The Galactic Center GeV Excess (GCE) remains a compelling but enigmatic signal from the inner regions of our galaxy. Muonphilic dark matter (DM), which couples exclusively to muons via a new mediator, provides a viable explanation for the GCE and relic density while naturally evading constraints from direct detection, collider searches, and other multimessenger observations. Based on the viable nonresonant parameter space identified in previous global fits, we perform a comprehensive study on the prospects for discovering such muonphilic DM in the context of a future 3 TeV muon collider, focusing on simplified models with a $Z_2$ -even mediator. Four distinct search strategies are investigated: visible on-shell mediator decays ( $\mu^{+}\mu^{-}\gamma$ final state), invisible on-shell mediator decays (mono-photon plus missing energy), mono-photon production via off-shell mediators, and vector boson fusion production. Through a detailed signal-background analysis using cut-and-count methods, we project the exclusion limits at $ 95 $ % confidence level for seven representative models across a wide range of mediator masses. Our results demonstrate that the projected limits cover a significant portion of viable parameter space that explains the GCE, establishing a muon collider as a decisive machine for testing the muonphilic DM hypothesis.

China

Wanyun Chen

Haoqi Li

Chih-Ting Lu

Qiulei Wang

Exploring muonphilic dark matter with the $\textit{Z}$ $_{2}$-even mediator at muon colliders * Chih-Ting Lu, Wanyun Chen and Haoqi Li are supported by the National Natural Science Foundation of China (NNSFC) (12335005, 12575118) and the Special funds for postdoctoral overseas recruitment, Ministry of Education of China

Positive and negative flows of the Chen-Lee-Liu model and its various reductions, including Burgers hierarchy, are formulated within the framework of Riemann-Hilbert-Birkhoff decomposition with the constant grade two generator. Two classes of vacua, namely zero vacuum and constant non-zero vacuum can be realized within a centerless Heisenberg algebra. The tau functions for soliton solutions are obtained by a dressing method and vertex operators are constructed for both types of vacua. We are able to select and classify the soliton solutions in terms of the type of vertices involved. A judicious choice of vertices yields in a closed form a particular set of multi soliton solutions for the Burgers hierarchy. We develop and analyze a class of gauge-Bäcklund transformations that generate further multi soliton solutions from those obtained by dressing method by letting them interact with various integrable defects.

Brazil

Ireland

Y.F. Adans

United States

H. Aratyn

C.P. Constantinidis

J.F. Gomes

G.V. Lobo

T.C. Santiago

New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its Bäcklund transformations

In this study, we compute the next-to-leading-order QCD corrections to the Dirac electromagnetic form factors of the Σ hyperons within the hard-collinear factorization framework at leading power. The corresponding short-distance coefficient functions are extracted from the relevant seven-point partonic correlation functions. We find that the one-loop radiative corrections to the leading-twist hard-scattering contributions are numerically significant over a broad range of momentum transfer. Combining the perturbatively calculated hard kernels with nonperturbative Σ distribution amplitudes determined from lattice QCD, we present state-of-the-art theoretical predictions for the Σ hyperon electromagnetic form factors.

Bo-Xuan Shi

Hui-Xin Yu

Xue-Chen Zhao

Next-to-leading-order QCD predictions for the Σ Dirac form factors * This research is supported by the National Natural Science Foundation of China (12475097, 12535006) and the Natural Science Foundation of Tianjin (25JCZDJC01190). Xue-Chen Zhao is supported by the Postdoctoral Fellowship Program of CPSF (GZB20250794)

We review the recent work by T.F. Dabash, M. Emam, and L. Schöppner (Eur. Phys. J. C 85, 1341, 2025) and identify an essential error in their analysis.

