The production of heavy-quark (HQ) jets is a new area that addresses the mass effect of jet quenching in heavy-ion physics. This paper presents a theoretical study of HQ jet yield suppression in Pb+Pb collisions at the Large Hadron Collider (LHC) and focuses on the energy loss of HQ jets produced by different mechanisms. The $\textit{p+p}$ baseline is provided by the generator simulation of high-energy reactions of particles (SHERPA), and the jet-medium interactions are described by the SHELL transport model, which considers the elastic and inelastic partonic energy loss in the quark-gluon plasma (QGP). In $\textit{p+p}$ collisions, our numerical results indicate that the HQ jets from gluon splitting ( $ g \rightarrow Q $ -jet) are the dominant contribution at high $ p_T $ , displaying more dispersive structures than the HQ-initiated ( $ Q \rightarrow Q $ -jet). In nucleus-nucleus collisions, our calculations were consistent with the inclusive and b-jet $ R_{AA} $ recently measured by the ATLAS collaboration, revealing a remarkable manifestation of the mass effect of jet energy loss. As a result of the dispersive substructure, the $ g \rightarrow Q $ -jet loses more energy than the $ Q \rightarrow Q $ -jet in the QGP. Due to the significant contribution of $ g \rightarrow c $ -jet, the $ R_{AA} $ of $\textit{c}$-jet is comparable or even smaller than that of inclusive jet. To experimentally distinguish the $ g \rightarrow Q $ -jet and $ Q \rightarrow Q $ -jet, we propose event selection strategies based on their topological features and test their performances. By isolating the $ c \rightarrow c $ -jet, $ b \rightarrow b $ -jet, and the jets initiated by heavy quarks, we predicted that the order of their $ R_{AA} $ are in line with the mass hierarchy of energy loss. Future measurements on the $ R_{AA} $ of $ Q \rightarrow Q $ -jet and $ g \rightarrow Q $ -jet will provide a unique opportunity for testing the flavor/mass dependence of energy loss at the jet level.

China

Sa Wang

Shuang Li

Yao Li

Ben-Wei Zhang

Enke Wang

Probing the mass effect of heavy quark jets in high-energy nuclear collisions * Supported by the MajorProject of Basic and Applied Basic Research of Guangdong Province, China (2020B0301030008, 2023A1515011460), and the National Natural Science Foundation of China (11935007, 12035007, 12247127, 12375137). Sa Wang is supported by the Open Foundation of Key Laboratory of Quark and Lepton Physics (MOE) (QLPL2023P01) and the Talent Scientific Star-up Foundation of the China Three Gorges University, China (CTGU) (2024RCKJ013)

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)

Studying percolation phase transitions offers valuable insights into the characteristics of phase transitions, shedding light on the underlying mechanisms that govern the formation of global connectivity within a system. We explore the percolation phase transition in the 3D cubic Ising model by employing two machine learning techniques. Our results demonstrate that machine learning methods can distinguish different phases during the percolation transition. Through the finite-size scaling analysis on the output of the neural networks, the percolation temperature and a correlation length exponent in the geometrical percolation transition are extracted and compared to those in the thermal magnetization phase transition within the 3D Ising model. These findings provide a valuable method for enhancing our understanding of the properties of the QCD critical point, which belongs to the same universality class as the 3D Ising model.

Ranran Guo

Xiaobing Li

Rui Wang

United Kingdom

Shiyang Chen

Yuanfang Wu

Zhiming Li

Exploring percolation phase transition in the three-dimensional Ising model with machine learning * Supported by the National Key Research and Development Program of China (2024YFE0110103, 2022YFA1604900), the National Natural Science Foundation of China (12275102), and the Chinese Scholarship Council Grant (202306770049)

Large density fluctuations of conserved charges have been proposed as a promising signature for exploring the QCD critical point in heavy-ion collisions. These fluctuations are expected to exhibit a fractal or scale-invariant behavior, which can be probed by intermittency analysis. Recent high-energy experimental studies reveal that the signal of critical fluctuations related to intermittency is very weak and thus could be easily obscured by the overwhelming background particles in the data sample. Employing a point cloud neural network with topological machine learning, we can successfully classify weak signal events from background noise by the extracted distinct topological features, and accurately determine the intermittency index for weak signal event samples.

