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)

We investigate the impact of a non-gravitational dark sector interaction on the growth of matter density perturbations within both the interacting $\textit{w}$CDM and the dynamical Chevallier–Polarski–Linder (CPL) scenarios. For $\textit{w}$CDM model, we develop a parameterization for the growth rate based on a second-order approximation for the growth index $$\gamma $$ that explicitly includes the coupling constant $$\alpha $$ . Our analysis reveals a theoretical degeneracy: the coupling induces a correction $$\Delta \gamma \simeq 1.1\alpha $$ in both models, allowing an interacting dark energy model to mimic the growth index predicted by certain modified gravity theories. Then, we confront the models with the latest multi-probe observations, including the Pantheon+ sample of Type Ia supernovae, Baryon Acoustic Oscillation (BAO) data from the Sloan Digital Sky Survey (SDSS) and the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI), Cosmic Microwave Background (CMB) measurements, Hubble parameter $\textit{H}$($\textit{z}$) data, and redshift-space distortion (RSD) measurements. Our analysis finds that the coupling constant is consistent with zero at approximately the $$3\sigma $$ and $$2\sigma $$ confidence levels for $\textit{w}$CDM and CPL models, respectively, showing no definitive statistical evidence for a departure from the standard $$\Lambda $$ CDM cosmology. The observational constraints strongly disfavor the region of parameter space where interacting dark energy can mimic modified gravity, restricting the growth index to a common approximate interval of $$0.53 \lesssim \gamma \lesssim 0.60$$ for both models. This reinforces the growth index as a robust diagnostic for distinguishing between a non-minimal interaction in the dark sector and a genuine modification of gravity with current data.

Fan Yang

Rongrong Zhai

Xiangyun Fu

Bing Xu

Kaiwen Liu

Chikun Ding

Yang Huang

Impact of interacting dark energy on the growth of matter density perturbations: observational constraints from DESI and multi-probe data

Pseudospin symmetry (PSS) is a relativistic symmetry of the Dirac Hamiltonian that is strictly conserved for single-particle resonant states in spherical nuclei when <math altimg='si27.svg'><mrow><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mo>&#8801;</mo><mi>S</mi><mo linebreak='goodbreak'>+</mo><mi>V</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, but whether this strict conservation persists in deformed nuclei, and how the sign of quadrupole deformation affects PSS breaking, remain open questions. This work aims to systematically investigate the conservation and breaking mechanisms of PSS for single-particle resonant states in both spherical and axially deformed nuclei, with special emphasis on the asymmetric role of the deformation sign&#8212;a dimension not explored in previous studies. The complex momentum representation (CMR) method is adopted, extended to quadrupole-deformed Woods-Saxon potentials, providing a unified description of bound states, resonances, and the continuum, and enabling the calculation of energies, widths, and Dirac wavefunction components in both coordinate and momentum spaces. In spherical nuclei at <math altimg='si1.svg'><mrow><msub><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mn>0</mn></msub><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, pseudospin partners have exactly the same energies, widths, and lower-component density distributions&#8212;strict conservation. In deformed nuclei, even at <math altimg='si1.svg'><mrow><msub><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mn>0</mn></msub><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, deformation lifts degeneracy; PSS becomes only approximately conserved, with a clear asymmetry: prolate ( <italic>&#946;</italic> <inf>2</inf>&#8239;&gt;&#8239;0) deformation yields small, stable splittings, while oblate ( <italic>&#946;</italic> <inf>2</inf>&#8239;&lt;&#8239;0) deformation induces larger, more sensitive splittings. For fixed <math altimg='si12.svg'><mrow><msub><mi>&#946;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>0.34</mn></mrow></math>, deepening the potential well increases splitting and drives resonances toward bound states, but does not alter the shape of density distributions. This work reveals, for the first time, that the sign of quadrupole deformation plays a crucial and asymmetric role in PSS breaking in resonant states&#8212;a dimension previously unexplored, providing a theoretical basis for understanding continuum coupling effects and exotic structures in weakly bound deformed nuclei.

Wei Zhou

Quan Liu

Meng-Jie Chen

Jian-You Guo

Sign of quadrupole deformation dictates pseudospin symmetry breaking in resonant states

We study the confining flux tube in the reconfined phase of trace deformed SU(2) Yang-Mills theory in (2+1) dimensions. Using lattice simulations above the standard deconfinement temperature, we analyze Polyakov-loop correlators and extract the ground state energy of the effective string. We show that the usual Nambu-Gotō effective string description, including its standard higher-order corrections, fails to reproduce the data as the trace deformation is increased. Remarkably, deep in the reconfined regime the results are instead accurately described by the Polchinski-Yang rigid-string solution, corresponding to an effective string dominated by an extrinsic-curvature term. We further investigate the transverse profile of the chromo-electric flux tube and find significant deviations from the standard Yang-Mills behavior, including a substantial modification of the intrinsic width. Finally, we present an exploratory study of the phase diagram, finding evidence for a transition from a continuous to a first order reconfinement line as the deformation parameter increases. These results suggest that the reconfined phase realizes a qualitatively different effective-string regime from ordinary confinement.

Claudio Bonati

Michele Caselle

Germany

Alessio Negro

Dario Panfalone

Lorenzo Verzichelli

Confining flux tube in the trace deformed (2+1) dimensional SU(2) gauge theory

It is well known that a strictly massless spin-3/2 particle can interact consistently only within supergravity. Recently, positivity arguments have shown that an effective field theory of a massive Majorana spin-3/2 particle admits an arbitrarily small mass only if a graviton is present and the four-fermion contact interactions are tuned to the values dictated by $$ \mathcal{N} $$ = 1 supergravity. In this work, we investigate how this limit is approached at finite mass. Assuming that the graviton $\textit{t}$-channel pole can be discarded, we derive non-forward, tree-level dispersive bounds on massive spin-3/2 contact operators and determine the region of effective couplings consistent with unitarity and analyticity. For sufficiently small $\textit{m}$, we find that the allowed parameter space forms a bounded, Planck-suppressed neighbourhood of the supergravity point, defined by the supergravity values of the four-fermion couplings. The supergravity point lies on the boundary of this region. In the regime $\textit{m}$ ≪ $\textit{M}$ , the volume of the allowed region scales parametrically as

Jay Desai

Diptimoy Ghosh

Saurabh Pant

Positivity in massive spin-3/2 EFTs and the Planck-suppressed neighbourhood of supergravity