The Taishan Antineutrino Observatory (TAO) is a tonne-scale gadolinium-doped liquid scintillator satellite experiment of the Jiangmen Underground Neutrino Observatory (JUNO). It is designed to measure the reactor antineutrino energy spectrum with unprecedented energy resolution, better than 2% at 1 MeV. To fully achieve its designed performance, precise vertex reconstruction is crucial. This work reports two distinct vertex reconstruction methods, the charge center algorithm (CCA) and the deep learning algorithm (DLA). We describe the efforts in optimizing and improving these two methods and compare their reconstruction performance. The results show that the CCA and DLA methods can achieve vertex position resolutions better than 20 mm (bias < 5 mm) and 12 mm (bias < 1.3 mm) at 1 MeV, respectively, fully meeting the requirements of the TAO experiment. The reconstruction algorithms developed in this study not only prepare the TAO experiment for its upcoming real data but also hold significant potential for application in other similar experiments.

China

Hangyu Shi

Jun Wang

Guofu Cao

Wei Wang

Yuehuan Wei

Vertex reconstruction in the TAO experiment

Motivated by the precise measurements of neutrino oscillation parameters at Jiangmen Underground Neutrino Observatory (JUNO), we investigate the possibility of probing the unitarity violation of lepton flavor mixing matrix solely with reactor antineutrinos. First, we stress that it is necessary to reconsider the production and detection of neutrinos in a self-consistent way, apart from neutrino propagation, when analyzing experimental sensitivities to unitarity violation. Then, concentrating on JUNO and its satellite experiment Taishan Antineutrino Observatory (TAO), we demonstrate how the event rates of inverse beta decays (i.e., <math altimg='si7.svg'><mrow><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>e</mi></msub><mo linebreak='goodbreak'>+</mo><mi>p</mi><mo>&#8594;</mo><msup><mi>e</mi><mo>+</mo></msup><mo linebreak='goodbreak'>+</mo><mi>n</mi></mrow></math>) for observing <math altimg='si8.svg'><mrow><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>e</mi></msub><mo>&#8594;</mo><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>e</mi></msub></mrow></math> oscillations, and those of elastic antineutrino-electron scattering (i.e., <math altimg='si9.svg'><mrow><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>&#945;</mi></msub><mo linebreak='goodbreak'>+</mo><msup><mi>e</mi><mo>&#8722;</mo></msup><mo>&#8594;</mo><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>&#945;</mi></msub><mo linebreak='goodbreak'>+</mo><msup><mi>e</mi><mo>&#8722;</mo></msup></mrow></math> with <math altimg='si10.svg'><mrow><mi>&#945;</mi><mo linebreak='goodbreak'>=</mo><mi>e</mi><mo>,</mo><mi>&#956;</mi><mo>,</mo><mi>&#964;</mi></mrow></math>) for <math altimg='si11.svg'><mrow><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>e</mi></msub><mo>&#8594;</mo><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>&#956;</mi></msub></mrow></math> and <math altimg='si12.svg'><mrow><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>e</mi></msub><mo>&#8594;</mo><msub><mover><mrow><mi>&#957;</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mi>&#964;</mi></msub></mrow></math> oscillations, depend on the parameters characterizing unitarity violation. Our investigation will be useful for JUNO and TAO to place independent constraints with more data in the near future.

Jihong Huang

Shun Zhou

Probing unitarity violation of lepton flavor mixing matrix with reactor antineutrinos at JUNO and TAO

We investigate the scenario of black holes coupled with the Euler–Heisenberg nonlinear electromagnetic field in the framework of <italic>f</italic>( <italic>R, T</italic>) gravity. The black hole solutions for electrically charged, magnetically charged and the dyonic case are separately analyzed, and we discuss the scalar curvature and the energy conditions of the black hole spacetime. In the magnetic charge solution, the <italic>f</italic>( <italic>R, T</italic>) correction appears in the 1/ <italic>r</italic> <sup>6</sup> Euler&#8211;Heisenberg electromagnetic field correction term, while the electrically charged black hole solution exhibits an <italic>r</italic> <sup>2</sup> term in the metric function, corresponding to an effective cosmological constant <math altimg='si20.svg'><mrow><msub><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mtext>eff</mtext></msub><mo linebreak='goodbreak'>=</mo><mi>&#946;</mi><mo linebreak='goodbreak'>/</mo><mrow><mo>(</mo><mn>3</mn><mi>&#960;</mi><mo>)</mo></mrow></mrow></math>, inducing asymptotically anti-de Sitter or de Sitter spacetimes depending on the sign of the coupling parameter <italic>&#946;</italic>. The dyonic solution is obtained through vacuum polarization quantum electrodynamics corrections, where electromagnetic duality is broken and the solution contains higher-order correction terms. The relationship between the event horizon and charge of dyonic extreme black holes is studied. Furthermore, we investigate the effective metric, photon trajectories, and innermost stable circular orbit under nonlinear electromagnetic effects, providing images of photon geodesic for varying electric and magnetic charge strengths and <italic>f</italic>( <italic>R, T</italic>) coupling parameter.

Yizhi Liang

Jun Tao

Rui Yang

Black holes in <italic>f</italic>( <italic>R, T</italic>) gravity coupled with Euler&#8211;Heisenberg electrodynamics

Xuewei Liu

Wei Dou

Japan

Benda Xu

Hanwen Wang

Erratum to: First-principle event reconstruction by time-charge readouts for TAO

In this paper, we study a mixed coupling function incorporating spontaneous and non-linear scalarization of the hairy black hole in the Einstein-Maxwell-scalar model. Recent researches have demonstrated that a series of hairy black holes exhibit multiple photon spheres outside the horizon. Compared to the spontaneous solution, the mixed coupling function leads to a smaller event horizon radius. Quasinormal modes describe the fundamental signal of the gravitational waves in the ringdown stage, providing an effective method for detection. The real part of quasinormal modes grows with the azimuthal quantum number, suggesting the positive correlation between quasinormal modes and the angular velocity of trajectories. Furthermore, the absolute value of quasinormal frequencies' imaginary part is connected to the Lyapunov exponents of the corresponding photon spheres. The result of quasinormal modes calculated by the WKB approximation indicates long-lived and sub-long-lived modes, which are associated with the stable and the outer unstable photon spheres.

