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)

Motivated by the observation of the doubly charmed tetraquark $ T_{cc}(3875)^+ $ , we present a systematic study of doubly heavy tetraquarks ( $ T_{QQ'\bar{q}\bar{q}'} $ ) using heavy antiquark-diquark symmetry (HADS) within a constituent quark model. By calibrating model parameters to known hadron spectra and incorporating the effective mass formula, we predict the masses for 38 ground-state tetraquarks with $ cc $ , $ bb $ , and $ bc $ heavy quark pairs, including the non-strange, single-strange, and double-strange configurations with quantum numbers $ J^P = 0^+, 1^+ $ and $ 2^+ $ . Notably, we identify several stable states below the relevant meson-meson thresholds, particularly in the $ bb\bar{q}\bar{q}' $ sector. The explicit connection between the doubly heavy tetraquark and the heavy baryon spectra through HADS reduces model dependence and reveals the fundamental systematics in the heavy-quark hadron landscape.

Liu-Yu Zhang

Tian-Wei Wu

Yong-Liang Ma

Bridging doubly heavy tetraquark mass spectrum with heavy baryons utilizing heavy antiquark-diquark symmetry * The work of Tian-Wei Wu is supported by the National Natural Science Foundation of China (12405108). Yong-Liang Ma is supported in part by the National Science Foundation of China (NSFC) (12347103) and Gusu Talent Innovation Program (ZXL2024363)

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)

We study the bifurcation phenomena between spherical and axisymmetric bosonic stars. By numerically solving for the zero-modes of spherical bosonic stars under specific axially symmetric perturbations, we discover that excited state spherical bosonic stars bifurcate into two types of axisymmetric bosonic stars under = 2 perturbations, with matter distributions resembling chains and rings, respectively. Meanwhile, = 4 axisymmetric perturbations lead spherical scalar bosonic stars to bifurcate into a new type of axisymmetric bosonic stars, exhibiting a mixed chain-like and ring-like matter distribution, which we refer to as gyroscope-like. Additionally, for the first time, we have constructed chains of scalar bosonic stars with 7 constituents and their corresponding ring-like scalar bosonic stars. Our results provide an explanation for the bifurcations in bosonic stars from the perspective of perturbations, and by analyzing physical quantities such as quadrupoles and energy densities we systematically discuss the impact of axisymmetric perturbations on spherical bosonic stars.

Portugal

Chen Liang

Carlos Herdeiro

Eugen Radu

Bifurcations in bosonic stars: chains and rings from spherical solutions

In this paper, we construct the multi-state Dirac stars (MSDSs) consisting of two pairs of Dirac fields. The two pairs of Dirac fields are in the ground state and the first excited state, respectively, with opposite spins to ensure that the system possesses spherical symmetry. We discuss the solutions of the MSDSs under synchronized and nonsynchronized frequencies. By varying the ratio of masses between the two sets of Dirac fields, different branches of solutions can be obtained. Furthermore, we analyze the characteristics of the various MSDSs solutions and analyze the relationship between the ADM mass M of the MSDSs and the synchronized and nonsynchronized frequencies. Subsequently, we calculate the binding energy  $$E_B$$  <math> <msub> <mi>E</mi> <mi>B</mi> </msub> </math>   of the MSDSs and discuss the stability of the solutions. Then, we investigated the solutions of the MSDSs under the single particle condition. Finally, we discuss the feasibility of simulating the dark matter halos using MSDSs.

Ji-Rong Ren

Shi-Xian Sun

Yong-Qiang Wang

Multi-state Dirac stars

Abstract The open N = 2 string theory is defined on the 4D space-time with the split signature (+, +, −, −). The string field theory action of the open N = 2 string theory is described by the 4D Wess–Zumino–Witten (WZW$_{4}$) model. The equation of motion of the WZW$_{4}$ model is the Yang equation, which is equivalent to the anti-self-dual Yang–Mills equation. In this paper, we study soliton-type classical solutions of the WZW$_{4}$ model in the split signature by calculating the action density of the WZW$_{4}$ model. We find that the action density of the one-soliton solutions is localized on a 3D hyperplane. This shows that there would be codimension-one-solitonic objects, or equivalently some kind of three-branes in the open N = 2 string theory. We also prove that, in the asymptotic region of the space-time, the action density of the n-soliton solutions is a “non-linear superposition” of n one-solitons. This suggests the existence of n intersecting three-branes in the N = 2 strings. Finally we make a reduction to a (1 + 2)D real space-time to calculate the energy densities of the soliton solutions. We can successfully evaluate the energy distribution for the two-soliton solutions and find that there is no singularity in the interacting region. This implies the existence of smooth intersecting codimension-one branes in the whole region. Soliton solutions in the Euclidean signature are also discussed.

