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)

<p>We study the nonleptonic weak decays of doubly charmed baryons (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>) into singly charmed baryons (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mi>c</mi></msub></math>) and vector mesons (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math>), denoted as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><msub><mi mathvariant="script">B</mi><mi>c</mi></msub><mi>V</mi></math>. The short-distance contributions are calculated within the naive factorization hypothesis, while the long-distance final-state interaction effects are modeled via hadronic triangle diagrams. Unlike previous approaches, which compute only the imaginary part using the Cutkosky cutting rule, we evaluate the complete loop integrals to obtain both the real and imaginary parts of the amplitudes. These provide the nontrivial strong phases essential for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation. The model parameters are determined using experimental data. With this improved calculation method, we predict the branching ratios and decay asymmetry parameters for various decay channels, as well as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violations for short-distance dominated and singly Cabibbo-suppressed channels. This strengthens our theoretical framework for future study of doubly charmed baryons. Certain decays, primarily driven by long-distance effects, have been calculated, and their observation in future experiments could help clarify the role of final-state interactions in charm baryon decays. Therefore, our calculation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><msub><mi mathvariant="script">B</mi><mi>c</mi></msub><mi>V</mi></math> provides crucial predictions for branching ratios, decay asymmetry parameters, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation, which are essential for guiding experimental study at LHCb.</p>

Xiao-Hui Hu

Fu-Sheng Yu

Ye Xing

Final-state rescattering mechanism of doubly-charmed baryon decays: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><msub><mi mathvariant="script">B</mi><mi>c</mi></msub><mi>V</mi></math>

Measurements of the production of the W $$^{\pm }$$ and Z $$^0$$ bosons at midrapidity in pp collisions at $$\sqrt{s} = 13$$ TeV with ALICE at the Large Hadron Collider (LHC) are presented. The W $$^{\pm }$$ and Z $$^0$$ bosons are detected via their (di)electronic decay channels, with the electron reconstruction performed in the midrapidity region $$(|y|< 0.6).$$ The $$p_{{\text {T}}}$$ -integrated and $$p_{\textrm{T}}$$ -differential production cross sections of electrons from W $$^{\pm }$$ decays in the interval $$30<p_{{\text {T}}}< 60$$ GeV/$\textit{c}$, as well as the $$p_{{\text {T}}}$$ -integrated production cross section of Z $$^0$$ bosons, are measured. The results are described by perturbative QCD calculations using different sets of parton distribution functions. The production of W $$^{\pm }$$ bosons and azimuthally correlated associated hadrons is also measured as a function of the charged-particle multiplicity for the first time at the LHC. The former increases approximately linearly with the charged-particle multiplicity, while for the latter, there are hints of a faster-than-linear increase. These observations are compared with theoretical calculations.