Yuling Weng

Yanqiang Liu

Yang Cao

Quasinormal modes of hairy black holes with mixed couplings

The Taishan Antineutrino Observatory (TAO) is a liquid-scintillator satellite experiment of the Jiangmen Underground Neutrino Observatory (JUNO) to measure the reference reactor neutrino spectrum with unprecedented energy resolution. We use inhomogeneous Poisson process and Tweedie generalized linear model (GLM) to characterize the detector response and the charge distribution of a SiPM. We develop a pure probabilistic model for time and charge of SiPMs from first principles to reconstruct point-like events in the TAO central detector. Thanks to our precise model and the high photo-coverage and quantum efficiency of the SiPM tiles at TAO, we achieve vertex position resolution better than $$20\,\hbox {mm}$$ , energy resolution of about $$2\%$$ at $$1\,\hbox {MeV}$$ and $$<0.5\%$$ non-uniformity, marking the world’s best performance of liquid scintillator detectors. With such resolution, we perceive $$\hbox {MeV}$$ events to exhibit track effects. It opens up an exciting possibility of computed tracking calorimeter for unsegmented liquid scintillator detector like TAO. Our methodology is applicable to other experiments that utilize PMTs for time and charge readouts.

First-principle event reconstruction by time-charge readouts for TAO

The merger of binary black holes produces a series of decaying oscillations, during which energy is radiated in gravitational waves. The characteristic signal in the ringdown phase can be described by complex oscillation frequencies called quasinormal modes (QNMs). In this paper, we investigate the ringdown spectrum resulting from scalar field perturbations of black holes surrounded by pseudo-isothermal dark matter halos. The complex frequencies of these quasinormal modes are numerically computed using the 6th-order WKB with Padé average approximation. Additionally, the time evolution of the scalar perturbations is examined using the finite difference method, considering various multipole numbers and dark matter halo parameters. For a static, spherically symmetric black hole, the photon sphere—composed of circular null geodesics—plays a crucial role in analyzing the black hole shadow. Furthermore, the connection between the black hole shadow and QNMs is explored in the eikonal limit.

Benrong Mu

Quasinormal modes of Schwarzschild-like black hole surrounded by the pseudo-isothermal dark matter halo

In this paper, we investigate the thermodynamic properties of the charged AdS Gauss–Bonnet black holes and their associations with the Lyapunov exponent. The chaotic features of the black holes and the isobaric heat capacity characterized by the Lyapunov exponent are studied to reveal the thermodynamic stability of the black hole phases. By considering both the timelike and null geodesics, we find that the relationship between the Lyapunov exponent and the Hawking temperature can accurately represent the features of the Small/Large phase transition and even the triple point. We also reveal the properties of the difference in the Lyapunov exponent as an order parameter. It is demonstrated that there is a negative correlation between the Lyapunov exponent and the size of the black hole shadow, which can be used to bridge the thermodynamic properties and the shadow of black holes.

Xin Lyu

Peng Wang

Probing the thermodynamics of charged Gauss Bonnet AdS black holes with the Lyapunov exponent

In this paper, we study topological numbers for uncharged and charged static black holes obtained in  $$z=3$$  <math> <mrow> <mi>z</mi> <mo>=</mo> <mn>3</mn> </mrow> </math>   Hořava–Lifshitz gravity theory in different ensembles, where z measures the degree of anisotropy between space and time. We first calculate the topological numbers for the uncharged black holes by changing the value of the dynamic coupling constant, and find that the black holes with spherical and flat horizons have the same topological number. When the black hole’s horizon is hyperbolic, different values of the coupling constant generate different topological numbers, which can be 1, 0 or  $$-1$$  <math> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </math>  . This shows that the coupling constant plays an important role in the topological classification. Then we study the topological numbers for the charged black holes in different ensembles. The black hole with a spherical horizon has the same topological number in canonical and grand canonical ensembles. When the horizons are flat or hyperbolic, they have different topological numbers in canonical and grand canonical ensembles. Therefore, the topological numbers for the uncharged black holes are parameter dependent, and those for the charged black holes are ensemble dependent.

Deyou Chen

Yucheng He

Wei Yang

Topology of Hořava–Lifshitz black holes in different ensembles

In this paper, we study the phase tranisions in the extended holographic thermodynamics of Born–Infeld AdS black holes. The extended gravitational thermodynamics of black holes is related to the thermodynamics of the dual field theory by varying both cosmological constant and Newton’s constant. With topological analysis and numerical calculation, we find that the reentrant large-small-large black hole phase transition still exists in  $$D=4$$  <math> <mrow> <mi>D</mi> <mo>=</mo> <mn>4</mn> </mrow> </math>  . Interestingly, a similar reentrant phase transition is also observed in the dual field theory, between the high-, low- and high-entropy thermal states. For higher dimension  $$D&gt;4$$  <math> <mrow> <mi>D</mi> <mo>&gt;</mo> <mn>4</mn> </mrow> </math>  , only the van der Waals like phase transition is observed, both in the bulk and the dual field theory.

Ning-Chen Bai

Li Song

Reentrant phase transition in holographic thermodynamicsof Born–Infeld AdS black hole