Japan

Masashi Hamanaka

Shan-Chi Huang

Hiroaki Kanno

Solitons in open = 2 String Theory Kahler-Chen-Simons theory A tour through N=2 strings On soliton solutions of the anti-self-dual Yang-Mills equations from the perspective of integrable systems Soliton solutions in an integrable chiral model in 2+1 dimensions On the space-time monopole equation A review on tachyon condensation in open string field theories Soliton equations as dynamical systems on infinite dimensional Grassmann manifold

In this paper, we construct Dirac-boson stars (DBSs) model composed of a scalar field and two Dirac fields. The scalar field and both Dirac fields are in the ground state. We consider the solution families of the DBSs for the synchronized frequency   <math> <mover> <mi>ω</mi> <mo>~</mo> </mover> </math>  $$ \overset{\sim }{\omega } $$  and the nonsynchronized frequency   <math> <msub> <mover> <mi>ω</mi> <mo>~</mo> </mover> <mi>D</mi> </msub> </math>  $$ {\overset{\sim }{\omega}}_D $$  cases, respectively. We find several different solutions when the Dirac field mass   <math> <msub> <mover> <mi>μ</mi> <mo>~</mo> </mover> <mi>D</mi> </msub> </math>  $$ {\overset{\sim }{\mu}}_D $$  and scalar field frequency   <math> <msub> <mover> <mi>ω</mi> <mo>~</mo> </mover> <mi>s</mi> </msub> </math>  $$ {\overset{\sim }{\omega}}_s $$  are taken in some particular ranges. In contrast, no similar case has been found in previous studies of multistate boson stars. Moreover, we discuss the characteristics of each type of solution family of the DBSs and present the relationship between the ADM mass M of the DBSs and the synchronized frequency   <math> <mover> <mi>ω</mi> <mo>~</mo> </mover> </math>  $$ \overset{\sim }{\omega } $$  or the nonsynchronized frequency   <math> <msub> <mover> <mi>ω</mi> <mo>~</mo> </mover> <mi>D</mi> </msub> </math>  $$ {\overset{\sim }{\omega}}_D $$ . Finally, we calculate the binding energy E  B  of the DBSs and investigate the relationship of E  B  with the synchronized frequency   <math> <mover> <mi>ω</mi> <mo>~</mo> </mover> </math>  $$ \overset{\sim }{\omega } $$  or the nonsynchronized frequency   <math> <msub> <mover> <mi>ω</mi> <mo>~</mo> </mover> <mi>D</mi> </msub> </math>  $$ {\overset{\sim }{\omega}}_D $$ .

Dirac-boson stars

In the present paper, the exact solutions of spherically symmetrical Einstein field equations describing wormholes supported by phantom energy that violates the null energy condition from Shan–Chen background fluid are obtained. We have considered the important case of the model parameter ψ≈1 , which corresponds to the “saturation effect”, and this regime corresponds to an effective form of “asymptotic freedom” for the fluids, but occurring at cosmological rather than subnuclear scales. Then we investigate the allowed range for the values of the model parameters g and ω when the spacetime metrics describe wormholes and discuss the possible singularities of the solutions, finding that the obtained spacetimes are geodesically complete. Furthermore, we construct two traversable wormholes through matching our obtained interior solutions to the exterior Schwarzschild solutions and analyze the traversablities of the wormholes. Finally, we consider the case of anisotropic pressure and discover that the transverse pressure also crosses the phantom divide -1 with the growth of the wormhole dimension, and it tends to be the same as the radial pressure with the growth of the wormhole radius.

Deng Wang

Xin-He Meng

Wormholes supported by phantom energy from Shan–Chen cosmological fluids