Electron-Positron Higgs Factory

• Electron-positron Higgs Factory is a high-luminosity lepton collider optimized for precision Higgs measurements, enabling absolute determinations of production cross sections and couplings.
• It leverages diverse machine concepts—circular storage rings, linear accelerators, and plasma-wakefield designs—to probe rare and exotic decay modes and CP-violation with sub-percent accuracies.
• Advanced detector systems and accelerator technologies minimize systematic uncertainties, empowering multi-permille level sensitivity to both Standard Model parameters and potential new physics.

An electron-positron Higgs factory is a high-luminosity lepton collider optimized for precision studies of the Higgs boson through reactions such as $e^+e^- \to ZH$. Such facilities are the highest-priority next collider within the global high energy physics strategy, providing unique model-independent sensitivity to Higgs couplings, rare and exotic decays, and potential physics beyond the Standard Model (BSM) through both absolute measurements and loop-induced observables. Multiple technological and conceptual realizations are in contention, including large-circumference circular storage rings (FCC-ee, CEPC, LEP3), linear colliders (ILC, CLIC, C³), and advanced asymmetric/hybrid plasma-wakefield concepts (HALHF), each with their own operational regimes, upgrade paths, and technical challenges (List, 2023, Black et al., 2022, Lindstrøm et al., 27 May 2025).

1. Scientific Objectives and Motivation

The primary goal of an electron-positron Higgs factory is to enable multi-permille to percent-level measurements of the Higgs boson’s properties that are inaccessible or systematically limited at the LHC. The clean initial state permits absolute determinations of production cross sections (using the recoil method against the Z), branching ratios for dominant and rare/exotic decay modes, and direct extractions of the total Higgs width and invisible width at the percent level. Out-of-the-box observables include:

• Higgsstrahlung process ($e^+e^- \to ZH$) cross section, peaking at $\sqrt{s} \simeq 240$–250 GeV.
• Z-pole and WW threshold scans, yielding the most precise $m_Z$, $m_W$, electroweak mixing angle, and BSM-sensitive observables.
• Measurement of Higgs couplings: $g_{HZZ}$, $g_{HWW}$, $g_{Hbb}$, $g_{Hcc}$, $g_{H\tau\tau}$, $g_{Hgg}$, $g_{H\gamma\gamma}$, $g_{H\mu\mu}$, with projected precisions at or below 0.2–1% for the dominant channels in leading designs.
• Searches for rare and forbidden decays (e.g., $H \to s\bar{s},\; u\bar{u},\; d\bar{d}$, FCNCs, invisible) with sensitivities two or more orders of magnitude beyond the LHC.
• Probes of CP-violation in the Higgs sector and anomalous couplings through multidimensional angular analyses and polarization asymmetries (1901.10218, Božović-Jelisavucić et al., 2022).
• Discrimination among SM extensions (2HDM, composite Higgs, singlet portals, SUSY) via loop-induced deviations in $e^+e^- \to hZ$ (Anisha et al., 23 Jun 2025).

The combination of large Higgs statistics (typically $10^5$–$10^6$ bosons per run), sub-percent systematics, modular upgrade paths, and unique kinematic handles on all Higgs states, define the scientific reach of an $e^+e^-$ Higgs factory (An et al., 2018, List, 2023).

2. Collider Concepts and Machine Parameters

The leading $e^+e^-$ Higgs factory proposals fall into two principal categories: circular storage rings and linear accelerators. Table 1 summarizes the main design parameters for currently prioritized machines (Black et al., 2022, Faus-Golfe et al., 2022).

Facility	$\sqrt{s}$ (GeV)	Luminosity per IP ($10^{34}\,\mathrm{cm}^{-2}\mathrm{s}^{-1}$)	Integrated L per run (ab$^{-1}$)	Polarization	Tunnel Length (km)
FCC-ee	240	5.0 (4 IPs)	10 (ZH run)	None	91–97
CEPC	240	2.0 (2 IPs)	5.6	None	50–100
ILC	250	1.35 (1 IP)	2.0	80% $e^-$, 30% $e^+$	20
CLIC	380	1.5 (1 IP)	1.0	80% $e^-$, 20% $e^+$	11
LEP3	230	1.8 (2 IPs)	2.2	None	26.7
HALHF	250	1.0	2.0	$e^-$ only	5

