Quantum chromodynamics (QCD) is a fundamental theory describing quark interactions. Thus far, various quark models based on QCD have been widely used to study the properties of hadrons, including their structures and mass spectra. However, unlike quantum electrodynamics and Bohr's model of the hydrogen atom, a direct classical analogy is lacking for hadronic structures. This paper presents a classical interpretation of the nonrelativistic quark potential model, providing a more intuitive and visualizable description of strong interactions through the quantitative formulation of color charge and color flux. In addition, we establish the relationship between meson mass and its structural radius in the nonrelativistic framework and estimate key parameters of our model using available data from $ \eta_b(1S) $ and $ \Upsilon(1S) $ . Subsequently, we extend this relationship to a broader range of excited meson states and obtain their structural radii, which show good agreement with the root mean square radius or charge radius predicted by QCD calculations.

China

Zhiguang Tan

Youneng Guo

Shengjie Wang

Hua Zheng

Classical interpretation of nonrelativistic quark potential model: Color charge definition and meson mass-radius relationship * Supported in part by the Department of Education (21A0541) and Natural Science Foundation (2025JJ50382) of Hunan province, China

Higgs self-coupling is crucial to understand the structure of the scalar potential and the mechanism of electroweak symmetry breaking. In this study, we utilize a deep neural network based on a particle Transformer model that relies on an attention mechanism to comprehensively analyze the measured trilinear Higgs self-coupling through Higgs pair production with subsequent decay into four $\textit{b}$-quarks ( $ HH\to b\bar{b}b\bar{b} $ ) at the LHC. The model processes the full event-level information as input and bypasses explicit jet pairing. It also serves as an event classifier. At HL-LHC, our approach constrains $ \kappa_\lambda $ to $ (-0.25,\,5.41) $ at 68% CL, and thus achieved an improvement of ~44% in precision over conventional cut-based analyses. The results of a comparison against alternative machine learning architectures demonstrate the outstanding performance of the Transformer-based model owing to its ability to capture correlations in high-dimensional collision data with the help of the attention mechanism. These findings highlight the potential of attention-based networks and end-to-end event classifiers in collider phenomenology.

Yongcheng Wu

Liang Xiao

Yan Zhang

Deep learning to improve the sensitivity of Higgs pair searches in the 4$\textit{b}$ channel at the LHC * Supported by the National Natural Science Foundation of China (NNSFC) (12305112)

Neutrino oscillation experiments have confirmed that neutrinos are massive particles and that lepton flavors are mixed. To explain the observed lepton mass spectra and flavor mixing patterns, flavor symmetry plays a crucial and unique role. In this paper, we propose a useful symmetry-breaking scheme by applying $S_{3L} \times S_{3R} \rightarrow $ $ S_{2L} \times S_{2R} \rightarrow \emptyset$ within both charged-lepton and neutrino sectors at the mass-matrix level. For the three distinct residual subgroups $S_{2L}^{(23)} \times S_{2R}^{(23)}$ , $S_{2L}^{(13)} \times S_{2R}^{(13)}$ , and $S_{2L}^{(12)} \times S_{2R}^{(12)}$ that are under consideration, we systematically analyze the various parameterizations of the lepton mass matrices. It is shown that all three scenarios are in good agreement with current neutrino oscillation data. Notably, within the latest best-fit values of neutrino oscillation parameters, the predicted values of the Dirac CP-violating phase $\textit{δ}$ are $294.6^\circ$ , $302.3^\circ$ , and $287.0^\circ$ , respectively. To further assess the viability of the model, a comprehensive numerical analysis is performed by utilizing neutrino oscillation parameters at the $3\sigma$ level. It is found that the allowed ranges of $\textit{δ}$ are $281.2^\circ \rightarrow 338.7^\circ$ , $287.0^\circ \rightarrow 342.2^\circ$ , and $282.7^\circ \rightarrow 297.0^\circ$ , which all fall within its $3\sigma$ range. These results indicate that the proposed symmetry-breaking scheme $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$ can naturally explain the realistic lepton mass hierarchy and mixing pattern, thereby providing valuable theoretical perspectives for future research.

