The flavor space of particles produced in collider environments contains informative quantum correlations. We present a systematic approach for constructing the complete flavor density matrix for a meson and antimeson system (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>M</mi><mover accent="true"><mrow><mi>M</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math>) in the Bloch vector space at a given time <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>t</mi></mrow></math>, which can be at or after production. We point out that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> systems are superior to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>d</mi><mn>0</mn></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup></math> systems for quantum tomography because of their flavor oscillation and decay properties. Performing quantum tomography for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>M</mi><mover accent="true"><mrow><mi>M</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> system can facilitate the study of production mechanisms, decoherence phenomena, quantum information variables, and potential new sources of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation.

United States

Kun Cheng

Tao Han

Matthew Low

Tong Arthur Wu

Quantum Tomography in Neutral Meson and Antimeson Systems

Experiments at the CERN Large Hadron Collider (LHC) have accumulated an unprecedented amount of data corresponding to a large variety of quantum states. Although searching for new particles beyond the Standard Model of particle physics remains a high priority for the LHC program, precision measurements of the physical processes predicted in the Standard Model continue to lead us to a deeper understanding of nature at high energies. We carry out detailed simulations for the process $\textit{pp}$ → $\textit{τ}$ $\textit{τ}$ $\textit{X}$ to perform quantum tomography and to measure the quantum entanglement and the Bell nonlocality of the $\textit{τ}$ $\textit{τ}$ two qubit state, including both statistical and systematic uncertainties. By using advanced machine learning techniques for neutrino momentum reconstruction, we achieve precise measurements of the full spin density matrix, a critical advantage over previous studies limited by reconstruction challenges for missing momenta. Our analysis reveals a clear observation of Bell nonlocality with high statistical significance, surpassing 5$\textit{σ}$, establishing $\textit{τ}$ $\textit{τ}$ as an ideal system for quantum information studies in high-energy collisions. Given its experimental feasibility and the high expected sensitivity for Bell nonlocality, we propose that $\textit{τ}$ $\textit{τ}$ should be regarded as the new benchmark system for quantum information studies at the LHC, complementing and extending the insights gained from the $$ t\overline{t} $$ system.

Yulei Zhang

China

Bai-Hong Zhou

Qi-Bin Liu

Tong Wu

Shu Li

Shih-Chieh Hsu

Entanglement and Bell nonlocality in $\textit{τ}$ + $\textit{τ}$ $\textit{−}$ at the LHC using machine learning for neutrino reconstruction

The Taishan Antineutrino Observatory (TAO) is a tonne-scale gadolinium-doped liquid scintillator satellite experiment of the Jiangmen Underground Neutrino Observatory (JUNO). It is designed to measure the reactor antineutrino energy spectrum with unprecedented energy resolution, better than 2% at 1 MeV. To fully achieve its designed performance, precise vertex reconstruction is crucial. This work reports two distinct vertex reconstruction methods, the charge center algorithm (CCA) and the deep learning algorithm (DLA). We describe the efforts in optimizing and improving these two methods and compare their reconstruction performance. The results show that the CCA and DLA methods can achieve vertex position resolutions better than 20 mm (bias < 5 mm) and 12 mm (bias < 1.3 mm) at 1 MeV, respectively, fully meeting the requirements of the TAO experiment. The reconstruction algorithms developed in this study not only prepare the TAO experiment for its upcoming real data but also hold significant potential for application in other similar experiments.

