Using Multi-Layer Perceptrons (MLP) and Kolmogorov–Arnold Networks (KAN), we construct a holographic model based on lattice QCD data for the heavy-quark potential in the 2+1 system. The deformation factor $\textit{w}$($\textit{r}$) in the metric is obtained using the two types of neural network. First, we numerically obtain $\textit{w}$($\textit{r}$) using MLP, accurately reproducing the QCD results of the lattice, and calculate the heavy quark potential at finite temperature and the chemical potential. Subsequently, we employ KAN within the Andreev–Zakharov model for validation purpose, which can analytically reconstruct $\textit{w}$($\textit{r}$), matching the Andreev–Zakharov model exactly and confirming the validity of MLP. Finally, we construct an analytical holographic model using KAN and study the heavy-quark potential at finite temperature and chemical potential using the KAN-based holographic model. This work demonstrates the potential of KAN to derive analytical expressions for high-energy physics applications.

China

Ou-Yang Luo

Xun Chen

Fu-Peng Li

Xiao-Hua Li

Kai Zhou

Neural network modeling of heavy-quark potential from holography

Using the holographic model of the finite end point momentum shooting string approach, we study the instantaneous energy loss of light quarks for the flavor-dependent systems with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> in the Einstein-Maxwell-dilaton framework. In particular, we investigate for the first time the impact of the flavor content of the strongly coupled quark-gluon plasma medium on the instantaneous energy loss of light quarks. It turns out that the instantaneous energy loss of light quarks is smallest for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>0</mn></math>, and adding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">)</mo></math> quarks and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> quark in the system increases this energy loss. In addition, we found that the instantaneous energy loss in the strongly coupled plasma is minimal near the critical temperature, but it increases as the system moves away from the critical end point due to rising temperature or chemical potential.

Le Zhang

Lu Yin

Guo-Dong Zhou

Chao-Jie Fan

Light quark energy loss in the flavor-dependent systems from holography

Detailed studies of two-neutrino double electron capture (2$\textit{ν}$DEC) is a crucial step towards searching for the neutrinoless mode to explore the Majorana nature of neutrinos. We have measured precisely the half-life of the 2$\textit{ν}$DEC process in Xe, utilizing a total exposure of 1.73 tonne year from the commissioning run and the first science run of the PandaX-4T experiment. A time-dependent background model in the $$ \mathcal{O} $$ (10 keV) energy is constructed for the first time in PandaX-4T data. With an unbinned maximum likelihood fit, we determine the half-life of the 2$\textit{ν}$DEC process to be (1.03 ± 0.15 ± 0.08 ) × 10 yr. Furthermore, we have evaluated the capture fraction for both electrons captured from the $\textit{K}$ shell ($\textit{KK}$) to be (65 ± 5)%, which aligns with the Xe nuclear model calculations within 1.8 $\textit{σ}$.

