We present the first lattice-QCD validation of multiple sum rules associated with quark-gluon decomposition of hadron mass by computing all relevant tensor components of the quark and gluon energy-momentum tensor matrix elements from first principles. We achieve this through nonperturbative renormalization of the QCD energy-momentum tensor, including its trace, in a gradient-flow scheme, followed by continuum extrapolations, two-loop matching to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><mi>MS</mi></mrow><mrow><mo stretchy="true">¯</mo></mrow></mover></mrow></math> scheme, and zero-flow-time extrapolations. These ingredients enable a direct and simultaneous verification, in a common renormalization scheme and scale, of multiple energy-density-based and trace-based mass decomposition sum rules proposed in the literature. We demonstrate the framework for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> charmonia using three fine lattice spacings with a physical strange-quark and near-physical up- and down-quark masses. We present the first lattice-QCD results for the gravitational form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>C</mi><mo stretchy="false">¯</mo></mover></math>. We find sizable gluonic contributions to charmonia masses at the hadronic scale, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>15</mn><mo>%</mo></math> in the Lorcé and Metz-Pasquini-Rodini decompositions. The trace-anomaly contribution in the Ji sum rule is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>∼</mo><mn>6</mn><mo>%</mo></mrow></math>, while the gluonic component of the trace anomaly in the Hatta-Rajan-Tanaka sum rule is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>35</mn><mo>%</mo></math>. The method is general and can be straightforwardly adopted for lattice-QCD calculations of mass and spin decompositions as well as gravitational form factors of other hadrons and nuclei.

United States

Dennis Bollweg

China

Heng-Tong Ding

Xiang Gao

Ran Luo

Swagato Mukherjee

Lattice-QCD Validation of Hadron Mass and Trace-Anomaly Decomposition Sum Rules

We present a lattice QCD study of the chiral properties of (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD in background magnetic fields at zero temperature with physical pion masses. Simulations are performed using the highly improved staggered quark action across four different lattice spacings to enable a controlled continuum extrapolation. We compute the renormalized chiral condensates together with pseudoscalar meson masses and decay constants for pions, kaons, and the fictitious <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>η</mi><mrow><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mn>0</mn></msubsup></math> pseudoscalar as functions of the magnetic-field strength <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>B</mi></math> up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>B</mi><mo>≃</mo><mn>1.2</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>. The chiral condensates exhibit clear magnetic catalysis, increasing monotonically with the field strength. In the meson sector, neutral pseudoscalar masses decrease steadily with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>B</mi></math>, whereas charged pseudoscalar masses display a nonmonotonic response: They rise at small fields, consistent with the lowest-Landau-level expectation, but then saturate and slightly decrease at larger fields, signaling sizable internal-structure effects. At the same time, neutral pseudoscalar decay constants are strongly enhanced by the magnetic field. To quantify deviations from chiral symmetry relations, we isolate the magnetic-field-induced shift in the Gell-Mann–Oakes–Renner corrections and find it to remain small for the neutral pion but to become sizable for the neutral kaon. To elucidate the origin of the magnetic response, we separately analyze the sea- and valence-quark contributions to both neutral and charged meson masses, finding that valence effects dominate at zero temperature. These results provide new insights into the interplay between QCD chiral symmetry breaking and strong magnetic fields.

Dan Zhang

Chiral properties of (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD in magnetic fields at zero temperature

We investigate the temperature dependence of the shear viscosity (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math>) and bulk viscosity (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi></math>) of the gluon plasma using lattice QCD over the range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.76</mn><mo>−</mo><mn>2.25</mn><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math>, extending from below the transition temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>c</mi></msub></math> across the transition region and into the deconfined phase. At each temperature, we employ three large, fine lattices, which enables controlled continuum extrapolations of the energy-momentum tensor correlators. Using gradient flow together with a recently developed blocking technique, we achieve percent-level precision for these correlators, providing strong constraints for a model-based spectral analysis. Since the inversion to real-time information is intrinsically ill posed, we extract viscosities by fitting spectral functions whose ultraviolet behavior is matched to the best available perturbative result, while the infrared region is described by a Lorentzian transport peak. The dominant modeling uncertainty associated with the transport peak width is bracketed by varying it over a physically motivated range set by thermal scales. We find that the shear-viscosity-to-entropy-density ratio, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>/</mo><mi>s</mi></math>, exhibits a minimum near the transition temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>c</mi></msub></math> and increases for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo>&gt;</mo><msub><mi>T</mi><mi>c</mi></msub></math>, whereas the bulk-viscosity-to-entropy-density ratio, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi><mo>/</mo><mi>s</mi></math>, decreases monotonically over the entire temperature range studied.

