We introduce a novel level crossing phenomenon in the mass mixing between QCD axions: one canonical QCD axion and one $ Z_{{\cal{N}}} $ axion. The level crossing can occur at or slightly before the QCD phase transition critical temperature, depending on the ratio of the axion decay constants, $ \sim 1.69 $ . The cosmological evolution of the mass eigenvalues in these two scenarios is similar; however, the transition of axion energy density differs significantly. Finally, we estimate the relic density of the QCD axion dark matter in this context. Additionally, this level crossing may have some interesting cosmological implications.

China

Hai-Jun Li

Yu-Feng Zhou

Mass mixing between QCD axions * Supported by the CAS Project for Young Scientists in Basic Research YSBR-006, the National Key R&D Program of China (2017YFA0402204), and the National Natural Science Foundation of China (11821505, 11825506, 12047503)

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

Xiaorong Zhou

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

We use a modified relativistic quark model to study the properties of excited charmed and charmed strange mesons. We calculate the masses and wave functions of conventional charmed and charmed strange mesons incorporating both spin and $\textit{S}$-$\textit{D}$ mixing effects and fit parameters of the potential model with known experimental states using differential evolution techniques. Using leading Born-Oppenheimer expansion, we compute the spectrum and wave functions of the first gluonic excited state of charmed and charmed strange mesons. We examine the effects of gluonic excitation on the spectrum of the resulting hybrid mesons. Using our calculated spectrum and wave functions, we determine the radiative transitions of the conventional and hybrid open charm mesons. We compare our calculations with experimental data and other works. We expect our results will be beneficial in the detection of charmed and charmed strange conventional and hybrid mesons.

Pakistan

Saba Noor

Faisal Akram

Bilal Masud

Study of excited $\textit{D}$ and D$_{s}$ mesons in a relativized quark model * F. A. acknowledges HEC grant 20-15728/NRPU/R&D/HEC/2021, Pakistan

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

United States

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

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

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

The isospin-singlet scalar meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> is hypothesized to consist of two energy eigenstates, forming a mixture of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mo stretchy="false">(</mo><mover accent="true"><mi>u</mi><mo stretchy="false">¯</mo></mover><mi>u</mi><mo>+</mo><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover><mi>d</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></math>. Building on this framework, we apply the quantum chromodynamics (QCD) sum rules approach in the background field theory to compute the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> decay constant, yielding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><msub><mi>f</mi><mn>0</mn></msub></msub><mo stretchy="false">(</mo><msub><mi>μ</mi><mn>0</mn></msub><mo>=</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0.386</mn><mo>±</mo><mn>0.009</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. Subsequently, we derive the first two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ξ</mi></math>-moments of the leading-twist light-cone distribution amplitude <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ϕ</mi><mrow><mn>2</mn><mo>;</mo><msub><mi>f</mi><mn>0</mn></msub></mrow></msub></math>. Using QCD light-cone sum rules, we then calculate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> transition form factor (TFF) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mo>+</mo></msub><mo stretchy="false">(</mo><msup><mi>q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math>, obtaining <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mo>+</mo></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0.51</mn><msubsup><mn>6</mn><mrow><mo>−</mo><mn>0.024</mn></mrow><mrow><mo>+</mo><mn>0.027</mn></mrow></msubsup></math> at the large-recoil region. We extend <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mo>+</mo></msub><mo stretchy="false">(</mo><msup><mi>q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> to the full physical region via a simplified series expansion parametrization, enabling calculations of the differential decay widths and the branching fraction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><mn>1.78</mn><msubsup><mn>3</mn><mrow><mo>−</mo><mn>0.189</mn></mrow><mrow><mo>+</mo><mn>0.227</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. Our theoretical predictions align well with the latest BESIII Collaboration measurements within reasonable errors.

Dan-Dan Hu

Xing-Gang Wu

Hai-Jiang Tian

Tao Zhong

Hai-Bing Fu

Light-cone sum rules analysis of the semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> decay incorporating the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> mixing state twist-2 distribution amplitudes

We propose a systematic approach to calculating $\textit{n}$-point one-loop parametric conformal integrals in $\textit{D}$ dimensions which we call the reconstruction procedure. It relies on decomposing a conformal integral over basis functions which are generated from a set of master functions by acting with the cyclic group ℤ . In order to identify the master functions we introduce a bipartite Mellin-Barnes representation by means of splitting a given conformal integral into two additive parts, one of which can be evaluated explicitly in terms of multivariate generalized hypergeometric series.