Circular designs deliver instantaneous luminosities up to $O(10^{35})\,\mathrm{cm}^{-2}\mathrm{s}^{-1}$ at the $Z$ pole and $O(10^{34})\,\mathrm{cm}^{-2}\mathrm{s}^{-1}$ at the Higgs maximum. Multiple IPs provide high statistics and parallel data streams. Synchrotron radiation (SR) loss per turn $\propto E^4/R$ is the limiting factor, requiring large radius and advanced cryomodules; ultimate energy reach caps at $\sqrt{s} \lesssim 365$ GeV. Linear colliders exploit single-pass, high-gradient RF or advanced plasma-wakefield acceleration (PWFA) to reach higher $\sqrt{s}$ (>500 GeV), allow beam polarization, and are naturally upgradeable, but typically operate with a single IP and somewhat lower Higgs yields for comparable running times (Agapov et al., 2022, Lindstrøm et al., 27 May 2025).

HALHF (hybrid asymmetric linear) and related concepts propose boosting electrons up to several hundred GeV in multi-stage PWFAs, with positrons accelerated to tens of GeV in a compact, high-gradient RF linac (Adli et al., 25 Mar 2025, Lindstrøm et al., 27 May 2025). The asymmetrical kinematics sidestep the technical barrier of positron PWFA while maintaining high Higgs yield and low capex.

3. Higgs Production, Coupling Extraction, and Precision Physics

At $\sqrt{s} \approx 240$–250 GeV, the cross section for Higgsstrahlung ($e^+e^- \to ZH$) reaches its maximum,

$$\sigma(e^+e^- \to ZH) = \frac{G_F^2\,m_Z^4}{96\pi\,s}\,(v_e^2 + a_e^2)\,\lambda^{1/2}\frac{\lambda + 12\,m_Z^2/s}{(1 - m_Z^2/s)^2},$$

with $$\lambda = [1 - (m_H + m_Z)^2/s][1 - (m_H - m_Z)^2/s]$$ (An et al., 2018). For $L = 5.6\,\text{ab}^{-1}$ and $\sigma(ZH) \simeq 205$ fb (CEPC), the total Higgs yield exceeds $10^6$ events, with further contributions from $WW$ fusion ($O(10^4)$ events/run).

Coupling precisions benefit from absolute normalization (recoil method), effective background rejection, and advanced flavor/jet identification. Estimated one-sigma uncertainties in the leading proposals are (An et al., 2018, List, 2023, Anastopoulos et al., 1 Apr 2025):

• $\Delta \kappa_Z \sim 0.13$–$0.3$\%
• $\Delta \kappa_W \sim 0.5$–$1.4$\%
• $\Delta \kappa_b \sim 0.3$–$1.8$\%
• $\Delta \kappa_g \sim 1.3$–$2.1$\%
• $\Delta \kappa_\gamma \sim 2.7$–$6.8$\%
• $\text{BR}(H \to \text{inv}) < 0.3\%$ (95% CL)
• $m_H$ reach: $\sim$5–6 MeV

Precision in $g_{HZZ}$, $g_{HWW}$, and $g_{Hff}$ in the 0.1–1% range probes BSM effects up to the multi-TeV scale, e.g., compositeness, singlet mixing, supersymmetric top partners, or loop-induced deviations from 2HDM or other non-minimal scenarios (Anisha et al., 23 Jun 2025). Rare decays such as $H \to s\bar{s}, d\bar{d}, u\bar{u}$ and FCNC modes can be probed down to ${\cal O}(10^{-3})$, two orders of magnitude beyond HL-LHC projections (Liang et al., 2023).

Coupling extraction utilizes multidimensional likelihood fits to total rates, angular (including $\cos\theta$, $\phi$) distributions, and, where feasible, polarization observables (1901.10218, Božović-Jelisavucić et al., 2022). Several model-independent and effective field theory frameworks are deployed to constrain higher-dimensional operators.