Chang-Qi Hu

Chun-Yuan Li

Xiao Liang

Xing-Hua Yang

Dai-Xing Zhang

Further study on lepton mass spectra and flavor mixing with $\textit{S}$ 3$\textit{L}$ × $\textit{S}$ 3$\textit{R}$ flavor symmetry * Supported in part by the National Natural Science Foundation of China (12105162, 12305106), the Natural Science Foundation of Shandong Province (ZR2021QA058, ZR2021QA040) and the Youth Innovation Technology Project of Higher School in Shandong Province (2023KJ146)

Symmetry studies represent one of the most promising frontiers in particle physics research. This investigation focuses on exploring P and $\rm CP $ symmetries in the charm system through the measurement of asymmetry decay parameters in the three-body decay of $ \Xi_c^{+} $ . By incorporating electron and positron beam polarization effects and utilizing the helicity formalism, we characterize the decay of $ \Xi_c^{+} $ and its secondary hyperons through asymmetry decay parameters. The complete angular distribution formula for these decays is systematically derived. Our study evaluates the sensitivity of the asymmetry parameters for the $ \Xi_c^{+} \to \Xi^{-}\pi^{+}\pi^{+} $ decay channel under various data sample sizes and beam polarization scenarios. The findings establish a robust theoretical framework for future experimental studies at the Super Tau-Charm Facility, providing valuable insights for symmetry investigations in the charm sector.

Yunlu Wang

Yunlong Xiao

Pengcheng Hong

Ronggang Ping

Study of P and CP symmetries in ${ \boldsymbol\Xi^{\bf +}_{\boldsymbol c}\rightarrow \boldsymbol\Xi^-\boldsymbol\pi^+\boldsymbol\pi^+ }$ at electron-positron collider

In this work, we investigate possible bound states in the $ D_s\bar{D}_s $ system using the Bethe-Salpeter (BS) formalism within both the ladder and instantaneous approximations. By numerically solving the Bethe-Salpeter equation with a kernel that incorporates contributions from $\textit{ϕ}$ and $ J/\psi $ meson exchanges, we confirm the existence of a loosely bound state. Furthermore, we explore the partial decay widths of the $ D_s\bar{D}_s $ bound state into the $ D\bar{D} $ , $ \eta_c\eta $ , and $ J/\psi\omega $ channels, and observe that these widths are sensitive to the model parameter $\textit{α}$. Notably, we find the dominant decay channel for the $ D_s\bar{D}_s $ bound state to be $ D\bar{D} $ .

Jing-Juan Qi

Zhen-Yang Wang

Zhu-Feng Zhang

Xin-Heng Guo

The properties of the $\textit{S}$-wave D$_{s}$ D $_{s}$ bound state * Supported by the National Natural Science Foundation of China (12405115, 12275024, 12105149)

We construct a formalism that describes the resonances decaying into four pseudoscalar meson final states. This method is fully covariant and can be directly applied to the partial-wave analysis of high statistical data. Two topologies of the process are considered: two intermediate resonances, each decaying into two final mesons, and cascade decay via three meson intermediate states. In particular, we consider the production of such states in the central collision reactions and in radiative $J/\Psi$ decay.

Russia

M.A. Matveev

A.T. Sitnikov

A.V. Sarantsev

Tensor formalism for the partial wave analysis of reactions with resonances decaying into four pseudoscalar mesons * Supported by the RSF (Grant No. 24-22-00322)

Recently, the BESIII Collaboration observed the three-body decays $ D_s^+\to \eta \omega\pi^+ $ , $ D^+\to K^0_S\pi^+\omega $ , and $ D^0\to K^-\pi^+\omega $ . In this study, we investigate the contributions of the subprocesses $ \rho^+\to \omega\pi^+ $ in these Cabibbo-favored decays $ D \to h\omega\pi $ , with $ \rho^+= \{\rho(770)^+, \rho(1450)^+, \rho(770)^+\&amp;\rho(1450)^+\} $ and $ h=\{ \eta, K^0_S, K^-\} $ , by introducing these subprocesses into the decay amplitudes of the relevant decay processes via the vector form factor $ F_{\omega\pi} $ , which has been measured in the related $\textit{τ}$ and $ e^+e^- $ processes. We provide the first theoretical predictions for the branching fractions of the quasi-two-body decays $ D_s^+\to\eta[\rho^+\to]\omega\pi^+ $ , $ D^+\to K^0_S[\rho^+\to]\omega\pi^+ $ , and $ D^0\to K^-[\rho^+\to]\omega\pi^+ $ . Our findings reveal that the contributions from the subprocess $ \rho(770)^+\to\omega\pi^+ $ are significant in these observed three-body decays $ D_s^+\to\eta \omega\pi^+ $ , $ D^+\to K^0_S \omega\pi^+ $ , and $ D^0\to K^- \omega\pi^+ $ , notwithstanding the contributions originating from the Breit-Wigner tail effect of $ \rho(770)^+ $ . The numerical results of this study suggest that the dominant resonance contributions for the three-body decays $ D_s^+\to\eta \omega\pi^+ $ and $ D^+\to K^0_S \omega\pi^+ $ originate from the $\textit{P}$-wave intermediate states $ \rho(770)^+ $ , $ \rho(1450)^+ $ and their interference effects.

