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Lepton flavor violation by three units
The conservation of lepton flavor is a prediction of the Standard Model and is still an excellent approximate symmetry despite our observation of neutrino oscillations. Lepton flavor violation by one or two units has been discussed for decades, with several dedicated experiments exploring the vast model landscape but no discoveries so far. Here, we explore operators and processes that violate at least one lepton flavor by three units and identify testable signatures. In the Standard Model effective field theory, such operators already arise at mass dimension 7 and can be tested through their contributions to Michel parameters in leptonic decays. True neutrinoless charged-lepton flavor violation arises at mass dimension 10 and can realistically only be seen in the tau decay channels 𝜏 → $𝑒𝑒𝑒\bar{𝜇}\bar{𝜇}$ or 𝜏 → $𝜇𝜇𝜇\bar{𝑒}\bar{𝑒}$, for example in Belle II. Testable rates for these tau decays require light new particles and subsequently predict an avalanche of remarkably clean but so-far unconstrained collider signatures.
Lepton flavor violation: From muon decays to muon colliders
We investigate the unique potential of a high-energy muon collider to probe lepton-flavor-violating signals arising from physics beyond the Standard Model (SM). Low-energy, precision searches for charged lepton flavor violation (LFV) are projected to dramatically improve their sensitivity in the coming years and could provide the first evidence of new physics. We interpret the sensitivity of these searches in terms of a set of LFV operators in the SM effective field theory. The same operators are then probed at the TeV scale via new, high-energy processes only available at a high-energy muon collider, such as 𝜇𝜇 → 𝜇𝜏 or the scattering of a muon of an electroweak gauge boson into LFV final states. We find that, for most operators, a muon collider could confirm signals if they are seen at future low-energy experiments, whereas for certain flavor combinations it extends the reach to scales well beyond those accessible at lower energies. We also project the sensitivity of a muon collider to lepton-flavor-violating decays of the SM Higgs boson and demonstrate improved sensitivity to ℎ → 𝑒𝜏 and ℎ → 𝜇𝜏 by an order of magnitude compared to the High-Luminosity LHC. The importance of having multiple, complementary probes is illustrated by considering both various combinations of operators and relative sizes of flavor-violating transitions between generations under various assumptions for the flavor structure of new physics.
General signals for charged lepton flavor violating decays
We explore the most general phenomenology of charged lepton flavor violating (CLFV) decays of muon and tau leptons to the three body final states ($\bar{e}ee, \bar{μ}μμ, \bar{e}μμ, \bar{μ}μe, \bar{μ}ee, \bar{e}eμ$). By constructing a complete basis of operators at each dimension, we derive the most general amplitudes for these decay processes. By considering constraints from unitarity and Large Electron-Positron Collider (LEP), we show that operators of mass dimension 6 and 7 are the most likely to be observed in next generation experiments. Focusing on these dimensions, we compute the results of unpolarized (spin-averaged) decays parametrized in terms of the invariant masses of the daughter particles. We also compute the differential decay rates for polarized decays, in anticipation of the experimental search Mu3e, which expects to have a muon beam with ∼ 90% polarization, and the chiral Belle proposal, which aims to have a 70% polarized electron beam. To determine the extent to which the operators may be distinguished experimentally, we plot the differential distributions for each operator, showing that they leave only a few possible degenerate explanations. Through a statistical analysis, we estimate the number of events needed to break the degeneracies using the angular information. These results are adapted to treat ℓ → ℓ′$v\bar{v}$, where the angular distribution of the outgoing charged lepton has enhanced distinguishing power. With many Standard Model extensions predicting these CLFV decays, these results will better enable upcoming searches to identify and/or constrain physics beyond the Standard Model.