Zihao Bo

Wei Chen

Yunhua Chen

Zhaokan Cheng

Xiangyi Cui

Yingjie Fan

Deqing Fang

Zhixing Gao

Lisheng Geng

Karl Giboni

Xunan Guo

Xuyuan Guo

Zichao Guo

Chencheng Han

Ke Han

Changda He

Jinrong He

Di Huang

Houqi Huang

Junting Huang

Ruquan Hou

Yu Hou

United States

Xiangdong Ji

Xiangpan Ji

Yonglin Ju

Chenxiang Li

Jiafu Li

Mingchuan Li

Shuaijie Li

Tao Li

Zhiyuan Li

Qing Lin

Jianglai Liu

Congcong Lu

Xiaoying Lu

Lingyin Luo

Yunyang Luo

Wenbo Ma

Yugang Ma

Yajun Mao

Yue Meng

Xuyang Ning

Binyu Pang

Ningchun Qi

Zhicheng Qian

Xiangxiang Ren

Dong Shan

Xiaofeng Shang

Xiyuan Shao

Guofang Shen

Manbin Shen

Wenliang Sun

Yi Tao

Anqing Wang

Guanbo Wang

Hao Wang

Jiamin Wang

Lei Wang

Meng Wang

Qiuhong Wang

Shaobo Wang

Siguang Wang

Wei Wang

Xiuli Wang

Xu Wang

Zhou Wang

Yuehuan Wei

Weihao Wu

Yuan Wu

Mengjiao Xiao

Xiang Xiao

Kaizhi Xiong

Yifan Xu

Shunyu Yao

Binbin Yan

Xiyu Yan

Yong Yang

Peihua Ye

Chunxu Yu

Ying Yuan

Zhe Yuan

Youhui Yun

Xinning Zeng

Minzhen Zhang

Peng Zhang

Shibo Zhang

Shu Zhang

Tao Zhang

Wei Zhang

Yang Zhang

Yingxin Zhang

Yuanyuan Zhang

Li Zhao

Jifang Zhou

Jiaxu Zhou

Jiayi Zhou

Ning Zhou

Xiaopeng Zhou

Yubo Zhou

Measurement of two-neutrino double electron capture half-life of

We perform a search of double beta decay of Xe to the excited state, $$ {0}_1^{+} $$ , of Ba (2$\textit{νββ}$- $$ {0}_1^{+} $$ ), using the dual-phase xenon detector of PandaX-4T with the first 94.9-day commissioning data. The multi-site events are reconstructed up to the MeV energy scale, which helps to improve the background model significantly. The background contribution from the stainless steel platform outside PandaX-4T cryostat is evaluated for the first time. No significant evidence for 2$\textit{νββ}$- $$ {0}_1^{+} $$ is observed, resulting in a lower limit on half-life of 7$\textit{.}$5 × 10 yr at the 90% confidence level. This is the first experimental limit on such a rare decay in a natural xenon-based detector.

Zhizhen Zhou

Search for double beta decay of

Based on the holographic model, which incorporates the equation of state and baryon number susceptibility for different flavors, we calculate the drag force, jet quenching parameter, and diffusion coefficient of the heavy quark at finite temperature and chemical potential. The holographic results for the diffusion coefficient align with lattice data for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math>, falling within their error margins. The holographic diffusion coefficient for heavy quark in the systems of different flavors is compatible with estimates from A Large Ion Collider Experiment data. The jet quenching parameter in our model demonstrates strong consistency with the estimations obtained from Bayesian analysis of data from both relativistic heavy ion collider and LHC for different flavors. We can confirm the model provides a good description of the transport properties of quark-gluon plasma. The work reinforces the potential of bottom-up holographic model in advancing our understanding of transport properties of hot and dense quark-gluon plasma.

Bing Chen

Xiaohua Li

Zhou-Run Zhu

Germany

Exploring transport properties of quark-gluon plasma in flavor-dependent systems with a holographic model

We present a novel constraint on light dark matter utilizing 1.54 metric ton/year of data acquired from the PandaX-4T dual-phase xenon time projection chamber. This constraint is derived through detecting electronic recoil signals resulting from the interaction with solar-enhanced dark matter flux. Low-mass dark matter particles, lighter than a few <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, can scatter with the thermal electrons in the Sun. Consequently, with higher kinetic energy, the boosted dark matter component becomes detectable via contact scattering with xenon electrons, resulting in a few keV energy deposition that exceeds the threshold of PandaX-4T. We calculate the expected recoil energy in PandaX-4T considering the Sun’s acceleration with heavy mediators and the detection capabilities of the xenon detector. The first experimental search results using the xenon detector yield the most stringent upper limits cross section of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3.51</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>39</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.08</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> for a solar boosted dark matter mass ranging from 0.02 to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></math>, achieving a 23-fold improvement compared with earlier experimental studies.

Search for Solar Boosted Dark Matter Particles at the PandaX-4T Experiment

We report a search for a lepton-portal dark matter model, where dark matter couples to a charged lepton in the standard model. This simplified model naturally leads to photon-mediated dark matter interactions with nuclei, making it suitable for direct dark matter detection experiments. Matching to the framework of non-relativistic effective field theory for dark matter, we report the first sensitive search for this model using data from the PandaX-4T commissioning run. Our results yield strong constraints on Dirac fermion dark matter but relatively weaker constraints on Majorana dark matter due to the suppression of effective photon interactions. These constraints complement those obtained from the collider and indirect detection experiments.

