In this work, we consider a spherically symmetric static black hole metric in Kalb–Ramond (KR) gravity, and investigate the impact of relevant parameters on the black hole shadow and polarization images. For black hole shadow images, we consider two geometrically thick accretion disk models such as a phenomenological RIAF-like model and an analytical BAAF disk model. In each case, we observe a bright ring-like structure corresponding to the higher-order images with a surrounding region of non-zero intensity that represents the primary image. The increasing values of $$\hat{\lambda }$$ or $$\hat{\gamma }$$ results in decrease the size of the higher-order image, while increasing values of observer inclination $$\theta _{o}$$ alter its shape and cause the horizons outline to be obscured. On the other hand, in BAAF disk model, at high observer inclinations, the obscuration of the horizons outline by radiation from outside the equatorial plane is weakened. Consequently, the brightness of the primary image in the phenomenological model is significantly greater than that in the BAAF disk model, indicating the strong gravitational lensing effect. For the polarized images, we use only the BAAF disk model with anisotropic radiation, assuming an infalling accretion flow matter. The obtained results illustrate that the polarization intensity $$P_{o}$$ in the higher-order image region is significantly stronger than as compare to other regions, and it is rapidly decreases away from this region. The variation in $$\hat{\lambda }$$ and $$\hat{\gamma }$$ depicts the intrinsic structure of the space-time and $$\theta _o$$ depends on the observers orientation, together they shape the polarization features.

China

Xiao-Xiong Zeng

Chen-Yu Yang

Pakistan

Muhammad Aslam

Rabia Saleem

Probing non-rotating black hole in Kalb–Ramond gravity: imaging and polarized signatures surrounded by different thick accretion flows

Using ray-tracing techniques, this paper investigates the optical and polarization images of rotating black holes in Kalb–Ramond (KR) gravity illuminated by thick accretion disks. We examine two accretion disk models: the phenomenological radiatively inefficient accretion flow (RIAF) model and the analytical ballistic approximation accretion flow (BAAF) model. The RIAF model incorporates both isotropic and anisotropic radiation. In all models, external bright rings corresponding to high-order images and an internal dark region associated with the event horizon are observed. At high observational inclinations, the inner shadow is obscured by radiation from the equatorial plane, which is significantly different from the thin accretion disk model. The primary distinction between isotropic and anisotropic radiation is that the latter causes distortion of the high-order image in the vertical direction, resulting in an elliptical structure. For the BAAF model, because certain regions become geometrically thinner under the conical approximation, the high-order images are narrower compared to those in the RIAF model. Furthermore, we find that an increase in the rotational parameter $\textit{a}$ leads to asymmetry in the intensity distribution of the high-order image, while an increase in the spontaneous Lorentz-violating parameters, $$\varsigma $$ and $$\varpi $$ , results in a decrease in the size of the high-order image. In the polarization image, linear polarization is found to be significantly influenced by the intensity, while it is relatively less affected by the parameters $$\varsigma $$ and $$\varpi $$ . The electric vector position angle is mainly affected by the parameters $$\varsigma $$ and $$\varpi $$ .

Huan Ye

Shadow and polarization images of rotating black holes in Kalb–Ramond gravity illuminated by several thick accretion disks

Based on the Comisso–Asenjo mechanism, we investigate the kinematic images of plasma before and after magnetic reconnection in Kerr–Anti-de Sitter(Kerr–AdS) black holes. Following a brief review of the Comisso–Asenjo process in Kerr–AdS black holes, we introduce the hotspot model and the imaging method. Building upon these foundational theories, we obtain the trajectory of the plasma and the temporal evolution of the hotspot images. It is found that there are three flares within the observing time, which is driven by the Comisso–Asenjo mechanism. We also discuss the influence of the cosmological parameter on the hotspot imaging. The results indicate that the hotspot image enlarges as the absolute value of $$\Lambda $$ increases, demonstrating that the cosmological constant significantly affects the hotspot.

