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2026 Vol. 50, No. 11

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PARTICLES AND FIELDS
Prospects for geoneutrino detection with JUNO
Thomas Adam, Shakeel Ahmad, Rizwan Ahmed, Fengpeng An, João Pedro Athayde Marcondes de André, Costas Andreopoulos, Giuseppe Andronico, Nikolay Anfimov, Vito Antonelli, Tatiana Antoshkina, Didier Auguste, Marcel Büchner, Weidong Bai, Nikita Balashov, Andrea Barresi, Davide Basilico, Eric Baussan, Marco Beretta, Antonio Bergnoli, Nikita Bessonov, Daniel Bick, Lukas Bieger, Svetlana Biktemerova, Thilo Birkenfeld, Simon Blyth, Manuel Boehles, Anastasia Bolshakova, Mathieu Bongrand, Matteo Borghesi, Dominique Breton, Augusto Brigatti, Riccardo Brugnera, Riccardo Bruno, Antonio Budano, Jose Busto, Anatael Cabrera, Barbara Caccianiga, Hao Cai, Xiao Cai, Stéphane Callier, Steven Calvez, Antonio Cammi, Guofu Cao, Jun Cao, Yaoqi Cao, Rossella Caruso, Cédric Cerna, Vanessa Cerrone, Jinfan Chang, Yun Chang, Tim Charisse, Auttakit Chatrabhuti, Chao Chen, Haotian Chen, Jiahui Chen, Jian Chen, Jing Chen, Junyou Chen, Pingping Chen, Shaomin Chen, Shiqiang Chen, Yixue Chen, Yu Chen, Ze Chen, Zhangming Chen, Zhiyuan Chen
2026, 50(11): 113001. doi: 10.1088/1674-1137/ae457d
Abstract:
Geoneutrinos—antineutrinos emitted during the decay of long-lived radioactive elements inside the Earth—serve as a unique tool for studying our planet's composition and heat budget. The Jiangmen Underground Neutrino Observatory (JUNO) experiment in China, which has recently completed construction, is expected to collect a sample comparable in size to the entire existing world geoneutrino dataset in less than a year. This paper presents an updated estimation of JUNO's sensitivity to geoneutrinos using the best knowledge available to date about the experimental site, the surrounding nuclear reactors, the detector response uncertainties, and the knowledge of the reactor antineutrino flux. To facilitate comparison with present and future geological models, our results cover a wide range of predicted signal strengths. Despite the significant background from reactor antineutrinos, the primary channel JUNO will use to determine the neutrino mass ordering, the experiment will measure the total geoneutrino flux with a precision comparable to that of existing experiments within its first few years, ultimately achieving a world-leading precision of about 8% over ten years. JUNO's large statistics will also allow separation of the Uranium-238 and Thorium-232 contributions with unprecedented precision, providing crucial constraints on models of Earth’s formation and composition. Observation of the mantle signal above the lithospheric flux will be possible but challenging. For models with the highest predicted mantle concentrations of heat-producing elements, a ~\begin{document}$3\sigma$\end{document} detection over six years requires knowledge of the lithospheric flux to within 15%. Together with complementary measurements from other locations, JUNO’s geoneutrino results will offer cutting-edge, high-precision insights into the Earth’s interior, of fundamental importance to both the geoscience and neutrino physics communities.
Extending the sensitivity of heavy sterile neutrino searches with solar neutrino experiments
Yutao Zhu, Haoyang Fu, Wentai Luo, Shaomin Chen, Litao Yang, Zhicai Zhang
2026, 50(11): 113003. doi: 10.1088/1674-1137/ae9929
Abstract:
A sensitivity study of the search for heavy sterile neutrinos (\begin{document}$ \nu_H $\end{document}) in the MeV mass range using solar neutrino experiments is presented. \begin{document}$ \nu_H $\end{document}, with masses ranging from a few MeV up to approximately 15 MeV, can be produced in the Sun through 8B decay and subsequently decays into \begin{document}$ \nu_e e^+ e^- $\end{document}. Its flux and lifetime strongly depend on the mixing parameter \begin{document}$ |U_{eH}|^2 $\end{document} and mass \begin{document}$ m_{\nu_H} $\end{document}. The \begin{document}$ \nu_H $\end{document} signal can be detected via its decay products, either the \begin{document}$ e^+e^- $\end{document} pair or \begin{document}$ \nu_e $\end{document}, depending on whether \begin{document}$ \nu_H $\end{document} decays inside or outside the detector. Expected signal yields for both detection methods (detecting \begin{document}$ e^+e^- $\end{document} or \begin{document}$ \nu_e $\end{document} signal) are presented across the full \begin{document}$ |U_{eH}|^2 $\end{document} and \begin{document}$ m_{\nu_H} $\end{document} parameter spaces. These two methods are found to be complementary in different regions of the \begin{document}$ |U_{eH}|^2 $\end{document} and \begin{document}$ m_{\nu_H} $\end{document} phase spaces. By combining both approaches, we anticipate observing at least a handful of signal events across most of the parameter space of \begin{document}$ 10^{-6} \lt |U_{eH}|^2 \lt 1 $\end{document} and 2 MeV \begin{document}$ \lt m_{\nu_H} \lt $\end{document} 15 MeV, assuming a 500-ton solar neutrino experiment operating for one year. Key variables, such as the energy spectra of \begin{document}$ \nu_e $\end{document} or \begin{document}$ e^+e^- $\end{document} and \begin{document}$ \nu_e $\end{document} solar angle, are also discussed to help distinguish the signal from major backgrounds, such as solar neutrino events.
Searching for ultralight dark matter with Mössbauer resonance
Peng-Long Zhang, Yu-Ming Yang, Xiao-Jun Bi, Qin Chang, Yu Gao, Hai-Bo Li, Wei Xu, Peng-Fei Yin
2026, 50(11): 113101. doi: 10.1088/1674-1137/ae9279
Abstract:
We investigate the feasibility of probing interactions between ultralight scalar dark matter and atomic nuclei using stationary Mössbauer spectroscopy. The exceptional energy resolution of the Mössbauer resonance enables searches for minute nuclear energy shifts induced by the local dark matter field. The dark matter mass range considered in this work is \begin{document}$10^{-18}$\end{document}–\begin{document}$10^{-8}\;\mathrm{eV}$\end{document}. We present projected constraints for two candidate Mössbauer isotopes, \begin{document}$^{109}\mathrm{Ag}$\end{document} and \begin{document}$^{45}\mathrm{Sc}$\end{document}, with \begin{document}$^{109}\mathrm{Ag}$\end{document} providing the strongest sensitivity. For \begin{document}$^{109}\mathrm{Ag}$\end{document}, projected sensitivities of approximately \begin{document}$10^{-19}$\end{document}, \begin{document}$10^{-22}$\end{document}, and \begin{document}$10^{-21}\; \mathrm{GeV^{-1}}$\end{document} can be achieved for the scalar DM–photon, DM–gluon, and DM–quark couplings \begin{document}$f_{\gamma}^{-1}$\end{document}, \begin{document}$f_{g}^{-1}$\end{document}, and \begin{document}$f_{\hat{m}}^{-1}$\end{document}, respectively. In the low-mass region, the projected sensitivity to the scalar DM–photon coupling approaches current constraints from equivalence-principle (EP) tests. These results demonstrate that Mössbauer-based techniques provide a promising and competitive approach to probing ultralight dark matter interactions with Standard Model particles.