Russia

Konstantin Alkalaev

Semyon Mandrygin

Multipoint conformal integrals in $\textit{D}$ dimensions. Part I. Bipartite Mellin-Barnes representation and reconstruction

We present the results of a first-principles theoretical study of the inclusive semileptonic decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> meson. We performed a state-of-the-art lattice QCD calculation using the gauge ensembles produced by the Extended Twisted Mass Collaboration with dynamical light, strange and charm quarks with physical masses and employed the so-called Hansen-Lupo-Tantalo (HLT) method to extract the decay rate and the first two lepton-energy moments from the relevant Euclidean correlators. We have carefully taken into account all sources of systematic errors, including the ones associated with the continuum and infinite-volume extrapolations and with the HLT spectral reconstruction method. We obtained results in very good agreement with the currently available experimental determinations and with a total accuracy at the few-percent level, of the same order of magnitude of the experimental error. Our total error is dominated by the lattice QCD simulations statistical uncertainties and is certainly improvable. From the results presented and thoroughly discussed in this paper we conclude that it is nowadays possible to study heavy mesons inclusive semileptonic decays on the lattice at a phenomenologically relevant level of accuracy. The phenomenological implications of our physical results are the subject of a companion Letter [A. De Santis et al., Inclusive semileptonic decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> meson: Lattice QCD confronts experiments, Phys. Rev. Lett. 135, 121901 (2025).].

Alessandro De Santis

Antonio Evangelista

Roberto Frezzotti

Giuseppe Gagliardi

Paolo Gambino

Marco Garofalo

Christiane Franziska Groß

Bartosz Kostrzewa

Vittorio Lubicz

Francesca Margari

Finland

Marco Panero

Francesco Sanfilippo

Silvano Simula

Antonio Smecca

Nazario Tantalo

Carsten Urbach

Inclusive semileptonic decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> meson: A first-principles lattice QCD calculation

We present the results of a first-principles theoretical study of the inclusive semileptonic decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> meson. We performed a state-of-the-art lattice QCD calculation by taking into account all sources of systematic errors. A detailed discussion of our lattice calculation, demonstrating that inclusive semileptonic decays can nowadays be studied on the lattice at a phenomenologically relevant level of accuracy, is the subject of a companion paper [A. De Santis et al., Inclusive semileptonic decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> meson: A first-principles lattice QCD calculation, Phys. Rev. D 112, 054503 (2025)]. Here, we focus on the phenomenological implications of our results. Using the current best estimates of the relevant Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, our theoretical predictions for the decay rate and for the first two lepton-energy moments are in very good agreement with the corresponding experimental measurements. We also argue that, while the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> channel is not yet competitive with the exclusive channels in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">|</mo></math> determination, the situation can be significantly improved in the near future.

Inclusive Semileptonic Decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> Meson: Lattice QCD Confronts Experiments

In this note, we present a novel formulation of <math altimg='si1.svg'><mrow><mn>4</mn><mi>d</mi></mrow></math> pure Yang-Mills theory within the unfolded framework of Vasiliev higher-spin gravity. This formulation is first-order and exhibits manifest diffeomorphism and gauge invariance. Our approach builds upon a recently proposed unfolding method, previously applied to scalar electrodynamics. Additionally, we discuss the features of various unfolding maps defined by the unfolded equations.

Nikita Misuna

Unfolded formulation of <math altimg='si1.svg'><mrow><mn>4</mn><mi>d</mi></mrow></math> Yang-Mills theory

In this paper, we explore the natural grand unified theory (GUT) with spontaneous supersymmetry (SUSY) breaking, focusing on the contribution to sfermion and Higgs masses. Natural GUTs solve various problems in SUSY GUTs with the natural assumption that all terms allowed by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>A</mi></msub></math> symmetry are introduced with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> coefficients. It is also possible to introduce spontaneous SUSY breaking in the natural GUT. This scenario predicts that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-term contribution to sfermion and Higgs masses dominates the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi></math>-term contribution, which potentially leads to the SUSY flavor problem. Fortunately, it also predicts high-scale SUSY, which avoids the SUSY flavor problem but leads to the instability of the electroweak scale. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-term domination results in the superheavy Higgsino, unless the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-term contribution becomes comparable with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi></math>-term contribution. We discuss whether it is possible to suppress the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-term contribution while maintaining the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi></math>-term contribution through the tuning of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> coefficients in the natural GUT with spontaneous SUSY breaking. Our results indicate that it is impossible. This also suggests that the mass spectrum of the sfermions can be predicted by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-term contributions and that the Higgsino is not a candidate for dark matter in the scenario.

Japan

Nobuhiro Maekawa

Taiju Tanii

Does finetuning make <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-term contributions smaller in natural grand unified theories with spontaneous supersymmetry breaking?