The beyond-the-standard-model scenario presented in this work is motivated by the observations of neutrino masses, the anomalous magnetic moments of the electron and muon, and dark matter in the Universe. We explain these observations by extending the standard model with two generations of vector-like fermions and an inert scalar doublet, all of which are odd under a $Z_2$ symmetry. The light neutrino masses and mixings are generated radiatively while maintaining consistency with bounds on lepton flavor violation. Loop diagrams featuring the same fields also explain the anomalous magnetic moments. Similarly, the correct dark matter relic abundance is reproduced without conflicting with direct detection constraints, or those from big bang nucleosynthesis or cosmic microwave background observations. Finally, prospective signatures at the LHC are discussed.

India

Vandana Sahdev

Neutrino masses, anomalous magnetic moments and dark matter with vector-like fermions and an inert scalar doublet * V.S. acknowledges the support from research grant no. CRG/2018/004889 of the SERB, India; T.R. Seshadri for providing resources during the initial stages of the work; and Brajesh Choudhary for providing access to computers bought under the aegis of Grant No. SR-MF/PS-0212014-DUB (G) of the DST (India)

We present an investigation of the $ K^*(1680) $ state in its strong decays into two-body final states within the flux-tube model and quark pair creation model. Since charge conjugation parity is not conserved in the strange sector, the conventional $ q\bar{q} $ states with $ J^{P(C)}=1^{-(-)} $ can mix with the lowest hybrid states with $ J^{P(C)}=1^{-(+)} $ . Our analysis of the $ K^*(1680) $ two-body strong decays indicates that the decay pattern of $ K^*(1680) $ cannot be explained by the conventional $ q\bar{q} $ scenario. Moreover, there is strong evidence for the $ q\bar{q} $ -hybrid mixing mechanism in the strange sector. The phenomenological consequences of such mixing are also discussed. Our study can provide guidance for future searches for hybrid multiplets in experiments at BESIII, LHCb, and Belle II.

China

Samee Ullah

Ye Cao

Ming-Xiao Duan

Hai-Bing Fu

Qiang Zhao

Nature of ${K^*(1680)}$ and ${q\bar{q}}$ -hybrid mixing as the $\textit{SU}$(3) partner of ${\eta_{1}(1855)}$ in the strange sector * Supported in part by the National Natural Science Foundation of China (12235018, 12265010, 12505098), and the Project of Guizhou Provincial Department of Science and Technology (MS[2025]219, CXTD[2025]030, ZD[2026]168, QN[2025]178), and the project of Guizhou Normal University (GZNUD[2025]05)

Uncovering physical laws from experimental data is a fundamental goal of theoretical physics. In this work, we apply the spline-based, interpretable Kolmogorov–Arnold Network (KAN) to investigate the algebraic structure underlying the baryon octet and decuplet mass spectra. Within a symbolic regression framework and without imposing theoretical priors, KAN recovers a symbolic representation equivalent to the classical Gell-Mann–Okubo mass relations, which can be transformed into the standard form through algebraic rearrangement. Compared with conventional fitting approaches, this method achieves comparable predictive accuracy while providing substantially improved interpretability and analytical transparency. Our results demonstrate the potential of KAN as a powerful tool for symbolic discovery in hadron physics and for bridging data-driven modeling with fundamental physical laws.

Jian-Yao He

Italy

Xun Chen

Xiao-Yan Zhu

Wen Luo

Discovering the Gell-Mann–Okubo formula with Kolmogorov-Arnold networks * Supported by the National Natural Science Foundation of China (NSFC) (12405154) and the European Union – Next Generation EU through research grant (P2022Z4P4B), ''SOPHYA - Sustainable Optimised PHYsics Algorithms: fundamental physics to build an advanced society'', under the PRIN 2022 PNRR program of the Italian Ministero dell'Università e Ricerca (MUR)