Confinement order parameters in QCD: a view from Schwinger–Dyson equations and related low energy QCD models
Aftab Ahmad, Muhammad Jamil
2026, 50(11): 113102. doi: 10.1088/1674-1137/ae8cf3
Abstract:
Confinement and dynamical chiral symmetry breaking are two emergent non-perturbative phenomena of quantum chromodynamics (QCD) that are responsible for the nature of hadron spectra. While it is well known that the chiral condensate \begin{document}$ -\langle\bar{\psi} \psi \rangle $\end{document} is an order parameter for the chiral transition, the Polyakov loop is the associated approximate order parameter for the confinement–deconfinement transition in the pure gauge sector with center symmetry. Nevertheless, this quantity cannot be derived from functional methods, and other quantities have therefore been proposed as order parameters for this transition. In the current investigation, we review and compare several proposed parameters that have been used to describe the confinement/deconfinement transition in QCD and related quantum field theories in the framework of Schwinger–Dyson equations.
Prospects for probing light photophobic axion-like particles via displaced vertex signals at the CEPC
Chong-Xing Yue, Xin-Yang Li
2026, 50(11): 113103. doi: 10.1088/1674-1137/ae91ce
Abstract:
In recent years, long-lived particles (LLPs) have attracted increasing attention in searches for physics beyond the Standard Model (SM). In this paper, we investigate the discovery prospects for light, long-lived ALPs predicted by the photophobic ALP scenario through displaced-vertex signals at the CEPC, with a center-of-mass energy of \begin{document}$ \sqrt{s}=91.2 $\end{document} GeV and an integrated luminosity of \begin{document}$ {\cal{L}}= $\end{document} 100 ab−1. After comparing several possible single-production processes for the photophobic ALP, we focus on the dominant process \begin{document}$ e^+ e^- \to Z \to a \gamma $\end{document}, in which the ALP a subsequently decays into a pair of charged leptons at a displaced vertex. Dedicated Monte Carlo simulations are performed for the \begin{document}$ \mu^+ \mu^- \gamma $\end{document} and \begin{document}$ \tau_h^+ \tau_h^- \not{E}_T \gamma $\end{document} signals. For the \begin{document}$ \mu^+\mu^-\gamma $\end{document} signal, the CEPC is sensitive to the parameter region \begin{document}$ g_{aWW} \in [1.27\times10^{-3},6.80\times10^{-1}]\; {\rm{TeV}}^{-1} $\end{document} for \begin{document}$ m_a \in [1,4]\; {\rm{GeV}} $\end{document}. For the \begin{document}$ \tau_h^+\tau_h^-\not{E}_T\gamma $\end{document} signal, the accessible region is \begin{document}$ g_{aWW} \in [7.00\times10^{-4},9.40\times10^{-3}]\; {\rm{TeV}}^{-1} $\end{document} for \begin{document}$ m_a \in [4,9]\; {\rm{GeV}} $\end{document}. These results demonstrate the substantial potential of the CEPC to explore light, long-lived ALPs through displaced-vertex signals, providing complementary coverage to existing searches at LEP and the LHC, as well as to the projected reach of the HL-LHC.
A B-factory continuum retune of PYTHIA 8 hadronization parameters using BELLE and BABAR identified-hadron data
Muhammad Ajaz, Haifa I. Alrebdi
2026, 50(11): 113104. doi: 10.1088/1674-1137/ae8f26
Abstract:
We refine the hadronization sector of a pp PYTHIA 8 tune for \begin{document}$ e^+e^-\to q\bar q $\end{document} production using selected BELLE and BABAR measurements near the \begin{document}$ \Upsilon(4S) $\end{document} region. The study is performed with PYTHIA 8.316 and Rivet 4.1.1 and is restricted to the parameters used in this \begin{document}$ e^+e^- $\end{document} setup. Starting from the five-parameter hadronization subset of the pp tune, we perform a staged extension guided by the remaining discrepancies with the BELLE and BABAR data. The final comparison uses a fixed common set of 20,803 bins and samples of 1,000,000 generated events per analysis and tune point. On this basis, the selected refined tune yields a bin-weighted score of 73.42, compared with 76.49 for the Skands \begin{document}$ e^+e^- $\end{document} reference and 79.22 for Monash 2013 \begin{document}$ e^+e^- $\end{document}. It remains the best-scoring tune for the BELLE charged-hadron, baryon, and single- and dihadron measurements, whereas Skands still performs better for the BABAR charged-hadron sample and the BELLE meson sample. The bin-weighted ordering is driven primarily by the BELLE 2020 sample. The refined tune provides a small but stable improvement for the selected BELLE and BABAR measurements, although clear differences among the individual datasets remain.
Mass relations in heavy hadrons from Jensen-like inequalities
Wen-Xuan Zhang, Wen-Nian Liu, Duojie Jia
2026, 50(11): 113105. doi: 10.1088/1674-1137/ae9925
Abstract:
We demonstrate that mass inequalities for hadrons containing one or more heavy quarks arise primarily from the concavity of binding energies in the quark model, reflecting short-range Coulombic interactions and long-range confinement. Empirical two-body bindings \begin{document}$ B_{i\bar{j}} $\end{document} are extracted from spin-averaged meson masses, ensuring model independence and direct use of experimental data. Fitting these quantities as functions of the reduced mass \begin{document}$ \mu_{ij} $\end{document} reveals a critical confinement scale of 1.34 fm, at which the bindings become positive. The concavity of \begin{document}$ B(1/\mu) $\end{document} motivates Jensen-like relations under flavor permutation, reproducing relations such as \begin{document}$ m_{x\bar{y}} \gt \dfrac{1}{2}(m_{x\bar{x}} + m_{y\bar{y}}) $\end{document} and the baryon analog \begin{document}$ m_{xyz} \gt \dfrac{1}{3}(m_{xxx} + m_{yyy} + m_{zzz}) $\end{document}. Hadron mass decomposition validates \begin{document}$ \Delta M_{ \rm{EXP}} \approx \Delta B + \Delta C $\end{document} with \begin{document}$ \sigma \sim 2.07 $\end{document} MeV for mesons and baryons. Using this decomposition, we obtain approximate mass estimates for unobserved heavy baryons (e.g., \begin{document}$ M(\Omega_{b}^{\ast})\approx 6076.6\, $\end{document}MeV, \begin{document}$ M(\Xi_{cc}^{\ast})\approx 3703.6\, $\end{document}MeV, and \begin{document}$ M(\Omega_{cc}^{\ast})\approx 3802.4\, $\end{document}MeV) and identify favored quark-exchange scattering channels. The present analysis is phenomenological and does not constitute a rigorous three-body derivation.
Study of the $ {{\boldsymbol J}/\boldsymbol\psi\bf\to \boldsymbol\Lambda\bar{\boldsymbol\Sigma}^{\bf 0}\boldsymbol\eta}$ reaction
Lian-Rong Dai, Wen-Tao Lyu, E. Oset
2026, 50(11): 113106. doi: 10.1088/1674-1137/ae8cee
Abstract:
We study the isospin-violating \begin{document}$J/\psi \to \Lambda\bar \Sigma^0 \eta $\end{document} reaction, recently measured by the BESIII collaboration, by considering the dominant terms involving \begin{document}$\bar \Sigma^0$\end{document} and pairs of pseudoscalar-baryon particles that together form an SU(3) singlet and can therefore couple to the \begin{document}$J/\psi$\end{document}. We then allow these pairs to undergo final-state interaction to produce the final \begin{document}$\eta \Lambda$\end{document}. We find that the relevant original channels are \begin{document}$\bar K N$\end{document} and \begin{document}$K \Xi$\end{document}, and that the incomplete cancellation of terms involving charged and neutral particles, owing to their different masses, is responsible for the reaction. With this mechanism, we find good agreement with the three experimental mass distributions.
