Searching for vector-like leptons decaying into an electron and missing transverse energy in e$^{+}$e$^{-}$ collisions with $\sqrt{s} = 240$ GeV at the FCC-ee

Abstract: This analysis delves into the lepton portal dark matter by utilizing Monte Carlo simulated samples from electron-positron collisions at the Future Circular Collider (FCC-ee), operating at a center of mass energy of 240 GeV and an integrated luminosity of 10.8 ab$<sup>{-1}$. The study explores a specific benchmark scenario in which dark matter is represented as a scalar particle produced as a byproduct of a vector-like lepton. The key signal signature features missing transverse energy alongside dilepton events. Should new physics not be detected, this study establishes 95\% confidence level exclusion limits on the mass of the vector-like leptons and the Yukawa coupling.

• The paper demonstrates the FCC-ee's ability to exclude vector-like leptons in the electron-philic channel with nearly degenerate mass spectra using a shape-based analysis.
• It combines Monte Carlo simulations with staged event selection and focuses on missing transverse energy and angular correlations to suppress standard model backgrounds.
• Exclusion limits extend up to 74.6–110 GeV for VLLs depending on ΔM scenarios and Yukawa couplings, offering a robust probe for BSM lepton portal dark matter.

Search for Vector-Like Leptons Decaying into Electron and Missing Transverse Energy in $e^+e^-$ Collisions at 240 GeV FCC-ee

Theoretical Motivation and Model Framework

The analysis investigates scenarios beyond the Standard Model (BSM), focusing on the lepton portal dark matter (LPDM) model that addresses the particle nature of dark matter via collider signatures. In this framework, a scalar dark matter candidate ($\chi$), singlet under the SM gauge group, interacts exclusively through Yukawa couplings ($\lambda_L^i$) with vector-like leptons (VLLs, denoted as $L$) that form electroweak doublets. To avoid lepton flavor violation, couplings are flavor-specific; this study concentrates on the electron-philic ($\lambda_L^1$) case.

Key theoretical parameters include:

• VLL mass ($M_L$),
• Scalar dark matter mass ($M_\chi$),
• Yukawa coupling ($\lambda_L$),
• Mass splitting $\Delta M = M_L - M_\chi$.

The stability of $\chi$ is ensured by an additional $\chi$0 or $\chi$1 symmetry.

VLL pair production occurs via both $\chi$2-channel (mediated by $\chi$3) and $\chi$4-channel (mediated by $\chi$5) processes, as depicted in the Feynman diagrams.

Figure 1: Feynman diagrams for vector-like lepton pair production via (a) $\chi$6-channel and (b) $\chi$7-channel, followed by decay into electrons and dark matter.

The $\chi$8-channel's importance increases with larger $\chi$9, making it relevant for the cross-section calculations. This study benchmarks two narrow mass splitting scenarios: $\lambda_L^i$0 GeV and $\lambda_L^i$1 GeV.

FCC-ee Simulation Setup and Signal Characterization

Monte Carlo event generation is performed at $\lambda_L^i$2 GeV, the Higgs factory running point of the FCC-ee, and with a projected integrated luminosity of $\lambda_L^i$3 ab$\lambda_L^i$4.

The main SM backgrounds involve processes yielding electron pairs and missing energy, dominantly $\lambda_L^i$5, $\lambda_L^i$6, $\lambda_L^i$7, $\lambda_L^i$8, and to a negligible extent, $\lambda_L^i$9 (the latter excluded due to tiny cross-sections at this energy).

Signal characteristics post-decay involve opposite-sign dielectron pairs and missing transverse energy ($L$0) from the undetected $L$1. The $L$2 distribution reflects the compressed spectrum—especially for small $L$3—making discrimination from SM backgrounds challenging.

The dependence of the VLL signal cross-section on $L$4 for varying $L$5 and $L$6 is shown in

Figure 2: Signal cross-section as a function of $L$7 for various $L$8 values with $L$9 GeV.

Production cross-sections are significantly enhanced for large $\lambda_L^1$0 due to the dominance of $\lambda_L^1$1-channel processes.