The rare exclusive decay of the Higgs boson, $ H \to J/\psi + \gamma $ , is a crucial channel for assessing the Yukawa coupling of the charm quark. In this article, we examine this process up to the next-to-next-to-leading order (NNLO) in QCD utilizing the Principle of Maximum Conformality (PMC). The PMC offers a systematic approach to eliminate renormalization scale uncertainties by resumming non-conformal $\textit{β}$ contributions into the QCD running coupling through the renormalization group equation (RGE). A PMC scale of $ Q_\star = 3.29\ {\rm{GeV}} $ is obtained, which reflects the low virtuality of the underlying QCD dynamics in the $ H \to J/\psi + \gamma $ process. Notably, this is an order of magnitude smaller than the scale estimated using the conventional method, $\textit{i.e.}$, $ \mu_r = m_H/2 $ . By removing the non-conformal $ \{\beta_i\} $ -terms from the perturbative QCD (pQCD) series, we observe that the PMC NLO QCD correction term is significantly enhanced, while the PMC NNLO QCD correction is suppressed. This indicates improved convergence of the pQCD series up to NNLO. Finally, we calculate the decay width $ \Gamma(H \to J/\psi + \gamma) = $ $ 14.183^{+0.249}_{-0.347} \pm 0.022 $ eV, where the first uncertainty arises from the factorization scale $ \mu_\Lambda \in [1, 2]\ {\rm{GeV}} $ , and the second is due to the estimation of unknown higher-order terms using the Pad $ \acute{e} $ approximant approach. The corresponding branching fraction is $ {\cal{B}}(H \to J/\psi + \gamma) = 3.485_{-0.161}^{+0.152} \times 10^{-6} $ .

Wen-Yuan Li

Ting Sun

Sheng-Quan Wang

Jian-Ming Shen

Hua Zhou

Xing-Gang Wu

Leonardo Di Giustino

Analysis of $\textit{H}$ → $\textit{J}$/$\textit{ψ}$ + $\textit{γ}$ up to Next-to-Next-to-Leading order QCD corrections * Supported in part by the Natural Science Foundation of China (12265011, 12175025, 12347101); the Project of Guizhou Provincial Department of Science and Technology (YQK[2023]016, ZK[2023]141, CXTD[2025]030); the Hunan Provincial Natural Science Foundation (2024JJ3004); the YueLuShan Center for Industrial Innovation (2024YCII0118), and the Natural Science Foundation of Sichuan Province (2024NSFSC1367)

This work presents a comprehensive analysis of polarization transfer in the decays of $\chi_{cJ}$ ( $J=0,1,2$ ) into octet baryon-antibaryon pairs in polarized electron-positron collisions. Using the spin density matrix formalism, we trace the polarization from the initial beams through the production chain $e^+e^- \to \psi(2S) \to \gamma \chi_{cJ}$ to the final-state baryon-antibaryon system. The helicity amplitude analysis for $\chi_{c1} \to B\bar{B}$ confirms the universal angular distribution parameter $\alpha = -1/3$ , as dictated by the charge-conjugation helicity selection rule. For $\chi_{c2}$ decays, $\textit{α}$ and the transverse polarization depend on two independent amplitudes, and our quark-model calculations agree with existing data. We demonstrate that the longitudinal beam polarization $P_z$ modifies the spin observables for $\chi_{c1}$ and $\chi_{c2}$ . This offers new experimental handles at future polarized facilities, such as the Super $\textit{τ}$-Charm Facility (STCF), to test decay mechanisms and explore baryonic spin entanglement as a quantum information resource.