South Africa

Chile

Andronikos Paliathanasis

Comment on: “Symmetry and conserved quantities in $$f\left( R\right) $$ -gravity: Mei vs. Noether approaches”

We solve the Dirac equation for a massive charged fermion in the near-extremal charged Nariai black hole with the near-horizon geometry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>dS</mi><mn>2</mn></msub><mo>×</mo><msup><mi mathvariant="normal">S</mi><mn>2</mn></msup></math>. At the one-loop level, contrary to the catastrophic emission of charged spinless bosons in C.-M. Chen et al., [<a href="http://dx.doi.org/10.1103/PhysRevD.110.085020">Phys. Rev. D 110, 085020 (2024)</a>], we show that the emission of fermions in a narrow timelike inner region between the cosmological horizon and black hole horizon saturates the bound from the Pauli blocking and does not give an amplification (quantum superradiance). Using the reciprocal relation, we find the Schwinger emission of fermions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>AdS</mi><mn>2</mn></msub><mo>×</mo><msup><mi mathvariant="normal">S</mi><mn>2</mn></msup></math>, and compare the Schwinger emission of fermions and bosons from near-extremal Nariai black holes.

South Korea

Taiwan

Chiang-Mei Chen

Chun-Chih Huang

Sang Pyo Kim

Saturation of Pauli blocking in near-extremal charged Nariai black holes

Electroweak (EW) amplitudes in the gauge-Goldstone five-component formalism have a distinctive property: gauge symmetry is imprinted in the amplitudes, manifested as the massive Ward identity (MWI) $ k^M{\cal{M}}_M=0 $ . In this study, we used the HELAS package to numerically study gauge symmetry in EW amplitudes. First, we directly tested gauge symmetry by examining the MWI of amplitudes. Second, we modified the couplings within a vertex and among vertices to check if and how the MWI changes. Third, we tested gauge symmetry by considering the couplings modified by operators from the standard model effective field theory (SMEFT). Similar to the standard model, there are relations between different couplings that are protected by gauge symmetry. We observed that, if we modify the couplings to deviate from the relations, the MWI is violated. In contrast, the MWI is restored when the relations between couplings reduce to those in the SMEFT.

Wang-Fa Li

Junmou Chen

Qian-Jiu Wang

Zhao-Huan Yu

Numerical study on the gauge symmetry of electroweak amplitudes * Junmou Chen is supported by National Natural Science Foundation of China (12205118), Wang-Fa Li, Qian-Jiu Wang, and Zhao-Huan Yu are supported by the Guangzhou Science and Technology Planning Project (2024A04J4026)

The Klein-Gordon and Dirac equation for a massive charged field in a uniform electric field has a symmetry of two-dimensional global de Sitter (dS) and anti–de Sitter (AdS) space. In the in-out formalism the mean numbers of spinors (spin-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> fermions) and scalars (spin-0 bosons) spontaneously produced by the uniform electric field are exactly found from the Bogoliubov relations both in the global and planar coordinates of (A)<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mtext>dS</mtext><mn>2</mn></msub></math> space. We show that the uniform electric field enhances the production of charged spinor and scalar pairs in the planar and global dS space while the AdS space reduces the pair production in which weak electric fields below the Breitenlohner-Freedman bound prohibits pair production. The leading Boltzmann factor in dS space can be written as the Gibbons-Hawking radiation or Schwinger effect enhanced by e-folding factors less than one that give the QED effect or the curvature effect. We observe that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> spaces are connected by QED, such as a reciprocal relation between the mean number of spinors and scalars provided that the spacetime curvature is analytically continued. The leading behavior of the mean numbers for spinors and scalars is explained as a residue sum of contour integrals of the frequency or momentum in the phase-integral formulation.

Kuan-Yen Lin

Reciprocal relation of Schwinger pair production between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>

