Based on a sample of $2.7\times10^{9}$ $\psi(3686)$ events collected by the BESIII detector operating at the BEPCII collider, the decay $\psi(3686)\to\gamma\chi_{cJ}, \chi_{cJ}\to\eta\eta\eta^{\prime}$ is analyzed. The decay modes $\chi_{c1}$ and $\chi_{c2}\to\eta\eta\eta^{\prime}$ are observed for the first time, and their corresponding branching fractions are determined to be ${\cal{B}}(\chi_{c1}\to\eta\eta\eta^{\prime}) = $ $ (1.40\, \pm 0.13\, (\text{stat.}) \pm 0.09\, (\text{sys.})) \times 10^{-4}$ and ${\cal{B}}(\chi_{c2}\to\eta\eta\eta^{\prime}) = (4.18\, \pm 0.84\, (\text{stat.}) \pm 0.48\, (\text{sys.})) \times 10^{-5}$ . An upper limit on the branching fraction of $\chi_{c0}\to\eta\eta\eta^{\prime}$ is set as $2.59 \times 10^{-5}$ at a 90% confidence level (CL). A partial wave analysis (PWA) of the decay $\chi_{c1}\to\eta\eta\eta^{\prime}$ is performed to search for the $1^{-+}$ exotic state $\eta_1(1855)$ . The PWA result indicates that the structure in the $\eta\eta^{\prime}$ mass spectrum is attributed to $f_0(1500)$ , while in the $\eta\eta$ mass spectrum, it is attributed to the $0^{++}$ phase space. The upper limit of ${\cal{B}}(\chi_{c1}\to\eta_{1}(1855)\eta) \cdot {\cal{B}}(\eta_{1}(1855)\to\eta\eta^{\prime}) \lt $ $ 9.79 \times 10^{-5}$ is set based on the PWA at 90% CL.

China

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.J. Chen

Z.K. Chen

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Search for $\textit{η}$ $_{1}$(1855) in $\textit{χ}$ $\textit{cJ}$ → $\textit{ηηη}$′ decays * Supported in part by National Key R&D Program of China (2023YFA1606000, 2023YFA1606704); National Natural Science Foundation of China (NSFC) (11635010, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS (YSBR-101); 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile (ANID PIA/APOYO AFB230003); German Research Foundation DFG (FOR5327); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea ( NRF-2022R1A2C1092335); National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources Institutional Development, Research and Innovation of Thailand ( B50G670107); Polish National Science Centre (2024/53/B/ST2/00975); Swedish Research Council (2019.04595); U. S. Department of Energy (DE-FG02-05ER41374)

Based on available experimental results on $ \chi _{cJ}(J=0,1,2) $ decays, we investigated the $ \chi_{cJ}\to PP $ , $ VV $ , $ PV $ , and $ PT $ decays using the $\textit{SU}$(3) flavor symmetry/breaking approach, where $\textit{P}$, $\textit{V}$, and $\textit{T}$ denote light pseudoscalar, vector, and tensor mesons, respectively. With the decay amplitude relations determined by $\textit{SU}$(3) flavor symmetry/breaking, we present the branching ratios for all $ \chi_{cJ}\to PP $ and $ \chi_{cJ}\to VV $ modes, including those without experimental data. While theoretical considerations strongly suppress or even forbid most $ \chi_{cJ}\to PV $ and $ PT $ decays, we also provide quantitative predictions constrained by existing experimental data. Our results are expected to be accessible in future experiments at BESIII and the planned Super Tau-Charm Facility.

Bo Lan

Qin-Ze Song

Jin-Huan Sheng

Yi Qiao

Ru-Min Wang

Study of χ$_{cJ}$ ($\textit{J}$ = 0,1,2) decays to light meson pairs based on $\textit{SU}$(3) flavor symmetry/breaking analysis * Supported by the National Natural Science Foundation of China (12175088, 12305100, 12365014) and Graduate Innovation Fund Project of Jiangxi Provincial Department of Education (YJS2024091)

We study the pole trajectory of the recently established subthreshold negative-parity nucleon pole, namely the $N^*(920)$ , with varying pion masses in the scheme of linear $\textit{σ}$ model with nucleons, using the $N/D$ unitarization method. We find that, as the pion mass increases, the pole moves toward the real axis. For larger pion masses, at tree level, the pole falls to a specific point on $\textit{u}$-channel cut and crosses to the adjacent Riemann sheet defined by the logarithmic $\textit{u-}$channel cut. At the one-loop level, the pole does not meet the $\textit{u}$-cut up to $m_\pi=0.36$ GeV. We also re-examined the $\textit{σ}$ pole trajectory and found it to be in good agreement with the Roy equation analysis result.

