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)

The Schwinger effect, a non-perturbative mechanism for particle production in strong fields, plays a crucial role in understanding quantum vacuum decay and high-energy phenomena, including heavy-ion collisions (HIC). Although holographic quantum chromodynamics (QCD) models have been widely used to study this effect, most treatments assume isotropy or consider only a single type of anisotropy, neglecting the interplay between spatial and magnetic anisotropies that arise in realistic HIC scenarios. A unified framework accounting for both anisotropies is needed to accurately model particle production. We investigate the Schwinger effect in a twice anisotropic holographic QCD model incorporating both spatial and magnetic anisotropies. Using the anti-de Sitter/conformal field theory correspondence, we compute the total potential of a particle-antiparticle pair to quantify how these anisotropies influence pair production. Our results show that the magnetic field (parameterized by $c_B$ and $q_3$ ) enhances the Schwinger effect by lowering and narrowing the potential barrier, while increasing spatial anisotropy (controlled by $\nu$ ) suppresses the process by raising and widening the barrier. These findings demonstrate that magnetic and spatial anisotropies exert competing effects on particle production, emphasizing the necessity of treating both concurrently in holographic models. This work advances the theoretical description of the Schwinger effect in anisotropic environments, with implications for understanding non-equilibrium dynamics in HIC and other strongly coupled systems.

Wen-Bin Chang

Defu Hou

Schwinger effect in a twice anisotropic holographic model * Defu Hou's research is supported in part by the National Key Research and Development Program of China (2022YFA1604900). Additionally, Defu Hou receives partial support from the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Wen-Bin Chang is supported by the Ph.D. Research Startup Project at Hubei Minzu University (RZ2500000857)

Space-based gravitational-wave detectors, such as the Laser Interferometer Space Antenna (LISA), provide a platform to probe new fundamental fields through extreme-mass-ratio inspirals (EMRIs), where a compact secondary object carrying scalar or vector charges inspirals into a massive primary. In a theory-agnostic framework, we compute the ultra-light vector and gravitational radiation emitted by eccentric EMRIs and determine the corresponding inspiral trajectories. We evaluate the impact of a massive vector (Proca) field on EMRIs waveform through dephasing and mismatches with predictions by general relativity. Using a Fisher information matrix analysis, we further assess LISA’s capability to constrain the Proca mass from future EMRIs observations. We find that orbital eccentricity can improve estimation accuracy of parameters, making the vector mass $$\mu $$ become detectable for the case of $$\mu =0.02$$ . Correlation analysis further reveals strong positive dependencies between the Proca mass and intrinsic source parameters, indicating that improved measurement of these parameters directly tightens constraints on vector mass. These results demonstrate that high-eccentricity EMRIs observed by LISA offer a powerful channel to detect or constrain massive vector-field extensions of GR in the strong-field regime.

Tieguang Zi

Fu-Wen Shu

Eccentric extreme-mass-ratio inspirals: a new window into ultra-light vector fields

This paper introduces a novel systematic construction of gapped domain walls (GDWs) within the Levin-Wen (LW) model. By gluing two LW models along their open sides in a compatible way, we achieve a complete GDW classification by subsets of bulk input data, which encompass the classifications in terms of bimodule categories. A generalized bimodule structure is introduced to capture domain-wall excitations. Furthermore, we demonstrate that folding along any GDW yields a gapped boundary (GB) described by a Frobenius algebra of the input UFC for the folded model, thus bridging our GDW classification and the GB classification in [1].

Yanyan Chen

Siyuan Wang

Yu Zhao

Yuting Hu

Yidun Wan

Classification of gapped domain walls of topological orders in 2+1 dimensions: a Levin-Wen model realization

In this paper, we extend the method of calculating the entanglement entropy of Hawking radiation of black holes using the “in” vacuum state, which describes one-sided asymptotically flat neutral black hole formed by gravitational collapse, to dynamic charged black holes. We explore the influence of charge on the position of the boundary of island $\textit{∂I}$ and the Page time. Due to their distinct geometric structures, we discuss non-extremal and extremal charged black holes separately. In non-extremal cases, the emergence of island saves the bound of entropy at late times, and the entanglement entropy of Hawking radiation satisfies the Page curve. Moreover, we also find that the position of the boundary of island $\textit{∂I}$ depends on the position of the cutoff surface (observers), differing from the behavior in eternal charged black holes. In extremal black holes, when the island exists, the entanglement entropy is approximately equal to the Bekenstein-Hawking entropy, while the entanglement entropy becomes ill-defined when island is absent. Our analysis underscores how different geometric configurations significantly influence the behavior of entropy.

