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)

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 present the first lattice QCD calculations of the isovector helicity transverse momentum-dependent parton distribution function (TMDPDF) and the flavor-dependent unpolarized TMDPDFs for up and down quarks in the proton. Our computations utilize domain-wall fermion discretization with physical quark masses. Employing Coulomb-gauge-fixed quark correlation functions within the large-momentum effective theory framework, we access nonperturbative transverse quark separations <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mi>T</mi></msub></math> up to approximately 1 fm, corresponding to transverse momenta as low as 200 MeV. Based on the quasi-TMD factorization theorem, we construct renormalization-group–invariant ratios that are equal to the corresponding light-cone TMDPDF ratios. At moderate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, our results reveal that the isovector helicity and unpolarized TMDPDFs exhibit nearly identical transverse structure up to a normalization factor, and the unpolarized distributions display only mild flavor dependence. These findings not only support key trends observed in recent global analyses but also provide robust, nonperturbative constraints that can distinguish between different parameterizations. This Letter establishes a first-principles benchmark for TMDPDFs, offering valuable input for ongoing and future experimental efforts to map the proton’s three-dimensional structure.

Dennis Bollweg

Xiang Gao

Swagato Mukherjee

Yong Zhao

Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses

We study magnetic properties of the hadron resonance gas in the presence of a strong (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>0</mn><mo>≤</mo><mi>B</mi><mo>≤</mo><mn>0.15</mn><mspace width="4pt"></mspace><msup><mrow><mi>GeV</mi></mrow><mn>2</mn></msup></mrow></math>) magnetic field, using physical values of the magnetic moments of hadrons, i.e., including their anomalous parts. The values of these moments are taken from experiment, or when unavailable, from theoretical estimates. We evaluate the conserved charge susceptibilities, finding the expected sizable effects of the anomalous magnetic moments, in particular for the octet baryons, such as the proton and neutron, where they are exceptionally large. We also study in detail the large effects of the magnetic moments of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Δ</mi><mo>(</mo><mn>1232</mn><mo>)</mo></mrow></math> states, for which various theoretical estimates and experimental values differ significantly. We compare our model results with the lattice quantum chromodynamics data and find reasonable agreement within the model uncertainty.

Rupam Samanta

Wojciech Broniowski

Magnetic properties of the hadron resonance gas with physical magnetic moments

We analyse a stationary, cylindrically symmetric spacetime endowed with an intrinsic helical twist, <math altimg='si95.svg'><mrow><mi>d</mi><msup><mi>s</mi><mn>2</mn></msup><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>d</mi><msup><mi>t</mi><mn>2</mn></msup><mo linebreak='goodbreak'>+</mo><mi>d</mi><msup><mi>r</mi><mn>2</mn></msup><mo linebreak='goodbreak'>+</mo><msup><mi>r</mi><mn>2</mn></msup><mi>d</mi><msup><mi>&#981;</mi><mn>2</mn></msup><mo linebreak='goodbreak'>+</mo><msup><mrow><mo>(</mo><mi>d</mi><mi>z</mi><mo>+</mo><mi>&#969;</mi><mspace width='0.16em' /><mi>r</mi><mspace width='0.16em' /><mi>d</mi><mi>&#981;</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></math>. Solving the Einstein equations exactly yields an anisotropic energy&#8211;momentum tensor whose density is negative and decays as <math altimg='si96.svg'><msup><mi>r</mi><mrow><mo>&#8722;</mo><mn>2</mn></mrow></msup></math>, thus violating the weak energy condition near the axis. Three notable features emerge: (i) axis-centred negative energy; (ii) unequal transverse stresses; (iii) a torsional momentum flux <math altimg='si97.svg'><mrow><msub><mi>T</mi><mrow><mi>&#981;</mi><mi>z</mi></mrow></msub><mo>&#8733;</mo><msup><mi>&#969;</mi><mn>3</mn></msup><mo linebreak='goodbreak'>/</mo><mi>r</mi></mrow></math>. We identify stable photon orbits and deflection angle, fully helical geodesics, and torsion-controlled wave optics modes, suggesting laboratory analogues in twisted liquid-crystal and photonic systems. The coupling between the torsion parameter <math altimg='si10.svg'><mi>&#969;</mi></math> and other physical parameters leads to significant effects, altering the motion along the positive or negative <math altimg='si98.svg'><mi>z</mi></math>-axis. These results make the twisted helical metric a useful test bed for studying the interplay of curvature, torsion, and matter in both gravitational and condensed-matter contexts.

