Inspired by the observation of the ${\eta}_{t}$ meson at the LHC and the promising prospect of the ${\eta}_{t}$ meson available at the approaching HL-LHC, branching ratios for the ${\eta}_{t}$ ${\to}$ $f\bar{f}$ , $gg$ , ${\gamma}{\gamma}$ , $W^{+}W^{-}$ , $Z^{0}Z^{0}$ , $Z^{0}{\gamma}$ , and $Z^{0}H$ decays are roughly estimated. It is found that tens of opposite-charge dilepton events from the ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ decay and hundreds of events from the ${\eta}_{t}$ ${\to}$ $Z^{0}H$ ${\to}$ ${\ell}^{+}{\ell}^{-}H$ decay using the single $Z^{0}$ boson tagging method are expected to be accessible. This estimation provides a reference for future experimental study on the ${\eta}_{t}$ meson.

China

Yueling Yang

Bingbing Yang

Jiazhi Li

Zhaojie Lü

Junfeng Sun

Searching for the toponium ${{\boldsymbol\eta}_{\boldsymbol t}}$ with the ${{\boldsymbol\eta}_{\boldsymbol t}}$ ${\boldsymbol\to}$ ${{\boldsymbol W}^{\bf +}{\boldsymbol W}^{\bf -}}$ decay * Supported by the National Natural Science Foundation of China (12275068, 12275067), the National Key R&D Program of China (2023YFA1606000), the Natural Science Foundation of Henan Province (252300421491, 242300420250), and the Science and Technology R&D Program Joint Fund Project of Henan Province (225200810030), as well as the Science and Technology Innovation Leading Talent Support Program of Henan Province (254200510039)

We investigate the discovery prospects of a leptophilic gauge boson $ Z_\ell $ at future $ e^+e^- $ colliders, focusing on a comparative study of the Circular Electron–Positron Collider (CEPC) and the International Linear Collider (ILC). Such a state naturally arises from an additional $ U(1)'_\ell $ gauge symmetry, under which quarks remain neutral while all leptons carry a universal charge, motivated by neutrino oscillations and scenarios of physics beyond the Standard Model. As a clean benchmark, we study the process $ e^+e^- \to \mu^+\mu^- $ , including realistic effects of initial-state radiation and beamstrahlung. Our results indicate that the CEPC, with its very high luminosity at $ \sqrt{s}=240 $ GeV, can probe couplings down to $ g_\ell \approx 10^{-3} $ for $ Z_\ell $ masses up to about 220 GeV. The ILC extends the sensitivity to heavier states in the multi-hundred GeV range through its higher $ \sqrt{s} $ stages. These findings demonstrate the strong complementarity of circular and linear colliders in exploring purely leptophilic interactions.

S.O. Kara

Discovery prospects for a leptophilic gauge boson Z$_{ℓ}$ at CEPC and ILC

Heavy Majorana neutrinos ($\textit{N}$) are predicted in many models of physics beyond the Standard Model. In this work, we explore the production and detection prospects of TeV-scale heavy neutrinos ( $ m_N \gtrsim 1 $ TeV) at a future 3 TeV Compact Linear Collider (CLIC). We focus on two distinct decay topologies: (i) $ N \to \ell^\pm W^\mp $ with hadronic $\textit{W}$ boson decay, leading to a final state with one charged lepton and a hadronic fat jet $ J_W $ ; and (ii) $ N \to \nu h $ with subsequent Higgs decay $ h \to b\bar{b} $ , yielding a Higgs-tagged fat jet $ J_h $ and $\not {E}_T$ . Based on comprehensive detector-level simulations and background analysis, we present both $ 2\sigma $ exclusion limits and $ 5\sigma $ discovery reaches in the $ m_N $ – $ |V_{\ell N}|^2 $ plane. We further extract 95% confidence level upper limits on the mixing parameter $ |V_{\ell N}|^2 $ and perform a detailed comparison with existing constraints from direct searches at future colliders and indirect global fits. Our findings demonstrate that a 3 TeV CLIC can improve the sensitivity to $ |V_{\ell N}|^2 $ by about two orders of magnitude compared with the projected reaches of future hadron colliders while remaining competitive with other CLIC search channels.

