Within the framework of Dyson-Schwinger equations (DSEs) and by means of the Multiple Reflection Expansion approximation, we study the finite volume effects on the constituent quark mass in a strong external magnetic field. Since the magnetic field influences the coupling constant, which controls the strength of strong interactions in QCD, we adopt the magnetic-field-dependent running coupling constant in our simulations. The results show that, in addition to the magnetic field, the masses of constituent quarks also have a significant dependence on the volume and the running coupling constant. The model behaves closely to the infinite volume limit for large sizes, but the effect of the finite volume is significant when the system size $\textit{R}$ is about $ 2-6 $ fm. The finite volume effects and the magnetic-field-dependent running coupling constant have considerable influence on the phase transition.

China

Li-Juan Zhou

De-Xian Wei

Zhong-Yi Liu

Hong-Wei Zhong

Dynamical quark mass and finite volume effects in the Dyson-Schwinger equations * Li-Juan Zhou has been supported by the National Natural Science Foundation of China (11865005), the Natural Science Foundation of Guangxi (China) (2025GXNSFAA069552). De-Xian Wei has been supported by the National Natural Science Foundation of China (12105057), the Natural Science Foundation of Guangxi (China) (2023GXNSFAA026020)

We report a feasibility study of the hyperon semileptonic decay $$\varLambda \rightarrow pe^{-} {\bar{\nu }}_{e}$$ by using a fast simulation software package at STCF. With an anticipated integrated luminosity of 3.4 trillion $$J/\psi $$ per year at a center-of-mass energy of 3.097 GeV, the statistical sensitivity of the branching fraction is determined to be 0.15%. The statistical sensitivities of form factors $$g_{av}$$ and $$g_w$$ are determined to be 0.4% and 2.15%, respectively. The projected sensitivity of $$|V_{us}|$$ is obtained by combining this result with $$g_1(0)$$ from Lattice QCD, to be 0.9%, including the systematic uncertainty from the LQCD input and the statistical uncertainties of input branching fraction and form factors. The precise measurement to be obtained at STCF will provide a rigorous test of the Standard Model.

Junxian Zhou

Shun Wang

Tao Luo

Xiaorong Zhou

Prospects of $$|V_{us}|$$ and axial vector form factors in $$\varLambda \rightarrow pe^{-}{\bar{\nu }}_{e}$$ decay at STCF

We present an investigation on cosmological implications resulting from spontaneous dark $ S U(2)_d $ symmetry breaking in conjunction with the Witten effect. Furthermore, we examine the mass of hidden monopoles generated by phase transition as well as the impact of axion-monopole interactions on the axion mass. Following spontaneous breaking of the PQ symmetry, axions emitted by cosmic strings or domain walls as well as hidden monopoles generated during this transition may collectively contribute to the observed dark matter relic density. Additionally, the stochastic gravitational wave background generated by sub-GeV phase transitions and by the decay of axionic domain walls formed during sub-ZeV phase transitions could account for the low-frequency gravitational wave signals detected by PTA experiments.

Ruiyu Zhou

Ligong Bian

Gravitational waves and dark matter with Witten effect * Supported by the National Key Research and Development Program of China (2021YFC2203004). Ruiyu Zhou is supported by the National Natural Science Foundation of China (12305109, 12147102), Chongqing Natural Science Foundation project (CSTB2022NSCQ-MSX0534), and Science and Technology Research Project of Chongqing Municipal Education Commission (KJQN202300614). Ligong Bian is supported by the National Natural Science Foundation of China (12322505, 12347101). Ligong Bian also acknowledges Chongqing Natural Science Foundation (CSTB2024NSCQ-JQX0022) and Chongqing Talents: Exceptional Young Talents Project (cstc2024ycjhbgzxm0020).

This study investigates the intrinsic electric dipole moment (EDM) of the $\textit{τ}$ lepton, which is an important quantity in the search for physics beyond the Standard Model (BSM). In preparation for future measurements at the Super Tau-Charm Facility (STCF), we employ Monte Carlo simulations of the $ e^+e^- \rightarrow \tau^+\tau^- $ process and optimize the analysis methodology for EDM extraction. Machine learning techniques are implemented to efficiently identify signal events ( $ \tau^\pm\rightarrow \pi^\pm\pi^0\nu_\tau $ ), which result in a significant improvement in signal-to-noise ratio. Our optimized event selection algorithm achieves 80.0% signal purity with 6.3% efficiency. We develop an analytical approach for $\textit{τ}$ lepton momentum reconstruction and derive the squared spin density matrix along with optimal observables, which maximize the sensitivity to $ d_\tau $ . The relationship between these observables and the EDM is established with the estimated sensitivity of $ |d_\tau| \lt 3.89\times 10^{-18}\,e\cdot\mathrm{cm} $ at a 68% confidence level. These results provide a foundation for future experimental measurements of the $\textit{τ}$ lepton EDM in STCF experiments.

