Tera-Z: Precision & BSM Probes

• Tera-Z Programmes are high-luminosity Z boson runs enabling unprecedented precision in electroweak measurements.
• They integrate innovative accelerator designs and advanced detector technologies to explore rare processes and BSM phenomena with high sensitivity.
• The programmes achieve significant impact through rigorous experimental methods and refined SMEFT operator analyses probing new physics up to 50 TeV.

The Tera-Z Programmes refer to future high-luminosity electron-positron collider runs at the Z boson resonance, notably envisioned for facilities such as FCC-ee and CEPC, where $\mathcal{O}(10^{12})$ Z bosons could be produced. In these programmes, both experimental and theoretical developments support transformative advances in particle physics, encompassing accelerator technology, electroweak precision measurement, flavour physics, and searches for physics Beyond the Standard Model (BSM). Tera-Z runs integrate ambitious technical goals with an indirect quantum probe of the TeV scale, advancing discovery potential for rare Standard Model (SM) processes and BSM phenomena.

1. Accelerator Concepts and High-Gradient Linac Development

The foundational accelerator principle underlying several TERA-Z initiatives is the cyclinac, a hybrid system combining a fast-cycling cyclotron with a high-frequency linear accelerator (linac) to efficiently produce ion beams suitable for hadrontherapy. The TERA collaboration, in partnership with CERN, developed high-gradient test protocols for accelerating structures, notably producing and testing 3 GHz and 5.7 GHz single-cell copper cavities (Amaldi et al., 2012), aiming to minimize linac length for hospital deployment.

Technical benchmarks include:

• Reliable operation of single-cell 3 GHz cavities at $E_{\max}=170$ MV/m peak surface field, equivalent to 35 MV/m on-axis.
• Adherence to stringent breakdown rate (BDR) tolerances required for clinical application: BDR $\le 3\times10^{-6}$ breakdowns per pulse per meter at 2.5 $\mu$s RF pulse length.
• Systematic simulation, precision machining, critical coupling design, and advanced diagnostics to reach thermal and electromagnetic stability, verified in test campaigns comprising $5\times10^7$ RF pulses.

These results cement the technical feasibility of cyclinacs, demonstrating that advanced linac structures can achieve compactness and reliability required for medical accelerators.

2. Quantum Precision and Electroweak Programme at Tera-Z

A central scientific goal of Tera-Z is exploiting extremely large Z samples to reach indirect sensitivity to new physics scales up to tens of TeV via electroweak precision measurements. Precision renormalisation analyses demonstrate that nearly all new BSM states generating dimension-six Standard Model Effective Field Theory (SMEFT) operators affect Z-pole electroweak observables—either directly or via one-loop renormalisation group (RG) evolution—even in scenarios lacking direct tree-level coupling to SM fields (Allwicher et al., 2024). Key features include:

• EWPOs (e.g. $R_b$, $A^b_\mathrm{FB}$, $m_W$, asymmetries, widths) are sensitive to SMEFT operators matched to possible BSM scenarios.
• Both tree-level and loop-level SMEFT operator matching, including detailed one-loop analytic coefficients for linear SM extensions (all scalar and fermion types) (Gargalionis et al., 2024).
• Projected reach: with $\mathcal{O}(1)$ couplings, new physics scales up to $10$–$50$ TeV are probed, and only highly unnatural coupling configurations evade these constraints.

The extreme statistical power of Tera-Z enables detection of loop-level quantum effects that are otherwise inaccessible, providing a nearly universal probe for heavy new physics.

3. Exotic Decays, Flavour Physics, and Rare Processes

With $N_Z\sim10^{12}$, Tera-Z offers a unique window into rare Z decays and rare $B$ hadron processes:

• Sensitivity to branching ratios for rare Z decays (e.g. $Z\to\nu\bar\nu\gamma$) down to $10^{-9}$, reaching SM loop-level predictions, and providing stringent upper bounds on anomalous couplings via EFT parameterisations (Denizli et al., 27 Oct 2025).
• Exotic signatures such as triple $Z'$ production ($Z\to Z'\phi\to Z'Z'Z'$), enabling kinetic mixing $\epsilon\gtrsim10^{-6}$ to be tested in dark photon models, with multi-lepton events well above background (Nomura et al., 2024).
• Measurement of rare neutral $B$ decays ($B^0_{(s)}\to\pi^0\pi^0,\eta\eta$) via advanced ECAL design ($\sigma_E/E=3\%/\sqrt{E/\text{GeV}}\oplus0.3\%$), achieving $0.45\%$ branching ratio sensitivity for $B^0\to\pi^0\pi^0$ (Wang et al., 2022). This unlocks sub-degree CKM angle ($\alpha$) resolution critical for unitarity triangle fits.
• Precision extraction of the electromagnetic coupling $\alpha_{em}(m_Z^2)$ at the $10^{-5}$ level using angular lepton distributions, surpassing previous limitations arising from hadronic vacuum polarization uncertainties and directly supporting EWPO accuracy (Riembau, 9 Jan 2025).

