Hadron-hadron interactions, being nonperturbative in nature, play a significant role in addressing phenomenological questions in particle physics. Femtoscopy is a powerful tool in heavy-ion collision experiments, enabling the extraction of hadron-hadron interactions via momentum-correlation functions (CFs). These CFs are typically expressed as a convolution of source functions and hadron-hadron wave functions, with the latter encoding information about the interactions. However, source functions remain poorly constrained and are commonly approximated by a Gaussian form. Reconstructing source functions from experimental correlation data constitutes an 'inverse problem.' To address this, we propose a toy model based on Tikhonov regularization. Using a square-well potential with four distinct strengths, we calculate the CFs for inputs of single Gaussian source functions and mixed Gaussian source functions. The resulting CFs are then used to reconstruct the source functions via Tikhonov regularization. Our results show that the Gaussian source function can be successfully reconstructed, highlighting the potential of this approach for extracting realistic source functions from hadron pairs of interest.

China

Ao-Sheng Xiong

Qi-Wei Yuan

Ming-Zhu Liu

Fu-Sheng Yu

Zhi-Wei Liu

Li-Sheng Geng

Solving the inverse source problem in femtoscopy with a toy model * Supported in part by the Fundamental and Interdisciplinary Disciplines Breakthrough Plan of the Ministry of Education of China (JYB2025XDXM204) and the National Natural Science Foundation of China (W2543006, 12435007). Ming-Zhu Liu acknowledges support from the National Natural Science Foundation of China (12575086). Zhi-Wei Liu acknowledges support from the National Natural Science Foundation of China (12405133) and from the Shenzhen Science and Technology Program (ZDSYS20230626091501002). Fu-Sheng Yu and Ao-Sheng Xiong acknowledge support from the Scientific Research Innovation Capability Support Project for Young Faculty (ZYGXQNJSKYCXNLZCXM-P2) and from the Fundamental Research Funds for the Central Universities (lzujbky-2023-stlt01, lzujbky-2024-oy02, lzujbky-2025-eyt01)

This paper investigates the repetitive Penrose process in accelerating Kerr black holes and explores the influence of the acceleration factor on the repetitive Penrose process. After a brief review of accelerating Kerr black holes, we study the fundamental equations of the Penrose process in this spacetime, examine the stopping conditions required for the repetitive Penrose process, and obtain corresponding numerical results. The conclusions indicate that, in addition to exhibiting previously observed similar phenomena, accelerating Kerr black holes exhibit stronger energy extraction capabilities compared to Kerr black holes during the repetitive Penrose process. Moreover, in prior studies, the energy utilization efficiency was difficult to exceed 50%. However, in accelerating Kerr black holes, when the decay radius is relatively small, the energy utilization efficiency can exceed 50%, indicating that the reduced extractable energy primarily transforms into extracted energy rather than irreducible mass. On the other hand, when the initial value of the acceleration factor is large, the extractable energy can decrease to nearly zero, which also differs from the case of Kerr black holes in previous studies.

Xiao-Xiong Zeng

Ke Wang

Repetitive Penrose process in accelerating Kerr black holes

Using the ballistic approximation accretion flow model, this paper investigates the shadow and polarization images of a Kerr-like black hole surrounded by a cold dark matter halo. By numerically solving the geodesic and radiative transfer equations, we analyze the effects of the critical density $$r_c$$ , the scale radius of the dark matter halo $$r_s$$ , the spin parameter $\textit{a}$, and the observer inclination $$\theta _o$$ on the resulting images. In all cases, a bright ring structure corresponding to higher-order images is observed, accompanied by an inner region of decreased intensity. The results show that both $$r_c$$ and $$r_s$$ increase the size of the higher-order images, while the spin parameter $\textit{a}$ and inclination $$\theta _o$$ modify the image morphology, producing a crescent-shaped bright region on the left side. In the polarization maps, the linear polarization degree $$P_o$$ is significantly lower in the higher-order image region, and the polarization vectors exhibit distinct distributions inside and outside the ring. Compared with the thin disk model, the thick disk model displays notable differences in both shadow and polarization images.