Ke Wang

Hotspot image driven by magnetic reconnection in Kerr–anti de Sitter black holes

This study investigates the polarization characteristics of solitonic boson stars surrounded by a thin accretion disk. By comparing their polarization images with corresponding optical images, we find a positive correlation between the polarization intensity distribution in the polarization images and the brightness in the optical images. Consequently, the strongest polarization occurs at the location corresponding to the direct image. The influence of the coupling strength of the sixtic potential on the polarization intensity distribution is not monotonic, under strong coupling, the polarization will concentrated on the left side of the image as the coupling strength increases, whereas under weak coupling, it is more evenly distributed across the entire direct image as the coupling strength increases. Moreover, we find that as the initial scalar field increases, both the lensing image and photon ring become more prominent. However, the polarization intensity at these regions remains weak. Due to the absence of the event horizon in solitonic boson stars, the polarization vector can penetrate the stellar interior, unlike in black holes, where no polarization signals exist within the event horizon. Our numerical simulations clearly reveal this phenomenon, suggesting that polarization features may serve as an effective tool for distinguishing solitonic boson stars from black holes.

Hao Yu

Ke-Jian He

Polarization images of solitonic boson stars

In the Kerr–Sen black hole, this study investigates the changes in hotspot images before and after the occurrence of magnetic reconnection. After reviewing the Comisso–Asenjo magnetic reconnection process and introducing the hotspot imaging method, we examine the temporal evolution of hotspot intensity, including when energy extraction occurs, when it does not occur, and when the observer’s azimuthal angle is altered. We also discuss the influence of the black hole’s expansion parameter and spin on hotspot imaging. The results indicate that the first flare may serve as a potential signature of ongoing energy extraction; changing the observer’s azimuthal angle may alter the time interval between the first and second flares; a larger expansion parameter makes it more difficult to identify the energy extraction signal, and a higher spin also makes it more challenging to detect the energy extraction signal.

Hotspot images driven by magnetic reconnection in Kerr–Sen black hole

The Kerr–Bertotti–Robinson (Kerr–BR) black hole, a theoretical model of a rotating black hole immersed in a uniform magnetic field, has been proposed recently by Podolsky and Ovcharenko. This study investigates the optical characteristics of the Kerr–BR black hole based on the exact solution. We analyze the black hole shadow and the optical image under two illumination models: a celestial light source and a geometrically thin accretion disk. We reveal distinct roles for the fundamental parameters in the model. Specifically, it is found that under both illumination models, the influence of the rotation parameter on the optical image of the Kerr–BR black hole is significant different from that of the magnetic field. As the magnetic field increases, the radii of both the shadow and the Einstein ring enlarge. We also attempt to use the data from M87* and Sgr A* to constrain the BR-like magnetic fields surrounding them. These results enhance our understanding of the optical characteristics of the Kerr–BR black hole and establish a theoretical foundation for interpreting future observations on the optical image of the black hole immersed in a uniform magnetic field. Finally, we point out that with advances in the resolution of the black hole image, it is possible to detect the BR-like magnetic fields surrounding black holes.

Optical characteristics of the Kerr–Bertotti–Robinson black hole

This study investigates the optical imaging characteristics of massive boson stars based on the Einstein–Klein–Gordon theory coupled to nonlinear electrodynamics. Under asymptotically flat boundary conditions, the field equations are solved numerically to obtain the spacetime metric of the massive boson stars. Employing the ray-tracing method, we analyze the optical images of the massive boson stars under two illumination conditions: a celestial light source and a thin accretion disk. The research reveals that the configurations and optical images of the massive boson stars can be tuned via the initial parameter $$\phi _0$$ and the coupling constant $$\Lambda $$ . The absence of the event horizon in the massive boson stars results in distinct optical image characteristics compared to those of black holes.

Optical images of massive boson stars with nonlinear electrodynamics

A future $ e^+e^- $ collider could run at the $\textit{Z}$-pole to perform important electroweak (EW) precision measurements, but such a run may not be viable for a future muon collider. However, this can be compensated for by measuring other EW processes utilizing the high energy and large luminosity of the muon collider. In this paper, we consider the measurements of the vector boson fusion processes of $ WW/WZ/W\gamma $ to a pair of fermions (along with a $ \nu_{\mu}\bar{\nu}_{\mu} $ or $ \nu_{\mu}\mu^+/\bar{\nu}_{\mu}\mu^- $ pair) at a high-energy muon collider and study their potential for probing EW observables. We consider two run scenarios for the muon collider with center-of-mass energies of 10 and 30 TeV, respectively, and focus on the processes involving $ f=b,c,\tau $ and the dimension-6 operators that directly modify the corresponding fermions coupling to the $ Z/W $ bosons. The invariant mass distribution of the $ f\bar{f} $ pair helps to separate the events from the $ Z/W $ and high-energy resonances, whereas the polar angle of the outing fermion provides additional information. Through a chi-squared analysis on the binned distributions and combining the information from the $\textit{WW}$ and $ WZ/W\gamma $ fusion processes, all relevant Wilson coefficients can be constrained simultaneously. The precision surpasses the current EW measurement constraints and is even competitive with future $ e^+e^- $ colliders. Our analysis can be included in a more complete framework that is required to fully determine the potential of muon colliders in EW precision measurements.

