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)

A recently developed topological approach offers novel insights into photon spheres, which are fundamental to the formation of black hole shadows. In this study, we extend this topological analysis to higher-dimensional, static, spherically symmetric, and asymptotically flat black holes. By examining the asymptotic properties of the vector field associated with the photon spheres, we demonstrate that their topological charge is consistently −1. This result is a dimensionally independent invariant, guaranteeing the existence of at least one standard (unstable) photon sphere outside the event horizon. We further explore this conclusion by analyzing two distinct regular black hole solutions derived from pure gravity theory, confirming that the topological charge remains −1 irrespective of the spacetime dimension. These results provide a robust and universal characterization of photon spheres in higher-dimensional spacetimes.

Jun-Lei Chen

Shan-Ping Wu

Shao-Wen Wei

The universal topological charge of black hole photon spheres in higher dimensions

We investigate the discovery potential of the $T_{bc}$ state with $J^P = 0^+$ in proton-proton ( $pp$ ) collisions at LHCb at a center-of-mass energy of $\sqrt{s} = 13~{\rm{TeV}}$ . The study focuses on the decay channel $T_{bc} \to B^- D^+$ . A phenomenological approach is employed to construct the background model based on the associated production of $\textit{B}$ and $\textit{D}$ mesons, incorporating previously published LHCb results. Background processes are simulated using ${\mathtt{MadGraph5\_aMC@NLO}}$ and ${\mathtt{Pythia8.3}}$ . We explore the parameter space of the $T_{bc}$ mass, width, production cross section, and the effective double-parton scattering cross section ( $\sigma_{{\rm{eff}}}$ ) relevant for the $B D$ meson background. The integrated luminosity required for a $5\sigma$ discovery at LHCb is evaluated under various assumptions. In particular, we consider three representative $T_{bc}$ production cross section scenarios: an optimistic estimate of $103~{\rm{nb}}$ , an intermediate value of $18~{\rm{nb}}$ obtained by scaling from the $T_{cc}^+$ production cross section, and a conservative lower bound of $0.3~{\rm{nb}}$ . We find that a $5\sigma$ observation is achievable for a production cross section of $103~{\rm{nb}}$ , which is expected to be within reach during Run4. In contrast, the more realistic cross section estimate of $18~{\rm{nb}}$ requires the full Run5 dataset ( $300~{\rm{fb}}^{-1}$ ) under the most favorable parameter choices. For the conservative scenario, no significant signal would be observable even with $300~{\rm{fb}}^{-1}$ . In addition, we estimate the minimum observable $\sigma(T_{bc}) \times {\cal{B}}(T_{bc} \to $ $ B^- D^+)$ for a $5\sigma$ discovery under different luminosity scenarios, providing guidance for future experimental searches at LHCb.

Mingjie Feng

Yiming Li

France

Hua-Sheng Shao

Prospects for discovering strongly decaying doubly heavy T$_{bc}$ tetraquark states at LHCb * Mingjie Feng and Yiming Li is Supported by the National Natural Science Foundation of China (NSFC) (2175245, 12188102, W2443008). Hua-Sheng Shao is Supported by the European Research Council (101041109, 'BOSON') and the French National Research Agency (grant ANR-20-CE31-0015, 'PrecisOnium')

<p>The Euclidean action provides a bridge between gravitational thermodynamics and the partition function. In this work, we further investigate the gravitational partition function under a fixed-volume constraint, generalizing the fixed-volume on-shell geometry in the massless case. Moving beyond this massless configuration, we construct solutions with nonvanishing mass functions, which give rise to a new class of volume-constrained Euclidean geometries (VCEGs). These geometries possess both a boundary and a horizon. However, closer inspection indicates that the boundary is not intrinsic, but rather artificially introduced and can be extended, leading to the extended volume-constrained Euclidean geometries (EVCEGs). The EVCEGs contain two horizons, each generically associated with a conical singularity. Their Euclidean action is given by one quarter of the sum of the areas of the two horizons. In general, the conical singularities at the two horizons cannot be simultaneously eliminated, except at a critical mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo>=</mo><msup><mi>m</mi><mo>*</mo></msup></math>, which defines the critical EVCEG. Configurations with unavoidable conical singularities are naturally interpreted as constrained gravitational instantons. An analysis of their contributions to the partition function, together with their topological properties, reveals a close analogy between the EVCEGs and the Euclidean Schwarzschild-de Sitter static patch. This suggests that the volume constraint effectively plays a role analogous to that of a cosmological constant in semiclassical quantum gravity.</p>

Peng Cheng

Gravitational partition function under volume constraints

We establish an exact duality between the extended thermodynamics of five-dimensional charged Gauss–Bonnet AdS black holes and the thermodynamic framework of the dual boundary conformal field theory (CFT). The thermodynamics of the dual CFT involves two central charges originating from the trace anomaly. We demonstrate a precise correspondence between the extended first laws on the bulk and boundary sides. Moreover, the topological charges of the CFT thermodynamics, associated with the phase transition and critical point, coincide with those of the corresponding bulk black hole.

