Search for the production of dark Higgs in the framework of Mono-Z$^{\prime}$ portal at the FCC-ee simulated electron-positron collisions at $\sqrt{s} = 240$ GeV

Abstract: In the present work, we study the possible production of the dark Higgs boson ($h_{D}$) candidates, which originated from a simplified-model scenario based on the Mono-Z$<sup>{\prime}$ model, in association with a neutral gauge boson (Z$<sup>{\prime}$). This study has been performed by studying events with dimuon plus missing transverse energy produced in the simulated electron-positron collisions at the foreseen Future Circular Collider in the Electron-Positron collision mode (FCC-ee), operating at 240 GeV center of mass energy and integrated luminosity of 10.8 ab$<sup>{-1}$. In case no new physics has been discovered, we set upper limits at a 95\% confidence level on the mass of the dark Higgs.

• The paper demonstrates a methodologically sound strategy analyzing particle and transverse momentum cuts for signal significance, finding at 240 GeV REC the entire dark Higgs production range from 20-80 GV may be effectively excluded with statistically significant findings and reduced background contamination,
• Across various simulated dark Higgs mass points from 20 to 80 GeV $ecause M_{Z'}$, a $5\sigma$ discovery reach for 35-45 GeV mass mass range. In low mass limits, the HV mass range is extended/improved 20-60 GeV. This simulates a discovery crossing an exclusion mass range of 20 to 80 Gentle report that
• The FCC-ee can search for Dark Higgs mass range of between 20 and 80 GeV and has \ can search with \sigma$ of {20-40,40-70,70-80} GeV in a discovery

Analysis overview

This paper presents a simulation-based search for a light dark Higgs boson ($h_D$) produced in association with a neutral gauge boson ($Z'$) at the Future Circular Collider in electron–positron mode (FCC-ee), using the mono-$Z'$ simplified model of Ref. (Autran et al., 2015). The analysis targets the final state $\mu^+\mu^- + E_{\text{miss}}$, where the on-shell $Z'$ decays to dimuons and the dark Higgs decays invisibly to a dark matter pair $\chi\bar{\chi}$. Events are generated for $e^+e^-$ collisions at $\sqrt{s}=240$ GeV with an integrated luminosity of 10.8 ab$^{-1}$, corresponding to the anticipated FCC-ee Run 1 conditions.

The free parameters of the simplified model are $M_{Z'}$, $Z'$0, and the couplings $Z'$1 (to SM leptons) and $Z'$2 (to the dark sector). Following existing constraints from LEP-2, ATLAS, and CMS, the lepton coupling is fixed at $Z'$3 for $Z'$4 between 10 and 90 GeV, while $Z'$5 follows LHC Dark Matter Working Group recommendations. The mass assumption ties $Z'$6 for $Z'$7 GeV, so seven benchmark mass points from 20 to 80 GeV are scanned. Signal cross sections times $Z'$8 range from about 0.74 fb at $Z'$9 GeV down to 0.57 fb at 80 GeV — small rates that make background suppression the central challenge of the analysis.

Simulation setup

Signal and background samples are produced privately with WHIZARD 3.1.1 at leading order, including initial-state radiation, interfaced to PYTHIA 6.24 for parton showering and hadronization, and passed through DELPHES fast simulation of the IDEA detector concept. The dominant irreducible backgrounds are $Z'$0 (4776 fb) and $Z'$1 (4826 fb), supplemented by diboson production: $Z'$2 (200.6 fb), $Z'$3 (5.0 fb), and $Z'$4 (0.6 fb). The dileptonic $Z'$5 channel is excluded due to its negligible cross section ($Z'$6 fb). A flat 10% systematic uncertainty is applied as an ad-hoc coverage of all systematic effects — a simplification that bears directly on the robustness of the projected limits discussed below.

Event selection

The pre-selection requires two opposite-charge muons with $Z'$7 GeV, $Z'$8, and track isolation ($Z'$9 in a cone of $\mu^+\mu^- + E_{\text{miss}}$0). At this stage, signal and background remain heavily mixed in both the dimuon invariant mass and recoil mass spectra, motivating tighter requirements on four kinematic variables:

• Energy balance: $\mu^+\mu^- + E_{\text{miss}}$1
• Azimuthal separation: $\mu^+\mu^- + E_{\text{miss}}$2 rad
• Back-to-back topology: $\mu^+\mu^- + E_{\text{miss}}$3
• Muon angular separation: $\mu^+\mu^- + E_{\text{miss}}$4

N-1 efficiency studies demonstrate that these cuts fully suppress the $\mu^+\mu^- + E_{\text{miss}}$5 and $\mu^+\mu^- + E_{\text{miss}}$6 backgrounds while strongly reducing diboson contamination, with signal efficiency remaining flat for leading-muon $\mu^+\mu^- + E_{\text{miss}}$7 above roughly 40 GeV. The recoil mass, computed from energy–momentum conservation as $\mu^+\mu^- + E_{\text{miss}}$8, is restricted to $\mu^+\mu^- + E_{\text{miss}}$9 GeV to avoid contamination from the $Z'$0 pole and SM Higgsstrahlung events. This recoil-mass-based approach is independent of how the dark Higgs decays, provided its decay products escape detection.

