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)

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)

We explore a supergravity model based on the modified Kähler potential $$\hat{K} = -3 \ln \left( \Phi + \Phi ^\dagger - \beta \, \mathcal {R} \bar{\mathcal {R}} -\right. \left. \gamma \, (\mathcal {R}\bar{\mathcal {R}})^2 \right) $$ ,where $$\Phi $$ is a chiral superfield containing the dilaton and $$\mathcal {R}$$ is the chiral curvature superfield. The quartic term $$-\gamma (\mathcal {R}\bar{\mathcal {R}})^2$$ ensures stabilization of the curvature sector, in line with recent proposals in modified supergravity, while the linear term $$-\beta \mathcal {R}\bar{\mathcal {R}}$$ yields a dilaton-modulated contribution to the effective $$R^2$$ coefficient. As clarified via the superfield Legendre transform, the model is equivalent to Einstein supergravity coupled to three chiral superfields ( $$\Phi $$ , $\textit{S}$, $\textit{T}$), yielding six physical scalars. Full stability requires both the curvature–sector stabilization (via $$\gamma $$ ) and a non-vanishing dilaton VEV. When the extra scalars are stabilized and $$\langle \phi \rangle = \mathcal {O}(M_P)$$ , the kinetic mixing is exponentially suppressed during inflation ( $$Z \propto e^{-\sigma /\sqrt{6}}$$ ), reducing the dynamics to an effectively single-field Starobinsky model. Thus, cosmological viability is inherited conditionally from the established success of Starobinsky inflation. To the best of our knowledge, this represents the first explicit realization of $\textit{dilaton-coupled modified supergravity}$, where a physical scalar (the dilaton) directly influences the curvature sector through the Kähler geometry. While chiral matter couplings to modified supergravity have been studied in the literature, the explicit coupling of the dilaton remains unexplored. The framework is presented as a phenomenological ansatz for exploring scalar–curvature unification in supersymmetry, with the understanding that a UV completion remains an open challenge.

Iran

Reza Baghbani

Dilaton coupling to $\textit{R}$

We confront the ghost-free non-local <italic>F</italic>( <italic>R</italic>) gravity theories with the latest Atacama Cosmology Telescope (ACT) constraints on the spectral index of the scalar perturbations and the updated constraints of Planck/BICEP on the tensor-to-scalar ratio. After reviewing how the ghost-free non-local version of <italic>F</italic>( <italic>R</italic>) gravity can be obtained, we show that the de Sitter solution can be obtained in this framework. Also, we show that the resulting theory can be cast in terms of an <italic>F</italic>( <italic>R, &#981;</italic>) theory of gravity. We analyze two models of non-local <italic>F</italic>( <italic>R</italic>) gravity, one power-law and the <italic>R</italic> 2 model, and we show that both models can be compatible with the ACT and updated Planck/BICEP constraints.

Japan

Shin’ichi Nojiri

Spain

Sergei Odintsov

Greece

Azerbaijan

V.K. Oikonomou

Ghost-free non-local <italic>F</italic>( <italic>R</italic>) gravity compatible with ACT

The Galactic Center excess (GCE) of GeV <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> rays may hint at dark matter (DM), yet its origin remains debated. Motivated by this, we survey weakly interacting massive particle (WIMP) models that can fit the GCE while satisfying relic-density, direct-detection (DD), and indirect-detection (ID) bounds. We group candidates into hadronic (Higgs portals; simplified scalar/vector mediators), leptonic [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>i</mi></msub><mo>−</mo><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math>], and mixed [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>-portal] classes. Across all cases, present DD and dwarf-spheroidal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray limits exclude wide regions, leaving mainly narrow resonant funnels with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mrow><mi>DM</mi></mrow></msub><mo>≃</mo><msub><mi>m</mi><mrow><mi>med</mi></mrow></msub><mo>/</mo><mn>2</mn></math> and portal couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≪</mo><mn>1</mn></math>. In hadronic setups, scalar and vector Higgs portals survive only in a thin strip near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>h</mi></msub><mo>/</mo><mn>2</mn><mo>≃</mo><mn>62.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> with portal couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, while the Dirac Higgs and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> portals are essentially excluded. The UV-complete vector Higgs portal retains resonant bands whose viable portal strength depends on the mixing angle. Simplified scalars allow small windows for complex-scalar or vector DM; Dirac DM is strongly disfavored, whereas a pseudoscalar with Dirac DM remains viable over a broader parameter range. For a simplified <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> mediator, a pure vector coupling leaves only a marginal region, while pure axial is excluded by DD/ID bounds. In leptonic scenarios, inverse-Compton emission is essential: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>e</mi></msub></math> (and, to a lesser extent, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math>) fits the GCE with near-thermal cross sections, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></math> is disfavored. Overall, viable WIMP explanations are constrained to the finely tuned resonant regime, with leptophilic vectors and pseudoscalar portals emerging as the most robust options.

United States

Chuiyang Kong

Italy

Mattia Di Mauro

Comprehensive study of WIMP models explaining the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi><mi>e</mi><mi>r</mi><mi>m</mi><mi>i</mi></math>-LAT Galactic Center excess

By using the integrable lattice model proposed by Maulik and Okounkov, we derive the (higher) Hamiltonians of the (generalized) trigonometric Calogero-Sutherland models. Then in terms of these (higher) Hamiltonians, we further construct certain nested structures and derive the commutative operators which coincide with the (higher) Hamiltonians of the (generalized) rational Calogero-Sutherland models.