We study the symmetries and conserved quantities in $$f(R)$$ gravity for the static, spherically symmetric Reissner–Nordström spacetime using two complementary frameworks: Noether symmetries and Mei symmetries. Starting from a canonical Lagrangian for radial metric functions and the curvature scalar $$R$$ , we derive the associated Hamiltonian and show that the Legendre map is regular whenever both the first derivative of $\textit{f}$($\textit{R}$) with respect to $\textit{R}$ and the second derivative with respect to $\textit{R}$ is non-zero. Within Noether’s approach (variational and Lie-derivative forms), we obtain general, canonical, and internal symmetry classes and identify explicit generators; for the quadratic model $$f(R)=R^{2}$$ these include radial translations and scaling symmetries. We then formulate Mei symmetry conditions as invariance of the Euler–Lagrange equations under the first prolongation, which yields an overdetermined partial differential equation (PDE) system for the generator components. Solving this system for $$f(R)=R^{2}$$ , we find eight independent Mei generators and construct the corresponding conserved currents, some with no direct Noether analogue. The analysis demonstrates that Mei symmetries extend the standard Noether framework for higher-order Lagrangians and provide additional conserved quantities relevant to black-hole dynamics in modified gravity. We conclude with a comparison of the two symmetry schemes and outline applications to broader $$f(R)$$ models and to rotating spacetimes.

Egypt

Tahia Dabash

Moataz Emam

Germany

Lukas Schöppner

Symmetry and conserved quantities in $$ f(R) $$ -gravity: Mei vs. Noether approaches

Kerr-Newman black holes in a de Sitter (dS) space have the limit of rotating Nariai black holes with the near-horizon geometry of a warped <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>dS</mi><mn>3</mn></msub><mo>×</mo><msup><mi mathvariant="normal">S</mi><mn>1</mn></msup><mo>/</mo><msub><mi>Z</mi><mn>2</mn></msub></math> when the black hole horizon and the cosmological horizon coincide or approach close to each other. We study the rotation effect on the spontaneous emission of charges in the near-extremal rotating charged Nariai black hole and compare it to those from the near-extremal Nariai black hole in [C.-M. Chen et al., <a href="http://dx.doi.org/10.1103/PhysRevD.110.085020">Phys. Rev. D 110, 085020 (2024)</a>] and near-extremal Kerr-Newman black hole in de Sitter space in [C.-M. Chen and S. P. Kim, <a href="http://dx.doi.org/10.1140/epjc/s10052-023-11380-7">Eur. Phys. J. C 83, 219 (2023)</a>]. In strong contrast to the near-extremal Kerr-Newman black hole in dS space, the near-extremal rotating Nariai black hole also has an exponential amplification for the emission of high-energy charges, which becomes catastrophic regardless of angular momentum when two horizons coincide. The radius of rotating Nariai black holes monotonically increases as the angular momentum and charge of black holes increase, which gives a weaker electric field on the horizon than Nariai black holes. Thus, the angular momentum of black holes that drags particles on the horizon decreases the mean number of charges by a factor not by an order. We observe a catastrophic emission of boson condensation for charges with an effective energy equal to the chemical potential in the spacelike outer region of the cosmological horizon. Remarkably, the Schwinger emission of charges in the standard particle model may prevent the rotating Nariai black holes from evolving into spacetimes with a naked singularity when the angular momentum is close to the allowed maximum, which Nariai black holes cannot avoid.

Chun-Yu Wei

Catastrophic emission of charges from near-extremal charged Nariai black holes. II. Rotation effect

Using both the in-out formalism and the monodromy method, we study the emission of charges from near-extremal charged Nariai black holes with the black hole event and cosmological horizons close to each other, whose near-horizon geometry is <math><msub><mi>dS</mi><mn>2</mn></msub><mo>×</mo><msup><mi>S</mi><mn>2</mn></msup></math>. The emission becomes catastrophic for a charge with energy greater than its chemical potential, whose leading exponential factor increases inversely proportional to the separation of two horizons. This effect may prevent near-extremal Nariai black holes with large charges that evaporate dominantly through the charge emission from evolving to black holes with a naked singularity, in analog to near-extremal RN-dS black holes that have the Breitenlohner-Friedman bound, below which they become stable against Hawking radiation and Schwinger effect of charge emission. The near-extremal Nariai black holes with small charges, which are close to near-extremal Schwarzschild-de Sitter black holes, emit dominantly charge-neutral particles and evolve to black holes with increasing charge to mass ratio. We illuminate the origin of the catastrophic emission in the phase-integral formulation and monodromy method by comparing near-extremal charged Nariai black holes with near-extremal Reissner-Nordtröm-dS black holes.

Catastrophic emission of charges from near-extremal Nariai black holes