Hangyu Shi

Jun Wang

Guofu Cao

Wei Wang

Yuehuan Wei

Vertex reconstruction in the TAO experiment

Motivated by the precise measurements of neutrino oscillation parameters at Jiangmen Underground Neutrino Observatory (JUNO), we investigate the possibility of probing the unitarity violation of lepton flavor mixing matrix solely with reactor antineutrinos. First, we stress that it is necessary to reconsider the production and detection of neutrinos in a self-consistent way, apart from neutrino propagation, when analyzing experimental sensitivities to unitarity violation. Then, concentrating on JUNO and its satellite experiment Taishan Antineutrino Observatory (TAO), we demonstrate how the event rates of inverse beta decays (i.e., <math altimg='si7.svg'><mrow><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>e</mi></msub><mo linebreak='goodbreak'>+</mo><mi>p</mi><mo>&#8594;</mo><msup><mi>e</mi><mo>+</mo></msup><mo linebreak='goodbreak'>+</mo><mi>n</mi></mrow></math>) for observing <math altimg='si8.svg'><mrow><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>e</mi></msub><mo>&#8594;</mo><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>e</mi></msub></mrow></math> oscillations, and those of elastic antineutrino-electron scattering (i.e., <math altimg='si9.svg'><mrow><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>&#945;</mi></msub><mo linebreak='goodbreak'>+</mo><msup><mi>e</mi><mo>&#8722;</mo></msup><mo>&#8594;</mo><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>&#945;</mi></msub><mo linebreak='goodbreak'>+</mo><msup><mi>e</mi><mo>&#8722;</mo></msup></mrow></math> with <math altimg='si10.svg'><mrow><mi>&#945;</mi><mo linebreak='goodbreak'>=</mo><mi>e</mi><mo>,</mo><mi>&#956;</mi><mo>,</mo><mi>&#964;</mi></mrow></math>) for <math altimg='si11.svg'><mrow><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>e</mi></msub><mo>&#8594;</mo><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>&#956;</mi></msub></mrow></math> and <math altimg='si12.svg'><mrow><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>e</mi></msub><mo>&#8594;</mo><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>&#964;</mi></msub></mrow></math> oscillations, depend on the parameters characterizing unitarity violation. Our investigation will be useful for JUNO and TAO to place independent constraints with more data in the near future.

Jihong Huang

Shun Zhou

Probing unitarity violation of lepton flavor mixing matrix with reactor antineutrinos at JUNO and TAO

In the third-generation (3G) gravitational-wave (GW) detector era, GW multi-messenger observations for binary neutron star merger events can exert significant effects on exploring the cosmic expansion history. Extending a previous work, we explore the potential of 3G GW standard siren observations in cosmological parameter estimation by considering their associated electromagnetic (EM) counterparts, including $$\gamma $$ -ray burst (GRB) coincidence observations by the Gravitational Wave High-energy Electromagnetic Counterpart All-sky Monitor and GW-triggered target-of-opportunity observations of kilonovae by different optical survey projects. During an assumed 10-year observation, we predict that the number of detectable GW-kilonova events is $$\sim 4900$$ with redshifts below $$\sim 0.4$$ under the GW detector network and Large Synoptic Survey Telescope in the $\textit{i}$ band, which is more than three times that of GW-GRB detections. For the cosmological analysis, we find that with the inclusion of GW-kilonova detections, the constraints on cosmological parameters from GW-EM detections are significantly improved compared to those from GW-GRB detections. In particular, GW-EM detections can tightly constrain the Hubble constant with precision ranging from $$0.076\%$$ to $$0.034\%$$ . Moreover, GW multi-messenger observations can effectively break the cosmological parameter degeneracies generated by the typical EM observations, CMB+BAO+SN (CBS). The combination of CBS and GW-EM can tightly constrain the equation-of-state parameters of dark energy $\textit{w}$ in the $\textit{w}$CDM model and $$w_0$$ in the $$w_0w_a$$ CDM model with precision of $$0.72\%$$ and $$0.99\%$$ , respectively, meeting the standard of precision cosmology. In conclusion, GW multi-messenger observations could play a crucial role in helping solve the Hubble tension and probing the fundamental nature of dark energy.

Jing-Fei Zhang

Xin Zhang

Multi-messenger standard-siren cosmology for third-generation gravitational-wave detectors: forecasts considering observations of gamma-ray bursts and kilonovae

Quantum entanglement and Bell nonlocality are two phenomena that occur only in quantum systems. In both cases, these are correlations between two subsystems that are classically absent. Traditionally, these phenomena have been measured in low-energy photon and electron experiments, but more recently they have also been measured in high-energy particle collider environments. In this work, we propose measuring the entanglement and Bell nonlocality in the $\textit{τ}$ $\textit{τ}$ state near and above its kinematic threshold at the Beijing Electron Positron Collider (BEPC). We find that in the existing dataset, entanglement is observable if systematic uncertainties are kept to 1%. In the upcoming run between 4.0 and 5.6 GeV, the entanglement is predicted to be measurable with a precision better than 4% and Bell nonlocality can be established at 5$\textit{σ}$ as long as systematic uncertainty can be controlled at level of 0$\textit{.}$5%–2$\textit{.}$0%, depending on the center-of-mass energy.