Yue Li

Fan Liu

Rui Wang

Jie Yang

The (higher) Hamiltonians of (generalized) trigonometric and rational Calogero-Sutherland models by MO <italic>R</italic>-matrix

In this paper, we investigate the traversable wormhole solutions in the presence of charge within the framework of <italic>f</italic>( <italic>R, &#981;</italic>) gravity, where <italic>R</italic> represents the Ricci scalar and <italic>&#981;</italic> denotes the scalar potential, respectively. We also consider the Karmarkar condition for the discussion of wormhole geometry. The obtained shape function satisfies all necessary Morris-Thorne criteria for traversability. We derive and graphically examine the physical characteristics, including energy density and pressure components, for a specific linear charge distribution. Our analysis confirms the violation of the null energy condition in the radial direction. The violation of these energy conditions indicates the presence of exotic matter, which is the main candidate for the existence of a wormhole. Under some sensible conditions, the analysis may give an assurance of the existence of wormhole geometries in the <italic>f</italic>( <italic>R, &#981;</italic>) theory of gravity. Furthermore, we investigate the stability of the wormhole through the Tolman-Oppenheimer-Volkov equation, namely the equilibrium condition. By comparing four distinct <italic>f</italic>( <italic>R, &#981;</italic>) models, we demonstrate the robustness of traversable wormhole solutions in this modified gravity setting and identify parameter ranges that minimize energy condition violations. The results affirm that <italic>f</italic>( <italic>R, &#981;</italic>) gravity, augmented by an electromagnetic field, can support stable, traversable wormhole geometries.

Pakistan

Adnan Malik

M. Waqas Aslam

Wenbin Lin

Muhammad Kashif Shafiq

Saudi Arabia

Fatemah Mofarreh

Ramy M. Hafez

Impact of charge on traversable wormhole solutions and modified <italic>f</italic>( <italic>R, &#981;</italic>) gravity

We investigate the gravitational baryogenesis scenario within the context of $\textit{F}$($\textit{R}$) gravity’s rainbow which incorporates both modified gravity and energy-dependent spacetime. This study explores a mechanism for generating baryon asymmetry based on the interaction between the derivative of the Ricci scalar $\textit{R}$ and the baryon current within the framework of $\textit{F}$($\textit{R}$) gravity’s rainbow. The rainbow functions, arising from quantum gravity effects, modify the gravitational interaction and the Friedmann equations, leading to a distinct evolution of the baryon asymmetry compared to standard $\textit{F}$($\textit{R}$) gravity. We analyze the conditions under which a viable baryon asymmetry can be produced, taking into account the constraints from cosmological observations and the specific form of the $\textit{F}$($\textit{R}$) function. By examining the cosmological equations in the context of $\textit{F}$($\textit{R}$) gravity’s rainbow, we obtain power-law solutions for these equations. We also identify the decoupling temperature and the ratio of baryonic number to entropy density in this model, depending on the model’s parameters. First, we discuss the acceptable intervals of the model’s parameters which are defined by constraints on the background quantity. We note that the decoupling temperature and the ratio of baryon-to-entropy in these models depend on the value of the rainbow function. We compare the predictions of this model with the existing observational data. Our results suggest that $\textit{F}$($\textit{R}$) gravity’s rainbow provides a novel mechanism for gravitational baryogenesis, potentially explaining the observed baryon asymmetry in the universe while incorporating quantum gravity corrections.

Parviz Goodarzi

Gravitational baryogenesis in $\textit{F}$($\textit{R}$) gravity’s rainbow

The minimal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-symmetric supersymmetric Standard Model with a seesaw mechanism extends the minimal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-symmetric supersymmetric Standard Model by incorporating right-handed neutrinos to generate neutrino masses via the type-I seesaw mechanism. This work presents a detailed analysis of lepton-flavor-violating (LFV) processes, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mo>ℓ</mo><mi>i</mi></msub><mo stretchy="false">→</mo><msub><mo>ℓ</mo><mi>j</mi></msub><mi>γ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mo>ℓ</mo><mi>i</mi></msub><mo stretchy="false">→</mo><mn>3</mn><msub><mo>ℓ</mo><mi>j</mi></msub></math>, and Higgs decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><msub><mo>ℓ</mo><mi>i</mi></msub><msub><mo>ℓ</mo><mi>j</mi></msub></math>. Based on the current experimental limitations, we carry out detailed parameter scanning and numerical calculations to analyze the effects of different sensitive parameters on LFV. The numerical results show that the nondiagonal elements involving the initial and final leptons are the main sensitive parameters and LFV sources.

Hao-yi Liu

Jin-Lei Yang

Ke-Sheng Sun

Tai-Fu Feng

Lepton-flavor violation in the minimal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-symmetric SSM with a seesaw mechanism

This paper studies the impact of bulk viscosity on the feasibility of the cosmological bounce solutions in the framework of $\textit{F}$($\textit{R}$) theory. In this perspective, the behavior of an isotropic homogeneous universe with a perfect matter configuration and new formulation of the bulk viscosity coefficient is explored. We select a specific mathematical form of the modified gravity model to see how it affects the dynamics of cosmic evolution. In addition, we analyze various cosmological parameters, exploring the presence of feasible cosmological bounce solutions. A physically acceptable bouncing scenario occurs when the energy density stays positive, pressure becomes negative, and the violation of null and strong energy conditions highlight the important role of bulk viscosity. We also study the cosmographic parameters and their paths in the $$r-s$$ diagnostic framework. Finally, a thermodynamic investigation is carried out to test the generalized second law of thermodynamics and the overall stability of the cosmological model. The results show that $\textit{F}$($\textit{R}$) gravity is a realistic and promising alternative to the standard cosmological model, giving deeper understanding of gravitational dynamics and the early evolution of cosmos.

M. Sharif

Eman Moneer

Nusrat Fatima

Russia

Euaggelos Zotos

Cosmic evolution beyond the singularity: a study of viscous bounce dynamics in $\textit{F}$($\textit{R}$) theory