Xulei Sun

Yongcheng Wu

Sensitivity study of the tau lepton electric dipole moment at the Super Tau-Charm Facility * Supported by the National Key R&D Program of China (2022YFA1602200, 2023YFA1607200); the National Natural Science Foundation of China (NSFC) (12341501, 12341503, 12341504); the international partnership program of the Chinese Academy of Sciences (211134KYSB20200057). Xulei Sun is supported by the Undergraduate Research Program of the University of Science and Technology of China and the Xinhe Scholar Program of the School of the Gifted Young

The neutrino floor, a theoretical sensitivity limit for dark matter (DM) direct detection, is being redefined as the boundary of a dynamic ''neutrino fog,'' where neutrino signals become inevitable, obscuring DM detection due to statistical and systematic uncertainties. This study provides the first site-specific analysis of the neutrino floor at China Jinping Underground Laboratory (CJPL), leveraging its unique geographic and environmental characteristics. We quantify how CJPL’s suppressed atmospheric neutrino flux (approximately 30% lower than that of Laboratori Nazionali del Gran Sasso (LNGS)) reshapes the neutrino floor, thereby enabling improved sensitivity to high-mass WIMPs (mass > 10 GeV). Using a gradient-based framework, we derive the CJPL’s neutrino floor and estimate the detection prospects for the PandaX-xT experiment. Our results demonstrate that a 500 tonne-year exposure with PandaX-xT could reach the floor, probing spin independent cross-sections down to $ \sigma_{n}\sim 3\times 10^{-49}\; {\rm{cm}}^2$ at a DM mass of 70 GeV/$\textit{c}$ $^{2}$.

Yingjie Fan

Xuewen Liu

Ning Zhou

Characterizing the CJPL’s site-specific neutrino floor as the neutrino fog boundary * Xuewen Liu is supported by the Project of Shandong Province Higher Educational Science and Technology Program (2022KJ271). Ning Zhou is supported by National Science Foundation of China (12325505)

In this study, we investigate the $R^2$ corrections to the dissociation of heavy quarkonium in the Gauss-Bonnet gravitational background. We analyze the impact of the Gauss-Bonnet parameter $\lambda_{\rm GB}$ on the spectral function of charmonium and bottomonium and examine the effect of $\lambda_{\rm GB}$ on the dissociation of heavy quarkonium. Our results show that $\lambda_{\rm GB}$ reduces the peak height and increases the peak width of the spectral function, suggesting that $\lambda_{\rm GB}$ enhances the dissociation of heavy quarkonium. We also discuss the variation in the dissociation of heavy quarkonium with the ratio of shear viscosity to entropy density and observe that the dissociation is easier in more perfect plasma. Additionally, we observe that the temperature decreases the peak height and widens the peak, thereby accelerating the dissociation.

Zhou-Run Zhu

Manman Sun

Rui Zhou

Jinzhong Han

$\textit{R}$ $^{2}$ corrections to holographic heavy quarkonium dissociation * Rui Zhou supported by the Science and Technology Development Plan Project of Henan Province, China (242102230085), the National Natural Science Foundation of China (12404470), the High Level Talents Research and Startup Foundation Projects for Doctors of Zhoukou Normal University, China (ZKNUC2023017). Manman Sun supported by the National Natural Science Foundation of China (12305076). Zhou-Run Zhu supported by the High Level Talents Research and Startup Foundation Projects for Doctors of Zhoukou Normal University, China (ZKNUC2023018)

Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant,  $$\alpha _s(Q^2)$$  <math> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </math>  , that varies with the energy scale  $$Q^2$$  <math> <msup> <mi>Q</mi> <mn>2</mn> </msup> </math>   characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of  $$\alpha _s$$  <math> <msub> <mi>α</mi> <mi>s</mi> </msub> </math>   at low momentum transfers limits perturbative calculations to the high-energy region where  $$Q^2\gg \varLambda _{{\textrm{QCD}}} ^2\simeq $$  <math> <mrow> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>≫</mo> <msubsup> <mi>Λ</mi> <mrow> <mtext>QCD</mtext> </mrow> <mn>2</mn> </msubsup> <mo>≃</mo> </mrow> </math>   (250 MeV) $$^2$$  <math> <msup> <mrow></mrow> <mn>2</mn> </msup> </math>  . Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large  $$N_c$$  <math> <msub> <mi>N</mi> <mi>c</mi> </msub> </math>  -limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected  $$q{{\bar{q}}}$$  <math> <mrow> <mi>q</mi> <mover> <mrow> <mi>q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson,  $$W^\pm $$  <math> <msup> <mi>W</mi> <mo>±</mo> </msup> </math>   or Z, is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude. The best is yet to come!