Magnetic dipole moments as probes of doubly-bottom molecular pentaquarks
Ulaş Özdem
2026, 50(11): 113107. doi: 10.1088/1674-1137/ae97e9
Abstract:
We investigate the magnetic dipole moments of doubly-bottom pentaquark states with spin-parities \begin{document}$J^P= {1}/{2}^-$\end{document} and \begin{document}$ {3}/{2}^-$\end{document}, interpreted as hadronic molecules in the \begin{document}$B\Sigma_b$\end{document}, \begin{document}$B\Sigma_b^{*}$\end{document}, and \begin{document}$B^{*}\Sigma_b$\end{document} configurations. The analysis is conducted within the framework of QCD light-cone sum rules employing photon distribution amplitudes. Our results demonstrate a strong sensitivity of the magnetic dipole moments to the internal spin structure and quark composition of the states. Specifically, the light-quark sector provides the dominant contribution in the \begin{document}$B\Sigma_b$\end{document} configuration, whereas the magnetic moment of \begin{document}$B\Sigma_b^{*}$\end{document} is largely governed by the heavy bottom quark. For the \begin{document}$B^{*}\Sigma_b$\end{document} molecular state, both light and heavy sectors contribute constructively, leading to a significantly enhanced magnetic dipole moment. These findings indicate that magnetic dipole moments serve as a sensitive probe of the internal structure of molecular-type doubly-bottom pentaquarks and provide testable predictions for future experimental studies.
Planar master integrals for two-loop NLO electroweak light-fermion contributions to gg → ZH
Shu-Xiang Li, Ren-You Zhang, Xiao-Feng Wang, Pan-Feng Li, Xiang-Jie Wei, Yi Wang, Yi Jiang, Qing-hai Wang
2026, 50(11): 113108. doi: 10.1088/1674-1137/ae8cf6
Abstract:
For the two-loop next-to-leading-order electroweak (NLO EW) corrections to \begin{document}$ gg \rightarrow ZH $\end{document}, the light-fermion contributions can be classified into eight distinct topologies. Using the canonical differential-equations method, we perform an analytic computation of the master integrals (MIs) associated with the four planar topologies. Canonical bases are constructed using the Magnus-expansion method, and the resulting alphabets consist of algebraic symbol letters involving nontrivial radicals. We develop a systematic framework for identifying the radical structures of the canonical MIs, enabling their organization into suitable subsystems and, whenever possible, their representation in terms of Goncharov polylogarithms (GPLs) up to \begin{document}$ {\cal{O}}(\epsilon^4) $\end{document}. Only a few MIs at \begin{document}$ {\cal{O}}(\epsilon^3) $\end{document} and \begin{document}$ {\cal{O}}(\epsilon^4) $\end{document} are instead represented as one-fold integrals over GPLs, due to the presence of nested square roots that obstruct the simultaneous rationalization of all radicals.
Rare exclusive decays of the Z-boson into S-wave quarkonia within the Bethe-Salpeter formalism
Asif Ali, Yi-Jie Li, Guang-Zhi Xu, Kui-Yong Liu
2026, 50(11): 113111. doi: 10.1088/1674-1137/ae9e9a
Abstract:
This paper investigates the rare decays of the Z boson into S-wave quarkonia within the Bethe-Salpeter formalism. Both double S-wave quarkonium production and radiative decays into a single S-wave quarkonium are analyzed. For double-quarkonium production, i.e., \begin{document}$ Z\to VV $\end{document} and \begin{document}$ Z\to VP $\end{document} (where V and P denote vector and pseudoscalar quarkonia, respectively), we consider the leading-order contributions from both QCD and electromagnetic transition via virtual photon (QED) amplitudes. The heavy-quark limit is adopted to simplify the calculations. In addition, we introduce another possible leading-order channel for Z-boson decays into double S-wave quarkonia, in which the Z boson decays into bottomonium plus charmonium via a QED amplitude. Such processes may include \begin{document}$ Z\to J/\psi+\Upsilon(1S) $\end{document}, \begin{document}$ Z\to\eta_{b}+J/\psi $\end{document}, and \begin{document}$ Z\to\eta_{c}+\Upsilon(1S) $\end{document}. Moreover, we study radiative Z-boson decays to S-wave quarkonium, namely \begin{document}$ Z\to X(Q\bar{Q})\gamma $\end{document}, where \begin{document}$ X(Q\bar{Q})=J/\psi $\end{document}, \begin{document}$\Upsilon $\end{document}, \begin{document}$ \eta_{c} $\end{document}, and \begin{document}$ \eta_{b} $\end{document}. Interestingly, for double-charmonium and radiative charmonium production, our results are larger than the NRQCD predictions, whereas for bottomonium they are comparatively smaller. This indicates that charmonium is a relativistic system, while bottomonium is a non-relativistic system.
NUCLEAR PHYSICS
Charge-exchange reactions accompanied by a single π+ production in medium-energy heavy-ion collisions
Xiaolei Chen, Jinyu Yang, Shikang Dong, Baowei Ding, Bitao Hu, Xiyu Qiu
2026, 50(11): 114101. doi: 10.1088/1674-1137/ae9050
Abstract:
Heavy-ion charge-exchange (CE) reactions provide a sensitive probe of isospin dynamics in nuclear collisions. We investigate the reaction \begin{document}$^{12}\mathrm{C}(^{12}\mathrm{C},\,^{12}{\rm N}\,{\pi}^{+})\,^{12}\mathrm{Be}$\end{document} at 400−600 A MeV using the ultra-relativistic quantum molecular dynamics model coupled with a phase-space coalescence approach. This reaction constitutes a nontrivial CE channel accompanied by single \begin{document}${\pi}^+$\end{document} production in heavy-ion collisions, thereby extending previous studies from lepton-induced to hadronic systems. The \begin{document}$^{12}{\rm N}$\end{document} fragment is formed via nucleon and meson exchange, while \begin{document}${\pi}^+$\end{document} production is primarily governed by ∆ resonance excitation and decay; this dual mechanism enables the simultaneous investigation of CE processes and ∆-induced pion production within the same reaction system. We calculate the reaction cross section and analyze the four-momentum distributions of \begin{document}$^{12}{\rm N}$\end{document} and \begin{document}${\pi}^+$\end{document}. Characteristic phase-space features reflect these distinct production mechanisms and offer guidance for future experimental design. Furthermore, this reaction could serve as a pathway for rare-isotope production.
Study of radiative proton capture by the 7Be nucleus with the use of ab initio approaches
D. M. Rodkin, Yu. M. Tchuvil'sky
2026, 50(11): 114102. doi: 10.1088/1674-1137/ae836e
Abstract:
A theoretical study of the 7Be(p, γ)8B reaction in the "astrophysical" energy range with the use of ab initio methods is presented. The used approaches are No-Core Shell Model and Cluster Channels Orthogonal Functions Method. The scheme also contains elements of R-matrix theory and procedures for extrapolating various data obtained in ab initio computations. The developed approach as a whole allows one not only to calculate the astrophysical S-factor and all nuclear characteristics that determine its value, but also to evaluate the reliability of the obtained results and to identify the dominant reaction mechanisms against a background of insignificant ones. The high accuracy of the obtained results and has been demonstrated.