Si-Jiang Yang

Yu-Xiao Liu

Topological perspective on bulk boundary thermodynamic equivalence

Within the framework of Dyson-Schwinger equations (DSEs) and by means of the Multiple Reflection Expansion approximation, we study the finite volume effects on the constituent quark mass in a strong external magnetic field. Since the magnetic field influences the coupling constant, which controls the strength of strong interactions in QCD, we adopt the magnetic-field-dependent running coupling constant in our simulations. The results show that, in addition to the magnetic field, the masses of constituent quarks also have a significant dependence on the volume and the running coupling constant. The model behaves closely to the infinite volume limit for large sizes, but the effect of the finite volume is significant when the system size $\textit{R}$ is about $ 2-6 $ fm. The finite volume effects and the magnetic-field-dependent running coupling constant have considerable influence on the phase transition.

Li-Juan Zhou

De-Xian Wei

Zhong-Yi Liu

Hong-Wei Zhong

Dynamical quark mass and finite volume effects in the Dyson-Schwinger equations * Li-Juan Zhou has been supported by the National Natural Science Foundation of China (11865005), the Natural Science Foundation of Guangxi (China) (2025GXNSFAA069552). De-Xian Wei has been supported by the National Natural Science Foundation of China (12105057), the Natural Science Foundation of Guangxi (China) (2023GXNSFAA026020)

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)

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)

In this paper, we investigate the dynamical evolution of the innermost stable circular orbit and light ring of a charged black hole under the influence of scalarization dynamics. This is achieved through a series of nonlinear simulations within the framework of the Einstein–Maxwell-dilaton theory. By combining these nonlinear simulations with a $$3+1$$ approach to geodesics in the dynamical spacetime, we derive the conditions for determining the ISCO and light ring in such a dynamical spacetime. Our results demonstrate how the ISCO and light ring evolve as a ‘hairless’ charged black hole transitions to a scalarized state. Moreover, we find that black hole scalarization leads to an increase in the areal radii of both the ISCO and light ring. These findings provide new insights into black hole scalarization, particularly concerning the dynamical evolution of the ISCO and light ring in a dynamically evolving spacetime.

Yu-Peng Zhang

Evolution of innermost stable circular orbit and light ring of a charged black hole induced by the scalarization

Heavy Majorana neutrinos ($\textit{N}$) are predicted in many models of physics beyond the Standard Model. In this work, we explore the production and detection prospects of TeV-scale heavy neutrinos ( $ m_N \gtrsim 1 $ TeV) at a future 3 TeV Compact Linear Collider (CLIC). We focus on two distinct decay topologies: (i) $ N \to \ell^\pm W^\mp $ with hadronic $\textit{W}$ boson decay, leading to a final state with one charged lepton and a hadronic fat jet $ J_W $ ; and (ii) $ N \to \nu h $ with subsequent Higgs decay $ h \to b\bar{b} $ , yielding a Higgs-tagged fat jet $ J_h $ and $\not {E}_T$ . Based on comprehensive detector-level simulations and background analysis, we present both $ 2\sigma $ exclusion limits and $ 5\sigma $ discovery reaches in the $ m_N $ – $ |V_{\ell N}|^2 $ plane. We further extract 95% confidence level upper limits on the mixing parameter $ |V_{\ell N}|^2 $ and perform a detailed comparison with existing constraints from direct searches at future colliders and indirect global fits. Our findings demonstrate that a 3 TeV CLIC can improve the sensitivity to $ |V_{\ell N}|^2 $ by about two orders of magnitude compared with the projected reaches of future hadron colliders while remaining competitive with other CLIC search channels.

Yao-Bei Liu

Jing-Wei Lian

Searches for heavy neutrinos at a 3 TeV CLIC in fat jet final states * Yao-Bei Liu is supported by the Natural Science Foundation of Henan Province, China (252300421988), Jing-Wei Lian is supported by the National Natural Science Foundation of China (12447140) and the Natural Science Foundation of Henan Province, China (252300421771)