These rare process measurements, often background-free at high $N_Z$, represent definitive probes for new physics and constraints on SM parameters.

4. BSM Probes: ALPs, SUSY, WIMPs, and Dark Matter

Tera-Z facilities are expected to provide comprehensive coverage for a range of key BSM models:

• Axion-like particles (ALPs)—Tera-Z and Higgs factories robustly exclude or discover ALP solutions to the muon $g-2$ anomaly for masses up to $85$ GeV (Z pole) and $160$ GeV (Higgs factory), via multi-photon and multi-lepton final states (Liu et al., 2022, Cacciapaglia et al., 2021). Projected sensitivity encompasses parameter space required by $(g-2)_\mu$ measurements.
• Natural SUSY—FCC-ee Tera-Z can probe stops and heavy Higgs masses well beyond the reach of LHC/HL-LHC, provided SM theory uncertainties are commensurate with experimental precision (Greljo et al., 3 Jul 2025). Observables like $R_b$, $S$, $T$, $W$, $Y$ reach unprecedented accuracy.
• Weakly Interacting Massive Particles (WIMPs) and quantum extensions—Indirect probes at Tera-Z can match or surpass sensitivity at higher energies for models contributing to oblique or Higgs-sector SMEFT operators via loop effects (Maura et al., 2024).
• Dark matter with t-channel mediators—Tera-Z enables powerful indirect discrimination and exclusion of DM portal models inaccessible to direct and indirect detection, especially in leptophilic and coannihilating cases. EWPO correlation patterns allow model differentiation even when DD/ID is absent (Olgoso et al., 23 Jul 2025).

The combination of rare process rates, ultra-precise EWPOs, and quantum sensitivity anticipates or exceeds the reach of high-energy runs, making Tera-Z an indispensable component for BSM discovery.

5. Theoretical and Experimental Synergy

The success of Tera-Z rests on simultaneous advances in experimental techniques, theoretical precision, and computational tools:

• Monte Carlo event generation, advanced showering, and fast detector simulation (e.g., MadGraph, Pythia, Delphes) are integral to extracting SM and BSM signals at projected luminosities (Denizli et al., 27 Oct 2025, Ali et al., 2018).
• SMEFT analytic matching and operator mapping, automated via public computational packages, ensure that EWPO constraints are interpreted robustly and comprehensively (Gargalionis et al., 2024).
• Detector design, notably in ECAL energy resolution, photon separation power, and $b$-tagging efficiency, is essential for realizing physics goals in rare decay and flavour sectors (Wang et al., 2022).

This synergy enables systematic and thorough exploration of the quantum and flavour frontiers, with Tera-Z data driving progress in both experiment and theory.

6. Scientific Outlook and Broader Impact

The Tera-Z Programmes redefine the LEP paradigm by combining extreme accuracy with innovative accelerator development and theoretical interpretation:

• Z-pole precision tests extend the scope of quantum exploration of the TeV scale, covering nearly all heavy new physics matching to SMEFT at tree or loop level (Allwicher et al., 2024, Gargalionis et al., 2024).
• Operator- and model-based analyses—combining on-pole and off-pole measurements—close parameter space for a diverse set of BSM scenarios, revealing complementarity or superiority over energy-frontier approaches (Maura et al., 2024).
• Discovery, constraint, and model discrimination for BSM physics, including validation or exclusion of theories such as Little Higgs models (Guo et al., 2013), axion models, SUSY, and various DM portals.
• Advances in accelerator technology (cyclinac, high-gradient linacs) feed directly into medical physics and broader accelerator applications.

In sum, Tera-Z runs uniquely complement and enhance energy-frontier physics, making them essential to the future collider landscape and the full exploitation of the quantum and precision frontiers.