Systematic investigation of nuclear incompressibility and finite-range exchange effects in density-dependent NN interactions on α-decay half-lives
M. M. Mesmh, M. Ismail, A. Adel, A. R. Abdulghany
2026, 50(11): 114103. doi: 10.1088/1674-1137/ae904e
Abstract:
We present a systematic investigation of α-decay half-lives for nuclei with \begin{document}$ 52 \leq Z \leq 122 $\end{document} within a microscopic double-folding framework. The α–nucleus potentials are constructed from the Michigan three-range Yukawa (M3Y) nucleon–nucleon interaction and its density-dependent variants (DDM3Y, CDM3Y, and BDM3Y), explicitly incorporating both direct and exchange terms. Special emphasis is placed on the role of finite-range exchange effects, which provide a more realistic description than the conventional zero-range approximation and lead to noticeable modifications in the Coulomb barrier region. Barrier penetrabilities are calculated using the WKB approximation with the Bohr–Sommerfeld quantization condition. The results demonstrate that nuclear deformation generally enhances the tunneling probability, resulting in shorter α-decay half-lives. Furthermore, the calculations indicate that increasing the nuclear incompressibility parameter K within the CDM3Y family tends to shorten the predicted half-lives by slightly enhancing the barrier penetrability. The calculated isotopic trends reflect the characteristic behavior near the neutron shell closures at \begin{document}$ N=82 $\end{document}, 126, and 184, highlighting the interplay between nuclear structure effects and decay dynamics. Overall, the results provide a systematic assessment of the sensitivity of α-decay half-lives to finite-range exchange, density dependence, deformation, and nuclear incompressibility within this microscopic double-folding approach.
Probing the jet transport coefficient of cold nuclear matter in electron-ion collisions
Peng Ru, Zhong-Bo Kang, Enke Wang, Hongxi Xing, Ben-Wei Zhang
2026, 50(11): 114105. doi: 10.1088/1674-1137/ae9924
Abstract:
We investigate transverse momentum broadening (TMB) in particle production in upcoming electron--ion collision experiments, an important manifestation of jet transport in cold nuclear matter. By incorporating the effects of parton multiple scattering in the nuclear medium within the high-twist expansion framework of perturbative QCD, we calculate the TMB of single-hadron production in semi-inclusive measurements, as well as the nuclear enhancement of the transverse momentum imbalance in di-hadron and heavy-meson pair production. A central input to our calculations is the effective jet transport coefficient \begin{document}$\hat{q} = \hat{q}(x,Q^2)$\end{document}, which depends on the parton momentum fraction x and the probing scale \begin{document}$Q^2$\end{document}. This quantity is obtained from an improved global analysis of existing data, with uncertainties quantified using the Hessian method. Our predictions show clear kinematic and color-state dependence of the nuclear-induced broadening and imbalance. These results demonstrate that future measurements of TMB will provide valuable insights into the kinematic dependence of jet transport properties, thereby substantially advancing jet tomography of cold nuclear matter.
Thermal effects on the moment of inertia and gravitational redshift of PSR J1012+5307: implications for hyperonic matter under SU(3) and SU(6) symmetries
Y. Xu, X. L. Huang, Y. B. Wang, Q. Yuan, W. B. Ding, N. An, Y. F. Shen, Z. Yu
2026, 50(11): 114106. doi: 10.1088/1674-1137/ae92f5
Abstract:
The temperature dependence of neutron star structure significantly alters the equation of state, thereby affecting observable properties such as the moment of inertia and gravitational redshift. Using relativistic mean-field (RMF) theory with hyperonic degrees of freedom under SU(3) flavor and SU(6) spin-flavor symmetries, we investigate thermal effects on the structural properties of protoneutron stars (PNSs) and cold neutron stars (CNSs). Focusing on PSR J1012+5307, we analyze the pronounced structural transformations that occur during the transition from a PNS to a CNS. For a 1.94 \begin{document}$M_{\odot}$\end{document} hyperonic star under SU(3) flavor symmetry, decreasing the temperature from \begin{document}$T = 30$\end{document} MeV to 0 MeV induces a radius contraction of approximately 50%, accompanied by a decrease in the moment of inertia of nearly 26% and a substantial increase in gravitational redshift of approximately 154%. Furthermore, we examine variations in the moment of inertia and gravitational redshift arising from the mass uncertainties of PSR J1012+5307. Taking SU(3) flavor symmetry at \begin{document}$T=20$\end{document} MeV as an example, increasing the mass across the range 1.72−\begin{document}$1.94 \,\, M_{\odot} $\end{document} leads to a radius contraction of 2.749 km, an ~8% increase in the moment of inertia, and a substantial ~40% increase in the gravitational redshift. We find that, in the cold regime and at fixed mass, the radius, moment of inertia, and gravitational redshift of hyperonic matter under SU(3) flavor symmetry differ only marginally from those of purely nucleonic matter. This makes it difficult to observationally confirm the presence of hyperons in the core of PSR J1012+5307. Moreover, future observations that can precisely constrain pulsar masses, ideally through long-term monitoring from birth, may help determine more conclusively whether hyperons or other exotic matter reside in individual pulsars.
Charge radii of calcium isotopes within relativistic configuration-interaction density functional theory
T. Qu, B. Li, Y. K. Wang
2026, 50(11): 114107. doi: 10.1088/1674-1137/ae9917
Abstract:
The charge radii of calcium isotopes are investigated within the framework of relativistic configuration-interaction density functional (ReCD) theory. The ReCD theory microscopically incorporates beyond-mean-field correlations through rotational symmetry restoration and configuration mixing among quasiparticle excited states, treating both even-even and odd-A isotopes on the same footing. It is found that beyond-mean-field correlations significantly soften the potential energy surfaces of calcium isotopes and shift the energy minima from nearly spherical mean-field solutions to deformed shapes. The quadrupole deformation parameters predicted by the ReCD theory show much better agreement with the available experimental data than the mean-field results, supporting the reliability of the calculated potential energy surfaces and highlighting the crucial role of beyond-mean-field correlations. Due to the sensitive dependence of charge radii on nuclear deformation, the charge radii obtained within the ReCD framework are generally larger than the mean-field predictions. The nearly identical charge radii of \begin{document}$ ^{40}\mathrm{Ca} $\end{document} and \begin{document}$ ^{48}\mathrm{Ca} $\end{document}, as well as the unexpectedly large charge radius of \begin{document}$ ^{52}\mathrm{Ca} $\end{document}, are well reproduced. Compared with the mean-field calculations, the description of the odd-even staggering is improved, particularly for the enhanced charge radii of \begin{document}$ ^{42}\mathrm{Ca} $\end{document} and \begin{document}$ ^{44}\mathrm{Ca} $\end{document}. It is also noteworthy that secondary local minima appear in the ReCD-based potential energy surfaces of the odd-A calcium isotopes \begin{document}$ ^{41,43,47}\mathrm{Ca} $\end{document}. The present results suggest that shape mixing between different local minima, which is not fully included in the current calculation, may further improve the description of the pronounced odd-even staggering observed in calcium isotopes.
Signature splitting and inversion in neutron-deficient 117–127Ba isotopes: a systematic total-Routhian-surface study
Jie Yang, Qing-Zhen Chai, Hua-Lei Wang, Kui-Peng Li
2026, 50(11): 114108. doi: 10.1088/1674-1137/aea10b
Abstract:
Signature splitting in the \begin{document}$ \nu h_{11/2} $\end{document} rotational bands of the odd-N neutron-deficient isotopes 117–127Ba is investigated systematically. Band crossings and shape evolution are studied using pairing- and deformation-self-consistent Woods-Saxon-Strutinsky calculations within the total-Routhian-surface (TRS) method in the \begin{document}$ (\beta_2,\gamma,\beta_4) $\end{document} deformation space. Calculated alignments and deformation-dependent Routhians indicate that proton-pair alignment is favored in 117–123Ba, whereas proton and neutron alignments compete in 125,127Ba. The signature splitting of the lowest \begin{document}$ h_{11/2} $\end{document} quasineutron Routhians is examined as a function of \begin{document}$ \beta_2 $\end{document} and γ, both below and above the first band crossing. The observed reduction and occasional inversion of the splitting are interpreted qualitatively in terms of competing γ-driving tendencies of the strongly coupled odd neutron and the aligned proton pair. For the heavier isotopes, the calculations associate large splitting with an aligned, oblate \begin{document}$ \nu h_{11/2} $\end{document} configuration; this association may help explain why only one member of a partner pair has been identified experimentally at high spin.