Cai-Ying Pang

Rong-Gang Ping

Dai-Hui Wei

Polarization analysis of χ$_{cJ}$ decay into octet baryonic pairs * Supported by the National Natural Science Foundation of China (NSFC) (12575112, 12465015)

The triangle singularity interpretation of the $a_1(1420)$ observed by the COMPASS Collaboration has been widely accepted. In this work, we investigate the triangle mechanism in the decay $B^0 \to D^- \pi^+ a_0(980)(\pi^0 \eta)$ , where the $a_0(980)$ is treated as a dynamically generated state. The $\bar{K}^{*0}$ - $K^+$ - $K^-$ triangle loop originates from the decay $B^0 \to D^- K^+ \bar{K}^{*0}$ , which has been observed by the Belle Collaboration, followed by the subsequent decay $\bar{K}^{*0} \to K^- \pi^+$ . The triangle amplitude develops a pronounced peak around 1420 MeV, which is reflected in the invariant mass spectrum of the $\pi a_0(980)$ system. The differential decay width is calculated and exhibits a narrow peak around $980~\mathrm{MeV}$ in the $\pi^0 \eta$ invariant mass distribution. Furthermore, the invariant mass distribution of the $\pi^+ \pi^0 \eta$ system shows a clear peak around $1420~\mathrm{MeV}$ , which further confirms the triangle singularity explanation of the $a_1(1420)$ . We expect that the proposed $B^0$ decay mode could provide a potential platform for further exploring the triangle-singularity nature of the $a_1(1420)$ and could be tested in future experiments such as LHCb, BESIII, and Belle II.

Wei Wang

Dazhuang He

Xuan Luo

The role of triangle singularity in the $ {B^0 \to D^- \pi^+ a_0(980)(\pi^0 \eta)}$ decay * Dazhuang He is supported by the Heze University doctoral fund project (010008002039037). Xuan Luo is supported by the National Natural Science Foundation of China (12205002)

The effective-one-body (EOB) framework, originally formulated within the post-Newtonian (PN) expansion, is central to modeling and interpreting gravitational-wave signals. Recent developments have incorporated the post-Minkowskian (PM) expansion into EOB theory. In this work, we focus on the bound state dynamics in the PM approximation up to the third order and construct the core ingredients of EOB: the effective metric. We examine two correspondence strategies, one based on the radial action variable and the other on the precession angle. We demonstrate that the radial action variable provides a consistent correspondence, which is further verified by the correspondence based on the precession angle. Building on these results, we adopt an isotropic gauge with a Schwarzschild-like parametrization to fix the remaining freedom. Within this parametrization, the effective metric coefficients are determined at 3PM order. Our results provide a consistent effective metric for the bound state dynamics.

Hanjun Zou

Sheng Long

Xiaokai He

Zhoujian Cao

Effective metric for bound state in an effective-one-body theory based on the third-post-Minkowskian approximation

<p>The first observation of a new meson state decaying into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> and a photon is presented using a dataset of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions at a center-of-mass energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math> collected by the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>140</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> mesons are reconstructed from a three-muon final state from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub><mi>X</mi></mrow></math> decays, along with photons reconstructed via conversions to electron-positron pairs in the detector material. The new state is observed with a significance that exceeds 8 standard deviations. The mass difference between the new meson state and the ground-state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> meson is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>64.5</mn><mo>±</mo><mn>1.4</mn><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><msubsup><mrow><mtext> </mtext></mrow><mrow><mo>−</mo><mn>1.4</mn></mrow><mrow><mo>+</mo><mn>1.0</mn></mrow></msubsup><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. This corresponds to a mass for the observed state of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>6339.0</mn><mo>±</mo><mn>1.4</mn><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><msubsup><mrow><mtext> </mtext></mrow><mrow><mo>−</mo><mn>1.4</mn></mrow><mrow><mo>+</mo><mn>1.0</mn></mrow></msubsup><mrow><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo></mrow><mo>±</mo><mn>0.3</mn><mrow><mo stretchy="false">(</mo><msub><mrow><mi>m</mi></mrow><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></msub><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>, where the last uncertainty is due to the precision of the best knowledge of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> meson mass. The low mass difference value matches the theory expectations for the lowest vector state of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></math> system, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></mrow></math> meson.</p>