Chen-Yu Yang

Ke-Jian He

Li-Fang Li

The impact of cold dark matter halo on black hole shadow and polarization images under thick disk illumination

Recently, Ref. [1] proved the energy conservation formula for particle decay in Kerr spacetime: <math altimg='si10.svg'><mrow><msub><mi>m</mi><mn>0</mn></msub><mo linebreak='goodbreak'>=</mo><msub><mi>m</mi><mn>1</mn></msub><mspace width='0.16em' /><msub><mi>&#947;</mi><mn>01</mn></msub><mo linebreak='goodbreak'>+</mo><msub><mi>m</mi><mn>2</mn></msub><mspace width='0.16em' /><msub><mi>&#947;</mi><mn>02</mn></msub></mrow></math>, where <italic>m</italic> <inf>0</inf> is the initial particle, <italic>m</italic> <inf>1</inf> and <italic>m</italic> <inf>2</inf> are the decay products, and <italic>&#947;</italic> <inf>01</inf>, <italic>&#947;</italic> <inf>02</inf> are the relative Lorentz factors between particle 0 and particle 1, and between particle 0 and particle 2, respectively. This conclusion shows that the particle splitting process exhibits a mass defect, which is converted into kinetic energy in the center-of-mass frame. In this paper, we extend it to Kerr&#8211;de Sitter spacetime. Through derivation, we obtain the same energy conservation result as in Kerr spacetime. In addition, we find that, for a fixed cosmological constant, a larger decay radius leads to a larger specific angular momentum of particle 0, larger masses of particles 1 and 2, a smaller absolute value of their specific energy, smaller relative Lorentz factors among the three particles, and smaller four-velocities of the three particles. For a fixed decay radius, a larger cosmological constant leads to larger specific angular momenta of particle 0 and particle 2, smaller masses of particles 1 and 2, a larger absolute value of their specific energy, larger relative Lorentz factors among the three particles, and larger four-velocities of the three particles.

Particle decay and energy conservation in Kerr-de Sitter spacetime

This study investigates the ultraviolet realization of semileptonic four-fermion operator $ O_{ledq}^{\alpha \beta 11} $ that incorporates Majorana dark matter (DM) in both lepton-flavor-conserving (LFC) and lepton-flavor-violating (LFV) scenarios at the one-loop level via box diagram, thereby effectively alleviating the lower bounds on the new physics scale. In addition, we investigate the interplay between model-independent constraints on the Wilson coefficients and DM direct detection, relic density, and collider searches in the context of fermion portal DM model with two mediators. We found that both the projected future constraint on the LFC Wilson coefficient $ C_{ledq}^{2211}/\Lambda^2 \lt $ $ (12.3\; \text{TeV})^{-2} $ from the measurements of neutrino non-standard interaction in the next-generation neutrino oscillation experiments, and the LFV constraint $ C_{ledq}^{1211}/\Lambda^2 \lt \left(2.2\times 10^3\; \text{TeV} \right)^{-2} $ from ongoing charged-lepton-flavor-violation searches, provide a complementary exploration of the parameter space encompassing the DM and scalar masses. With a colored mediator mass of approximately $ 2\; \text{TeV} $ , the sensitivity of the indirect constraints on the four-fermion operator can surpass those of collider searches and DM direct detection, in scenarios where the masses of the DM and scalar are close. By ensuring the correct DM relic density, however, we find that the collider searches and DM direct detection are more sensitive to the electroweak-scale DM and scalar than indirect constraints.