Brazil

Edilberto O. Silva

Frankbelson dos S. Azevedo

India

Faizuddin Ahmed

Helically twisted spacetime: Study of geometric and wave optics, and physical analysis

Lepton number violation decay $ \omega \to \pi^+ \pi^+ e^-e^- +c.c. $ is searched for via $ J/\psi \to \omega\eta $ using a data sample of $ (1.0087 \pm 0.0044) \times 10^{10} $ $ J/\psi $ events collected via the BESIII detector at the BEPCII collider. No significant signal is observed, and the upper limit on the branching fraction of $ \omega \to \pi^+ \pi^+ e^-e^- +c.c. $ at the 90% confidence level is determined for the first time to be $ 2.8 \times 10^{-6} $ .

Z.H. Duan

Search for the lepton number violation decay $\textit{ω}$→$\textit{π}$ $^{+}$ $\textit{π}$ $^{+}$ $\textit{e}$ $^{−}$ $\textit{e}$ $^{−}$+$\textit{c}$.$\textit{c}$. * Supported in part by National Key R&D Program of China (2023YFA1606000, 2023YFA1606704); National Natural Science Foundation of China (NSFC) (12035009, 11875170, 11635010, 11935015, 11935016, 11935018, 12025502, 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); ERC (758462); 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; Polish National Science Centre (2024/53/B/ST2/00975); STFC (United Kingdom); Swedish Research Council (2019.04595); U. S. Department of Energy (DE-FG02-05ER41374)

In this paper, we study the different properties of static spherically symmetric black hole solutions of Einstein–Bel–Robinson gravity (EBR), a modified four-dimensional theory of gravity quartic in curvature. We look at the implications of EBR gravity on the orbit of massless and massive test bodies, derive modified expressions, and show how the higher curvature term influences the behavior of particle trajectories near black holes. Specifically, computing the innermost stable circular orbit and photon sphere, and finding them smaller than their Einstein counterparts in general relativity. Next, we obtain the deflection angle and shadow of an EBR black hole and find that both decrease compared to a non-rotating black hole in general relativity. Using the Shapiro time delay, we obtain a bound value for the coupling constant. Then, we explore the EBR black hole’s lifetime and find that it decreases to Einstein’s gravity. Quasinormal modes (QNMs) are computed using Padé averaged sixth-order WKB method, showing that increasing the coupling constant lowers the damping rate of ring-down gravitational waves (GWs). The oscillation frequency of scalar QNMs decreases with the coupling constant, whereas it increases for electromagnetic QNMs. We also provide an analytically rigorous bound on the greybody factor. We show that the coupling constant has a small effect on the greybody factor. Finally, correspondence between the greybody factor and quasinormal modes is also considered.