Charged Lepton Flavor Violating Experiments with Muons
We report on the status of charged lepton flavor violating (CLFV) experiments with muons. We focus on the three "golden channels": $\mu^{+} \rightarrow e^{+} \gamma$, $\mu^{+} \rightarrow e^{+} e^{-} e^{+}$ and $\mu^{-} N \rightarrow e^{-} N$. The collection of upcoming experiments aim for sensitivity improvements up to $10^{4}$ with respect to previous searches. The MEG II experiment, searching for $\mu^{+} \rightarrow e^{+} \gamma$, is currently in its 4th year of physics data-taking with a published result from its first year of data. The Mu3e experiment is an upcoming experiment searching for $\mu^{+} \rightarrow e^{+} e^{-} e^{+}$ with plans of physics data-taking as soon as 2025. The Mu2e and COMET experiments are upcoming searches for $\mu^{-} N \rightarrow e^{-} N$ with the goal of physics data-taking starting in 2027 and 2026 respectively. This proceeding summarizes the signal signature, expected background, resolutions, and timelines for the mentioned searches.
Crystal Calorimetry for Charged Lepton Flavor Violation Searches
The Mu2e experiment at Fermilab aims to search for Charged Lepton Flavor Violation (CLFV) through the coherent conversion of a muon into an electron in the field of an aluminum nucleus. This process, highly suppressed in the Standard Model, would clearly indicate new physics if observed. A crucial component of Mu2e is its electromagnetic calorimeter, which enhances the identification and measurement of conversion electrons. The calorimeter consists of two disks of undoped CsI crystals read out by custom-designed SiPMs and fast front-end electronics. This paper presents an overview of the calorimeter’s design, its custom SiPM technology, the readout and data acquisition system, and the results from commissioning tests.Building on the experience from Mu2e, the proposed Mu2e-II upgrade aims to enhance further the experiment’s sensitivity by an order of magnitude. This requires significant advancements in calorimeter technology, particularly in crystal materials and photodetector performance. Studies on BaF$_2$ and LYSO crystals, as well as the development of radiation-hard Silicon Photomultipliers (SiPMs), are currently underway. Test beam results demonstrate promising improvements in energy resolution and timing capabilities, ensuring the feasibility of next-generation calorimetry solutions for Mu2e-II.
Search for lepton-flavor-violating tau decays to ℓα at Belle
We report a search for the lepton-flavor-violating decays τ ± → ℓ ± α (ℓ = e, μ), where α is an undetected spin-0 particle, such as an axion-like particle using 736 × 10 6 tau lepton pairs collected by the Belle detector at the KEKB asymmetric-energy e + e − collider. We find no evidence of signal and obtain the most stringent upper limits on the branching fractions at 95% confidence level: $\mathcal{B}$ (τ ± → e ± α) < (0.4–6.4) × 10 −4 and $\mathcal{B}$ (τ ± → μ ± α) < (0.2–3.5) × 10 −4 at 95% confidence level for an α mass in the range 0.0 ≤ m α ≤ 1.6 GeV/c 2 .
Distinguishing Charged Lepton Flavor Violation Scenarios with Inelastic 𝜇 → 𝑒 Conversion
The Mu2e and COMET experiments are expected to improve existing limits on charged lepton flavor violation (CLFV) by roughly 4 orders of magnitude. 𝜇 → 𝑒 conversion experiments are typically optimized for electrons produced without nuclear excitation, as this maximizes the electron energy and minimizes backgrounds from the free decay of the muon. Here we argue that Mu2e and COMET will be able to extract additional constraints on CLFV from inelastic 𝜇 → 𝑒 conversion, given the 27 Al target they have chosen and backgrounds they anticipate. We describe CLFV scenarios in which inelastic CLFV can induce measurable distortions in the near-endpoint spectrum of conversion electrons, including cases where certain contributing operators cannot be probed in elastic 𝜇 → 𝑒 conversion. We extend the nonrelativistic EFT treatment of elastic 𝜇 → 𝑒 conversion to include the new nuclear operators needed for the inelastic process, evaluate the associated nuclear response functions, and describe several new-physics scenarios where the inelastic process can provide additional information on CLFV.
