Electroweak (EW) amplitudes in the gauge-Goldstone five-component formalism have a distinctive property: gauge symmetry is imprinted in the amplitudes, manifested as the massive Ward identity (MWI) $ k^M{\cal{M}}_M=0 $ . In this study, we used the HELAS package to numerically study gauge symmetry in EW amplitudes. First, we directly tested gauge symmetry by examining the MWI of amplitudes. Second, we modified the couplings within a vertex and among vertices to check if and how the MWI changes. Third, we tested gauge symmetry by considering the couplings modified by operators from the standard model effective field theory (SMEFT). Similar to the standard model, there are relations between different couplings that are protected by gauge symmetry. We observed that, if we modify the couplings to deviate from the relations, the MWI is violated. In contrast, the MWI is restored when the relations between couplings reduce to those in the SMEFT.

China

Wang-Fa Li

Junmou Chen

Qian-Jiu Wang

Zhao-Huan Yu

Numerical study on the gauge symmetry of electroweak amplitudes * Junmou Chen is supported by National Natural Science Foundation of China (12205118), Wang-Fa Li, Qian-Jiu Wang, and Zhao-Huan Yu are supported by the Guangzhou Science and Technology Planning Project (2024A04J4026)

A muon collider represents a promising candidate for the next generation of particle physics experiments after the expected end of LHC operations in the early 2040s. Rare or hard-to-detect processes at the LHC, such as the production of multiple gauge bosons, become accessible at a TeV muon collider. We present here the prospects of detecting quantum entanglement and the violation of Bell inequalities in H → ZZ → 4ℓ events at a potential future muon collider. We show that the spin density matrix of the Z boson pairs can be reconstructed using the kinematics of the charged leptons from the Z boson decays. Once the density matrix is determined, it is straightforward to obtain the expectation values of various Bell operators and test the quantum entanglement between the Z boson pair. Through a detailed study based on Monte-Carlo simulation, we show that the generalized CGLMP inequality can be maximally violated, and testing Bell inequalities could be established with high significance.

Alim Ruzi

Youpeng Wu

Ran Ding

Sitian Qian

Andrew Levin

Qiang Li

Testing Bell inequalities and probing quantum entanglement at a muon collider

In the deep learning era, improving the neural network performance in jet physics is a rewarding task, as it directly contributes to more accurate physics measurements at the LHC. Recent research has proposed various network designs in consideration of the full Lorentz symmetry, but its benefit is still not systematically asserted, given that there remain many successful networks without taking it into account. We conduct a detailed study on the Lorentz-symmetric design. We propose two generalized approaches for modifying a network—these methods are experimented on Particle Flow Network, ParticleNet, and LorentzNet and exhibit a general performance gain. We also reveal that the notable improvement attributed to the “pairwise mass” feature in the network is due to its introduction of a structure that fully complies with Lorentz symmetry. We confirm that Lorentz-symmetry preservation serves as a strong inductive bias of jet physics, hence calling for attention to such general recipes in future network designs.

Congqiao Li

CERN

Huilin Qu

Qi Meng

Shiqi Gong

Jue Zhang

Tie-Yan Liu

Does Lorentz-symmetric design boost network performance in jet physics?

Majorana properties of neutrinos have long been a focus in the pursuit of possible new physics beyond the standard model, which has motivated lots of dedicated theoretical and experimental studies. A future same-sign muon collider is an ideal platform to search for Majorana neutrinos through the lepton number violation process: <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><mo>→</mo><msup><mi>W</mi><mo>+</mo></msup><msup><mi>W</mi><mo>+</mo></msup></math>. Specifically, this t-channel kind of process is less kinematically suppressed and has a good advantage in probing Majorana neutrinos at high mass regions up to 10 TeV. In this paper, we perform a detailed fast Monte Carlo simulation study by examining three different final states: (1) pure leptonic state with electrons or muons, (2) semileptonic state, and (3) pure hadronic state in the resolved or merged categories. Furthermore, we perform a full simulation study on the pure leptonic final state to validate our fast simulation results.

Ruobing Jiang

Tianyi Yang

Yong Ban

Jingshu Li

Zhengyun You

Searching for Majorana neutrinos at a same-sign muon collider

Charged lepton flavor violation (CLFV) represents a transition between charged leptons of different generations that violates lepton flavor conservation, which is a clear signature of possible new physics beyond the standard model. By exploiting a typical example model of extra Z′ gauge boson, we perform a detailed comparative study on CLFV searches at several future lepton colliders, including a 240 GeV electron-positron collider and a TeV scale muon collider. Based on detailed signal and background Monte-Carlo studies with fast detector simulations, we derive the potentials in searching for Z′ mediated CLFV couplings with eμ, eτ and μτ of different future colliders. The results are compared with the current and prospect limits set by either low-energy experiments or the high-energy LHC experiments. The sensitivity of the τ related CLFV coupling strength at future lepton colliders will be significantly improved in comparison to the current best constraints and the prospect constraints for the μτ channel.