Youle Su

Entanglement and Bell nonlocality in $\textit{τ}$

We discuss the landscape of flavor physics at the Circular Electron-Positron Collider (CEPC), based on the nominal luminosity outlined in its Technical Design Report. The CEPC is designed to operate in multiple modes to address a variety of tasks. At the $\textit{Z}$ pole, the expected production of 4 Tera $\textit{Z}$ bosons will provide unique and highly precise measurements of $\textit{Z}$ boson couplings, while the substantial number of boosted heavy-flavored quarks and leptons produced in clean $\textit{Z}$ decays will facilitate investigations into their flavor physics with unprecedented precision. We investigate the prospects of measuring various physics benchmarks and discuss their implications for particle theories and phenomenological models. Our studies indicate that, with its highlighted advantages and anticipated excellent detector performance, the CEPC can explore beauty and $\textit{τ}$ physics in ways that are superior to or complementary with the Belle II and Large-Hadron-Collider-beauty experiments, potentially enabling the detection of new physics at energy scales of 10 TeV and above. This potential also extends to the observation of yet-to-be-discovered rare and exotic processes, as well as testing fundamental principles such as lepton flavor universality, lepton and baryon number conservation, etc., making the CEPC a vibrant platform for flavor physics research. The $\textit{WW}$ threshold scan, Higgs-factory operation and top-pair productions of the CEPC further enhance its merits in this regard, especially for measuring the Cabibbo-Kobayashi-Maskawa matrix elements, and Flavor-Changing-Neutral-Current physics of Higgs boson and top quarks. We outline the requirements for detector performance and considerations for future development to achieve the anticipated scientific goals. The role of machine learning for innovative detector design and advanced reconstruction algorithms is also stressed. The CEPC flavor physics program not only develops new capabilities for exploring flavor physics beyond existing projects but also enriches the physics opportunities of this machine. It should be remarked that, given the richness of the CEPC flavor physics, this manuscript is not meant to be a comprehensive survey, but rather an investigation of representative cases. Uncovering the full potential of flavor physics at the CEPC will require further dedicated explorations in the future.