Wen-Fei Wang

Jiao-Yuan Xu

Si-Hong Zhou

Spain

Pan-Pan Shi

Contributions of $\textit{ρ}$(770,1450)→$\textit{ωπ}$ to Cabibbo-favored $\textit{D}$→$\textit{hωπ}$ decays * Supported in part by the National Natural Science Foundation of China (12465017) and the Foundation of Shanxi '1331 Project' Key Subjects Construction

The charmed baryon was first observed experimentally in 1975, one year after the charm quark's confirmation via the discovery of the $ J/\psi $ particle. Studying charmed baryon decays provides a pathway to investigate both strong and weak interactions, leveraging the weak decays of the embedded charm quark. However, for approximately three decades following its discovery, experimental knowledge of charmed baryons remained significantly limited compared to those of the hidden-charm $\textit{ψ}$ mesons and open-charm $ D_{(s)} $ mesons. This situation changed markedly starting in 2014, when dedicated data collection for charmed baryons commenced at BESIII. In this article, we review the experimental progress achieved since 2014 in understanding the weak decays of the charmed baryons.

Pei-Rong Li

Xiao-Rui Lyu

Yangheng Zheng

Experimental overview on the charmed baryon decays * The authors thank Fusheng Yu for useful discussions. The authors are supported in part by National Natural Science Foundation of China (12221005, 12422504); CAS Project for Young Scientists in Basic Research (YSBR-117); Fundamental Research Funds for the Central Universities, Lanzhou University (lzujbky-2025-ytB01, lzujbky-2023-stlt01, lzujbky-2023-it32), University of Chinese Academy of Sciences

The decay of the Higgs boson and the nature of dark matter remain fundamental challenges in particle physics. We investigate the 95 GeV diphoton excess and dark matter within the framework of the triplet-extended minimal supersymmetric standard model (TMSSM). In this model, an additional hypercharge $ Y=0 $ , $ S U(2)_L $ triplet superfield is introduced. Mixing between the triplet and doublet Higgs states enhances the diphoton signal strength of the 95 GeV Higgs boson, resulting in $ \mu_{\gamma\gamma}^{{\rm{CMS+ATLAS}}} = 0.24_{-0.08}^{+0.09} $ , which is consistent with experimental observations. This enhancement arises primarily from charged Higgs and chargino loop contributions, together with an LEP excess in the $ Zb\bar{b} $ channel around the same mass within the $ 2\sigma $ range. Additionally, the model accommodates viable dark matter candidates in the form of a bino-dominated neutralino. The relic density is reduced to the observed value through resonance-enhanced annihilation via the Higgs portal or co-annihilation with the triplino or higgsino. This reduction remains consistent with constraints from direct and indirect detection experiments. A comprehensive parameter scan demonstrates that the TMSSM can simultaneously explain the 95 GeV diphoton excess, observed 125 GeV Higgs mass, and dark matter relic density, establishing a compelling and theoretically consistent framework.

Zetian Li

Ning Liu

Bin Zhu

Interplay of 95 GeV diphoton excess and dark matter in supersymmetric triplet model * Supported by the National Natural Science Foundation of China (NNSFC) (12275232, 12335005) and Bin Zhu is also supported by the Natural Science Foundation of Shandong Province (ZR2025QA20)

An $\textit{SU}$(3) flavor projection operator technique is implemented to construct the baryon-meson scattering amplitude within the framework of the $1/N_c$ expansion of quantum chromodynamics (QCD), where $N_c$ represents the number of color charges. The operator technique is implemented to evaluate not only the lowest-order scattering amplitude but also effects from the first-order perturbative $\textit{SU}$(3) flavor symmetry breaking and strong isospin breaking. The most general expression is obtained by explicitly accounting for the effects of the decuplet-octet baryon mass difference. At order ${\cal{O}}(1/N_c^2)$ , a large number of unknown operator coefficients appear, and therefore, there is little additional predictive power unless leading and subleading terms are retained. Although the resultant expression is sufficiently general that it can be applied to any incoming and outgoing baryons and pseudo scalar mesons, provided that the Gell-Mann--Nishijima scheme is respected, results for $N\pi\to N\pi$ scattering processes are explicitly considered.

Víctor Miguel Banda Guzmán

Rubén Flores-Mendieta

Johann Hernández

Use of $\textit{SU}$(3) flavor projection operators to construct baryon-meson scattering amplitudes in the 1/ N$_{c}$ expansion * The authors are grateful to Consejo Nacional de Humanidades, Ciencias y Tecnologías (Mexico) for support through the $\textit{Ciencia de Frontera}$ project CF-2023-I-162