Comparing EPOS-4, EPOS-LHC, and SMASH for identified-hadron observables in the NICA energy range
Murad Badshah, Haifa I. Alrebdi, Sana Raza Khan, Muhammad Ajaz
2026, 50(11): 114110. doi: 10.1088/1674-1137/ae9922
Abstract:
We report a systematic generator-level study of identified-hadron production in minimum-bias Au+Au collisions at \begin{document}$\sqrt{s_{NN}}=6$\end{document}, 7, and 8 GeV using EPOS-LHC, EPOS-4, and SMASH. These frameworks represent different microscopic approaches, ranging from string/core-corona and hydrodynamic descriptions to purely hadronic transport. We compare rapidity distributions, transverse-momentum spectra, two-dimensional \begin{document}$p_T-y$\end{document} density maps, particle-yield ratios, and number-of-constituent-quark-scaled elliptic flow. Charged and neutral pions provide a relatively model-insensitive baseline dominated by bulk production and resonance feed-down, whereas \begin{document}$K^\pm$\end{document}, protons, and \begin{document}$\Lambda$\end{document} baryons exhibit stronger model dependence. The \begin{document}$p_T-y$\end{document} maps identify the longitudinal and transverse phase-space regions in which the model predictions diverge, although conclusions for rare strange particles are limited to statistically populated regions. Elliptic flow is presented as \begin{document}$v_2/n_q$\end{document} versus transverse kinetic energy per constituent quark, \begin{document}$(m_T-m_0)/n_q$\end{document}. All three models exhibit an approximately common trend at low and intermediate transverse kinetic energy, with the closest visual grouping in EPOS-LHC; deviations and statistical uncertainties increase at larger \begin{document}$(m_T-m_0)/n_q$\end{document}. Because each sample contains 50,000 events, no quantitative conclusions are drawn from sparsely populated forward-rapidity or high-\begin{document}$p_T$\end{document} regions. The results provide exploratory model baselines and identify strange-particle spectra, \begin{document}$K^-/K^+$\end{document}, \begin{document}$\Lambda/\pi^+$\end{document}, double-differential \begin{document}$p_T-y$\end{document} measurements, and identified-particle elliptic flow as priority observables in the NICA energy range.
Investigation for antimagnetic rotational structure in 107,109,111Pd
Pooja Chauhan, Nithin V, Dalip Singh Verma, S. Sihotra
2026, 50(11): 114111. doi: 10.1088/1674-1137/ae9f35
Abstract:
Partial level schemes of \begin{document}$ ^{107,109,111} {\rm{Pd}}$\end{document} have been reported in the literature, and antimagnetic rotational bands were recently predicted within the cranked shell model for the negative-parity bands of \begin{document}$ ^{107} {\rm{Pd}}$\end{document} and \begin{document}$ ^{109} {\rm{Pd}}$\end{document}, although lifetime data and semiclassical particle-rotor model studies are still unavailable. Electric quadrupole (\begin{document}$ E2 $\end{document}) transitions have also been observed in the negative-parity band of \begin{document}$ ^{111} {\rm{Pd}}$\end{document}, for which the rotational structure has not yet been theoretically investigated within the semiclassical particle-rotor framework. Over the past decade, the semiclassical particle-rotor model has been extensively applied to antimagnetic rotational bands in various nuclei, successfully explaining the generation of angular momentum through the shears mechanism and reproducing the observed systematics of excitation energies and \begin{document}$ B(E2) $\end{document} transition rates. In the present work, the negative-parity bands of \begin{document}$ ^{107,109,111} {\rm{Pd}}$\end{document} are investigated within the semiclassical particle-rotor model, where angular momentum is generated through the closing of proton-hole shears toward the neutron-particle angular momentum vector involving high-j orbitals. The calculated \begin{document}$ B(E2) $\end{document} values decrease with increasing spin, while the ratio \begin{document}$ \Im^{(2)}/B(E2) $\end{document} increases for the negative-parity bands of \begin{document}$ ^{107,109,111} {\rm{Pd}}$\end{document}, consistent with the characteristic signatures of antimagnetic rotation.
Self-consistent phonon inputs for vibrationally corrected combinatorial nuclear level densities
Jing-Zhu Hao, Nuo-Cheng Tang, Guan-Bin He, Yuan Tian, Ying Cui, Rui-Rui Xu
2026, 50(11): 114112. doi: 10.1088/1674-1137/aea283
Abstract:
Phenomenological vibrational prescriptions are widely used in microscopic combinatorial nuclear level-density (NLD) calculations, but they introduce empirical phonon-energy systematics that are not generated by the underlying nuclear-structure model. This empirical input limits the predictive consistency of the model, especially for nuclei for which low-lying collective spectra are unavailable. To reduce this empirical component, we construct self-consistent phonon inputs for vibrationally corrected combinatorial NLDs by calculating the first 2+, 3-, and 4+ phonon states with the relativistic quasiparticle random-phase approximation (RQRPA) built on the relativistic Hartree–Bogoliubov ground state. The corresponding RQRPA excitation energies are used in place of the phenomenological phonon energies, while the intrinsic combinatorial density and the established combinatorial vibrational prescription are kept unchanged. The method is benchmarked in selected even-even Sn isotopes against the phenomenological prescription and Oslo-normalized level densities. The RQRPA-based calculation approximately preserves the average vibrational enhancement of the phenomenological prescription and achieves agreement with the Oslo-normalized data comparable to that of the phenomenological calculation. These results demonstrate, for the selected semi-magic Sn isotopes, that self-consistent microscopic phonon energies can serve as collective inputs for vibrationally corrected combinatorial NLDs without using experimental low-lying spectra as model inputs.
Constraint on particle mass of dark matter based on XTE J1814-338 observation and DANS model
Lin Wang, Dehua Wen
2026, 50(11): 114113. doi: 10.1088/1674-1137/ae9ea6
Abstract:
The small observed radius of the neutron star XTE J1814-338 (with a mass of \begin{document}$1.21_{-0.05}^{+0.05} M_{\odot}$\end{document} and a radius of \begin{document}$7_{-0.4}^{+0.4} \text{km}$\end{document}) poses a significant challenge to the conventional neutron star model composed of normal nuclear matter. The dark matter-admixed neutron star (DANS) model offers a possible solution to this challenge. By employing a self-interacting fermionic dark matter model, we investigate the effects of dark matter parameters, including the particle mass, self-interaction strength, and dark matter mass fraction, on the properties of DANSs. Our results indicate that the joint constraints from the observations of XTE J1814-338 and the astrophysical limits on the dark matter self-interaction cross section derived from observations of different colliding galaxy clusters can effectively constrain the dark matter particle mass. Specifically, to simultaneously satisfy the small radius of XTE J1814-338 and the self-interaction limit, the particle mass of self-interacting fermionic dark matter is constrained to the range from sub-GeV to a few GeV.