France

G. Aad

Norway

E. Aakvaag

United States

B. Abbott

United Arab Emirates

S. Abdelhameed

Germany

K. Abeling

N.J. Abicht

S.H. Abidi

M. Aboelela

Morocco

A. Aboulhorma

Israel

H. Abramowicz

B.S. Acharya

A. Ackermann

Switzerland

J. Ackerschott

C. Adam Bourdarios

Poland

L. Adamczyk

S.V. Addepalli

United Kingdom

M.J. Addison

J. Adelman

Türkiye

A. Adiguzel

T. Adye

A.A. Affolder

Y. Afik

Spain

M.N. Agaras

A. Aggarwal

Romania

C. Agheorghiesei

A. Ahmad

F. Ahmadov

S. Ahuja

X. Ai

G. Aielli

A. Aikot

M. Ait Tamlihat

Sweden

T.P.A. Åkesson

Japan

D. Akiyama

N.N. Akolkar

S. Aktas

G.L. Alberghi

Canada

J. Albert

U. Alberti

P. Albicocco

S. Alderweireldt

Z.L. Alegria

CERN

M. Aleksa

I.N. Aleksandrov

C. Alexa

Greece

T. Alexopoulos

F. Alfonsi

M. Algren

M. Alhroob

Czechia

B. Ali

H.M.J. Ali

S. Ali

S.W. Alibocus

South Africa

M. Aliev

G. Alimonti

C. Allaire

B.M.M. Allbrooke

D.R. Allen

J.S. Allen

J.F. Allen

Australia

C.S. Alley

E.R. Almazan

A. Aloisio

Argentina

F. Alonso

C. Alpigiani

A. Alvarez Fernandez

M. Alves Cardoso

M.G. Alviggi

Brazil

Y. Amaral Coutinho

C. Amelung

M. Amerl

T. Amezza

B. Amini

K. Amirie

A. Amirkhanov

D. Amperiadou

C. Anastopoulos

T. Andeen

J.K. Anders

A.C. Anderson

A. Andreazza

S. Angelidakis

A. Angerami

A.V. Anisenkov

A. Annovi

C. Antel

E. Antipov

M. Antonelli

F. Anulli

M. Aoki

T. Aoki

M.A. Aparo

L. Aperio Bella

M. Apicella

C. Appelt

A. Apyan

R. Arakida

M. Arampatzi

S.J. Arbiol Val

C. Arcangeletti

Observation of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></mrow></math> Meson with the ATLAS Detector

<p>By analyzing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2712.4</mn><mo>±</mo><mn>14.3</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mtext> </mtext><mtext> </mtext><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> events collected with the BESIII detector operating at the BEPCII collider, the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>η</mi><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi></math>. (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2) are observed for the first time, with statistical significances exceeding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mi>σ</mi></math> for all three <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> states. The measured branching fractions are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>η</mi><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>5.3</mn><mo>±</mo><mn>0.7</mn><mo>±</mo><mn>0.5</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>η</mi><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>9.8</mn><mo>±</mo><mn>0.6</mn><mo>±</mo><mn>0.6</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>η</mi><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>9.3</mn><mo>±</mo><mn>0.6</mn><mo>±</mo><mn>0.6</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, where the first uncertainties are statistical and the second are systematic. Structures consistent with the known hyperon resonances <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1520</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo></math> are seen in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>η</mi></math> invariant mass spectra, respectively. The reported branching fractions include both resonant and nonresonant contributions. These results provide new experimental information on hadronic decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave charmonium states and contribute to the understanding of baryon production and hadronization dynamics in the nonperturbative QCD regime.</p>

M. Ablikim

Russia

M.N. Achasov

P. Adlarson

X.C. Ai

C.S. Akondi

R. Aliberti

A. Amoroso

Q. An

Y.H. An

M.S. Anderson

Y. Bai

JINR

O. Bakina

H.R. Bao

X.L. Bao

M. Barbagiovanni

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

D. Cabiati

Observation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> decays into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>η</mi><mo>+</mo><mrow><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></mrow></math>