We present a novel deep generative framework that uses probabilistic diffusion models for ultrafast, event-by-event simulations of heavy-ion collision output. This new framework is trained on ultrarelativistic quantum molecular dynamics (UrQMD) cascade data to generate a full collision event output containing 26 distinct hadron species. The output is represented as a point cloud, where each point is defined by a particle's momentum vector and its corresponding species information. Our architecture integrates a normalizing flow-based condition generator that encodes global event features into a latent vector, and a diffusion model that synthesizes a point cloud of particles based on this condition. A detailed description of the model and an in-depth analysis of its performance is provided. The conditional point-cloud diffusion model learns to generate realistic output particles of collision events which successfully reproduce the UrQMD distributions for multiplicity, momentum, and rapidity of each hadron type. The flexible point-cloud representation of the event output preserves full event-level granularity, enabling direct application to inverse problems and parameter estimation tasks while also making it easily adaptable for accelerating any event-by-event model calculation or detector simulation.

Germany

Manjunath Omana Kuttan

China

Kai Zhou

Jan Steinheimer

Horst Stoecker

Ultrafast, event-by-event heavy-ion simulations for next-generation experiments

A novel point-cloud diffusion model for relativistic heavy-ion collisions, capable of ultrafast generation of complete, event-by-event collision output, is introduced. When trained on ultrarelativistic quantum molecular dynamics cascade simulations, the model generates realistic collision event output containing 26 distinct hadron species, as a list of particle momentum vectors along with their particle ID. From solving inverse problems to accelerating model calculations or detector simulations, the model can be a promising general-purpose tool for heavy-ion collisions beneficial to both theoretical studies and experimental applications.

Toward a foundation model for heavy-ion collision experiments based on point-cloud diffusion

We present an investigation on cosmological implications resulting from spontaneous dark $ S U(2)_d $ symmetry breaking in conjunction with the Witten effect. Furthermore, we examine the mass of hidden monopoles generated by phase transition as well as the impact of axion-monopole interactions on the axion mass. Following spontaneous breaking of the PQ symmetry, axions emitted by cosmic strings or domain walls as well as hidden monopoles generated during this transition may collectively contribute to the observed dark matter relic density. Additionally, the stochastic gravitational wave background generated by sub-GeV phase transitions and by the decay of axionic domain walls formed during sub-ZeV phase transitions could account for the low-frequency gravitational wave signals detected by PTA experiments.

Ruiyu Zhou

Ligong Bian

Gravitational waves and dark matter with Witten effect * Supported by the National Key Research and Development Program of China (2021YFC2203004). Ruiyu Zhou is supported by the National Natural Science Foundation of China (12305109, 12147102), Chongqing Natural Science Foundation project (CSTB2022NSCQ-MSX0534), and Science and Technology Research Project of Chongqing Municipal Education Commission (KJQN202300614). Ligong Bian is supported by the National Natural Science Foundation of China (12322505, 12347101). Ligong Bian also acknowledges Chongqing Natural Science Foundation (CSTB2024NSCQ-JQX0022) and Chongqing Talents: Exceptional Young Talents Project (cstc2024ycjhbgzxm0020).

The neutrino floor, a theoretical sensitivity limit for dark matter (DM) direct detection, is being redefined as the boundary of a dynamic ''neutrino fog,'' where neutrino signals become inevitable, obscuring DM detection due to statistical and systematic uncertainties. This study provides the first site-specific analysis of the neutrino floor at China Jinping Underground Laboratory (CJPL), leveraging its unique geographic and environmental characteristics. We quantify how CJPL’s suppressed atmospheric neutrino flux (approximately 30% lower than that of Laboratori Nazionali del Gran Sasso (LNGS)) reshapes the neutrino floor, thereby enabling improved sensitivity to high-mass WIMPs (mass > 10 GeV). Using a gradient-based framework, we derive the CJPL’s neutrino floor and estimate the detection prospects for the PandaX-xT experiment. Our results demonstrate that a 500 tonne-year exposure with PandaX-xT could reach the floor, probing spin independent cross-sections down to $ \sigma_{n}\sim 3\times 10^{-49}\; {\rm{cm}}^2$ at a DM mass of 70 GeV/$\textit{c}$ $^{2}$.

Yingjie Fan

Xuewen Liu

Ning Zhou

Characterizing the CJPL’s site-specific neutrino floor as the neutrino fog boundary * Xuewen Liu is supported by the Project of Shandong Province Higher Educational Science and Technology Program (2022KJ271). Ning Zhou is supported by National Science Foundation of China (12325505)