Hai-Tao Shu

Cheng Zhang

Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD

The Jiangmen Underground Neutrino Observatory (JUNO) started physics data taking on 26 August 2025. JUNO consists of a 20-kton liquid scintillator central detector, surrounded by a 35 kton water pool serving as a Cherenkov veto, and almost 1000 m$^{2}$ of plastic scintillator veto on top. The detector is located in a shallow underground laboratory with an overburden of 1800 m.w.e. This paper presents the performance results of the detector, extensively studied during the commissioning of the water phase, the subsequent liquid scintillator filling phase, and the first physics runs. The liquid scintillator achieved an attenuation length of 20.6 m at 430 nm, while the high coverage PMT system and scintillator together yielded about 1785 photoelectrons per MeV of energy deposit at the detector centre, measured using the 2.223 MeV $\textit{γ}$ from neutron captures on hydrogen with an Am-C calibration source. The reconstructed energy resolution is 3.4% for two 0.511 MeV $\textit{γ}$ at the detector centre and 2.9% for the 0.93 MeV quenched $^{214}$Po alpha decays from natural radioactive sources. The energy non-linearity is calibrated to better than 1%. Intrinsic contaminations of $^{238}$U and $^{232}$Th in the liquid scintillator are below 10$^{-16}$ g/g, assuming secular equilibrium. The water Cherenkov detector achieves a muon detection efficiency better than 99.9% for muons traversing the liquid scintillator volume. During the initial science runs, the data acquisition duty cycle exceeded 97.8%, demonstrating the excellent stability and readiness of JUNO for high-precision neutrino physics.

Chile

Angel Abusleme

France

Thomas Adam

Germany

Kai Adamowicz

David Adey

Pakistan

Shakeel Ahmad

Rizwan Ahmed

Finland

Timo Ahola

Italy

Sebastiano Aiello

Fengpeng An

Guangpeng An

United Kingdom

Costas Andreopoulos

Giuseppe Andronico

João Pedro Athayde Marcondes de André

Russia

Nikolay Anfimov

Vito Antonelli

Tatiana Antoshkina

Thailand

Burin Asavapibhop

Didier Auguste

Margherita Buizza Avanzini

Slovakia

Andrej Babic

Jingzhi Bai

Weidong Bai

Nikita Balashov

Roberto Barbera

Andrea Barresi

Davide Basilico

Eric Baussan

Beatrice Bellantonio

Marco Bellato

JeanLuc Beney

Marco Beretta

Antonio Bergnoli

Enrico Bernieri

Nikita Bessonov

David Biaré

Daniel Bick

Lukas Bieger

Svetlana Biktemerova

Thilo Birkenfeld

David Blum

Simon Blyth

Sara Boarin

Manuel Boehles

Anastasia Bolshakova

Mathieu Bongrand

Aurélie Bonhomme

Clément Bordereau

Matteo Borghesi

Augusto Brigatti

Timothee Brugiere

Riccardo Brugnera

Riccardo Bruno

Jonas Buchholz

Antonio Budano

Max Buesken

Mario Buscemi

Severino Bussino

Jose Busto

Ilya Butorov

Marcel Büchner

Anatael Cabrera

Barbara Caccianiga

Boshuai Cai

Hao Cai

Xiao Cai

Yanke Cai

Yi-zhou Cai

Zhiyan Cai

Stéphane Callier

Steven Calvez

Antonio Cammi

Agustin Campeny

Dechang Cai

Chuanya Cao

Dewen Cao

Guofu Cao

Jun Cao

Yaoqi Cao

Rossella Caruso

Aurelio Caslini

Cédric Cerna

Vanessa Cerrone

Daniele Cesini

Chi Chan

Jinfan Chang

Yun Chang

Milo Charavet

Tim Charissé

Auttakit Chatrabhuti

Chao Chen

Guoming Chen

Haitao Chen

Haotian Chen

Jiahui Chen

Jian Chen

Jing Chen

Junyou Chen

Lihao Chen

Mali Chen

Mingming Chen

Initial performance results of the JUNO detector * We acknowledge financial and institutional supportfrom the Chinese Academy of Sciences, the National KeyR&D Program of China, the People's Government of Guangdong Province, and the Tsung–Dao Lee Institute of Shanghai Jiao Tong University in China.We appreciate the contributions from the Institut Na-tional de Physique Nucléaire et de Physique des Partic-ules (IN2P3) in France, the Istituto Nazionale di Fisica Nucleare (INFN) in Italy, the Fonds de la Recherche Sci-entifique (F.R.S.–FNRS) and the Institut Interuni-versitaire des Sciences Nucléaires (IISN) in Belgium, and the Conselho Nacional de Desenvolvimento Científico eTecnológico (CNPq) in Brazil.We also acknowledge the support of the AgenciaNacional de Investigación y Desarrollo (ANID) and the ANID–Millennium Science Initiative Program (ICN2019044) in Chile; the European Structural and In-vestment Funds, the Ministry of Education, Youth and Sports, and the Charles University Research Center inthe Czech Republic; the Deutsche Forschungsgemeinsch-aft (DFG), the Helmholtz Association, and the Cluster ofExcellence PRISMA+ in Germany; and the Joint Insti-tute for Nuclear Research (JINR) and Lomonosov Mo-scow State University in Russia.We further thank the Slovak Research and Develop-ment Agency in the Slovak Republic, the National Science and Technology Council (NSCT) and MOE, China, the Program Management Unit for Hu-man Resources & Institutional Development, Research and Innovation (PMU–B), Chulalongkorn University, and Suranaree University of Technology in Thailand, the Science and Technology Facilities Council (STFC) in the United Kingdom, and the University of California atIrvine and the National Science Foundation (NSF) in the United States

