Measurements of $H ightarrow W^+W^-$ in the Fully Leptonic Decay Mode at the FCC-ee

The expected precision on measuring the $σ(e^+ e^- \rightarrow ZH) \times Br(H\rightarrow W^+W^-)$ in the fully leptonic decay mode at the Future Circular Collider (FCC) is presented. We consider two FCC-ee scenarios: $\sqrt{s} =240$ GeV centre-of-mass energy with a luminosity of 10.8$\rm{~ab}^{-1}$ and $\sqrt{s} =365$ GeV centre-of-mass energy with a luminosity of 3.12$\rm{~ab}^{-1}$. Our results indicate that a relative uncertainty of 2.9% and 6.8% can be achieved on measurements of $σ(e^+ e^- \rightarrow ZH) \times Br(H\rightarrow W^+W^-)$ in the fully leptonic decay mode at $\sqrt{s} =240$ GeV and $\sqrt{s} =365$ GeV, respectively.

💡 Research Summary

This paper evaluates the prospective precision of measuring the product of the Higgs‑strahlung cross‑section and the branching ratio for H→WW* in the fully leptonic final state at the Future Circular Collider operating as an electron‑positron machine (FCC‑ee). Two operating scenarios are considered: a centre‑of‑mass energy of 240 GeV with an integrated luminosity of 10.8 ab⁻¹, and 365 GeV with 3.12 ab⁻¹. The analysis focuses on the process e⁺e⁻→ZH where the Z boson decays to a pair of charged leptons (electrons or muons) and the Higgs boson decays to a pair of W bosons, each subsequently decaying leptonically, yielding a final state of four charged leptons plus missing energy from the neutrinos.

Signal and background event samples are generated using Whizard interfaced with Pythia 6 for the signal and Pythia 8 for the dominant backgrounds (ZZ, WW, tt̄). A fast detector simulation based on Delphes with the IDEA detector model is employed. Leptons with p_T > 100 MeV and |η| < 2.56 are assumed to be reconstructed with 100 % efficiency, and electron/muon identification efficiencies are set to 99 % for E > 2 GeV. Missing transverse energy is used to tag the neutrinos.

Six orthogonal final‑state categories are defined according to the flavour composition of the four leptons: (1) Z(μμ)H(eeνν), (2) Z(μμ)H(eμνν), (3) Z(μμ)H(μμνν), (4) Z(ee)H(eeνν), (5) Z(ee)H(eμνν), and (6) Z(ee)H(μμνν). Pre‑selection requires at least four leptons with |p| > 5 GeV and missing energy >5 GeV. The Z boson is reconstructed from the opposite‑sign, same‑flavour lepton pair whose invariant mass lies within 80–100 GeV; the remaining lepton pair is assigned to the Higgs decay. The recoil mass against the reconstructed Z, calculated from energy‑momentum conservation, serves as a powerful discriminant because signal events peak near the Higgs mass (125 GeV) while the main backgrounds do not.

A traditional cut‑flow analysis applies sequential requirements on the Z mass window, lepton transverse momentum (< 80 GeV), recoil mass (110–150 GeV), and the pseudorapidity of the missing momentum (|η_miss| < 2.0). At 240 GeV the Z→μμH→ee and Z→eeH→μμ channels achieve post‑cut significances of about 8 σ, with the four‑electron and four‑muon channels reaching 7–8 σ. At 365 GeV the initial significances are modest (0.6–1.9 σ) due to larger background contributions and lower signal yields.

To improve sensitivity, a multivariate analysis based on a Gradient‑Boosted Decision Tree (BDT) implemented with XGBoost is employed. Forty‑four input features are used, including low‑level quantities (four‑momenta of each lepton, missing momentum components, η) and high‑level observables (invariant masses of dilepton pairs, angular separations ΔR, reconstructed Z mass, recoil mass, missing‑energy fraction). The BDT is trained separately for each channel with a maximum tree depth of five, 1 000 estimators, early stopping after 50 rounds, and regularisation to avoid over‑training. Events with a BDT score above 0.6 are retained. This strategy yields a 50–70 % increase in signal efficiency and a 30–50 % reduction in background relative to the cut‑based approach. Consequently, the overall significance at 240 GeV rises to 12–19 σ across channels, while at 365 GeV it improves to 1.3–2.0 σ.

Statistical extraction of the signal strength μ (the ratio of measured to Standard Model σ·Br) is performed using a Poisson likelihood with profiling of nuisance parameters. Systematic uncertainties (lepton efficiency, energy scale, background normalisation) are not included in the baseline estimate, representing an optimistic scenario. Under these assumptions the relative uncertainties on σ(e⁺e⁻→ZH)·Br(H→WW) are 2.9 % at 240 GeV and 6.8 % at 365 GeV. These precisions surpass those achievable at the LHC and HL‑LHC and would enable a model‑independent determination of the Higgs‑W coupling g_HWW at the few‑percent level.

The study highlights several key points: (i) the fully leptonic final state, despite its low branching fraction, benefits from negligible jet‑related backgrounds and excellent lepton reconstruction; (ii) the recoil mass and missing‑energy kinematics provide strong discrimination against ZZ and WW backgrounds; (iii) machine‑learning techniques substantially enhance sensitivity, especially at higher energies where signal‑to‑background ratios are lower; (iv) the high integrated luminosities and clean environment of FCC‑ee are ideally suited for precision Higgs measurements. The authors note that future work should incorporate realistic systematic uncertainties, combine all leptonic and semi‑leptonic channels, and explore full global fits to Higgs couplings within the FCC‑ee physics program.