⚛️ phenomenology

Probing Lepton Flavor Violation at FCC-ee

This paper demonstrates that the FCC-ee's high-statistics $Z$ -pole run will significantly enhance sensitivity to lepton flavor violation in $\tau$ decays, often surpassing the reach of direct $Z \to \tau\ell$ and $h \to \tau\ell$ searches for various SMEFT operators, particularly semileptonic ones.

Original authors: L. Allwicher, R. Bartocci, M. Cepeda, C. Cornella, L. P. S. Leal, A. Lusiani, C. Martin Perez, P. Paradisi, E. Scantamburlo, O. Sumensari

Published 2026-10-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: L. Allwicher, R. Bartocci, M. Cepeda, C. Cornella, L. P. S. Leal, A. Lusiani, C. Martin Perez, P. Paradisi, E. Scantamburlo, O. Sumensari

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the universe of particle physics, there is a set of rules that governs how the smallest building blocks of matter interact. One of these rules, deeply embedded in the Standard Model, is that a specific type of particle called a lepton should never change its family identity. There are three families: electrons, muons, and tau particles. Under normal circumstances, a tau particle should decay into other particles while staying true to its own family line, never turning into an electron or a muon. This conservation of family identity is so strict that if a tau were to suddenly transform into a lighter cousin, it would be a clear signal that the known laws of physics are incomplete. Such an event, known as lepton flavor violation, has never been observed, yet many theories about the universe suggest it should happen, just very rarely. Finding it would be like discovering a new continent on a map that was thought to be fully explored, pointing directly to the existence of new, undiscovered forces or particles.

Scientists are preparing for a future machine called the FCC-ee, a massive circular collider designed to produce an unprecedented number of particles. In its initial phase, this machine will act as a "Z-pole" factory, creating roughly 6 trillion Z bosons. Because the Z boson frequently decays into pairs of tau particles, this run is expected to generate about 200 billion tau-lepton pairs. This sheer volume of data offers a unique opportunity to hunt for those rare, forbidden transformations. Researchers have used a theoretical framework called the Standard Model Effective Field Theory to predict what might happen if new physics exists at energy scales far beyond what current machines can directly reach. They asked a specific question: if new physics is hiding in the tau sector, will looking for the rare decay of a tau particle into an electron or muon be a better way to find it than looking for the Z boson or the Higgs boson to decay into these same forbidden combinations?

The researchers found that for the search involving the Z boson, the answer is a decisive yes. While the FCC-ee will be incredibly powerful at spotting a Z boson turning into a tau and a lighter lepton, the direct decay of the tau particle itself is an even more sensitive probe. The study shows that by watching how the tau particles decay, scientists can set limits on new physics that are significantly tighter than those obtained by watching the Z boson decay. In fact, for certain types of interactions, the tau decay channel is so sensitive that it can probe energy scales hundreds of times higher than the direct Z boson search. This is because the tau decay process is influenced by a wider variety of theoretical interactions, and the massive number of tau particles available at the FCC-ee allows these subtle effects to be detected with great precision. The team calculated that the FCC-ee could improve current limits on these tau decays by factors ranging from 30 to 800, depending on the specific channel, making it the most powerful tool for this specific type of search.

The situation is more nuanced when it comes to the Higgs boson, the particle responsible for giving mass to other particles. If the new physics directly alters how the Higgs interacts with tau particles, then looking for the Higgs to decay into a tau and a lighter lepton is the most effective method. In this specific scenario, the direct observation of the Higgs decay provides the strongest constraints. However, the researchers discovered that this hierarchy is not absolute. If the new physics involves interactions with quarks that only indirectly cause the Higgs to decay into a tau and a lighter lepton, the situation flips. In these cases, the indirect effects show up much more strongly in the tau decays themselves. Consequently, watching the tau particles break apart becomes the leading way to detect these specific types of new physics, surpassing the sensitivity of the direct Higgs search.

This work suggests that a dedicated program to study tau-lepton decays at the FCC-ee is essential. It is not enough to simply look at the Z and Higgs bosons; the tau particles themselves hold the key to a broader range of potential discoveries. The study indicates that these decays can test new physics that is completely out of reach for the Z boson searches and, in some specific theoretical scenarios, even outperform the Higgs searches. While the projections rely on simulations and extrapolations that will need to be confirmed with detailed detector studies, the potential gain in sensitivity is substantial. The findings provide a strong motivation for experimentalists to refine their plans for observing these rare events, ensuring that when the FCC-ee begins its run, it is fully prepared to catch the faintest whisper of a tau particle breaking the rules of the Standard Model.

Technical Summary: Probing Lepton Flavor Violation at FCC-ee

Problem Statement
Lepton Flavor Violation (LFV) is forbidden in the Standard Model (SM) due to accidental global symmetries, though neutrino oscillations imply these symmetries are broken. However, charged LFV processes induced by light neutrino masses are suppressed by factors of $m_\nu^2/m_W^2$ , rendering them unobservable. Consequently, any observation of charged LFV would constitute unambiguous evidence of new physics (NP). While current constraints are strongest in the muon sector (e.g., $\mu \to e\gamma$ ), scenarios with hierarchical couplings involving third-generation leptons can weaken these bounds, making $\tau$ -lepton processes complementary or leading probes. Future high-luminosity $e^+e^-$ colliders, specifically the FCC-ee operating at the Z-pole (Tera-Z run) and at $\sqrt{s} = 240$ GeV, offer unprecedented statistics ( $\sim 2 \times 10^{11}$ $\tau$ pairs and $\sim 10^6$ Higgs bosons). Previous studies of LFV at these facilities have focused primarily on $Z \to \tau\ell$ and $h \to \tau\ell$ decays. This paper investigates whether direct searches for LFV $\tau$ decays ( $\tau \to \ell\gamma$ and $\tau \to 3\ell$ ) at the same facility can provide comparable or superior sensitivity to the underlying SMEFT operators.

