Long-lived Left-Right signals at the FCC-ee

We give an extensive discussion of the displaced signals of heavy Majorana neutrino production at future electron-positron colliders operating at various proposed energies in the context of the Left-Right symmetric model. A comprehensive collection of channels is taken into account, ranging from those featuring $W$ and $W_R$ mediation to those induced by scalar mixing and gauge/scalar boson fusion, with connections to the mechanism of neutrino mass origin. The emerging signatures feature possibly multiple displaced heavy neutrinos that are in some cases accompanied by prompt activity and forward leptons. We derive the corresponding total production rates and differential distributions, which allow us to differentiate the channels and have analytical estimates of the signal yield. We then develop realistic estimates of the selection efficiencies using a dedicated vertexing algorithm which establishes the displaced decay positions and supplies a reliable proxy for reconstructing the full four-momenta of long-lived particles. This allows to determine the realistic reaches in the parameter space of the Left-Right symmetric model across the various channels, and we show that these can strongly surpass the LHC ones, demonstrating that future lepton colliders are sensitive to left-right symmetry breaking scales in the deep multi-TeV regime.

💡 Research Summary

This paper presents a comprehensive study of displaced signatures arising from heavy Majorana neutrino (N) production in the minimal Left‑Right Symmetric Model (LRSM) at the Future Circular Collider in its electron‑positron mode (FCC‑ee). The authors consider the full spectrum of production mechanisms that are relevant at the various planned centre‑of‑mass energies of the FCC‑ee, ranging from the Z‑pole (√s≈91 GeV) through the Higgs‑factory stage (√s≈240 GeV) up to the top‑pair threshold (√s≈350 GeV). The channels examined include: (i) s‑channel Z/γ exchange leading to e⁺e⁻→NN and Z→NN; (ii) t‑channel right‑handed W_R exchange producing e⁺e⁻→Nν and e⁺e⁻→NN; (iii) associated production with a scalar triplet Δ (e⁺e⁻→ZΔ, ZhΔ) and vector‑boson fusion (e⁺e⁻→e⁺e⁻Δ). The scalar triplet Δ, the “Majorana Higgs”, mixes with the SM‑like Higgs and provides a direct probe of the Yukawa coupling Y_N that generates the heavy‑neutrino mass via the vacuum expectation value of Δ_R.

The theoretical framework is laid out in detail: the gauge sector features left‑ and right‑handed gauge bosons (W_L, W_R, Z, Z_{LR}) with masses set by the electroweak scale v≈174 GeV and the right‑handed breaking scale v_R≳1 TeV. Mixing between W_L and W_R is suppressed by ε=v/v_R, and the neutral sector mixing is treated to second order in ε. Heavy neutrino decay modes (N→ℓW, νZ, νh) are computed, showing lifetimes ranging from 10⁻⁴ s down to 10⁻⁸ s for masses between a few GeV and the kinematic limit √s/2. Such lifetimes lead to macroscopic decay lengths (centimetres to metres) that produce displaced vertices inside the FCC‑ee detector.

Cross sections are obtained both analytically and with MadGraph5_aMC@NLO using a dedicated FeynRules implementation (mrsm‑1.2). At the Z‑pole, the NN pair production via Z exchange yields σ≈10 fb for m_N≈10–30 GeV. Associated production with the scalar triplet, e⁺e⁻→ZΔ→ZNN, can dominate when m_Δ≲150 GeV, thanks to the sizable Δ–h mixing. At higher energies, the t‑channel W_R exchange becomes the leading source, with σ∝g_R⁴/M_{W_R}⁴, allowing sensitivity to M_{W_R} well into the multi‑TeV regime.

A key methodological advance is the use of a graph‑based displaced‑vertex reconstruction algorithm. This tool clusters tracks, fits multiple vertices simultaneously, and reconstructs the full four‑momentum of each long‑lived particle. Simulation studies show an average reconstruction efficiency of about 60 % for neutrino masses between 10 GeV and 30 GeV, decreasing for masses approaching the kinematic limit due to geometric acceptance. The algorithm exploits the clean environment of an e⁺e⁻ collider, where background from SM processes is negligible once a displaced vertex with transverse displacement of a few millimetres is required.

Sensitivity projections assume the FCC‑ee luminosity scenarios: 5 ab⁻¹ at the Z‑pole, 150 ab⁻¹ at the Higgs‑factory, and 1 ab⁻¹ at √s=350 GeV. The 95 % confidence‑level exclusion limits are:

• Right‑handed gauge boson mass M_{W_R} up to ≈12 TeV from Z‑pole NN production, and up to ≈15 TeV from the 350 GeV run via t‑channel exchange.
• Scalar triplet mass m_Δ up to ≈150 GeV (below the WW threshold) provided the Yukawa coupling Y_N≳10⁻³, allowing observation of the Δ→NN decay chain.
• Heavy‑neutrino masses m_N can be probed up to the kinematic ceiling √s/2, with optimal sensitivity in the 10–50 GeV window where displaced signatures are most pronounced.

These reaches surpass current LHC limits (M_{W_R}≈4.5 TeV) by a factor of two to three, demonstrating the power of a high‑luminosity, low‑background e⁺e⁻ machine for probing left‑right symmetry breaking scales deep into the multi‑TeV domain. The authors also discuss the possibility of combining multiple channels in a global fit to extract the underlying LRSM parameters (M_{W_R}, m_Δ, Y_N) and to test the hypothesis that the heavy neutrino mass originates from the vacuum expectation value of Δ_R.

In conclusion, the study establishes FCC‑ee as an unparalleled laboratory for exploring the Majorana nature of heavy neutrinos, lepton‑number violation, and the dynamics of left‑right symmetry breaking. The combination of diverse production modes, sophisticated displaced‑vertex reconstruction, and the clean experimental environment enables sensitivity to new physics far beyond the capabilities of present hadron colliders, and provides a concrete physics case for the inclusion of dedicated long‑lived particle detection capabilities in the design of future lepton colliders.