The study of extra charged gauge bosons beyond the Standard Model has always been of great interest. Future muon colliders will have a significant advantage in discovering exotic particles. In this paper, by studying the $ \mu^+ \mu^- \to W^{\prime +} W^{\prime -} \to e^+ e^- n_e \bar{n}_e $ process, we explore the properties of $ W^\prime $ in the alternative left-right model. The cross section and angular distribution of the final electron are investigated in a scenario of different $ W^\prime $ masses and right-handed coupling constants. The forward-backward asymmetry is also an important observable to reflect the properties of $ W^\prime $ . We provide a method to effectively suppress the background processes by imposing constraints on the transverse momentum $ P_T $ and azimuthal angle of the final-state electrons $\textit{α}$. With cuts of $ 600 \lt P_T \lt 3500 $ GeV and $ 0.5 \lt \alpha \lt 3 $ , the significance exceeds 5$\textit{σ}$ for 4.8 TeV $ W^\prime $ at a collision energy of 10 TeV.

China

Liuxin Zhao

Honglei Li

Zhi-Long Han

Fei Huang

Xinyi Yan

Extra charged gauge boson $\textit{W}$′ in Alternative Left-Right Model at future muon collider * This work is supported by the Natural Science Foundation of Shandong Province (ZR2022MA065, ZR2024QA138), and University of Jinan Disciplinary Cross-Convergence Construction Project 2024 (XKJC-202404)

High-precision regression of physical parameters from black hole images generated by General Relativistic Ray Tracing (GRRT) is essential for investigating spacetime curvature and advancing black hole astrophysics. However, owing to limitations in observational resolution, high observational costs, and imbalanced distributions of positive and negative samples, black hole images often suffer from data scarcity, sparse parameter spaces, and complex structural characteristics. These factors pose significant challenges to conventional regression methods based on simplified physical models. To overcome these challenges, this study introduces the Multiscale Adaptive Network (MANet), a novel regression framework grounded in deep learning. MANet integrates an Adaptive Channel Attention (ACA) module to selectively enhance features in physically informative regions. Meanwhile, a Multiscale Enhancement Feature Pyramid (MEFP) is employed to capture fine-grained spatial structures, such as photon rings and accretion disks, while alleviating information loss due to downsampling. Experimental evaluations on GRRT-simulated datasets demonstrate that MANet substantially improves parameter estimation accuracy and generalization capability in high-dimensional parameter spaces, outperforming existing baseline approaches. This framework presents a promising avenue for high-precision parameter regression in Event Horizon Telescope (EHT) data analysis and broader astrophysical imaging applications characterized by sparse and noisy data.

Jialei Wei

Ao Liu

Dejiang Li

Cuihong Wen

Physical parameter regression from black hole images using a multiscale adaptive neural network * Supported by the Natural Science Foundation of Hunan Province under grant No. 2023JJ30384; the National Natural Science Foundation of China under Grants No. 12374408; the University Students' Innovation and Entrepreneurship Training Program Project

We present a Physics-Informed Neural Network (PINN) framework for reconstructing the redshift-dependent Hubble parameter $$H(z)$$ within the Tsallis Holographic Dark Energy (THDE) model extended by massive neutrinos. In this approach, the modified Friedmann equation is incorporated into the neural network loss function, enabling training on Cosmic Chronometers data up to $$z \le 2$$ . The framework allows for the simultaneous estimation of the Hubble constant $$H_0$$ , the neutrino density parameter $$\Omega _\nu $$ , and the Tsallis non-extensivity index $$\delta $$ . Uncertainty quantification is performed through dropout simulations, resulting in statistically consistent $$1\sigma $$ confidence bands. Our results show that the THDE+ $$\nu $$ model, reconstructed via PINN, alleviates the statistical Hubble tension from the canonical $$\sim 5\sigma $$ level down to a range of $$0.5\sigma \le T \le 2.2\sigma $$ , depending on the redshift sampling. Additionally, we constrain the total neutrino mass to $$\Sigma m_\nu < 0.11\,\text {eV}$$ . A detailed comparison with the traditional Markov Chain Monte Carlo (MCMC) analysis demonstrates the consistency of both methods, while highlighting the competitiveness of the PINN-based THDE framework as a robust, data-driven approach for non-parametric cosmological inference within generalized thermodynamics.