Yao-Bei Liu

Jing-Wei Lian

Searches for heavy neutrinos at a 3 TeV CLIC in fat jet final states * Yao-Bei Liu is supported by the Natural Science Foundation of Henan Province, China (252300421988), Jing-Wei Lian is supported by the National Natural Science Foundation of China (12447140) and the Natural Science Foundation of Henan Province, China (252300421771)

One-loop contributions for the decay process $ H^{\pm} \rightarrow W^{\pm}Z $ within the Two-Higgs-Doublet Model (THDM) are computed in the general $ {\cal{R}}_{\xi} $ gauge, and its phenomenological applications at future muon–TeV colliders are investigated. Analytic results are confirmed by several consistency tests, including those of $\textit{ξ}$-independence, renormalization-scale stability, and the ultraviolet finiteness of the one-loop amplitude. We first perform an updated parameter scan of the Type-X THDM in phenomenological studies. The production of charged Higgs boson pairs at future muon–TeV colliders is then investigated through two processes: $ \mu^+\mu^- \rightarrow H^+H^- \rightarrow W^{\pm}W^{\mp}Zh $ and $ \mu^+\mu^- \rightarrow \gamma\gamma \rightarrow H^+H^- \rightarrow W^{\pm}W^{\mp}Zh $ . Both signal events and their significance are evaluated considering the corresponding Standard Model backgrounds. We find that the signal significances can exceed $ 5\sigma $ at several benchmark points in the viable parameter space of the Type-X THDM.

Vietnam

Dzung Tri Tran

Quang Hoang-Minh Pham

Khoa Ngo-Thanh Ho

Khiem Hong Phan

One-loop expressions for ${H^\pm \rightarrow W^\pm Z} $ and their implications at muon-TeV colliders * This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) (103.01-2023.16)

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.

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

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

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 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)

In this study, we investigate the isospin-violating decays of $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ , which may provide additional information for the determination of the properties of $ B_{c}(1P)^{+} $ , the first orbital excitation states of the $B_c $ meson. By assuming a dual relation between the $\textit{U}$(1) anomaly soft-gluon coupling for $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ and the intermediate meson loop transitions, we can quantify the isospin-violating decay effects for these four $\textit{P}$-wave states. We observe that the partial decay width of $ B_{c0}^{*+}\to B_{c}^{+}\pi^{0} $ is approximately three orders of magnitude larger than that for $ B_{c2}^{*+}\to B_{c}^{+}\pi^{0} $ . This indicates that $ B_{c0}^{*+} $ can be established in the $ B_{c}^{+}\pi^{0} $ decay channel as a single state. Meanwhile, the two axial-vector states $ B_{c1}^{+}/B_{c1}'^{+} $ can be possibly identified in $ B_{c1}^{+}/B_{c1}'^{+}\to B_{c}^{*+}\pi^{0} $ with comparable strengths. Although these isospin-violating decays are observed to be small, the theoretical predictions should be useful for guiding future experimental efforts.

Jun Wang

Qiang Zhao

Predictions for the isospin-violating decays of ${{\boldsymbol B}_{\boldsymbol c}({\boldsymbol{1P}})^{\bf +}{\bf\to}{\boldsymbol B}_{\boldsymbol c}^{({\bf *})+}\boldsymbol\pi^{\bf 0}}$ * Supported, in part, by the National Natural Science Foundation of China (12235018), DFG and NSFC funds to the Sino-German CRC 110 'Symmetries and the Emergence of Structure in QCD' (12070131001, DFG Project-ID 196253076), National Key Basic Research Program of China (2020YFA0406300) and Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302)