Xiaocong Ai

Wolfgang Altmannshofer

Peter Athron

Xiaozhi Bai

Lorenzo Calibbi

Germany

Lu Cao

Yuzhi Che

Chunhui Chen

Ji-Yuan Chen

Long Chen

Mingshui Chen

Shanzhen Chen

Xuan Chen

Shan Cheng

Cheng-Wei Chiang

Switzerland

Andreas Crivellin

Hanhua Cui

France

Olivier Deschamps

Sébastien Descotes-Genon

Xiaokang Du

Shuangshi Fang

Yu Gao

Yuanning Gao

Li-Sheng Geng

Pablo Goldenzweig

Jiayin Gu

Feng-Kun Guo

Yuchen Guo

Zhi-Hui Guo

Hong-Jian He

Jibo He

Miao He

Xiaogang He

Yanping Huang

Gino Isidori

Quan Ji

Jianfeng Jiang

Xu-Hui Jiang

Slovenia

Jernej F. Kamenik

Tsz Hong Kwok

Gang Li

Geng Li

Haibo Li

Haitao Li

Hengne Li

Honglei Li

Liang Li

Lingfeng Li

Qiang Li

Xiaomei Li

Xin-Qiang Li

Yiming Li

Yubo Li

Yuji Li

Zhao Li

Hao Liang

Zhijun Liang

Libo Liao

Zoltan Ligeti

Jia Liu

Jianbei Liu

Tao Liu

Yi Liu

Yong Liu

Zhen Liu

Xinchou Lou

Peng-Cheng Lu

Italy

Alberto Lusiani

Hong-Hao Ma

Kai Ma

Farvah Mahmoudi

Yajun Mao

Yaxian Mao

David Marzocca

Juan-Juan Niu

Soeren Prell

Huirong Qi

Sen Qian

Zhuoni Qian

Qin Qin

Ariel Rock

Jonathan L. Rosner

Manqi Ruan

Dingyu Shao

Chengping Shen

Xiaoyan Shen

Haoyu Shi

United Kingdom

Liaoshan Shi

Zong-Guo Si

Cristian Sierra

Huayang Song

Shufang Su

Wei Su

Zhijia Sun

Michele Tammaro

Dayong Wang

En Wang

Flavor physics at the CEPC: a general perspective * We acknowledge financial support from the National Natural Science Foundation of China (NSFC) (12125507, 12047503, 12035008, 2211530479, 12475094, 12135006, 12075097, 12375086, 2022YFA1601903, 12061141007, 12375091, 12342502, 12235018, 12335003, 12105100, 12475106, 11961141015, 12188102, 12175245, 12205171, 12321005, tsqn202312052, 2024HWYQ-005, 12405121, 12447167, 12061141006, 12405102, 12125503,12305115, 12075213, 12335005, 12235008); the Chinese Academy of Sciences (YSBR-101, XDB34030000); the National Key R&D Program of China (2022YFE0116900, 2023YFA1606703, 2022YFA1601901); the National Key Research and Development Program of China (2023YFA1606300); the Excellent Postdoctoral Program of Jiangsu Province (2023ZB891); the Shenzhen Science and Technology Program (202206193000001, 20220816094256002); the Natural Science Foundation for Distinguished Young Scholars of Henan Province (242300421046); the Beijing Municipal Natural Science Foundation (JQ22002); the Area of Excellence (AoE/P-404/18-3) and the General Research Fund (16304321) (both grants are issued by the Research Grants Council of Hong Kong S.A.R); the MOST National Key R&D Program (2023YFA1606303); the Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (Ministry of Education), Shanghai Jiao Tong University

In high-energy collisions far above the electroweak scale, the effects of electroweak symmetry breaking are expected to become parametrically small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>δ</mi><mo>∼</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>W</mi></mrow></msub><mo>/</mo><mi>E</mi></mrow></math>. This defines the extent to which the electroweak gauge symmetry is restored: (i) the physics of the transverse gauge bosons and fermions is described by a massless theory in the unbroken phase; (ii) the longitudinal gauge bosons behave like the Goldstone bosons and join the Higgs boson to restore the unbroken O(4) symmetry in the original Higgs sector. Using the unique feature of the radiation amplitude zeros in gauge theory, we propose to study the electroweak symmetry restoration quantitatively by examining the processes for the gauge boson pair production <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>W</mi></mrow><mrow><mo>±</mo></mrow></msup><mi>γ</mi><mo>,</mo><msup><mrow><mi>W</mi></mrow><mrow><mo>±</mo></mrow></msup><mi>Z</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>W</mi></mrow><mrow><mo>±</mo></mrow></msup><mi>H</mi></mrow></math> at the LHC and muon colliders.

Rodolfo Capdevilla

Electroweak Symmetry Restoration and Radiation Amplitude Zeros

Lepton flavor violation (LFV) offers a powerful probe of physics beyond the Standard Model, particularly in models addressing neutrino masses and the baryon asymmetry of the universe. In this study, we investigate LFV processes within the framework of type II seesaw leptogenesis, where the Standard Model is extended by an $S U(2)_L$ triplet Higgs field. We focus on key LFV processes, including $\mu^+\to e^+\gamma$ , $\mu^+ \to e^+e^-e^+$ , and $\mu \rightarrow e$ conversion in nuclei, deriving stringent constraints on the parameter space from current experimental data. We scan the 3$\textit{σ}$ range of neutrino oscillation parameters and identify the most conservative bounds consistent with existing measurements. Our results reveal that the MEG experiment currently provides the most stringent constraints in the normal ordering (NO) scenario, while the SINDRUM experiment offers comparable sensitivity in the inverted ordering (IO) case. Future experiments, such as MEG II, Mu3e, Mu2e, and COMET, are predicted to significantly improve the sensitivity, testing larger regions of the parameter space.

Chengcheng Han

Yijun Han

Sihui Huang

Zhanhong Lei

Probing type II seesaw leptogenesis through lepton flavor violation * Chengcheng Han acknowledges supports from the National Key R&D Program of China (2023YFA1606100), the Sun Yat-Sen University Science Foundation, the Fundamental Research Funds for the Central Universities at Sun Yat-sen University (24qnpy117) and the Key Laboratory of Particle Astrophysics and Cosmology (MOE) of Shanghai Jiao Tong University

Spin correlation observables of particles produced at colliders generally depend on the coordinate basis. While spin correlations and their associated basis dependence have been studied in top-quark pair production, the basis dependence of spin correlations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>W</mi><mo>±</mo></msup></math> pairs has not been studied. In this work, we focus on the azimuthal-angle correlation in the decay of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>W</mi><mo>±</mo></msup></math> pairs, which encodes spin information in the direction transverse to the rotational axis. We quantitatively describe the basis dependence of the relative azimuthal angle. We further present the optimal coordinate direction to define the azimuthal angle between the decay products of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>W</mi><mo>±</mo></msup></math> bosons to achieve the maximal spin correlation based on symmetry considerations. The results can be used to optimize the measurement of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-even and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-odd interactions, and have applications to quantum information observables in the vector boson pair system.

Yi-Jing Fang

Maximizing the azimuthal-angle correlation in the decay of vector boson pairs