New Particles at the Z-Pole: Tera-Z factories as discovery and precision machines

TL;DR

The paper addresses the potential of future Z-pole factories to discover and study light long-lived particles (LLPs) by producing vast numbers of Z-bosons, encapsulating the production and decay physics in a compact, analytic EFT-like framework with small parameters $\varepsilon_{\rm pro}$ and $\varepsilon_{\rm dec}$. It develops general formulas for the observable LLP yield $N_{\rm obs}$ as a function of $N_Z$, detector geometry, and lifetimes, and identifies the dominant limitations from integrated luminosity, detector size, and backgrounds. The authors illustrate the approach with two benchmark LLPs—heavy neutral leptons and axion-like particles—demonstrating discovery reach well beyond HL-LHC and the potential for percent-level measurements of decay patterns, thereby turning Tera-Z factories into both exotics factories and precision probes of new physics. While inherently approximate, the analytic framework captures the correct scaling and provides fast, design-iteration insights. A public code is provided to generate sensitivity curves for various models, enabling rapid exploration of detector configurations and LLP parameter spaces.

Abstract

Several proposed future lepton colliders are capable of producing trillions of Z-bosons, including FCC-ee, CEPC, LEP3 and LEP-Z. Such Tera-Z factories can discover new elementary particles with couplings to the Z-boson that are orders of magnitude smaller than current bounds. For couplings near the currently excluded parameter regions they could produce sufficiently large samples to study the new particles' properties in detail, hence acting as a discovery and precision machine in one. Using simple analytic estimates, we quantify the dependence of the expected event yield in long-lived particle searches on the number of produced Z-bosons and on the detector dimensions. From this, we derive estimates for both the discovery reach and the measurement precision attainable at such facilities. While the precision of such estimates of course falls short of proper simulations, the analytic approach is suitable for a quick assessment of the sensitivity for a given design. We illustrate this with two examples, heavy neutral leptons and axion-like particles. Under optimistic assumptions, these could be produced in the millions and billions, respectively, effectively turning future lepton colliders into exotics factories. We provide a code that quickly generates the sensitivity curves displayed in this work and can be extended to other models at https://github.com/liyuanzhen98/LLPatTeraZ.

Figures (7)

• Figure 1: Left: Production of an LLP $X$ along with $\mathcal{A}_\alpha$. Right: Subsequent decay of $X$ into a multiparticle state $\mathcal{B}_\beta$.
• Figure 2: Left: Feynman diagram representing the HNL production from the decay of an on-shell Z-boson. Right: Feynman diagram symbolically summarising the various HNL decay channels mediated by both the neutral current \ref{['HNLdecaysNC']} and charged current \ref{['HNLdecaysCC']}, here represented by a four-fermion interaction because the gauge boson is off-shell.
• Figure 3: The dashed lines represent the expected total number of HNL decays inside a cylindrical fiducial volume of diameter $d_{\rm cyl}=10$ m and length $l_{\rm cyl}=8.6$ m with $N_Z = 6\times 10^{12}$ and $U^2=U_\mu^2$, as obtained from \ref{['NobsGeneral']}. We set $l_0 = 0$ to emphasise the fact that any event inside the fiducial volume can in principle be observed. The green line is based on \ref{['Kenny2']} and indicates the regime in which more than $N_{\rm min}=4$ events with displacements exceeding $l_0 = 400 \, \mu$m are expected, a cut which we assume to remove most SM backgrounds. The red and blue lines indicate the corresponding limitations coming from the integrated luminosity and the detector dimensions for $N_{\rm min}=4$, based on \ref{['Kenny']} and \ref{['Methusalix']}, respectively. The gray shaded areas represent the parameter regions excluded by experimental searches Abdullahi:2022jlv and big bang nucleosynthesis Boyarsky:2020dzc. The brown band represents the seesaw floor\ref{['seesaw']}, its width indicates the uncertainty in this lower bound when varying the sum of SM neutrino masses between the lowest possible value consistent with oscillation data Esteban:2024eli and the upper bound from Planck observations Planck:2018vyg. Heavy neutrinos with masses and mixings anywhere in the white region above this lower bound can simultaneously explain the light neutrino masses and the matter-antimatter asymmetry of the universe for technically natural parameter choices Drewes:2021nqr. A significant fraction of the wedge between the blue line, the seesaw floor and the BBN-disfavoured region can be explored with fixed target experiments or additional detectors at the LHC or future colliders Beacham:2019nyxAgrawal:2021dbo; the most sensitive approved experiments are the near detector of DUNE DUNE:2015lolDUNE:2020ypp and SHiP SHiP:2015vadAlekhin:2015byhSHiP:2025ows.
• Figure 4: The dashed lines indicate the integrated luminosity for which $N_{\rm min}=4$ HNL decays are expected within the fiducial volume, with all other parameter choices as in Fig. \ref{['fig:HNLdiscovery1']}. The colourful lines represent the reach that could be achieved with the numbers given in table \ref{['tab:NZ']}, reflecting the current planning for several proposed Tera-Z factories.
• Figure 5: The dashed lines indicate the precision at which the branching ratios in HNL decays can be measured based on \ref{['HNLprecision']} with $l_0 = 400 \mu m$ and all other parameters as in Fig. \ref{['fig:HNLdiscovery1']}. In the upper panel we assume a ratio $U_e^2:U_\mu^2:U_\tau^2 = 1:1:1$, in the lower panel we assume $U_e^2:U_\mu^2:U_\tau^2 = 2 : 199 : 199$. The former is favoured for an inverted ordering of the light neutrino masses, the latter for a normal ordering, cf. Drewes:2022akb and references therein.