Yun-Feng Qu

Yi-Ling Lan

Hongwei Yu

Wen-Cong Gan

Entanglement island and Page curve for one-sided charged black hole

In our previous work (Zhang and Shu in Eur Phys J. C 84(3):256, 2024), we have explored quantum gravity induced entanglement of masses (QGEM) in curved spacetime, observing entanglement formation between particles moving along geodesics in a Schwarzschild spacetime background. We find that long interaction time induces entanglement, even for particles with microscopic mass, addressing decoherence concerns. In this work, we build upon our previous work (Zhang and Shu 2024) by extending our investigation to a time-dependent spacetime. Specifically, we explore the entanglement induced by the mutual gravitation of massive particles in the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. With the help of the phase shift and the QGEM spectrum, our proposed scheme offers a potential method for observing the formation of entanglement caused by the quantum gravity of massive particles as they propagate in the FLRW universe. Consequently, it provides insights into the field of entanglement in cosmology.

Chi Zhang

United States

Gravity-induced entanglement between two massive microscopic particles in curved spacetime: II. Friedmann–Lemaître–Robertson–Walker universe

The experiment involving the entanglement of two massive particles through gravitational fields has been devised to discern the quantum attributes of gravity. In this paper, we present a scheme to extend this experiment’s applicability to more generalized curved spacetimes, with the objective of validating universal quantum gravity within broader contexts. Specifically, we direct our attention towards the quantum gravity induced entanglement of masses (QGEM) in astrophysical phenomena, such as particles traversing the interstellar medium. Notably, we ascertain that the gravitational field within curved spacetime can induce observable entanglement between particle pairs in both scenarios, even when dealing with particles significantly smaller than mesoscopic masses. Furthermore, we obtain the characteristic spectra of QGEM across diverse scenarios, shedding light on potential future experimental examinations. This approach not only establishes a more pronounced and extensive manifestation of the quantum influences of gravity compared to the original scheme but also opens avenues for prospective astronomical experiments. These experiments, aligned with our postulates, hold immense advantages and implications for the detection of quantum gravity and can be envisioned for future design.

Gravity-induced entanglement between two massive microscopic particles in curved spacetime: I. The Schwarzschild background

It is believed that gravity can be considered as a quantum coherent mediator. In this study, we propose a plan to test the existence of extra dimensions using the quantum gravity induced entanglement of masses (QGEM) experiment. This experiment involves two freely falling test masses passing through a Stern–Gerlach-like device. We investigate the entanglement witness between these masses within the framework of the Randall–Sundrum II model (RS-II). Our findings indicate that the system reaches entanglement more rapidly in the presence of extra dimensions, particularly when the radius of the extra dimension is large.

Shuai Feng

Bao-Min Gu

Quantum gravity induced entanglement of masses with extra dimensions

Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the Drinfeld center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensation. We also describe the classification of anyons in Levin-Wen models via representation theory of the tube algebra, and use a variant of the tube algebra to classify low-energy localized excitations in the condensed phase.

Jessica Christian

David Green

Peter Huston

David Penneys

A lattice model for condensation in Levin-Wen systems

In this paper we analyze and discuss 2D Jackiw-Teitelboim (JT) gravity coupled to primary fermion fields in asymptotically anti-de Sitter (AdS) spacetimes. We obtain a particular solution of the massless Dirac field outside the extremal black hole horizon and find the solution for the dilaton in JT gravity. As two dimensional JT gravity spacetime is conformally flat, we calculate the two point correlators of primary fermion fields under the Weyl transformations. The primary goal of this work is to present a standard technique, called resolvent, rather than using CFT methods. We redefine the fields in terms of the conformal factor as fermion fields and use the resolvent technique to derive the renormalized entanglement entropy for massless Dirac fields in JT gravity.