Yuxuan He

Gang Li

Jia Liu

Xiao-Ping Wang

Xiang Zhao

Lepton flavor of four-fermion operator and fermion portal dark matter * Gang Li and Xiang Zhao are supported by the National Natural Science Foundation of China (12347105, 12505127), the Guangdong Basic and Applied Basic Research Foundation (2024A1515012668). The work of Jia Liu is supported by the National Science Foundation of China (12235001, 12475103) and State Key Laboratory of Nuclear Physics and Technology (NPT2025ZX11). The work of Xiao-Ping Wang is supported by National Science Foundation of China (12375095) and the Fundamental Research Funds for the Central Universities

This paper investigates the shadow images of rotating charged black holes in Kalb–Ramond (KR) gravity, using an accretion disk that is both optically and geometrically thin and located on the equatorial plane as the light source model. The results show that, compared to Sgr A*, the observational data of M87* impose stronger constraints on the charge parameter $\textit{Q}$ and the Lorentz-violating parameter $$\mathcal {G}$$ . Under the thin accretion disk model, a larger observer inclination $$\theta _o$$ deforms the central brightness depression into a hat-like structure. The parameters $$(a, Q, \mathcal {G})$$ mainly affect the size of the central brightness depression and the brightness of the critical curve, where increasing these parameters reduces the shadow size and enhances the distinguishability of the critical curve. In the retrograde accretion disk case, the crescent-shaped bright area appears on the side opposite to that in the prograde case. In addition, we compute the distribution of the redshift factor on the projection screen. The results indicate that the Doppler effect induced by large $$\theta _o$$ enhances the blueshift in the image, while the light emitted by particles plunging into the black hole leads to strong redshift near the central brightness depression. Finally, we study the polarization images under synchrotron radiation and find that the polarization intensity $$\mathcal {P}_o$$ reaches its maximum around the lensed image and higher-order images, whereas no polarization vectors appear within the central brightness depression. This stands in sharp contrast to horizonless compact objects. These findings contribute to a deeper understanding of the shadow properties of charged black holes within Lorentz-violating gravity.

Observational signatures and polarized images of rotating charged black holes in Kalb–Ramond gravity

In this analysis, we investigate the polarization radiation imaging of Kerr–Newman black holes, with a particular focus on the impact of black hole charge on photon propagation and polarization characteristics. By extending the traditional Walker–Penrose method, which is limited by its reliance on specific symmetric structures and Killing tensors, we overcome these limitations by constructing an ordinary differential equations (ODEs) numerical framework that combines the photon orbit equation with the polarization parallel transport equation. This allows for the self-consistent evolution of photon trajectories and polarization states in any spacetime backgrounds without relying on specific symmetries. Using this framework, we analyze the effects of black hole spin and charge on the polarization characteristics of radiation from both prograde and retrograde accretion disks. Our results show that black hole charge can significantly modify photon trajectories and polarization patterns: increasing charge compresses and distorts the EVPA structure on photon-ring scales, inducing localized rotations and asymmetries that may provide a potential diagnostic of a nonzero black hole charge.

Xin Li

Sen Guo

Pei Wang

En-Wei Liang

Huan Deng

Yu Liang

Brazil

Kai Lin

Qing-Quan Jiang

Polarized radiative transfer of Kerr–Newman black hole

Recently, references [1, 2] found that the repetitive Penrose process cannot extract all the extractable rotational energy of a Kerr black hole, and reference [3] found that the repetitive electric Penrose process cannot extract all the electrical energy of a Reissner-Nordström (RN) black hole. In this paper, we intend to study the repetitive Penrose process in the Kerr-de Sitter (Kerr-dS) black hole. We will explore influences of the cosmological parameter on the repetitive Penrose process. The results show that, apart from the comparable features documented earlier, the Kerr-dS black hole yields a higher energy return on investment (EROI) and single-extraction energy capability compared to the Kerr black hole. Specifically, the larger the cosmological parameter, the stronger the EROI and the single-extraction energy capability. Furthermore, we also find that at a lower decay radius, the Kerr black hole exhibits a higher energy utilization efficiency (EUE) and more extracted energy after the repetitive Penrose process is completed. However, at a higher decay radius, the situation is reversed, i.e., the Kerr-dS black hole exhibits a higher EUE and more extracted energy, which is due to the existence of stopping condition of the iteration.

Repetitive Penrose process in Kerr-de Sitter black holes

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.

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