PARTICLE AND NUCLEAR ASTROPHYSICS AND COSMOLOGY
Photon regions, shadow observables and constraints from M87* of a Kerr-Newman-like black hole in Bumblebee gravity surrounded by plasma
Jian-Peng Zhang, Yu Zhang, Li Han
2026, 50(11): 115101. doi: 10.1088/1674-1137/ae8cf0
Abstract:
In this paper, we investigate the photon regions, shadow, and observational constraints of a Kerr-Newman-like black hole in Bumblebee gravity within a plasma medium. Using a specific non-homogeneous power-law plasma model to ensure the separability of the Hamilton-Jacobi equation, we derive the null geodesic equations, analyze the photon regions, and construct the black hole shadow. Furthermore, we introduce two sets of shadow observables to systematically analyze the distinct effects of each physical parameter (spin a, charge \begin{document}$ Q_0 $\end{document}, Lorentz-violating parameter ℓ, and plasma parameter k) on the shadow geometry. Specifically, we find that a and ℓ mainly enhance the distortion of the shadow, whereas \begin{document}$ Q_0 $\end{document} and k primarily lead to radial shrinkage. In addition, a brief evaluation of the energy emission rate shows that increasing these parameters generally suppresses the emission peak. Finally, by modeling M87* as a charged, rotating black hole in Bumblebee gravity surrounded by plasma, we constrain the physical parameters using observations from the Event Horizon Telescope (EHT). For a fixed viewing angle of \begin{document}$ 17^\circ $\end{document}, the angular diameter \begin{document}$ \theta_d = 42 \pm 3 \, \mu\mathrm{as} $\end{document} narrows the viable parameter space, while the circularity deviation \begin{document}$ \Delta C \lesssim 0.1 $\end{document} and axis ratio \begin{document}$ 1 \lt D_x \lesssim 4/3 $\end{document} satisfy the EHT limits. This suggests that the charged, rotating black hole in Bumblebee gravity surrounded by plasma may be a candidate for real astrophysical black holes.
Rational orbits and gravitational waves in static spherical spacetimes: an open-source numerical framework
Dan Li, Shiyang Hu, Chen Deng, Shijie Tan, Guansheng He
2026, 50(11): 115102. doi: 10.1088/1674-1137/ae8db3
Abstract:
Timelike orbits constitute a crucial probe for exploring the intrinsic properties of curved spacetimes, and the accompanying gravitational radiation signals provide a direct window into strong field gravity. In this paper, we develop a versatile computational framework based on Mathematica and the OpenMP parallel architecture to simulate the rational orbits of timelike particles and their gravitational radiation in static spherically symmetric spacetimes. Specifically, with only the user defined covariant metric as input, this numerical tool can efficiently calculate rational orbits for various configurations, as well as the corresponding gravitational wave polarization states and characteristic strains. The package presented here provides an efficient and comprehensive tool for investigating the properties of curved spacetimes and their potential observational signatures. To demonstrate the reliability and capability of our code, we apply it to the Schwarzschild spacetime as a test case, illustrating its functionality in several key aspects, including the effective potential, stable orbital regions, rational and irrational orbits, and gravitational wave signals. Furthermore, we show that the gravitational waves emitted by an extreme-mass-ratio inspiral system composed of an intermediate mass black hole and the Galactic Center supermassive black hole could be detected by future space detectors.
Observable thin accretion disk around a self-dual black hole in loop quantum gravity
Tursunali Xamidov, Javokhir Sharipov, Sanjar Shaymatov
2026, 50(11): 115103. doi: 10.1088/1674-1137/ae97ea
Abstract:
In this paper, we study a self-dual black hole (BH) in loop quantum gravity (LQG) by analyzing both timelike and null geodesics. Using observational data from Mercury’s perihelion shift and the orbit of the S2 star around Sagittarius A* (Sgr A*), we derive constraints on the polymeric function P. We also investigate photon trajectories near the self-dual BH under various scenarios to assess their observational relevance. Finally, we examine the properties of accretion disks around the self-dual BH in LQG, including their direct and secondary images. We further study the redshift and observed energy-flux distribution across the accretion disk, as measured by distant observers at different inclination angles. Our findings provide new insights into the physical nature and accretion properties of self-dual BHs in LQG and their possible observational consequences.
Observational constraints on fractional holographic dark energy in the light of DESI DR2
Qihong Huang, Yuchen Zhang, Bing Xu, Kaituo Zhang
2026, 50(11): 115104. doi: 10.1088/1674-1137/ae9926
Abstract:
Based on the fractional entropy from fractional quantum mechanics, fractional holographic dark energy (FHDE) has been proposed with the Hubble horizon as the IR cutoff (FHDEH). We extend this framework by adopting the future event horizon and the particle horizon as the IR cutoff and proposing the FHDEF and FHDEP models. Using the SN+OHD+DESI DR2 dataset to constrain these models, we find that all three models provide a marginally lower \begin{document}$\chi^{2}_{\min}$\end{document} compared to ΛCDM but without significant preference according to AIC and BIC. When CMB distance priors are included, the FHDEH and FHDEP models are strongly ruled out. We further analyze the cosmological evolution for these models, and find that only the FHDEF model predicts nearly identical evolutions of \begin{document}$ \Omega_{m} $\end{document} and \begin{document}$ \Omega_{\rm de} $\end{document} to those of the ΛCDM model across cosmic history, but its deceleration parameter q deviates from the ΛCDM model in the future, indicating richer late time dynamics beyond the standard ΛCDM cosmology.
Energy–momentum–squared gravity: charged quark star solutions with unified interacting matter
Ayan Banerjee, Bobur Turimov, Javlon Rayimbaev, Faisal Javed, Gulnoza Palvanova, Sulton Usanov
2026, 50(11): 115105. doi: 10.1088/1674-1137/ae8cf4
Abstract:
We investigate the equilibrium structure of electrically charged quark stars within the framework of energy-momentum-squared gravity (EMSG), adopting a unified interacting quark-matter equation of state that incorporates perturbative quantum chromodynamics (QCD) corrections, color superconductivity, and finite strange-quark mass effects. By solving the modified Tolman-Oppenheimer-Volkoff (TOV) equations across a broad range of EMSG coupling strengths and interaction parameters, we show that including electric charge substantially increases both the maximum mass and the radius relative to neutral configurations. For strong negative couplings and pronounced interaction strengths, the resulting stellar models reach masses close to \begin{document}$3\,M_{\odot}$\end{document}, with compactness ratios of order \begin{document}$0.34$\end{document}, placing them within the mass range inferred for the secondary component of GW190814, whose nature remains observationally undetermined. The presence of charge reduces the central density at maximum mass by approximately \begin{document}$10\%$\end{document}–\begin{document}$15\%$\end{document} while satisfying causality requirements. Furthermore, comparisons with observational constraints from PSR J1614\begin{document}$-$\end{document}2230, J0348\begin{document}$+$\end{document}0432, J0740\begin{document}$+$\end{document}6620, J0952\begin{document}$-$\end{document}0607, and recent NICER radius measurements indicate that charged EMSG configurations remain consistent with current astrophysical bounds across a wide parameter space. These results demonstrate that moderate electric charge, combined with nonlinear matter-geometry coupling, can support quark stars that are significantly more massive than those predicted by general relativity, underscoring the potential observational relevance of charged compact objects in modified gravity and multimessenger astrophysics.
Tuning a rotating black hole spectrum with dark matter halo: quasibound states, scalar cloud, black hole bomb and superradiant scattering
David Senjaya
2026, 50(11): 115106. doi: 10.1088/1674-1137/ae8cf1
Abstract:
We investigate the spectral dynamics of a rotating black hole embedded in a Dehnen \begin{document}$(1,4,\gamma)$\end{document} dark matter halo, in which quasibound states and superradiant scattering jointly characterize the physical response of the system. Starting from an exact Schwarzschild–Dehnen solution, we construct its rotating counterpart via the Newman–Janis algorithm, thereby obtaining a consistent axisymmetric geometry that incorporates the influence of a structured halo. Through its inner slope parameter γ, the Dehnen profile introduces a controlled deformation of both the near-horizon and asymptotic regions of the spacetime. Using the analytical asymptotic matching method, we derive the quasibound-state spectrum and show that the real part of the frequency retains a hydrogen-like structure but is systematically shifted by the leading-order halo correction proportional to \begin{document}$\rho_0 r_0^3/(3-\gamma)$\end{document}. In particular, denser, more extended, and cuspier halos strengthen the binding of the quasibound states, lower the critical mass required for the onset of instability, and typically suppress the growth rate of the black hole bomb. In the scattering sector, we obtain an analytic expression for the superradiant amplification factor and find that the same halo properties that strengthen the binding effects also tend to narrow the superradiant window. These results demonstrate that quasibound states and superradiant scattering are complementary manifestations of a unified spectral structure, with the Dehnen halo acting as an environmental tuner that directly imprints its properties onto both the resonance spectrum and the energy-extraction channels of the rotating black hole.