Qu-Zhi Li

Zhiguang Xiao

Han-Qing Zheng

On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses * Supported by China National Natural Science Foundation (12335002, 12375078). This work is also supported by “the Fundamental Research Funds for the Central Universities”

By capturing the characteristics of the Bethe-Salpeter amplitude for the pion excitation state, we construct an algebraic model to provide the overall features of the pion’s first excitation state parton distribution amplitude and distribution function. We find that, at the hadronic scale, the distribution amplitude of the excited state exhibits nodes, while the distribution function is unimodal, with a peak at $x=1/2 $ and distinct concave and convex fluctuations in the valence region. These findings provide new insights into the partonic structure of excited mesons and contribute significantly to our understanding of hadronic excitations.

Xiaobin Wang

Lei Chang

Unveiling the inner structure of the Pion’s first excited state * This work is financially supported by the National Natural Science Foundation of China (12135007)

Axions and axion-like particles can be generated in the early universe through mechanisms such as misalignment production, thermal processes, and the decay of topological defects. In this study, we show that scalar perturbations in the early universe can produce a significant amount of these particles primarily through mass parametric resonance effects. Scalar perturbations induce temperature fluctuations during the particle mass transition era, e.g., during the QCD phase transition. These temperature fluctuations modulate the particle mass, transferring energy into the field through parametric mass resonance, a nonlinear process. This mechanism exhibits substantially unstable regions that could lead to explosive particle production. Notably, it does not generate additional isocurvature perturbations.

Ruifeng Zheng

Puxian Wei

Qiaoli Yang

Generation of axions and axion-like particles through mass parametric resonance induced by scalar perturbations in the early universe

The study of extra charged gauge bosons beyond the Standard Model has always been of great interest. Future muon colliders will have a significant advantage in discovering exotic particles. In this paper, by studying the $ \mu^+ \mu^- \to W^{\prime +} W^{\prime -} \to e^+ e^- n_e \bar{n}_e $ process, we explore the properties of $ W^\prime $ in the alternative left-right model. The cross section and angular distribution of the final electron are investigated in a scenario of different $ W^\prime $ masses and right-handed coupling constants. The forward-backward asymmetry is also an important observable to reflect the properties of $ W^\prime $ . We provide a method to effectively suppress the background processes by imposing constraints on the transverse momentum $ P_T $ and azimuthal angle of the final-state electrons $\textit{α}$. With cuts of $ 600 \lt P_T \lt 3500 $ GeV and $ 0.5 \lt \alpha \lt 3 $ , the significance exceeds 5$\textit{σ}$ for 4.8 TeV $ W^\prime $ at a collision energy of 10 TeV.

Liuxin Zhao

Honglei Li

Zhi-Long Han

Fei Huang

Xinyi Yan

Extra charged gauge boson $\textit{W}$′ in Alternative Left-Right Model at future muon collider * This work is supported by the Natural Science Foundation of Shandong Province (ZR2022MA065, ZR2024QA138), and University of Jinan Disciplinary Cross-Convergence Construction Project 2024 (XKJC-202404)

High-precision regression of physical parameters from black hole images generated by General Relativistic Ray Tracing (GRRT) is essential for investigating spacetime curvature and advancing black hole astrophysics. However, owing to limitations in observational resolution, high observational costs, and imbalanced distributions of positive and negative samples, black hole images often suffer from data scarcity, sparse parameter spaces, and complex structural characteristics. These factors pose significant challenges to conventional regression methods based on simplified physical models. To overcome these challenges, this study introduces the Multiscale Adaptive Network (MANet), a novel regression framework grounded in deep learning. MANet integrates an Adaptive Channel Attention (ACA) module to selectively enhance features in physically informative regions. Meanwhile, a Multiscale Enhancement Feature Pyramid (MEFP) is employed to capture fine-grained spatial structures, such as photon rings and accretion disks, while alleviating information loss due to downsampling. Experimental evaluations on GRRT-simulated datasets demonstrate that MANet substantially improves parameter estimation accuracy and generalization capability in high-dimensional parameter spaces, outperforming existing baseline approaches. This framework presents a promising avenue for high-precision parameter regression in Event Horizon Telescope (EHT) data analysis and broader astrophysical imaging applications characterized by sparse and noisy data.