United States

I. Abualrob

S. Acharya

Switzerland

G. Aglieri Rinella

L. Aglietta

N. Agrawal

Z. Ahammed

S. Ahmad

Slovakia

I. Ahuja

Indonesia

Z. Akbar

A. Akindinov

Germany

V. Akishina

M. Al-Turany

D. Aleksandrov

B. Alessandro

Mexico

R. Alfaro Molina

B. Ali

A. Alici

South Korea

A. Alkin

Norway

J. Alme

G. Alocco

T. Alt

I. Altsybeev

Romania

C. Andrei

United Kingdom

N. Andreou

A. Andronic

E. Andronov

M. Angeletti

V. Anguelov

F. Antinori

P. Antonioli

N. Apadula

H. Appelshäuser

S. Arcelli

R. Arnaldi

I. Arsene

M. Arslandok

A. Augustinus

R. Averbeck

M. Azmi

Japan

H. Baba

A. Babu

A. Badalà

J. Bae

Y. Bae

Y. Baek

X. Bai

R. Bailhache

Y. Bailung

R. Bala

France

A. Baldisseri

Poland

B. Balis

S. Bangalia

Z. Banoo

V. Barbasova

F. Barile

L. Barioglio

Greece

M. Barlou

B. Barman

Hungary

G. Barnaföldi

L. Barnby

E. Barreau

V. Barret

Brazil

L. Barreto

K. Barth

E. Bartsch

N. Bastid

G. Batigne

D. Battistini

B. Batyunya

D. Bauri

Peru

J. Bazo Alba

Denmark

I. Bearden

P. Becht

D. Behera

S. Behera

I. Belikov

V. Bella

F. Bellini

R. Bellwied

L. Beltran

Y. Beltran

G. Bencedi

A. Bensaoula

S. Beole

Y. Berdnikov

A. Berdnikova

L. Bergmann

L. Bernardinis

L. Betev

P. Bhaduri

T. Bhalla

A. Bhasin

B. Bhattacharjee

S. Bhattarai

L. Bianchi

Czechia

J. Bielčík

J. Bielčíková

A. Bilandzic

A. Binoy

G. Biro

Measurements of the production of W $$^{\pm }$$ and Z $$^0$$ bosons in pp collisions at $$\sqrt{s} = 13$$ TeV

We study the non-equilibrium dynamics, thermalisation and attractor behaviour of charm quarks in a longitudinally expanding Quark–Gluon Plasma within the Relativistic Boltzmann Transport approach in 1+1D Bjorken expansion. Considering both a strong AdS/CFT coupling scenario with constant <math altimg='si2.svg'><mrow><mn>2</mn><mi>&#960;</mi><mi>T</mi><msub><mi>D</mi><mi>s</mi></msub><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math> and a temperature-dependent diffusion coefficient <math altimg='si1.svg'><mrow><msubsup><mi>D</mi><mi>s</mi><mtext>lQCD</mtext></msubsup><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math> from the recent unquenched lattice QCD data, we analyse the evolution of effective temperature, momentum moments and distribution functions for different initial conditions, including FONLL and EPOS4HQ spectra. We find that charm quarks exhibit dynamical attractors; however, the temperature dependence of <math altimg='si1.svg'><mrow><msubsup><mi>D</mi><mi>s</mi><mtext>lQCD</mtext></msubsup><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math> leads to significantly longer relaxation times compared to the strong coupling limit. While the memory loss of initial conditions occurs within <math altimg='si16.svg'><mrow><mo>&#8764;</mo><mn>2</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>3</mn><mrow><mspace width='0.16em' /></mrow><mi>f</mi><mi>m</mi></mrow></math> for <math altimg='si2.svg'><mrow><mn>2</mn><mi>&#960;</mi><mi>T</mi><msub><mi>D</mi><mi>s</mi></msub><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math>, they are delayed to &#8239;&#8764;&#8239;8&#8201;fm for <math altimg='si1.svg'><mrow><msubsup><mi>D</mi><mi>s</mi><mtext>lQCD</mtext></msubsup><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math>, becoming comparable to the lifetime of the Quark-Gluon Plasma phase in ultra-relativistic collisions. This indicates that charm quarks may not fully thermalise, especially in small systems such as peripheral or light-ion collisions. We further show that, for <math altimg='si1.svg'><mrow><msubsup><mi>D</mi><mi>s</mi><mtext>lQCD</mtext></msubsup><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math>, the deviation from equilibrium becomes as large as <math altimg='si17.svg'><mrow><mi>&#948;</mi><msub><mi>f</mi><mrow><mi>H</mi><mi>Q</mi></mrow></msub><mo linebreak='goodbreak'>/</mo><msub><mi>f</mi><mrow><mi>e</mi><mi>q</mi></mrow></msub><mspace width='0.33em' /><mo>&#8764;</mo><msubsup><mi>p</mi><mi>T</mi><mi>&#946;</mi></msubsup><mo>&#8764;</mo><mi mathvariant='script'>O</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math> already at <italic>p<inf>T</inf></italic>&#8239;&#8818;&#8239;2.5&#8201;GeV, rising with <italic>&#946;</italic>&#8239;&#8819;&#8239;4, thus questioning the applicability of viscous hydrodynamics to charm dynamics.

Shile Chen

Vincenzo Nugara

Maria Lucia Sambataro

Salvatore Plumari

Vincenzo Greco

Non-equilibrium dynamical attractors and thermalisation of charm quarks in nuclear collisions at the LHC energy

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>Derived a novel representation of 2&#8239;&#8594;&#8239;2 scattering left-hand cuts using right-hand cut imaginary parts.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>Provides exact extraction of logarithmic branch left-cuts for arbitrary isospin and angular momentum partial waves.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>Enables systematic quantification of left-hand cut uncertainties in unitarization methods like IAM and <italic>N</italic>/<italic>D</italic>.</para></list-item></list>

Spain

Alexandre Salas-Bernárdez

The left-cut for partial waves in terms of physical amplitudes