Methodology
The authors analyze the reach of LFV searches at FCC-ee within the Standard Model Effective Field Theory (SMEFT) framework, assuming NP scales $\Lambda$ well above the electroweak scale.

Framework: The analysis utilizes the Warsaw basis of dimension-six operators, focusing on four classes: dipole operators ( $\psi^2 X H$ ), Higgs-current operators ( $\psi^2 H^2 D$ ), Yukawa-like operators ( $\psi^2 H^3$ ), and four-fermion operators ( $\psi^4$ ).
Renormalization Group (RG) Evolution: Wilson coefficients are evolved from a high scale $\Lambda$ (set to 10 TeV) down to the electroweak scale using one-loop RG equations. The SMEFT is then matched onto the Low-Energy Effective Field Theory (LEFT), where heavy degrees of freedom ( $W, Z, h, t$ ) are integrated out. For $\tau$ decays, coefficients are further evolved to the $\tau$ mass scale.
Correlations: The study maps the projected experimental sensitivities of various channels onto the SMEFT Wilson coefficients. It explicitly calculates the correlations between:
- $Z \to \tau\ell$ and $\tau \to \ell\gamma, \tau \to 3\ell$ .
- $h \to \tau\ell$ and $\tau \to \ell\gamma, \tau \to 3\ell$ .
Experimental Inputs: The analysis incorporates current bounds and future projections for Belle II, the HL-LHC, and FCC-ee. The FCC-ee projections for $\tau \to \ell\gamma$ and $\tau \to 3\ell$ are based on existing dedicated studies and fast simulations, while $Z \to \tau\ell$ and $h \to \tau\ell$ sensitivities are reassessed using updated reconstruction performance and statistical scaling assumptions.

Key Contributions and Results
The paper compares the sensitivity of $\tau$ decays against direct $Z$ and Higgs boson decay searches for specific SMEFT operators:

LFV Z Interactions vs. $\tau$ Decays:
- For operators contributing to $Z \to \tau\ell$ at tree level (Higgs-current operators $O_{Hl}^{(1,3)}, O_{He}$ and dipole operators $O_{eB}, O_{eW}$ ), $\tau$ decays provide significantly stronger constraints than direct $Z \to \tau\ell$ searches.
- Specifically, for dipole operators, $\tau \to \mu\gamma$ probes scales of $\mathcal{O}(10^3)$ TeV, whereas direct $Z \to \tau\mu$ searches at FCC-ee only reach $\mathcal{O}(20)$ TeV.
- For Higgs-current operators, $\tau \to 3\mu$ probes scales of $\sim 40$ TeV compared to $\sim 25$ TeV for $Z \to \tau\mu$ .
- For four-lepton operators ( $O_{ll}, O_{ee}, O_{le}$ ), which contribute to $\tau \to 3\ell$ at tree level but only induce $Z \to \tau\ell$ via loop mixing, $\tau$ decays offer the leading constraint.
- Conclusion: Even with the projected four-order-of-magnitude improvement in $Z \to \tau\ell$ sensitivity at FCC-ee, rare $\tau$ decays remain the most sensitive probes for the same underlying interactions.
LFV Higgs Interactions vs. $\tau$ Decays:
- Yukawa-like Operators ( $O_{eH}$ ): For operators that modify SM Yukawa couplings at tree level, direct searches for $h \to \tau\mu$ provide the strongest sensitivity. The contribution to $\tau \to \mu\gamma$ arises from loop effects, including the Barr-Zee contribution and two-loop RG mixing, suppressing the $\tau$ decay rate relative to the Higgs decay. At FCC-ee, $h \to \tau\mu$ probes $\Lambda \approx 11$ TeV, while $\tau \to \mu\gamma$ probes only $\approx 4.5$ TeV.
- Semileptonic Operators ( $O_{lequ}^{(1)}, O_{ledq}$ ): For operators that generate LFV Higgs couplings only radiatively (via RG mixing), the hierarchy reverses. $\tau$ decays become the leading probe. For $O_{lequ}^{(1)}$ , $\tau \to \mu\gamma$ and $\tau \to 3\mu$ at FCC-ee probe scales of $\sim 55$ TeV and $\sim 29$ TeV, respectively, compared to $\sim 8$ TeV for $h \to \tau\mu$ .

Significance and Claims
The authors claim that their analysis fundamentally alters the perspective on LFV searches at future $e^+e^-$ colliders. While previous literature emphasized $Z$ and Higgs decays, this work demonstrates that:

$\tau$ decays are superior for Z-sector physics: They offer stronger constraints on $Z \to \tau\ell$ interactions and probe a broader range of SMEFT operators (including four-fermion operators) than direct $Z$ searches.
Hierarchy depends on operator structure: The relative sensitivity between Higgs decays and $\tau$ decays is not generic. While direct Higgs searches dominate for tree-level Yukawa modifications, $\tau$ decays become the leading probe for operators that induce Higgs LFV only through radiative corrections.
Motivation for dedicated programs: The results strengthen the case for a dedicated LFV program in the $\tau$ -lepton sector at FCC-ee. The projected improvements (factors of 30 to 800 over current limits for $\tau$ branching fractions) suggest these processes can test new physics beyond the reach of LFV $Z$ searches and, in specific operator scenarios, beyond LFV Higgs searches.

The paper concludes that these encouraging prospects motivate detailed Monte Carlo simulations to confirm the projected sensitivities and further studies of complementary probes, such as hadronic $\tau$ decays.

More like this