Jialei Wei

Ao Liu

Dejiang Li

Cuihong Wen

Physical parameter regression from black hole images using a multiscale adaptive neural network * Supported by the Natural Science Foundation of Hunan Province under grant No. 2023JJ30384; the National Natural Science Foundation of China under Grants No. 12374408; the University Students' Innovation and Entrepreneurship Training Program Project

We perform the first computation of phase-transition parameters to cubic order in $ \lambda\sim m^2/T^2 $ , where $\textit{m}$ is the scalar mass and $\textit{T}$ is the temperature, in a simple model resembling the Higgs sector of the SMEFT. We use dimensional reduction, including 1-loop matching corrections for terms of dimension 6 (in 4-dimensional units), 2-loop contributions for dimension-4 ones and 3-loops for the squared mass. We precisely quantify the size of the different corrections, including renormalization-group running as well as quantum effects from light fields in the effective theory provided by the Coleman-Weinberg potential, and discuss briefly the implications for gravitational waves. Our results suggest that, for strong phase transitions, 1-loop corrections from dimension-6 operators can compete with 2-loop ones from quartic couplings and largely surpass those from 3-loop thermal masses.

Spain

Mikael Chala

Luis Gil

Zhe Ren

Phase transitions in dimensional reduction up to three loops * Supported by MCIN/AEI (10.13039/501100011033) and ERDF (grants PID2021-128396NB-I00 and PID2022-139466NB-C22), from the Junta de Andalucía grants FQM 101 and P21-00199 and from Consejería de Universidad, Investigación e Innovación, Gobierno de España and Unión Europea – NextGenerationEU under grants AST22 6.5 and CNS2022-136024. MC and LG are further supported by the RyC and FPU programs under contract numbers RYC2019-027155-I and FPU23/02026, respectively.

This paper presents a systematic study of hyperon non-leptonic two-body decays induced by light quark transitions, particularly the $ s \rightarrow u\bar{u}d $ process, within the framework of $\textit{SU}$(3) flavor symmetry. The effective weak Hamiltonian is decomposed into irreducible $\textit{SU}$(3) representations, including the 27-plet and octet components, and applied to analyze decays of octet and decuplet baryons and charmed baryons. Both the irreducible representation amplitude (IRA) approach and the topological diagrammatic analysis (TDA) are employed to construct decay amplitudes and constrain the parameter space. $\textit{SU}$(3) symmetry-breaking effects arising from the strange quark mass are incorporated systematically. A global fit to current experimental data allows us to extract form factors and predict branching ratios and asymmetry parameters for several decay channels. Our results demonstrate the predictive power of $\textit{SU}$(3) flavor symmetry while highlighting significant symmetry-breaking effects, especially in amplitudes related to the 27-plet. Notably, the $ \Sigma^+ \rightarrow p\pi^0 $ decay channel exhibits a deviation exceeding $ 1\sigma $ from experimental measurements, suggesting the possible presence of new decay mechanisms or contributions beyond the Standard Model. Besides, we also evaluate the size of symmetry breaking. However, the large uncertainty of the experimental data makes it difficult to precisely determine the value of symmetry breaking. We strongly recommend that future experimental efforts aim to reduce the measurement uncertainties, especially for the processes $ \Lambda^0\to p\pi^- $ and $ \Lambda^0\to n\pi^0 $ , which have larger experimental errors compared to other data and play an important role in determining the symmetry breaking parameter. This study provides a systematic framework for future tests of the Standard Model and the search for new physics in hyperon decays.

Xin Wu

Qi Chen

Ye Xing

Zhi-Peng Xing

Ruilin Zhu

$\textit{SU}$(3) flavor symmetry analysis of hyperon non-leptonic two body decays * Ruilin Zhu is supported by NSFC (12322503, 12075124) and the Natural Science Foundation of Jiangsu (BK20211267). Zhi-Peng Xing is supported by NSFC (12375088, 12335003, 12405113). Ye Xing is supported by NSFC (12005294)

We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the surface in question to its four closest neighbors, forming quads. We then focus on the simplices of $$d=2$$ , or triangles embedded in these quads, which make up a pure simplicial complex with $$d=2$$ . This allows us to numerically compute the local metric along with zweibeins, which subsequently leads to a derivation of discrete curvature defined at every triangle or face. We provide an efficient algorithm with $$\mathscr {O}(N \log {N})$$ complexity that first orients two-dimensional surfaces, solves the nonlinear system of equations of the spin-connections resulting from the torsion condition, and returns the value of curvature at each face.

Lebanon

Ali Chamseddine

Ola Malaeb

Sara Najem

Curvature of an arbitrary surface for discrete gravity and for $$d=2$$ pure simplicial complexes