Wanyue Wang

Xunye Cai

Chuxue Yang

Meng Lu

A comparative study of Z′ mediated charged lepton flavor violation at future lepton colliders

Anomalies from the LHCb lepton flavour universality and Fermilab muon anomalous magnetic moment show tantalizing hints of possible new physics from the lepton sectors. Due to its large mass and shorter lifetime than muon, the tau lepton is believed to couple more to possible new physics beyond the Standard Model. Traditionally, tau leptons are probed through their decay products due to tau’s short lifetime. On the other hand, at a high energy scale, a large fraction of tau leptons could be boosted to a much longer lifetime and fly a visible distance from several centimetres up to kilometer length scale yet very informative to new physics beyond the standard model or high energy cosmic rays. In this article, we investigate rare, yet promising, tau-physics phenomena, where long-lived taus are exploited either as a microscope (for the measurement of tau’s anomalous magnetic moment to an unprecedented level of accuracy) or as a macroscope (for the detection of 1 TeV to 1 PeV cosmic neutrinos).

Zhe Guan

Sen Deng

Yunxuan Song

Tianyu Mu

Jie Xiao

Siguang Wang

Yajun Mao

Boosted Tau Lepton as a Microscope and Macroscope

Deep learning methods have been increasingly adopted to study jets in particle physics. Since symmetry-preserving behavior has been shown to be an important factor for improving the performance of deep learning in many applications, Lorentz group equivariance — a fundamental spacetime symmetry for elementary particles — has recently been incorporated into a deep learning model for jet tagging. However, the design is computationally costly due to the analytic construction of high-order tensors. In this article, we introduce LorentzNet, a new symmetry-preserving deep learning model for jet tagging. The message passing of LorentzNet relies on an efficient Minkowski dot product attention. Experiments on two representative jet tagging benchmarks show that LorentzNet achieves the best tagging performance and improves significantly over existing state-of-the-art algorithms. The preservation of Lorentz symmetry also greatly improves the efficiency and generalization power of the model, allowing LorentzNet to reach highly competitive performance when trained on only a few thousand jets.

Weitao Du

Zhi-Ming Ma

An efficient Lorentz equivariant graph neural network for jet tagging

The LHCb Collaboration recently gave an update on testing lepton flavour universality with B + → K +ℓ+ℓ − , in which a 3.1 standard deviations from the standard model prediction was observed. The g-2 experiment also reports a 3.3 standard deviations from the standard model on muon anomalous magnetic moment measurement. These deviations could be explained by introducing new particles including leptoquarks. In this paper, we show the possibility to search for heavy spin-1 leptoquarks at a future TeV scale muon collider by performing studies from three channels: 1) same flavour final states with either two bottom or two light quarks, 2) different flavour quark final states, and 3) a so-called “VXS” process representing the scattering between a vector boson and a leptoquark to probe the coupling between leptoquark and tau lepton. We conclude that a 3 TeV muon collider with 3 ab −1 of integrated luminosity is already sufficient to cover the leptoquark parameter space in order to explain the LHCb lepton flavour universality anomaly.

Fanqiang Meng

Searching for heavy leptoquarks at a muon collider

Measuring longitudinally polarized vector boson scattering in, e.g., the <math><mi>Z</mi><mi>Z</mi></math> channel is a promising way to investigate the unitarization scheme from the Higgs and possible new physics beyond the Standard Model. However, at the LHC, it demands the end of the high-luminosity-LHC lifetime luminosity, <math><mrow><mn>3000</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>, and advanced data analysis technique to reach the discovery threshold due to its small production rates. Instead, there could be great potential at future colliders. In this paper, we perform a Monte Carlo study and examine the projected sensitivity of longitudinally polarized <math><mi>Z</mi><mi>Z</mi></math> scattering at a TeV scale muon collider. We conduct studies at 14 and 6 TeV muon colliders respectively and find that a 5 standard deviation discovery can be achieved at a 14 TeV muon collider, with <math><mn>3000</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of data collected. While a 6 TeV muon collider can already surpass high-luminosity LHC, reaching 2 standard deviations with around <math><mrow><mn>4</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>ab</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> of data. The effect from lepton isolation and detector granularity is also discussed, which may be more obvious at higher energy muon colliders, as the leptons from longitudinally polarized <math><mrow><mi>Z</mi></mrow></math> decays tend to be closer.

Longitudinally polarized <math><mi>Z</mi><mi>Z</mi></math> scattering at a muon collider

An electron-muon collider with an asymmetric collision profile targeting multi-ab-1 integrated luminosity is proposed. This novel collider, operating at collision energies of, e.g., 20–200 GeV, 50–1000 GeV, and 100–3000 GeV, would be able to probe charged lepton flavor violation and measure Higgs boson properties precisely. The collision of an electron and muon beam leads to less physics background compared with either an electron-electron or a muon-muon collider, since electron-muon interactions proceed mostly through higher-order vector boson fusion and vector boson scattering processes. The asymmetric collision profile results in collision products that are boosted towards the electron beam side, which can be exploited to reduce beam-induced background from the muon beam to a large extent. With this in mind, one can imagine a lepton collider complex, starting from colliding order 10 GeV electron and muon beams for the first time in history and to probe charged lepton flavor violation, then to be upgraded to a collider with 50-100 GeV electron and 1-3 TeV muon beams to measure Higgs properties and search for new physics and finally to be transformed to a TeV-scale muon-muon collider. The cost should vary from order 100 million to a few billion dollars, corresponding to different stages, which make the funding situation more practical.

Andrew Michael Levin

Antonios Agapitos

The Physics Case for an Electron-Muon Collider