Iran

Muhammad Yarahmadi

Amin Salehi

Towards a machine learning solution for hubble tension: Physics-Informed Neural Network (PINN) analysis of Tsallis Holographic Dark Energy in presence of neutrinos

For de Sitter spacetime, when the parameters of spacetime satisfy certain conditions, black hole horizon and cosmological horizon coexist in the spacetime. In this region, due to the existence of two horizons with different radiation temperatures, the spacetime does not satisfy the thermodynamic equilibrium stability requirements. This paper considers the spacetime as an overall thermodynamic system and, under the boundary conditions, provides the effective temperature that reflects the entire de Sitter spacetime. Through discussion, it is found that when the effective potential remains unchanged in time, the heat capacity of the de Sitter spacetime exhibits a curve similar to the Schottky specific heat of a two-level system. Moreover, this curve highly coincides with the heat capacity curve when the two horizons are considered as a two-level system. By comparing the maximum values of the heat capacity curves, the number of microscopic particles between the two horizons in the spacetime is estimated. This discovery provides a deeper understanding of de Sitter spacetime. This conclusion opens a new avenue for studying the interactions of microscopic particles inside black holes and simulating the evolution process of the universe, aiming to explore the intrinsic factors driving the accelerated expansion of the universe.

Yubo Ma

Huihua Zhao

Schottky anomaly of a perturbed Reissner–Nördstrom de Sitter spacetime

We carry out a systematic study of the 1$\textit{S}$-wave hidden and double charm-strange tetraquarks $$cs\bar{c}\bar{s}$$ and $$cc\bar{s}\bar{s}$$ in a nonrelativistic potential quark model framework with the explicitly correlated Gaussian method, and the mass spectra, color-spin configurations and possible decay modes are obtained. We find that although these states are all above their open flavor thresholds, their rearrangement decay widths are rather narrow which can be understood by the mismatching of the wave functions between the initial and final states. It implies that the tetraquarks of $$cs\bar{c}\bar{s}$$ and $$cc\bar{s}\bar{s}$$ may have a good chance to exist as genuine tetraquark states. It also shows that the color-spin configurations of the $$cs\bar{c}\bar{s}$$ and $$cc\bar{s}\bar{s}$$ systems are quite different. We find that for a physical state of $$cs\bar{c}\bar{s}$$ its color configurations can be dominated by either the $$|11\rangle _{c}$$ or $$|88\rangle _{c}$$ ones. It suggests that some hidden charm-strange tetraquark states may strongly couple to two color-singlet hadrons if the kinematics and dynamics allow. In contrast, we find that the color configurations $$|11\rangle _{c}$$ and $$|88\rangle _{c}$$ in a double charm-strange $$cc\bar{s}\bar{s}$$ state are rather compatible. It may suggest that an overall color-singlet tetraquark (i.e. a genuine color-singlet) should always play a role in the $$T_{cc\bar{s}\bar{s}}$$ states. We also demonstrate that our formalism contain the spin symmetry relations in the heavy quark symmetry and heavy quark spin symmetry limit which are the same as those derived in the Born–Oppenheimer model. Discussions taking into account some experimental candidates are presented, and suggestions on further experimental searches are also made.

Fengxiao Liu

Ru-Hui Ni

Xian-Hui Zhong

Qiang Zhao

Hidden and double charm-strange tetraquarks and their decays in a potential quark model

