}{TeV}$, $\SI{1.5}{TeV}$ and $\SI{3}{TeV}$, the accessible mass range extends to approximately $\SI{490}{GeV}$, $\SI{740}{GeV}$ and $\SI{1440}{GeV}$, which represents a substantially improvement over the detection limits of existing hadron collider experiments.

💡 Research Summary

This paper investigates the prospects for discovering first‑generation weak‑isosinglet vector‑like leptons (VLLs), denoted E±, through pair production at future high‑energy electron‑positron colliders such as the ILC and CLIC. The authors adopt a realistic simulation framework that includes polarized beams, full detector modeling, and a detailed treatment of Standard Model backgrounds.

The theoretical setup introduces a minimal extension of the Standard Model by adding a Dirac fermion E with quantum numbers (1,1,−1). Mixing with the SM electron is parameterised by a Yukawa‑like coupling ε, chosen to be 0.01, which yields a small mixing angle (θL≈εv/M) consistent with electroweak precision constraints while ensuring prompt decays of E±. After electroweak symmetry breaking the dominant decay modes are E±→W±νe, E±→Ze±, and E±→he±, with branching ratios approaching the pattern 2:1:1 in the heavy‑mass limit.

Pair production proceeds via s‑channel Z/γ exchange. The authors exploit a single optimized beam‑polarisation configuration, (Pe−=+0.8, Pe+=−0.2), which enhances the right‑handed coupling (|aR|>|aL|) and raises the cross section by roughly a factor of two compared with the unpolarised case. Cross‑section curves are presented for centre‑of‑mass energies √s = 1 TeV, 1.5 TeV and 3 TeV, showing values of order 100 fb near threshold and decreasing to a few fb at the highest masses.

Two complementary multilepton signatures are studied:

• Case 1 (2ℓ + 2j + E_T) – one VLL decays to Z (e→jj) and the other to W (ℓν), yielding two opposite‑sign leptons, two light‑flavour jets, and missing transverse energy.
• Case 2 (3ℓ + 2j + E_T) – the Z decays leptonically while the W decays hadronically, giving three leptons, two jets and missing energy.

Signal and background events (ZW, tt̄Z, tt̄) are generated at leading order with MadGraph5_aMC@NLO, showered with PYTHIA 8.20, and passed through DELPHES detector cards (ILD for ILC, CLIC for the higher‑energy stage). Object reconstruction follows basic kinematic cuts (pT>10 GeV, |η|<3, ΔR>0.4).

A three‑step cut flow is applied:

1. Lepton selection – exact lepton multiplicity, charge requirement, pT thresholds that scale with √s, and a Z‑mass veto for the opposite‑sign lepton pair.
2. Missing‑energy and transverse‑mass cuts – E_T > 100–200 GeV (depending on √s) and MT(ℓ) > 100 GeV.
3. Invariant‑mass reconstruction – for √s=1 TeV and 1.5 TeV a dijet mass window |Mjj−mZ|<20 GeV together with a lower bound on Mjjℓ (≥300–400 GeV); for √s=3 TeV a fat‑jet with 60 GeV<Mj1<110 GeV and pT>300 GeV is required, plus Mj1ℓ > 600 GeV.

These selections retain roughly 30 % of the signal while suppressing backgrounds to the 10⁻³ level. Statistical significance is evaluated using the simple S/√B metric. For integrated luminosities of 25 fb⁻¹ (1 TeV), 90 fb⁻¹ (1.5 TeV) and 1000 fb⁻¹ (3 TeV), the 5σ discovery reach extends to E± masses of approximately 490 GeV, 740 GeV and 1.44 TeV, respectively. Corresponding 2σ exclusion limits are slightly lower but still well beyond the current LHC bounds of ≈ 320 GeV for singlet VLLs.

The authors conclude that future e⁺e⁻ colliders, equipped with polarized beams and high‑precision detectors, can probe weak‑isosinglet VLLs up to the kinematic limit of each energy stage, offering a dramatic improvement over hadron‑collider searches. They suggest further work on varying the mixing parameter ε, exploring displaced‑vertex signatures for smaller ε, and extending the analysis to doublet or triplet VLL scenarios.