Search for the lepton-flavor-violating τ − → e ∓ ℓ ± ℓ − decays at Belle II
We present the result of a search for the charged-lepton-flavor violating decays τ − → e ∓ ℓ ± ℓ − , where ℓ is a muon or an electron, using a data sample with an integrated luminosity of 428 fb −1 recorded by the Belle II experiment at the SuperKEKB e + e − collider. The selection of e + e − → τ + τ − events containing a signal candidate is based on an inclusive-tagging reconstruction and on a boosted decision tree to suppress background. Upper limits on the branching fractions between 1.3 and 2.5 × 10 −8 are set at the 90% confidence level. These results are the most stringent bounds to date for four of the modes.
Search for charged lepton flavor violating 𝑍 and 𝑍′ boson decays in proton-proton collisions at $\sqrt{s}$ = 13 TeV
A search for flavor violating decays of the 𝑍 boson to charged leptons is performed using data from proton-proton collisions at $\sqrt{s}$ =13 TeV collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb −1 . Each of the decays 𝑍 → 𝑒𝜇, 𝑍 → 𝑒𝜏, and 𝑍 → 𝜇𝜏 is considered. The data are consistent with the backgrounds expected from standard model processes. For the 𝑍 → 𝑒𝜇 channel the observed (expected) 95% confidence level upper limit on the branching fraction is 1.9(2.0) × 10 −7 , which is the most stringent direct limit to date on this process; the corresponding limits for the 𝑍 → 𝑒𝜏 and 𝑍 → 𝜇𝜏 channels are 13.8(11.4) × 10 −6 and 12.0(5.3) × 10 −6 , respectively. Additionally, the 𝑒𝜇 final state is used to search for lepton flavor violating decays of 𝑍′ resonances in the mass range from 110 to 500 GeV. No significant excess is observed above the predicted background levels.
Lepton-flavor-violating ALP signals with TeV-scale muon beams
We explore the feasibility of using TeV-energy muons to probe lepton-flavor-violating (LFV) processes mediated by an axion-like particle (ALP) a with mass O(10 GeV). We focus on µτ LFV interactions and assume that the ALP is coupled to a dark state χ, which can be either less or more massive than a. Such a setup is demonstrated to be consistent with χ being a candidate for dark matter, in the experimentally relevant regime of parameters. We consider the currently operating NA64-µ experiment and proposed FASERν2 detector as both the target and the detector for the process µA → τA a, where A is the target nucleus. We also show that a possible future active muon fixed-target experiment operating at a 3 TeV muon collider or in its preparatory phase can provide an impressive reach for the LFV process considered, with future FASERν2 data providing a pilot study towards that goal. The implications of the muon anomalous magnetic moment (g - 2) µ measurements for the underlying model, in case of a positive signal, are also examined, and a sample UV completion is outlined.
Search for lepton-flavor-violating ${\tau }^{-}\to {{\ell}}^{-}{K}_{s}^{0}$ decays at Belle and Belle II
We present the results of a search for charged-lepton-flavor violating decays ${\tau }^{-}\to {{\ell}}^{-}{K}_{s}^{0}$, where ℓ − is either an electron or a muon. We combine e + e − data samples recorded by the Belle II experiment at the SuperKEKB collider (428 fb −1 ) with samples recorded by the Belle experiment at the KEKB collider (980 fb −1 ) to obtain a sample of 1.3 billion e + e − → τ + τ − events. We observe 0 and 1 events and set 90% confidence level upper limits of 0.8 × 10 −8 and 1.2 × 10 −8 on the branching fractions of the decay modes ${\tau }^{-}\to {e}^{-}{K}_{S}^{0}$ and ${\tau }^{-}\to {\mu }^{-}{K}_{S}^{0}$, respectively. These are the most stringent upper limits to date.