United States

Franz Gross

Germany

Eberhard Klempt

Stanley Brodsky

Andrzej Buras

Volker Burkert

Gudrun Heinrich

Karl Jakobs

Curtis Meyer

Kostas Orginos

Michael Strickland

Johanna Stachel

Giulia Zanderighi

Nora Brambilla

Peter Braun-Munzinger

Daniel Britzger

Simon Capstick

Tom Cohen

Volker Crede

Martha Constantinou

United Kingdom

Christine Davies

Luigi Debbio

Achim Denig

Carleton DeTar

Alexandre Deur

Russia

Latvia

Yuri Dokshitzer

Hans Dosch

Jozef Dudek

Monica Dunford

Evgeny Epelbaum

Spain

Miguel Escobedo

Harald Fritzsch

Japan

Kenji Fukushima

Italy

Paolo Gambino

Canada

Sweden

Dag Gillberg

Steven Gottlieb

CERN

Per Grafstrom

Switzerland

Massimiliano Grazzini

Boris Grube

JINR

Alexey Guskov

Toru Iijima

Xiangdong Ji

Frithjof Karsch

Stefan Kluth

John Kogut

Frank Krauss

Shunzo Kumano

Australia

Derek Leinweber

Heinrich Leutwyler

Hai-Bo Li

Yang Li

France

Bogdan Malaescu

Chiara Mariotti

Pieter Maris

Simone Marzani

Wally Melnitchouk

Johan Messchendorp

Harvey Meyer

Ryan Mitchell

Chandan Mondal

Frank Nerling

Sebastian Neubert

Marco Pappagallo

Saori Pastore

José Peláez

Andrew Puckett

Jianwei Qiu

Klaus Rabbertz

Alberto Ramos

Patrizia Rossi

Azerbaijan

Anar Rustamov

Andreas Schäfer

Stefan Scherer

Matthias Schindler

Steven Schramm

Mikhail Shifman

Edward Shuryak

Torbjörn Sjöstrand

George Sterman

Iain Stewart

Joachim Stroth

Eric Swanson

Costa Rica

Guy Téramond

Ulrike Thoma

Antonio Vairo

Danny Dyk

James Vary

Javier Virto

Marcel Vos

Christian Weiss

Markus Wobisch

Sau Wu

Christopher Young

Feng Yuan

Xingbo Zhao

50 Years of quantum chromodynamics

To avoid the impact from the background events directly from <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilations or <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays, we propose a novel approach to investigate <math><mi>η</mi></math> decays, in particular for its rare or forbidden decays, by using <math><msup><mi>η</mi><mo>′</mo></msup><mo>→</mo><mi>π</mi><mi>π</mi><mi>η</mi></math> produced in <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays at the <math><mi>τ</mi></math>-charm factories. Based on the Monte Carlo studies of a few typical decays, <math><mi>η</mi><mo>→</mo><mi>π</mi><mi>π</mi></math>, <math><mrow><mi>γ</mi><msup><mrow><mi>l</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>l</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><mi>l</mi><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></math>, <math><msup><mi>l</mi><mo>+</mo></msup><msup><mi>l</mi><mo>−</mo></msup></math>, as well as <math><msup><mi>l</mi><mo>+</mo></msup><msup><mi>l</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>, the sensitivities could be obviously improved by taking advantage of the extra constraint of <math><msup><mi>η</mi><mo>′</mo></msup></math>. Using <math><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>12</mn></msup><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></math> events accumulated at the super <math><mi>τ</mi></math>-charm facility, the precision on the investigation of <math><mi>η</mi></math> decays could be improved significantly and the observation of the rare decay <math><mi>η</mi><mo>→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> is even accessible.

Xiaolin Kang

Yuyao Ji

Xiaoqing Yuan

Benhou Xiang

Haiping Peng

Xingtao Huang

Shuangshi Fang

Novel approach to investigate <math><mi>η</mi></math> decays via <math><msup><mi>η</mi><mo>′</mo></msup><mo>→</mo><mi>π</mi><mi>π</mi><mi>η</mi></math>

Polarized hyperon-antihyperon pairs shed light on various unresolved puzzles in contemporary physics: How the strong interaction confines quarks into hadrons, how accurately the Standard Model describes microcosmos and even why our universe consists of so much more matter than antimatter. Thanks to their weak, parity violating decays, hyperons reveal their spin properties. This can be exploited e.g. the decomposition of the electromagnetic structure of hyperons, precision tests of flavour symmetry and searches for CP violation. At the BESIII experiment at BEPC-II, Beijing, China, hyperon-antihyperon pairs can be produced in abundance. Recently collected large data samples have triggered the development of new methods that provide unprecedented precision and a plethora of new results have emerged. When applied at future high-intensity facilities like PANDA and STCF, precision physics will be taken to a new level which can contribute to the solution to the aforementioned puzzles.

Karin Schönning

Poland

Varvara Batozskaya

Patrik Adlarson

Production and decay of polarized hyperon-antihyperon pairs  

A special class of four-point correlation functions in the maximally supersymmetric Yang-Mills theory is given by the square of the Fredholm determinant of a generalized Bessel kernel. In this note, we re-express its logarithmic derivatives in terms of a two-dimensional Riemann-Hilbert problem. We solve the latter in the null limit making use of the Deift-Zhou steepest descent. We reproduce the exact octagonal anomalous dimension in 't Hooft coupling and provide its novel formulation as the convolution of a non-linear quasiclassical phase with the Fermi distribution in the limit of the infinite chemical potential.

A.V. Belitsky

Null octagon from Deift-Zhou steepest descent