We study nonthermal resonant leptogenesis in a general setting, where a heavy Majoron <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> decays to right-handed neutrinos (RHNs) whose further out-of-equilibrium decay generates the required lepton asymmetry. Domination of the energy budget of the Universe by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> or the RHNs alters the evolution history of the primordial gravitational waves (GWs) of inflationary origin, which re-enter the horizon after inflation, modifying the spectral shape. The decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> and RHNs release entropy into the early Universe, while nearly degenerate RHNs facilitate low- and intermediate-scale leptogenesis. A characteristic damping of the GW spectrum resulting in kneelike features would provide evidence for low-scale nonthermal leptogenesis. We explore the parameter space for the lightest right-handed neutrino mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mn>1</mn></msub><mo>∈</mo><mo stretchy="false">[</mo><msup><mn>10</mn><mn>2</mn></msup><mo>,</mo><msup><mn>10</mn><mn>14</mn></msup><mo stretchy="false">]</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and washout parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> that depends on the light-heavy neutrino Yukawa couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>, in the weak (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo>&lt;</mo><mn>1</mn></math>) and strong (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo>&gt;</mo><mn>1</mn></math>) washout regimes. The resulting novel features compatible with observed baryon asymmetry are detectable by future experiments, like LISA and Einstein Telescope. By estimating the signal-to-noise ratio for upcoming GW experiments, we investigate the effect of the Majoron mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>ϕ</mi></msub></math> and reheating temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>ϕ</mi></msub></math>, which depends on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mo>−</mo><mi>N</mi></math> Yukawa couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>y</mi><mi>N</mi></msub></math>.

India

Zafri A. Borboruah

Poland

Anish Ghoshal

Lekhika Malhotra

Urjit Yajnik

Inflationary gravitational wave spectral shapes as a test for low-scale leptogenesis

We show that the inference problem of constraining the dipole amplitude with inclusive deep inelastic scattering data can be written into a discrete linear inverse problem, in an analogous manner as can be done for computed tomography. To this formulation of the problem, we apply standard inverse problems methods and algorithms to reconstruct known dipole amplitudes from simulated reduced cross section data with realistic precision. The main difference of this approach to previous works is that this implementation does not require any fit parametrization of the dipole amplitude. The freedom from parametrization also enables us for the first time to quantify the uncertainties of the inferred dipole amplitude in a novel more general framework. This mathematical approach to small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> phenomenology opens a path to parametrization bias-free inference of the dipole amplitude from HERA and Electron-Ion Collider data.

Finland

H. Hänninen

United States

A. Kykkänen

H. Schlüter

Reconstruction of the dipole amplitude in the dipole picture as a mathematical inverse problem