Polarization modes of gravitational waves in general symmetric teleparallel gravity
Yu-Qi Dong, Xiao-Bin Lai, Yu-Zhi Fan, Yu-Xiao Liu
2026, 50(11): 115108. doi: 10.1088/1674-1137/ae9264
Abstract:
This study investigates the polarization modes of gravitational waves within the most general symmetric teleparallel gravity theory that allows for second-order field equations. We consider scenarios where test particles either carry or do not carry a hypermomentum charge. Our findings reveal the existence of tensor, vector, and scalar modes of gravitational waves. First, the theory supports the + and × tensor modes propagating at the speed of light. Second, in the case where particles do not carry hypermomentum, vector modes propagating at the speed of light exist only within a very specific parameter space. However, when particles do carry hypermomentum, there are two shear modes that propagate at the speed of light, while the vector-x and vector-y modes emerge only under very specific conditions. Third, in the presence of hypermomentum, there is always a longitudinal mode propagating at the speed of light. The universal existence of the shear modes and the longitudinal mode in the presence of hypermomentum is a key feature of symmetric teleparallel gravity, distinguishing it from the Riemannian framework through gravitational wave polarization detection. We also analyze the polarization modes in two widely studied special theories: f(Q) theory and quadratic non-metricity theory.
Frequencies spectra and gravitational ringing around Hayward-AdS black holes immersed in a string fluid
G. Mustafa, Faisal Javed, Dhruba Jyoti Gogoi, S. K. Maurya, Akram Ali, Farruh Atamurotov
2026, 50(11): 115109. doi: 10.1088/1674-1137/ae8ced
Abstract:
We investigate the dynamics of test particles in a Hayward–AdS black hole with string fluid, with particular emphasis on how the relevant parameters influence particle motion. The stability of circular orbits is studied using the effective potential method, which yields analytic expressions for the particle energy and angular momentum in terms of the black hole parameters. The effects of these parameters on the innermost stable circular orbit and the effective force are also examined. In addition, we calculate the pericenter precession frequency and investigate the small oscillatory motion of a particle around a stable orbit, examining how the corresponding frequency is modified by the black hole parameters. We further compare particle dynamics in the Hayward–AdS spacetime with string fluid to those in the Hayward–AdS, the Hayward Reissner Nordstrom, and the conventional Hayward black holes. Lastly, we examine the influence of the string fluid and the Hayward parameter on the quasinormal spectrum and the time-domain dynamics of electromagnetic perturbations, and find that these two terms have reciprocal effects on the quasinormal scale.
Photon spheres and shadows of black holes with modified entropy-inspired metrics
Fang Liu, Yu-Bo Ma, Yun-Zhi Du, Huai-Fan Li
2026, 50(11): 115110. doi: 10.1088/1674-1137/ae9916
Abstract:
Starting from the first law of black hole thermodynamics, we establish an explicit correspondence between the corrected entropy and the metric function under the condition of fixed black hole energy and horizon location. Using the corrected metric, we then compute the photon sphere radius and shadow size, demonstrating that different entropy corrections produce characteristic optical shifts. By comparing these results with Event Horizon Telescope observations of Sgr A*, we constrain the parameter range associated with the corrected entropy. This analysis provides a feasible approach for testing generalized entropy frameworks and probing deviations from the Bekenstein--Hawking area law.
Topological signatures in Kerr-Sen AdS black hole thermodynamics
Mohd Rehan, Md Sabir Ali, Sushant G. Ghosh
2026, 50(11): 115111. doi: 10.1088/1674-1137/ae9278
Abstract:
Black hole thermodynamics and topology have emerged as a robust foundation for a coordinate-independent understanding of phase transitions. Using both Duan’s topological current theory and a novel complex residue method, we conduct a topological study of the Kerr-Sen AdS black hole arising in heterotic string theory. Specifically, we identify the zero points corresponding to on-shell black hole states and calculate their winding numbers to determine the global topological charge by constructing the generalized off-shell free energy and examining the corresponding vector field in a parametric space. Our analysis reveals that the Kerr-Sen AdS black hole exhibits three distinct thermodynamic phases—small, intermediate, and large black hole branches—characterized by critical points with winding numbers \begin{document}$ +1 $\end{document}, \begin{document}$ -1 $\end{document}, and \begin{document}$ +1 $\end{document}, respectively, culminating in a total topological charge \begin{document}$ W = +1 $\end{document}. Significantly, this topological number remains invariant under variations of the dilaton charge parameter, indicating that the dilaton field does not alter the fundamental topological class established for Kerr-AdS and RN-AdS black holes. However, the rotation parameter proves crucial in determining the phase structure and the emergence of multiple critical points. We systematically examine three limiting configurations: the full Kerr-Sen AdS spacetime, the GMGHS AdS limit (\begin{document}$ a = 0 $\end{document}), and the asymptotically flat Kerr-Sen case (\begin{document}$ \Lambda = 0 $\end{document}). The GMGHS AdS black hole yields a vanishing total topological charge, with winding numbers \begin{document}$ +1 $\end{document} and \begin{document}$ -1 $\end{document} canceling each other, while the Kerr-Sen black hole (\begin{document}$ \Lambda = 0 $\end{document}) similarly exhibits \begin{document}$ W = 0 $\end{document} despite possessing two distinct phase branches. Furthermore, we propose a novel approach by analytically continuing the thermodynamic characterization to the complex plane. The resulting complex function, derived from the off-shell Gibbs free energy, possesses isolated singular points whose residues directly encode the winding numbers. Our results indicate that topology offers profound insights into black hole phase transitions, with potential implications for understanding holographic dualities.
A comprehensive cosmographic and thermodynamic analysis of non-metric-matter coupled gravity
M. Zeeshan Gul, Shamraiza Shabbir, Fei Ni, Muhannad Mohammed Alfehaid
2026, 50(11): 115112. doi: 10.1088/1674-1137/ae8cef
Abstract:
The main objective of this manuscript is to explore the viable cosmological bounce solutions in the background of \begin{document}$f(Q,L_{m},T)$\end{document} gravity, where Q denotes the non-metricity scalar describing the curvature of spacetime, \begin{document}$L_m$\end{document} represents the matter-Lagrangian density, and T is the trace of the energy-momentum tensor. For this purpose, we consider an isotropic and homogeneous universe with bulk viscous fluid to examine the implications of this framework on the dynamics of the early universe. The central focus of this work is to uncover the role of bulk viscosity on the cosmic evolution, especially in non-singular bounces. Furthermore, we investigate the behavior of various cosmological parameters to identify the viable bounce solutions. We find that the positive energy density, negative pressure profile and violation of energy conditions (ECs) support the realization of a cosmological bounce. These results emphasize the importance of bulk viscosity in shaping the cosmic dynamics. We demonstrate that system's entropy evolution satisfies the second law of thermodynamics, confirming its thermodynamic consistency over time. Moreover, the examination of cosmographic parameters and adiabatic sound speed demonstrates the model's kinematic feasibility and stability. Our findings imply that \begin{document}$f(Q,L_{m},T)$\end{document} gravity stands as a consistent and alternative theory for standard cosmology, providing a significant theoretical framework to study the gravitational interactions. This modified gravitational theory (MGT) successfully accommodates important aspect of cosmic evolutions and offers a new perspective on geometric and coupling effects that may govern the dynamics of the universe beyond the predictions of general relativity.