Search for lepton portal dark matter in the PandaX-4T experiment

Axionlike particles (ALPs) and dark photons (DPs) are viable dark matter particle candidates. We have searched for possible ALP/DP signals in the PandaX-4T liquid xenon detector using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>440</mn><mtext> </mtext><mtext> </mtext><mi>kg</mi><mo>·</mo><mi>yr</mi></mrow></math> of data. A binned likelihood fit is constructed to search for possible mono-energetic peaks induced by the absorption processes between ALPs/DPs and atomic electrons of xenon. A detailed temporal model of decays associated with xenon isotopes is introduced to constrain the number of background events. No signal excess over background expectations is observed, and we have established the most stringent exclusion limits for most ALP/DP masses across the range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>150</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>. The improvement is particularly significant within the mass range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>150</mn><mi>–</mi><mn>400</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, with the average factor of 3.5 compared to previous results.

Search for MeV-Scale Axionlike Particles and Dark Photons with PandaX-4T

QCD phase diagram in the − plane and the equation of state for pure gluon, 2-flavor, 2+1-flavor systems, and 2+1+1-flavor systems have been investigated using the Einstein-Maxwell-Dilaton (EMD) framework at finite temperature and chemical potential. By inputting lattice QCD data for the equation of state and baryon number susceptibility at zero chemical potential into holographic model, all the parameters can be determined with the aid of machine learning algorithms. Our findings indicate that the deconfinement phase transition is of first order for the pure gluon system with critical temperature = 0.265 GeV at vanishing chemical potential. The phase transition for the 2-flavor, 2+1-flavor systems, and 2+1+1-flavor systems are crossover at vanishing chemical potential and first-order at high chemical potential, and the critical endpoint (CEP) in the plane locates at ( $$ {\mu}_B^c $$ = 0.46 GeV, = 0.147 GeV), ( $$ {\mu}_B^c $$ = 0.74 GeV, = 0.094 GeV), and ( $$ {\mu}_B^c $$ = 0.87 GeV, = 0.108 GeV), respectively. Additionally, the thermodynamic quantities of the system for different flavors at finite chemical potential are presented in this paper. It is observed that the difference between the 2+1-flavor and 2+1+1-flavor systems is invisible at vanishing chemical potential and low temperature. The location of CEP for 2+1+1-flavor system deviates explicitly from that of the 2+1-flavor system with the increase of chemical potential. Both 2+1-flavor and 2+1+1-flavor systems differ significantly from the 2-flavor system. Moreover, at zero temperature, the critical chemical potential is found to be = 1.1 GeV, 1.6 GeV, 1.9 GeV for the 2-flavor, 2+1-flavor and 2+1+1-flavor systems, respectively.

Mei Huang

Flavor dependent critical endpoint from holographic QCD through machine learning

We investigate the effects of rotation on deconfinement and chiral phase transitions in the framework of the dynamical holographic QCD model. Instead of transforming to the rotating system by Lorentz boost, we construct an anisotropic gravitational background by incorporating the rotating boundary current. We first investigate the pure gluon system under rotation to extract deconfinement phase transition from the Polyakov loop then add two-flavor probe for chiral restoration phase transition from the chiral condensate. It is observed that at low chemical potentials, the deconfinement phase transition of pure gluon system is of first order and the chiral phase transition of a two-flavor system is of crossover. Both the critical temperatures of deconfinement and chiral phase transitions decrease/increase with imaginary/real angular velocity (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Ω</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>/</mo><mi mathvariant="normal">Ω</mi></mrow></math>) as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo>/</mo><msub><mi>T</mi><mi>c</mi></msub><mo>∼</mo><mn>1</mn><mo>−</mo><msub><mi>C</mi><mn>2</mn></msub><msubsup><mi mathvariant="normal">Ω</mi><mi>I</mi><mn>2</mn></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo>/</mo><msub><mi>T</mi><mi>c</mi></msub><mo>∼</mo><mn>1</mn><mo>+</mo><msub><mi>C</mi><mn>2</mn></msub><msup><mi mathvariant="normal">Ω</mi><mn>2</mn></msup></math>, which is consistent with lattice QCD results. In the temperature-chemical potential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo>−</mo><mi>μ</mi></math> phase diagram, the critical end point moves toward regions of higher temperature and chemical potential with real angular velocity.

Yidian Chen

Danning Li

Deconfinement and chiral restoration phase transition under rotation from holography in an anisotropic gravitational background