Chengrui Qiu

Singapore

Chuan-Shen Hu

Identifying weak critical fluctuations of intermittency in heavy-ion collisions with topological machine learning

We investigate the constraints of the ( <italic>&#946;</italic>-deformed) partition functions with <italic>W</italic>-representations in the literature, which can be realized by the interpolating two-matrix models (two <italic>&#946;</italic>-ensembles). For the non-deformed partition functions, we construct their Virasoro and higher order constraints using the total derivative operators. For the <italic>&#946;</italic>-deformed partition functions, we derive their Virasoro constraints in terms of the constructed Virasoro operators. Meanwhile, we obtain a new realization of the Virasoro algebra in terms of the Dunkl operators and the conserved quantities in the rational Calogero model.

Yu-Sen Zhu

Ren Cuo Ji

Min-Li Li

On constraints of the ( <italic>&#946;</italic>-deformed) partition functions with <italic>W</italic>-representations

We construct the ( $$\beta $$  <math> <mi>β</mi> </math>  -deformed) higher order total derivative operators and analyze their remarkable properties. In terms of these operators, we derive the higher order constraints for the ( $$\beta $$  <math> <mi>β</mi> </math>  -deformed) Hermitian matrix models. We prove that these ( $$\beta $$  <math> <mi>β</mi> </math>  -deformed) higher order constraints are reducible to the Virasoro constraints. Meanwhile, the Itoyama–Matsuo conjecture for the constraints of the Hermitian matrix model is proved. We also find that through rescaling variable transformations, two sets of the constraint operators become the W-operators of W-representations for the ( $$\beta $$  <math> <mi>β</mi> </math>  -deformed) partition function hierarchies in the literature.

Higher order constraints for the ( $$\beta $$  <math> <mi>β</mi> </math>  -deformed) Hermitian matrix models

We construct the generalized  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed partition functions through W representations, where the expansions are respectively with respect to the generalized Jack and Macdonald polynomials labeled by N-tuple of Young diagrams. We find that there are the profound interrelations between our deformed partition functions and the 4d and 5d Nekrasov partition functions. Since the corresponding Nekrasov partition functions can be given by vertex operators, the remarkable connection between our  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed W-operators and vertex operators is revealed in this paper. In addition, we investigate the higher Hamiltonians for the generalized Jack and Macdonald polynomials.

Fan Liu

Jie Yang

Wei-Zhong Zhao

Generalized  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed partition functions with W-representations and Nekrasov partition functions

In this letter we continue the development of W-representations. We propose several generalizations of the known models, such as the hypergeometric Hurwitz τ-functions. We construct W-representations for multi-character expansions, which involve a generic number of sets of time variables. We propose integral representations for such kind of partition functions which are given by tensor models and multi-matrix models with multi-trace couplings. We further propose the β-deformation of the discussed W-representation for the Hurwitz case for two sets of times as well as for the multi-character case.

Lu-Yao Wang

Russia

V. Mishnyakov

A. Popolitov

-representations for Multi-character Partition Functions and Their -deformations

We construct the supersymmetric  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed Hurwitz–Kontsevich partition functions through W-representations and present the corresponding character expansions with respect to the Jack and Macdonald superpolynomials, respectively. Based on the constructed  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed superoperators, we further give the supersymmetric  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed partition function hierarchies through W-representations. We also present the generalized super Virasoro constraints, where the constraint operators obey the generalized super Virasoro algebra and null super 3-algebra. Moreover, the superintegrability for these (non-deformed) supersymmetric hierarchies is shown by their character expansions, i.e.,  $$&lt;character&gt;\sim character$$  <math> <mrow> <mo>&lt;</mo> <mi>c</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>a</mi> <mi>c</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> <mo>&gt;</mo> <mo>∼</mo> <mi>c</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>a</mi> <mi>c</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </math>  .

Supersymmetric partition function hierarchies and character expansions

We follow the general recipe for constructing commutative families of W-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to a <math><mo>(</mo><mi>q</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-deformation of the earlier studied models. As before, a key role is played by an appropriate deformation of the cut-and-join rotation operator. We outline its expression both in terms of generators of the quantum toroidal algebra and in terms of the Macdonald difference operators.

A. Mironov

A. Morozov

( , )-deformed (skew) Hurwitz -functions