Hao-Qiao Li

Hai-Ning Yan

Jiayin Gu

Germany

Xiao-Ze Tan

Probing $\textit{Z}$/$\textit{W}$ pole physics at high-energy muon colliders via vector-boson-fusion processes * Supported by the National Natural Science Foundation of China (NSFC) (12035008, 12375091, 12347171), and the Innovation Program for Quantum Science and Technology (2024ZD0300101). Xiao-Ze Tan also acknowledges the support from Helmholtz – OCPC (Office of China Postdoctoral Council) Postdoctoral Fellowship Program

We study $ \cos2\phi $ azimuthal asymmetry in doubly longitudinally polarized proton-proton Drell-Yan collisions within the transverse momentum dependent factorization framework. The asymmetry arises from the convolution of the longitudinal transversity distribution $ h_{1L}^{\perp} $ for both protons. Using the Bacchetta-Delcarro-Pisano-Radici-Signori parameterization for the nonperturbative Sudakov form factor and the Wandzura-Wilczek approximation for collinear $ h_{1L}^{\perp} $ , we predict the double spin asymmetry $ A_{LL}^{\cos2\phi} $ at RHIC and NICA kinematics. Our results demonstrate sensitivity to sea quark distributions, with the asymmetry reaching up to 25% for maximal sea quark contributions. These predictions highlight the potential of polarized Drell-Yan measurements to probe sea quark dynamics and advance our understanding of nucleon structures.

Hui Li

Ting Hu

Liang-Liang Liu

Xiao-Yu Wang

Zhun Lu

Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization * Hui Li is supported by Fundamental Research Program of Shanxi Province (202203021222224) and Natural Science Foundation of Shanxi Normal University (JCYJ2023021). Xiao-Yu Wang is supported by the Natural Science Foundation of Henan Province (242300421377, 232300421140)

We propose a search strategy at the HL-LHC for a new neutral particle $\textit{X}$ that couples to $\textit{W}$-bosons, using the process $ p p \to W^{\pm} X (\to W^{+} W^{-}) $ with a tri-$\textit{W}$-boson final state. Focusing on events with two same-sign leptonic $\textit{W}$-boson decays into muons and a hadronically decaying $\textit{W}$-boson, our method leverages the enhanced signal-to-background discrimination achieved through a machine-learning-based multivariate analysis. Using the heavy photophobic axion-like particle (ALP) as a benchmark, we evaluate the discovery sensitivities on both production cross section times branching ratio $ \sigma(p p \to W^{\pm} X) \times \text{Br}(X \to W^{+} W^{-}) $ and the coupling $ g_{aWW} $ for particle mass over a wide range of 170–3000 GeV at the HL-LHC with center-of-mass energy $ \sqrt{s} = 14 \, \text{ TeV} $ and integrated luminosity $ {\cal{L}} = 3 \, \text{ab}^{-1} $ . Our results show significant improvements in discovery sensitivity, particularly for masses above 300 GeV, compared to existing limits derived from CMS analyses of Standard Model (SM) tri-$\textit{W}$-boson production at $ \sqrt{s} = 13 \, \text{ TeV} $ . This study demonstrates the potential of advanced selection techniques in probing the coupling of new particles to $\textit{W}$-bosons and highlights the HL-LHC's capability to explore physics beyond the SM.

Ying-nan Mao

Kechen Wang

Yiheng Xiong

Sensitivities of new resonance couplings to $\textit{W}$-bosons at the LHC * Ying-nan Mao and Yihen Xiong are supported by the National Natural Science Foundation of China (12205227). Kechen Wang is supported by the National Natural Science Foundation of China (11905162), the Excellent Young Talents Program of the Wuhan University of Technology (40122102), and the research program of the Wuhan University of Technology (2020IB024). The simulation and analysis work of this article was completed with the computational cluster provided by the Theoretical Physics Group at the Department of Physics, School of Physics and Mechanics, Wuhan University of Technology