Thailand

Seyed Sajadi

Supakchai Ponglertsakul

Azerbaijan

Dhruba Gogoi

Physical properties of black hole solutions in Einstein–Bel–Robinson gravity

By analyzing a $\psi(3686)$ data sample containing $(107.7\pm0.6)\times10^{6}$ events taken with the BESIII detector at the BEPCII storage ring in 2009, the $\chi_{c0}$ resonance parameters are precisely measured using $\chi_{c0,c2} \to \pi^+\pi^-/K^+K^-$ events. The mass of $\chi_{c0}$ is determined to be $M(\chi_{c0})=(3415.63\pm0.07\pm0.07\pm0.07$ ) MeV/ $c^2$ , and its full width is $\Gamma(\chi_{c0})=(12.52\pm0.12\pm0.13)~{\rm{MeV}}$ , where the first uncertainty is statistical, the second systematic, and the third for mass comes from $\chi_{c2}$ mass uncertainty. These measurements improve the precision of $\chi_{c0}$ mass by a factor of four and width by one order of magnitude over the previous individual measurements, and significantly boost our knowledge about the charmonium spectrum. Together with additional $(345.4\pm2.6)\times10^{6}$ $\psi(3686)$ data events taken in 2012, the decay branching fractions of $\chi_{c0,c2}\to\pi^+\pi^-/K^+K^-$ are measured as well, with precision improved by a factor of three compared to previous measurements. These $\chi_{c0}$ decay branching fractions provide important inputs for the study of glueballs.

O. Afedulidis

I. Balossino

G. Chelkov

C. Chen

Z.Y. Chen

I. Denisenko

Y. Fang

Y.T. Feng

M. Fritsch

C.D. Fu

J.L. Fu

Y.W. Fu

H. Gao

X.B. Gao

Precise measurement of the $\textit{χ}$ $\textit{c}$0 resonance parameters and branching fractions of $\textit{χ}$ $\textit{c}$0,$\textit{c}$2 → $\textit{π}$ $^{+}$ $\textit{π}$ $^{−}$/$\textit{K}$ $^{+}$ $\textit{K}$ $^{−}$ * Supported in part by National Key R&D Program of China (2020YFA0406300, 2020YFA0406400, 2023YFA1606000); National Natural Science Foundation of China (NSFC) (11635010, 11735014, 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; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U1832207); 100 Talents Program of CAS; (ZR2022JQ02, ZR2024QA151) supported by Shandong Provincial Natural Science Foundation; supported by the China Postdoctoral Science Foundation (2023M742100); The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG (FOR5327, GRK 2149); 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 (B16F640076, B50G670107); Polish National Science Centre (2019/35/O/ST2/02907); Swedish Research Council (2019.04595); The Swedish Foundation for International Cooperation in Research and Higher Education (CH2018-7756); U. S. Department of Energy (DE-FG02-05ER41374)

This study investigates finite-volume effects in physical processes that involve the combination of long-range hadronic matrix elements with electroweak loop integrals. We adopt the approach of implementing the electroweak part as the infinite-volume version, which is denoted as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>EW</mi></mrow><mi>∞</mi></msub></math> method in this work. A general approach is established for correcting finite-volume effects in cases where the hadronic intermediate states are dominated by either a single particle or two particles. For the single-particle case, this work derives the infinite volume reconstruction method from a new perspective. For the two-particle case, we provide the correction formulas for power-law finite-volume effects and unphysical terms with exponentially divergent time dependence. The finite-volume formalism developed in this study has broad applications, including the QED corrections in various processes and the two-photon exchange contribution in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mi>L</mi></msub><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> decays.

Xin-Yu Tuo

Xu Feng

Finite-volume formalism for physical processes with an electroweak loop integral

Two distinct non-singular interior models that describe anisotropic spherical configurations are presented in this work. We develop the Einstein field equations and the associated mass function in accordance with a static spherical spacetime. We then discuss certain requirements that must be satisfied for compact models to be physically validated. Two distinct limitations are taken into account to solve the field equations, including different forms of the radial geometric component and anisotropy, which ultimately leads to a couple of relativistic models. In both cases, solving the differential equations result in the appearance of integration constants. By equating the Schwarzschild exterior metric and spherical interior line element on the interface, these constants are explicitly obtained. The disappearance of the radial pressure on the hypersurface is also used in this context. We further use estimated radii and masses of six different stars to graphically visualize the physical properties of new solutions. Both of our models are deduced to be well-aligned with all physical requirements, indicating the superiority of the presence of anisotropy in compact stellar interiors over the perfect isotropic fluid content.

Pakistan

M. Sharif

Tayyab Naseer

Hira Shadab

Physical existence of relativistic stellar models within the context of anisotropic matter distribution