4. Detector and Reconstruction Requirements

The detector and reconstruction strategy for a Higgs factory is tightly coupled to physics goals:

• Vertexing: impact parameter resolution at the few-$\mu$m level for $b/c$ tagging, crucial for $H \to b\bar{b}$, $c\bar{c}$ separation (Liang et al., 2023).
• Tracking: CMOS MAPS, low-mass structures, and TPCs for minimal multiple scattering and high $p_T$ resolution ($\sigma_{p_T}/p_T^2 \sim 2$–$3\times10^{-5}$ GeV$^{-1}$) (Wang et al., 11 Nov 2024).
• Calorimetry: fine-grained ($1\times 1$ cm$^2$ ECAL, $2\times 2$ cm$^2$ HCAL), 30–50 layers, time resolution $\sigma_t\lesssim 100$ ps ("5D" calorimetry) to minimize confusion and double-counting (Wang et al., 11 Nov 2024).
• Particle identification: MRPC-based time-of-flight systems with $<35$ ps for full barrel coverage, enabling $\pi/K$ separation up to $\sim$3 GeV/c; TPC $dE/dx$ for charged hadron PID (Sun et al., 2023).
• Jet clustering and origin identification: graph neural network algorithms (e.g., ParticleNet-style), flavor tagging ($b$, $c$, $s$) with efficiencies $67$–$92\%$ and mis-ID (jet-charge flip) rates $7$–$24\%$ (Liang et al., 2023).
• One-to-one correspondence reconstruction ("1-1 correspondence," Editor's term) with transformer-based classifiers achieves $>90\%$ visible energy mapping, $97$–$99\%$ per-particle identification for charged tracks and $\sim75\%$ for neutral hadrons, improving hadronic Higgs mass resolution by $25\%$ and enhancing discovery power for invisible/exotic decays by up to a factor two (Wang et al., 11 Nov 2024).
• Full event reconstruction leverages advanced particle flow algorithms, high-throughput front-ends, multi-level calibrations and real-time ML in the data stream.

These detector requirements guarantee statistical and systematic uncertainties are kept at or below the percent level, robustly supporting the ambitious physics agenda (Agapov et al., 2022, Black et al., 2022).

5. Accelerator Physics, Staging, and Technology Drivers

Beam properties are dictated by the luminosity and precision requirements:

• Circular machines: $\sim$50–100 km circumference, top-up injection at full energy, ultra-low emittance beam optics ($\epsilon_y\sim1$ pm-rad), final focus $\beta^*_y\sim 1$ mm, beam currents up to 25 mA, bunch populations typically $O(10^{11})$, 200–250 bunches per beam (Agapov et al., 2022).
• Synchrotron radiation loss per turn at $E$ (in GeV) and arc radius $R$ (in m): $U_0 \sim 88.5 \frac{E^4}{R}$ MeV, imposing a tradeoff between energy reach, ring size, and power ($P_{SR}\sim100$–300 MW).
• Top-up injection maintains quasi-constant luminosity in the face of short ($\sim$20 min) beam lifetimes at high energy.
• Linear colliders: gradient in SCRF $\sim$31.5 MV/m (ILC), 72 MV/m in X-band (CLIC), or up to 1 GV/m for PWFAs (HALHF), normalized emittance $\epsilon_n\,(\mu\text{m})\sim 5$–30, beamspot at IP $\sim$nm scale, train repetition up to 5–50 Hz, bunch charge $\sim 2\times 10^{10}$ (Lindstrøm et al., 27 May 2025, Agapov et al., 2022).
• HALHF and similar advanced concepts utilize multi-stage PWFAs for electrons (gradient $1$ GV/m, 48 stages) and $3$ GHz Cu-LN$_2$-cooled RF linacs for positrons (40 MV/m), with asymmetrical energies and bunch charges to optimize both cost and wall-plug efficiency. The design supports modular upgrades to higher $\sqrt{s}$ (Lindstrøm et al., 27 May 2025).
• Key R&D includes high-Q$_0$ SCRF, high-power klystrons ($>80\%$), precision timing and alignment for plasma stages ($<10$ fs, $O(100~\mathrm{nm})$), and industrialization of large-area, high-granularity detector modules (List, 2023).