Results

A shape-based analysis is performed in recoil-mass bins of width 10 GeV centered on each assumed $Z'$1, using the profile likelihood ratio test statistic with systematics treated as nuisance parameters. The expected yields after final selection show that the $Z'$2 process dominates the surviving background, ranging from about 179 events in the lowest bin to nearly 2000 events in the highest, while the DH signal yields peak around 2100 events in the 35–45 GeV bin.

The projected statistical significances are strong across most of the mass range:

$Z'$3 window (GeV)	Background yield	Signal yield	Significance
[15, 25]	179.2	128.4	3.4σ
[25, 35]	410.6	2077.0	13.8σ
[35, 45]	649.1	2119.1	12.3σ
[45, 55]	878.4	2039.2	9.6σ
[55, 65]	1154.2	1854.8	7.5σ
[65, 75]	1568.3	1561.4	4.9σ
[75, 85]	2001.8	832.4	4.2σ

For $Z'$4 GeV, a 5σ discovery is reachable with only 1.21 ab$Z'$5 of integrated luminosity; for $Z'$6 GeV, 3.5 ab$Z'$7 suffices. Both thresholds are well below the full Run 1 luminosity of 10.8 ab$Z'$8, implying that discovery potential in this scenario does not hinge on the later FCC-ee running phases.

In the absence of a signal, expected 95% CL upper limits on $Z'$9 are derived using the CL$\chi\bar{\chi}$0 modified frequentist construction with asymptotic approximations. Under the benchmark coupling assumptions ($\chi\bar{\chi}$1, $\chi\bar{\chi}$2), the entire dark Higgs mass range from 20 to 80 GeV can be excluded. The authors emphasize that this extends the reach below previous limits: the LEP working group's invisible-Higgs searches excluded only masses above 60 GeV (60–112.1 GeV hadronically, 60–91.3 GeV leptonic), whereas this analysis lowers the exclusion threshold to 20 GeV. Notably, this low-mass region remains unexplored by the LHC, since hadron colliders lose sensitivity when the $\chi\bar{\chi}$3 couples exclusively to leptons.

Limitations and open questions

Several caveats qualify these projections. First, the results rest entirely on leading-order cross sections and a fast detector simulation (DELPHES/IDEA); no full GEANT-based detector study validates the muon reconstruction efficiencies and resolutions assumed here. Second, the systematic uncertainty treatment is deliberately coarse — a flat 10% nuisance — rather than derived from detector-level studies, so the reported significances and limits should be regarded as optimistic benchmarks pending realistic uncertainty modeling. Third, the analysis fixes $\chi\bar{\chi}$4 and $\chi\bar{\chi}$5; sensitivity at other coupling values, particularly smaller $\chi\bar{\chi}$6 or larger $\chi\bar{\chi}$7 already constrained by four-muon searches, is not quantified. Fourth, the claim that the electron-philic $\chi\bar{\chi}$8 decay mode would yield comparable results assumes similar reconstruction performance for electrons and muons, which is asserted but not demonstrated. Finally, the degenerate mass assumption $\chi\bar{\chi}$9 restricts the parameter space; scenarios with off-shell or non-degenerate mediators fall outside this study.

Conclusion

This work establishes, through a cut-based recoil-mass analysis of simulated FCC-ee data at $e^+e^-$0 GeV, that the mono-$e^+e^-$1 dark Higgs scenario with $e^+e^-$2 and $e^+e^-$3 would be discoverable at more than 5σ across most of the 20–80 GeV mass range within the first 10.8 ab$e^+e^-$4 of FCC-ee operation, with the strongest sensitivity near $e^+e^-$5–40 GeV. In the null hypothesis, the same analysis excludes the full 20–80 GeV mass window at 95% CL, extending existing LEP exclusions downward by 40 GeV into territory inaccessible to the LHC for lepton-philic mediators. The main open question left by the study is whether these projections survive a full detector simulation and realistic systematic uncertainty treatment, which would be required before they can inform the FCC-ee physics program quantitatively.