Extremely weak long-range forces may lead to apparent violations of the equivalence principle. The final MICROSCOPE result, leading at 95% CL to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>δ</mi><mo stretchy="false">|</mo><mo>&lt;</mo><mn>4.5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>15</mn></mrow></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6.5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>15</mn></mrow></msup></math> for a positive or negative Eötvös parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>δ</mi></math>, requires taking into account the spin of the mediator, and the sign of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mi>Q</mi><mo>/</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>r</mi></mrow></msub><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mtext>Ti</mtext><mi mathsize="small">−</mi><mtext>Pt</mtext></mrow></msub></mrow></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> denoting the new charge involved). A coupling to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> should verify <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>g</mi><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub><mo stretchy="false">|</mo><mo>&lt;</mo><mn>1.1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>25</mn></mrow></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>g</mi><mi>B</mi></msub><mo stretchy="false">|</mo><mo>&lt;</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>25</mn></mrow></msup></math>, for a spin-1 mediator of mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo>&lt;</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>14</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>eV</mi><mo stretchy="false">/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, with slightly different limits of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>25</mn></mrow></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6.6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>25</mn></mrow></msup></math> in the spin-0 case. The limits increase with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi></math>, in a way which depends on the density distribution within the Earth. This involves an hyperbolic form factor, expressed through a bilateral Laplace transform as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Φ</mi><mo stretchy="false">(</mo><mi>x</mi><mo>=</mo><mi>m</mi><mi>R</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">⟨</mo><mi>sinh</mi><mi>m</mi><mi>r</mi><mo>/</mo><mi>m</mi><mi>r</mi><mo stretchy="false">⟩</mo></mrow></math>, related by analytic continuation to the Earth form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Φ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">⟨</mo><mi>sin</mi><mi>m</mi><mi>r</mi><mo>/</mo><mi>m</mi><mi>r</mi><mo stretchy="false">⟩</mo></math>. It may be expressed as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Φ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo stretchy="false">(</mo><mi>cosh</mi><mi>x</mi><mo>−</mo><mfrac><mrow><mi>sinh</mi><mi>x</mi></mrow><mi>x</mi></mfrac><mo stretchy="false">)</mo><mo>×</mo><mover accent="true"><mi>ρ</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>/</mo><msub><mi>ρ</mi><mn>0</mn></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>ρ</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> is an effective density, decreasing from the average <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mn>0</mn></msub></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo>=</mo><mn>0</mn></math> down to the density at the periphery. We give general integral or multishell expressions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Φ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math>, evaluating it, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>ρ</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math>, in a simplified 5-shell model. <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Φ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> may be expanded as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∑</mo><mfrac><msup><mi>x</mi><mrow><mn>2</mn><mi>n</mi></mrow></msup><mrow><mo stretchy="false">(</mo><mn>2</mn><mi>n</mi><mo stretchy="false">+</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">!</mo></mrow></mfrac><mfrac><mrow><mo stretchy="false">⟨</mo><msup><mi>r</mi><mrow><mn>2</mn><mi>n</mi></mrow></msup><mo stretchy="false">⟩</mo></mrow><msup><mi>R</mi><mrow><mn>2</mn><mi>n</mi></mrow></msup></mfrac><mo>≃</mo><mn>1</mn><mo>+</mo><mo>.</mo><mn>0827</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mo>.</mo><mn>00271</mn><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>4.78</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mn>5.26</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup><msup><mi>x</mi><mn>8</mn></msup><mo>+</mo><mo>⋯</mo></math>, absolutely convergent for all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> and potentially useful up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>≈</mo><mn>5</mn></math>. The coupling limits increase at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> like <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>m</mi><mi>R</mi><mtext> </mtext><msup><mrow><mi>e</mi></mrow><mrow><mi>m</mi><mi>z</mi><mo>/</mo><mn>2</mn></mrow></msup><mo>/</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mi>m</mi><mi>r</mi></mrow></msqrt></mrow></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi><mo>=</mo><mi>r</mi><mo>−</mo><mi>R</mi></math> being the satellite altitude), getting multiplied by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>≃</mo><mtext> </mtext><mn>1.9</mn></mrow></math>, 34, or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.2</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo>=</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>13</mn></mrow></msup><mo>,</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>12</mn></mrow></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>11</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>eV</mi><mo stretchy="false">/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, respectively.

France

Pierre Fayet

Yukawa potential of a nonhomogeneous sphere with new limits on an ultralight boson

This study explores the Chern–Simons portal model, an extension of the Standard Model that introduces a massive neutral vector boson $\textit{X}$ associated with a $$U_X(1)$$ gauge symmetry. Motivated by gauge anomaly cancellation, the model incorporates heavy chiral fermions that induce observable effects through topological Chern–Simons interactions, despite being inaccessible at Large Hadron Collider energies. We investigate the associated production of the $\textit{X}$ boson with a $\textit{W}$ boson and jets at the high-luminosity LHC with a center-of-mass energy of 14 TeV, considering different $\textit{X}$ masses benchmarks. A multivariate analysis using boosted decision trees is employed to separate signal from background processes. Detector effects are modeled using a fast simulation tuned to the HL-LHC environment, including realistic pile-up conditions with an average of 200 interactions per bunch crossing. We derive expected $$95\%$$ confidence level exclusion limits in two-dimensional parameter spaces involving the $\textit{X}$ boson couplings. Our results demonstrate that the HL-LHC can achieve high sensitivity to gauge-anomaly-induced interactions, setting robust constraints on the $\textit{X}$ boson coupling to the $\textit{W}$ boson down to $$\mathcal {O}(10^{-4})$$ , depending on $$m_X$$ .

Mohammad Nourbakhsh

Switzerland

Mojtaba Najafabadi

Probing the Chern–Simons portal at the HL-LHC through displaced vertices from W boson associated production

A sensitivity of the collider FCC-hh to anomalous quartic gauge couplings (aQGCs) of neutral bosons in lead-lead collisions is studied. Examining diphoton production, the bounds on aQGCs at 5$\textit{σ}$ and 95% C.L. are obtained depending on systematic uncertainties.

Türkiye

S. İnan

Russia

A. Kisselev

A search for anomalous quartic gauge couplings in lead-lead collisions at the FCC-hh