Typical staging sequences include initial Z-pole ($\sqrt{s}=91$ GeV, Tera-Z), WW threshold ($\sqrt{s}\approx160$ GeV), followed by the Higgs factory ($\sqrt{s}=240$–250 GeV), then top threshold ($\sqrt{s}=350$–380 GeV) and multi-TeV upgrades for BSM searches (List, 2023).

6. Projected Sensitivities: BSM, CPV, and Rare Decays

Sensitivity studies consistently show that sub-percent measurements of $g_{HZZ}$ and $g_{HWW}$ at future $e^+e^-$ factories can resolve indirect BSM effects from radiative corrections at 0.5–2% level, covering phase transition scenarios in 2HDM, singlet-extended models, composite Higgs, and top partner loops that evade LHC signatures (Anisha et al., 23 Jun 2025, An et al., 2018).

• In a dimension-6 EFT framework, $\Lambda/\sqrt{c}\gtrsim$ few TeV is reached for $HZZ$ operators using the $e^+e^-\to ZH$ total cross section and angular spectra. Bounds for anomalous couplings $|g_3'|\lesssim 10^{-2}$, $|g_1|\lesssim 10^{-2}$, and for CP-odd $\tilde g$ to a few$\times 10^{-2}$, vastly exceeding LHC limits (1901.10218).
• CP properties can be probed via $h\to\tau^+\tau^-$ azimuthal correlations (measurement of mixing angle $\varphi$ to $75$ mrad, constraining $|\tan\varphi|<0.08$) and in $ZZ$-fusion at high energy ($\psi_{CP}$ in $HZZ$ coupling to a few degrees), restricting anomalous form factors to $10^{-2}$–$10^{-3}$ (Božović-Jelisavucić et al., 2022).
• Rare and forbidden decays: Reach for $H\to s\bar s$ at $7.5\times10^{-4}$ (three times the SM prediction), FCNC channels e.g. $H\to sb$ at $2.2\times10^{-4}$; $H\to \text{inv}$ below $0.3\%$ (Liang et al., 2023, An et al., 2018).
• Sensitivity to EW baryogenesis: Precision Higgs and $Z$-pole data will test parameter space for SFOEWPT in 2HDM via one-loop $\sim1\%$ shifts in $e^+e^-\to hZ$, only accessible at sub-percent-level Higgs factories even if LHC and $Z$-pole yields are SM-like (Anisha et al., 23 Jun 2025).

Any measured nonzero deviation above these levels would constitute clear evidence of BSM dynamics in the Higgs sector.

7. Timelines, Sustainability, and Future Evolution

Current generation designs target data-taking windows from the late 2030s (ILC, CEPC) to mid-2040s (FCC-ee, LEP3 fallback) (Anastopoulos et al., 1 Apr 2025). Capital costs lie in the range of \%%%%144$s$145%%%%300$$MW. Environmental and sustainability criteria (construction GWP, power efficiency) are central to design and optimization (<a href="/papers/2311.17472" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">List, 2023</a>, <a href="/papers/2505.21654" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Lindstrøm et al., 27 May 2025</a>).</p> <p>Circular machines are compatible with future upgrades to$$100$ TeV hadron colliders (FCC-hh, SppC, site-filler scenarios), ensuring long-term strategic utility. Linear/plasma designs may be extended to probe multi-TeV scales, and the advanced detector/analysis ecosystem is being co-developed for all architectures, with significant opportunities for international collaboration in software, hardware, and physics research (Black et al., 2022, Faus-Golfe et al., 2022).

Rigorous project timing, funding decisions, and international partnerships remain to be finalized in the next European Strategy and U.S. P5 cycles; R&D in plasma-wakefield, cryogenics, high-luminosity optics, and advanced reconstruction is expected to define technical readiness over the next 5–10 years (Lindstrøm et al., 27 May 2025, Black et al., 2022).

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References:

(An et al., 2018, 1901.10218, Black et al., 2022, Božović-Jelisavucić et al., 2022, Agapov et al., 2022, Faus-Golfe et al., 2022, Liang et al., 2023, List, 2023, Wang et al., 11 Nov 2024, Adli et al., 25 Mar 2025, Anastopoulos et al., 1 Apr 2025, Lindstrøm et al., 27 May 2025, Anisha et al., 23 Jun 2025, Sun et al., 2023)