We present a unified free field realization of the Ding-Iohara algebra at arbitrary levels, which satisfies a generalized form of the Serre relations. This realization, constructed using six free boson fields, arises from a specialized factorization of the structure function in the defining relations of the algebra. Based on this construction, we then develop intertwining operators for the Ding-Iohara algebra.

Zitao Chen

Xiang-Mao Ding

Free field realization of the Ding-Iohara algebra at general levels

We investigated the impact of a constant external magnetic field on the dressed propagators of up-, down-, and strange quarks. In the weak field limit, we derive a general momentum-space representation for the propagator and numerically solve the corresponding gap equation. Our analysis reveals that the vector term of the propagator can be decomposed into components parallel and perpendicular to the magnetic field, resulting in anisotropic effective masses, with the transverse mass consistently exceeding the longitudinal mass. This mass disparity exhibits a power law dependence on the magnetic field strength and is less pronounced for the strange quark compared to up and down quarks. Additionally, the magnetic field induces axial-vector and tensor terms, highlighting the Zeeman effect, resulting from quark interactions with the magnetic field. These findings have important implications for (inverse) magnetic catalysis and phenomena such as vector meson and pion condensations.

Minghui Ding

Fei Gao

Sebastian M. Schmidt

Anisotropic quark propagation and Zeeman effect in an external magnetic field * Fei Gao is supported by the National Science Foundation of China (12305134). Minghui Ding appreciates the support received from the Helmholtz-Zentrum Dresden-Rossendorf High Potential Programme

We present continuum-estimated (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor lattice QCD results for the leading-order Taylor expansion coefficients of the equation of state in strong magnetic fields and at nonzero baryon chemical potential. Simulations employ the highly improved staggered quark action with physical pion masses on lattices of temporal extent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>8</mn></math>, 12, covering <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>145</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>≲</mo><mi>T</mi><mo>≲</mo><mn>165</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>B</mi><mo>≲</mo><mn>0.8</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>, imposing strangeness neutrality with baseline results at electric charge to baryon number ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi><mo>=</mo><mn>0.4</mn></math>. We determine the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mi>–</mi><mi>e</mi><mi>B</mi></math> dependence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>q</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>s</mi><mn>1</mn></msub></math> (electric charge and strangeness chemical potential ratios), pressure coefficient <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mn>2</mn></msub></math>, baryon number density coefficient <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>N</mi><mn>1</mn><mi mathvariant="normal">B</mi></msubsup></math>, and energy-related coefficients <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Θ</mi><mn>2</mn></msub></math> (trace anomaly), <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ε</mi><mn>2</mn></msub></math> (energy density), and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>σ</mi><mn>2</mn></msub></math> (entropy density). Magnetic fields induce temperature-band crossings for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>q</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mn>2</mn></msub></math> and nonmonotonic structures in the energy-related coefficients, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Θ</mi><mn>2</mn></msub></math> at strong fields possibly vanishing or turning negative at higher <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>, indicating dominance of the pressure term over the energy contribution. We also examine the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi></math>-dependence, finding that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi><mo>=</mo><mn>0</mn></math> (charge-neutral matter) shows the most muted magnetic-field enhancement of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mn>2</mn></msub></math> despite larger <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>q</mi><mn>1</mn></msub><mo stretchy="false">|</mo></math>, providing a useful reference for neutron-star–relevant conditions. Comparisons with the hadron resonance gas model show qualitative agreement at low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> and weak <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>B</mi></math>, with clear deviations near the crossover and at strong fields. These results provide useful input for constraining models and effective theories of QCD matter in strong magnetic fields at finite baryon density.

Jin-Biao Gu

Arpith Kumar

Sheng-Tai Li

Leading-order QCD equation of state in strong magnetic fields at nonzero baryon chemical potential

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

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

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

Tao Han

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

Shu Li

Xiaomei Li

Xin-Qiang Li

Yiming Li

Yubo Li

Yuji Li

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