Search for Lepton-Flavor-Violating Decay Modes 𝐵 0 →𝐾$^0_𝑆$𝜏 ± ℓ ∓ with Hadronic 𝐵 Tagging at Belle and Belle II
We present the first search for the lepton-flavor-violating decay modes 𝐵 0 →𝐾$^0_𝑆$𝜏 ± ℓ ∓ (ℓ=𝜇,𝑒) using the 711 and 365 fb −1 data samples recorded by the Belle and Belle II detectors, respectively. We use a hadronic 𝐵-tagging technique to fully reconstruct a 𝐵 meson and search for signal decays in the system recoiling against the tagged meson, considering 𝜏 decays to either light leptons, one charged hadron, or one charged hadron and a neutral pion. We find no evidence for 𝐵 0 →𝐾$^0_𝑆$𝜏 ± ℓ ∓ decays and set 90% confidence level upper limits on the branching fractions in the range of [0.8,3.6] ×10 −5 .
Search for charged-lepton flavor violation in the production and decay of top quarks using trilepton final states in proton-proton collisions at $\sqrt{s}$ =13 TeV
A search is performed for charged-lepton flavor violating processes in top quark (𝑡) production and decay. The data were collected by the CMS experiment from proton-proton collisions at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 138 fb −1 . The selected events are required to contain one opposite-sign electron-muon pair, a third charged lepton (electron or muon), and at least one jet of which no more than one is associated with a bottom quark. Boosted decision trees are used to distinguish signal from background, exploiting differences in the kinematics of the final states particles. The data are consistent with the standard model expectation. Upper limits at 95% confidence level are placed in the context of effective field theory on the Wilson coefficients, which range between 0.024–0.424 TeV −2 depending on the flavor of the associated light quark and the Lorentz structure of the interaction. These limits are converted to upper limits on branching fractions involving up (charm) quarks, 𝑡 → 𝑒𝜇𝑢 (𝑡 → 𝑒𝜇𝑐), of 0.032(0.498) × 10 −6 , 0.022(0.369) × 10 −6 , and 0.012(0.216) × 10 −6 for tensorlike, vectorlike, and scalarlike interactions, respectively.
Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation
We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let S be a set of spurion fields introduced to organize the breaking of a global symmetry G f , and H S be the subgroup of G f that remains unbroken under a generic vacuum expectation value ⟨S⟩; we show that the EFT Lagrangian constructed from the spurion analysis saturates the EFT Lagrangian without the spurions but restricted to H S invariance, provided that arbitrary powers of the spurion fields are allowed. As examples, we study several implementations of the Minimal Lepton Flavor Violation (MLFV) principle, corresponding to various origins of the neutrino masses. In each scenario, we compute the Hilbert series to obtain the numbers of independent lepton flavor covariants that appear in the corresponding EFT at mass dimension 6. These numbers agree with the number of H S invariants in the EFT without the spurions, demonstrating the saturation theorem.
Proposal for Direct Detection of Ultralight Dark Matter via Charged Lepton Flavor Violation
We propose a dark matter direct-detection strategy using charged particle decays at accelerator-based experiments. If ultralight ( m ϕ ≪ eV ) dark matter has a misalignment abundance, its local field oscillates in time at a frequency set by its mass. If it also couples to flavor-changing neutral currents, rare exotic decays such as μ → e ϕ ′ and τ → e ( μ ) ϕ ′ inherit this modulation. Focusing on such charged lepton flavor-violating decays, we show that sufficient event samples can enable detection of ultralight dark matter candidates at Mu3e, Belle-II, and FCC-ee.
Neutron stars can shine a light on elusive lepton-flavor-violating dark matter
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Search for lepton flavor-violating decay modes B 0 → K* 0 τ ± ℓ ∓ (ℓ = e, μ) with hadronic B-tagging at Belle and Belle II
We present the results of a search for the charged-lepton-flavor violating decays B 0 → K *0 τ ± ℓ ∓ , where ℓ ∓ is either an electron or a muon. The results are based on 365 fb −1 and 711 fb −1 datasets collected with the Belle II and Belle detectors, respectively. We use an exclusive hadronic B-tagging technique, and search for a signal decay in the system recoiling against a fully reconstructed B meson. We find no evidence for B 0 → K* 0 τ ± ℓ ∓ decays and set upper limits on the branching fractions in the range of (2.9–6.4)×10 −5 at 90% confidence level.