Optical images of the braneworld black hole surrounded by an optically thin accretion disk
Wen-Hao Deng, Sen Guo, Qing-Quan Jiang, Kai Lin, Pei Wang
2026, 50(11): 115114. doi: 10.1088/1674-1137/ae973b
Abstract:
This work examines the observational signatures of rotating black holes with tidal charge in the Randall–Sundrum braneworld scenario. By combining an elliptic-integral-based analytical treatment with numerical ray tracing, we characterize photon motion around braneworld black holes in detail. At small observer inclinations, secondary images remain embedded within the primary emission rings. As the inclination increases, the primary and secondary images gradually separate, producing a strongly asymmetric image morphology. We show that the image asymmetry and deformation of the inner shadow are jointly governed by the black hole spin, tidal charge, and observer inclination. To analyze frequency shifts across the accretion disk, we extend the emitting region from the ISCO to the event horizon by including the plunging flow. The results indicate that the observer inclination is the dominant factor controlling the frequency-shift distribution. In addition, we reconstruct braneworld black hole images using a fisheye-lens ray-tracing model. The optical morphology and brightness distribution exhibit a clear dependence on the observing frequency, particularly when comparing 230 GHz with 86 GHz. We also compare the brightness distributions of prograde and retrograde disks and find that both the total intensity and peak intensity at 86 GHz are higher than those at 230 GHz. For negative tidal-charge values, we further investigate the corresponding frequency-shift behavior and 230 GHz intensity profiles, which may provide useful theoretical guidance for future studies of extra-dimensional gravity models.
Chaos bound for spinning particles: violation in Kerr black holes
Chuanhong Gao, Tetvui Chong
2026, 50(11): 115115. doi: 10.1088/1674-1137/ae9b89
Abstract:
In this work, we investigate the Lyapunov exponents that characterize the chaotic dynamics of neutral spinning particles around a Kerr black hole and perform a stringent test of the chaos bound in this framework. We carry out a systematic analysis of the dependence of these exponents on the black hole angular momentum, the particle spin, and its total angular momentum. For a non-extremal Kerr black hole with rotational parameter \begin{document}$a=\pm 0.90$\end{document}, no violation of the chaos bound is observed when the black hole rotation is aligned with the z-axis. In the anti-aligned configuration, violations occur only when the particle spin magnitude or total angular momentum exceeds a critical threshold. In the extremal case, which corresponds to a zero-temperature thermal state, the surface gravity vanishes. Within the parameter ranges for which unstable equilibrium orbits exist, the exponents are found to be positive. These results provide clear evidence of violation of the bound by a spinning particle in Kerr spacetime.
Constraining f (R) gravity with a space-borne superconducting gradiometer via precision measurement of the planetary gravitomagnetic field
Li-Fang Li, Xiaokai He, Manjia Liang, Pan Li, Xing Bian, Peng Xu
2026, 50(11): 115116. doi: 10.1088/1674-1137/ae8ce5
Abstract:
This paper investigates constraints on the parameters of \begin{document}$ f(R) $\end{document} modified gravity through high-precision, space-based gravity gradiometer measurements of the planetary gravitomagnetic Lense-Thirring effect. As a generalization of general relativity, \begin{document}$ f(R) $\end{document} gravity introduces an additional scalar degree of freedom. In the weak-field limit, it can effectively behave as a scalar-tensor theory and thus may alter gravitomagnetic effects. We derive the metric solution within the parametrized post-Newtonian (PPN) framework and obtain the gravitomagnetic potential containing the \begin{document}$ f(R) $\end{document} parameter \begin{document}$ \eta \equiv G_{{\rm{eff}}}/G $\end{document}. We propose a differential measurement scheme using two freely falling test masses in a near-Earth orbit to detect the transverse tidal signal induced by the gravitomagnetic field. Solving the geodesic deviation equation at first post-Newtonian order yields a signal proportional to η. For a satellite at an altitude of 1500 km with a gradiometer sensitivity of \begin{document}$ 10^{-2} {{s}}^{-2}/\sqrt{{\rm{Hz}}} $\end{document} at 0.1 mHz, one year of data can constrain \begin{document}$ |\eta - 1| \lesssim 0.0025 $\end{document}, corresponding to an upper bound on the quadratic coupling parameter \begin{document}$ \alpha/a^2 \lesssim 1.1\times 10^{-3} $\end{document}, where a is the radius of the satellite orbit. This work establishes a measurement framework for gravitomagnetic effects in \begin{document}$ f(R) $\end{document} gravity and provides a new approach for testing modified gravity with future space-based gradiometer missions.
Causal structure of spacetime singularities and their observable signatures
Bina Patel, Jahnvi Mistry, Ayush Bidlan, Parth Bambhaniya
2026, 50(11): 115117. doi: 10.1088/1674-1137/ae9c23
Abstract:
We analyze the causal structure of horizonless compact objects through the light-cone geometry and conformal compactification of the Joshi-Malafarina-Narayan (JMN-1) and Janis-Newman-Winicour (JNW) spacetimes. Penrose diagrams reveal that JMN-1 undergoes a transition from timelike \begin{document}$ (0<M_0<2/3) $\end{document} to null \begin{document}$ (2/3<M_0<4/5) $\end{document} singularities, whereas JNW remains timelike throughout, in contrast to the spacelike singularity of the Schwarzschild spacetime. We show that photon spheres exist in Schwarzschild and JNW spacetimes, but arise in JMN-1 only when the singularity is null. For the class of spacetimes considered here, this result reveals a correspondence between the causal character of the singularity and null-geodesic trapping. We further demonstrate that radial timelike geodesics develop turning points in certain parameter regimes in both JMN-1 and JNW spacetimes, indicating the emergence of such turning points in the strong-field region. These features lead to distinct shadow signatures that may be testable by very-long-baseline interferometric observations such as those of the Event Horizon Telescope.
Effects of plasma medium and King dark matter halo surrounding black holes on weak gravitational lensing
Shokhzod Jumaniyozov, Javlon Rayimbaev, Yassine Sekhmani, Satimbay Palvanov, Ahmadjon Abdujabbarov, Chengxun Yuan
2026, 50(11): 115118. doi: 10.1088/1674-1137/ae9fbe
Abstract:
This work examines how a Schwarzschild black hole embedded within a King dark matter halo and immersed in a dispersive, cold plasma leaves observable imprints on photon trajectories. For the King profile \begin{document}$ (\mu,\nu,\alpha)=(3,2,0) $\end{document} we obtain a closed-form analytic metric that recovers the Schwarzschild solution once the dark matter contribution vanishes. Applying the Hamilton–Jacobi method to photon propagation in a plasma, we evaluate the photon-sphere radius and the black-hole shadow for both homogeneous and spatially varying plasma configurations. We find that plasma pushes the photon sphere to larger radii while simultaneously shrinking the shadow's apparent size relative to the vacuum case. Comparing these predictions with Event Horizon Telescope shadow measurements of M87* and Sgr A* yields only weak upper limits on the halo's central density and core radius, showing that physically realistic King halos remain consistent with the observed shadows. We further obtain analytic and semi-analytic deflection-angle and magnification formulas in the weak-lensing regime for three plasma configurations: uniform, singular isothermal sphere (SIS), and non-singular isothermal sphere (NSIS). Of these, the homogeneous plasma yields the largest enhancement of both the deflection angle and the magnification relative to vacuum, whereas the SIS profile, despite likewise enhancing the deflection, produces the smallest such enhancement of the models studied. These findings indicate that plasma contributions cannot be neglected when weak gravitational lensing is employed to constrain dark matter concentrations around supermassive black holes.
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