Event Selection and Background Suppression

The analysis employs a staged event selection:

• Pre-selection: Both electrons must satisfy $\lambda_L^1$2 GeV, $\lambda_L^1$3, and an electromagnetic-to-hadronic energy deposit ratio $\lambda_L^1$4.
• Final selection: Tighter kinematic requirements on:
  • Relative $\lambda_L^1$5 misalignment between dielectrons and $\lambda_L^1$6 ($\lambda_L^1$7),
  • Angular separation $\lambda_L^1$8,
  • Three-dimensional angular correlation $\lambda_L^1$9(Angle$M_L$0) $M_L$1.

The $M_L$2 spectrum for SM backgrounds and several signal $M_L$3 hypotheses, before and after final selection, is shown for both $M_L$4 and $M_L$5 GeV.

Figure 3: Measured missing transverse energy spectrum post-preselection for SM backgrounds and VLL signals with $M_L$6 GeV (a) and $M_L$7 GeV (b).

After final selection, additional key discriminants include the $M_L$8 ratio, dielectron $M_L$9, and the $M_\chi$0(Angle$M_\chi$1) variable.

Figure 4: Distributions for $M_\chi$2, $M_\chi$3, and $M_\chi$4(Angle$M_\chi$5) for signal and backgrounds with cut values indicated.

The "N–1" efficiency plots (efficiency for each variable after applying all other cuts) confirm that background events are robustly suppressed in the relevant $M_\chi$6 regime.

Figure 5: N–1 efficiency distributions versus leading electron $M_\chi$7 for selection variables, for signal ($M_\chi$8 GeV) and backgrounds.

Statistical Analysis and Exclusion Limits

A shape-based analysis using $M_\chi$9 distributions allows interpretation in terms of 95% confidence level (CL) exclusion limits. For $\lambda_L$0 and $\lambda_L$1 GeV, vector-like leptons with masses from 10 to 74.6 GeV are excluded. For $\lambda_L$2 GeV and $\lambda_L$3, $\lambda_L$4 exclusion extends up to 110 GeV. The cross-section limits as a function of $\lambda_L$5 for selected $\lambda_L$6 values are shown below.

Figure 6: 95% CL limit on expected VLL production cross-section as a function of $\lambda_L$7, with several $\lambda_L$8 values and $\lambda_L$9 GeV (a) and $\Delta M = M_L - M_\chi$0 GeV (b).

The exclusion in the $\Delta M = M_L - M_\chi$1–$\Delta M = M_L - M_\chi$2 parameter plane is explicitly demonstrated.

Figure 7: 95% CL exclusion contours in the $\Delta M = M_L - M_\chi$3–$\Delta M = M_L - M_\chi$4 plane for $\Delta M = M_L - M_\chi$5 and $\Delta M = M_L - M_\chi$6 GeV at $\Delta M = M_L - M_\chi$7 GeV.

The FCC-ee sensitivity notably diminishes for lower $\Delta M = M_L - M_\chi$8 (below $\Delta M = M_L - M_\chi$9 for $\chi$0 GeV, $\chi$1 for $\chi$2 GeV).

Practical and Theoretical Implications

This work shows that the FCC-ee, in its anticipated Run I configuration, can extend coverage to VLL scenarios with nearly degenerate spectra—regions that are largely inaccessible to hadron colliders like the LHC due to overwhelming SM backgrounds and limited kinematic reach. This is particularly relevant for models with $\chi$3–$\chi$4 GeV.

The analysis sets strict exclusion limits on VLL masses in the electron-philic scenario. Extensions to the muon-philic channel should yield similar sensitivity, given equivalent reconstruction performance, but tau-philic modes remain more challenging due to the complex tau signatures.

Future directions include:

• Extending analyses to tau-philic scenarios with advanced reconstruction and ML-based discriminators,
• Incorporating systematic uncertainties correlated across detector subsystems,
• Exploring different FCC-ee running energies for broader mass reach,
• Extending phenomenological studies for alternative dark sector mediators and signatures.

Conclusion

A detailed simulation-based search for electron-philic vector-like leptons decaying into $\chi$5 at the FCC-ee demonstrates robust sensitivity for compressed mass spectrum scenarios. For Yukawa couplings $\chi$6 and small $\chi$7, vector-like leptons up to 74.6–110 GeV can be excluded depending on $\chi$8. This complements existing LHC constraints and indicates the FCC-ee's uniqueness in probing lepton-portal dark sectors characterized by soft visible decay products and substantial missing energy. These results inform both the design of future lepton collider search strategies and the parameter space for BSM models incorporating vector-like matter.