We present a Bayesian holographic model constructed by integrating the equation of state and baryon number susceptibility at zero chemical potential from lattice quantum chromodynamics (QCD). The model incorporates error estimates derived from lattice data. With this model, we systematically investigate the thermodynamic properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>-flavor QCD system. Using Bayesian inference, we perform precise calibration of the model parameters and determined the critical end point (CEP) position under the maximum a posterior (MAP) estimation to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>T</mi><mi>c</mi></msup><mo>,</mo><msubsup><mi>μ</mi><mi>B</mi><mi>c</mi></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>0.0859</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>,</mo><mn>0.742</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo stretchy="false">)</mo></math>. Additionally, we predict the CEP positions within 68% and 95% confidence levels, yielding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>T</mi><mi>c</mi></msup><mo>,</mo><msubsup><mi>μ</mi><mi>B</mi><mi>c</mi></msubsup><msub><mo stretchy="false">)</mo><mrow><mn>68</mn><mo>%</mo></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mn>0.0820</mn><mo>−</mo><mn>0.0889</mn><mo>,</mo><mn>0.71</mn><mo>−</mo><mn>0.77</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>T</mi><mi>c</mi></msup><mo>,</mo><msubsup><mi>μ</mi><mi>B</mi><mi>c</mi></msubsup><msub><mo stretchy="false">)</mo><mrow><mn>95</mn><mo>%</mo></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mn>0.0816</mn><mo>−</mo><mn>0.0898</mn><mo>,</mo><mn>0.71</mn><mo>−</mo><mn>0.79</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, respectively. Moreover, to validate the reliability and predictive power of our approach, we conduct a comprehensive comparison between our predictions and potential CEP locations proposed by other theoretical models. This work not only establishes a novel Bayesian framework for holographic modeling but also provides valuable insights and theoretical support for exploring phase transitions in strongly interacting matter under extreme conditions.

Liqiang Zhu

Italy

Xun Chen

Hanzhong Zhang

Mei Huang

Bayesian inference of the critical end point in a (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor system from holographic QCD

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.

Ou-Yang Luo

Fu-Peng Li

Xiao-Hua Li

Hong Kong

Neural network modeling of heavy-quark potential from holography

In this study, we investigate the $R^2$ corrections to the dissociation of heavy quarkonium in the Gauss-Bonnet gravitational background. We analyze the impact of the Gauss-Bonnet parameter $\lambda_{\rm GB}$ on the spectral function of charmonium and bottomonium and examine the effect of $\lambda_{\rm GB}$ on the dissociation of heavy quarkonium. Our results show that $\lambda_{\rm GB}$ reduces the peak height and increases the peak width of the spectral function, suggesting that $\lambda_{\rm GB}$ enhances the dissociation of heavy quarkonium. We also discuss the variation in the dissociation of heavy quarkonium with the ratio of shear viscosity to entropy density and observe that the dissociation is easier in more perfect plasma. Additionally, we observe that the temperature decreases the peak height and widens the peak, thereby accelerating the dissociation.

Zhou-Run Zhu

Manman Sun

Rui Zhou

Jinzhong Han

$\textit{R}$ $^{2}$ corrections to holographic heavy quarkonium dissociation * Rui Zhou supported by the Science and Technology Development Plan Project of Henan Province, China (242102230085), the National Natural Science Foundation of China (12404470), the High Level Talents Research and Startup Foundation Projects for Doctors of Zhoukou Normal University, China (ZKNUC2023017). Manman Sun supported by the National Natural Science Foundation of China (12305076). Zhou-Run Zhu supported by the High Level Talents Research and Startup Foundation Projects for Doctors of Zhoukou Normal University, China (ZKNUC2023018)

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

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

We have conducted an extensive study using a diverse set of equations of state (EoSs) to uncover strong relationships between neutron star (NS) observables and the underlying EoS parameters using symbolic regression method. These EoS models, derived from a mix of agnostic and physics-based approaches, considered neutron stars composed of nucleons, hyperons, and other exotic degrees of freedom in beta equilibrium. The maximum mass of a NS is found to be strongly correlated with the pressure and baryon density at an energy density of approximately 800 MeV.fm &#8722;3. We have also demonstrated that the EoS can be expressed as a function of radius and tidal deformability within the NS mass range 1-2 <math altimg='si1.svg'><msub><mrow><mi>M</mi></mrow><mrow><mo>&#8857;</mo></mrow></msub></math>. These insights offer a promising and efficient framework to decode the dense matter EoS directly from the accurate knowledge of NS observables.

India

N.K. Patra

Portugal

Tuhin Malik

Helena Pais

B.K. Agrawal

Constança Providência

Inferring the equation of state from neutron star observables via machine learning

In this paper, we introduce a novel approach in quantum field theories to estimate actions using artificial neural networks (ANNs). The actions are estimated by learning system configurations governed by the Boltzmann factor,   $ e^{-S} $  , at different temperatures within the imaginary time formalism of thermal field theory. Specifically, we focus on the 0+1 dimensional quantum field with kink/anti-kink configurations to demonstrate the feasibility of the method. Continuous-mixture autoregressive networks (CANs) enable the construction of accurate effective actions with tractable probability density estimation. Our numerical results demonstrate that this methodology not only facilitates the construction of effective actions at specified temperatures but also adeptly estimates the action at intermediate temperatures using data from both lower and higher temperature ensembles. This capability is especially valuable for detailed exploration of phase diagrams.