Jets selected with high internal charged-particle multiplicity exhibit markedly different substructure patterns compared to inclusive jet samples. Such correlations motivate a systematic study of jet observables as a function of the normalized multiplicity, $\textit{ν}$ = $\textit{N}$ /〈$\textit{N}$ 〉 . In this work, we develop a theoretical framework for the full charged-particle multiplicity distribution of exclusive and inclusive jets, formulated within the jet-function approach. The hard production and jet function are evaluated at NLO + LL accuracy. The internal parton dynamics governing the multiplicity distribution are described by coupled nonlinear branching equations with angular ordering, supplemented by a nonperturbative modeling term that accounts for hadron-level effects. The resulting predictions are validated against P 8 simulations and compared with CMS data. We examine the effects of both nonperturbative and perturbative components in shaping the multiplicity distribution, and show that Koba-Nielsen-Olesen (KNO) scaling is notably violated in the region $\textit{ν >}$ 2 in the full solution, with a trend consistent with Monte Carlo results. This framework that numerically solves the nonlinear multiplicity evolution goes beyond DLA-like approximations and reproduces key features seen in event generators, providing a solid foundation for future investigations of multiplicity-conditioned jet substructure within the jet function formalism.

China

Pi Duan

Weiyao Ke

Guang-You Qin

Lei Wang

Internal multiplicity distributions of jets from nonlinear evolution within the jet function framework

Machine learning techniques have emerged as powerful tools for tackling nonperturbative challenges in quantum chromodynamics. In this study, we introduce a data-driven framework employing deep neural networks to systematically predict the temperature-dependent behavior of the screening mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>m</mi><mi>D</mi></msub><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math> and the strong coupling constant <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>α</mi><mi>s</mi></msub><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math> within a quark-gluon plasma medium. These medium-sensitive quantities are subsequently employed to compute the thermal widths <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi mathvariant="normal">Γ</mi><mtext>n</mtext></msub><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math> and binding energies <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>E</mi><mi>B</mi></msub><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math> of heavy quarkonia states, specifically charmonia and bottomonia, by numerically solving the Schrödinger equation with medium-modified heavy quark potentials. To estimate the dissociation temperatures <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>d</mi></msub></math> of various quarkonia states, we employ two complementary dissociation criteria: the conventional one, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><msub><mi>E</mi><mi>B</mi></msub><mrow><mo>(</mo><msub><mi>T</mi><mi>d</mi></msub><mo>)</mo></mrow><mo>=</mo><msub><mi mathvariant="normal">Γ</mi><mtext>n</mtext></msub><mrow><mo>(</mo><msub><mi>T</mi><mi>d</mi></msub><mo>)</mo></mrow></mrow></math>, and an additional lower bound criterion defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>E</mi><mi>B</mi></msub><mrow><mo>(</mo><msub><mi>T</mi><mi>d</mi></msub><mo>)</mo></mrow><mo>=</mo><mn>3</mn><msub><mi>T</mi><mi>d</mi></msub></mrow></math>. This dual-criterion approach provides a more constrained and physically motivated estimate of the temperature range over which quarkonia states dissolve in the quark-gluon plasma (QGP) environment. Our machine learning-enhanced predictions show excellent agreement with available lattice quantum chromodynamics results, especially for the ground states <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Υ</mi><mo>(</mo><mn>1</mn><mi>S</mi><mo>)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>, and offer new perspectives on the sequential suppression pattern detected in relativistic heavy-ion collision experiments. Overall, this work advances the quantitative description of quarkonium suppression and demonstrates the prospect of modern machine learning methods to bridge theoretical predictions and experimental observations, thereby contributing significantly to QGP tomography.

Mohammad Yousuf Jamal

Fu-Peng Li

Long-Gang Pang

Melting of heavy quarkonia in QGP using deep neural networks

In a talk at an IHEP-Beijing symposium celebrating the 50th anniversary of the discovery of the <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math>, I reminisced about some of the interesting phenomena that were observed in <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> decays in the BES, BESII, and BESIII detectors during the 35 year long BES experimental program. The three order of magnitude increase in the <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> event samples and the improved detector capabilities that occurred during this time led to a persistent series of interesting discoveries and new insights. As more <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> events were collected, the scientific interest in them increased and the breadth of physics topics that are addressed by them expanded. In addition, I speculated on what might happen if, in the next few decades, the magnitude of <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> data samples and the detector capabilities continued to increase at similar paces. In particular, I emphasize the possibilities of searches for <math altimg='si111.svg'><mi mathvariant='script'>C</mi></math> <math altimg='si112.svg'><mi mathvariant='script'>P</mi></math> violation in strange hyperon decays and testing the <math altimg='si111.svg'><mi mathvariant='script'>C</mi></math> <math altimg='si112.svg'><mi mathvariant='script'>P</mi></math> <math altimg='si113.svg'><mi mathvariant='script'>T</mi></math> theorem with strangeness-tagged neutral kaon decays.

South Korea

Stephen Lars Olsen

You never have enough <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> events - The case for a <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> factory

To accurately determine the nuclear equation of state (EoS) at finite baryon chemical potential ( <math altimg='si1.svg'><msub><mrow><mi>&#956;</mi></mrow><mrow><mi>B</mi></mrow></msub></math>) remains a challenging yet essential goal in the study of QCD matter under extreme conditions. In this study, we develop a deep learning assisted quasi-parton model, which utilizes three deep neural networks, to reconstruct the QCD EoS at zero <math altimg='si1.svg'><msub><mrow><mi>&#956;</mi></mrow><mrow><mi>B</mi></mrow></msub></math> and predict the EoS and transport coefficient <math altimg='si2.svg'><mi>&#951;</mi><mo stretchy='false'>/</mo><mi>s</mi></math> at finite <math altimg='si1.svg'><msub><mrow><mi>&#956;</mi></mrow><mrow><mi>B</mi></mrow></msub></math>. The EoS derived from our quasi-parton model shows excellent agreement with lattice QCD results obtained using Taylor expansion techniques. The temperature of smallest <math altimg='si2.svg'><mi>&#951;</mi><mo stretchy='false'>/</mo><mi>s</mi></math> is found to be approximately 175 MeV and decreases with increasing chemical potential within the confidence interval. This model not only provides a robust framework for understanding the properties of the QCD EoS at finite <math altimg='si1.svg'><msub><mrow><mi>&#956;</mi></mrow><mrow><mi>B</mi></mrow></msub></math> but also offers critical input for relativistic hydrodynamic simulations of nuclear matter produced in heavy-ion collisions by the RHIC beam energy scan program.

QCD equation of state at finite <italic>&#956;</italic> <inf><italic>B</italic></inf> using deep learning assisted quasi-parton model

The nuclear modification factor (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mi>AA</mi></msub></math>) of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> mesons in high-energy nuclear collisions provides a novel probe of heavy quark interactions with the quark-gluon plasma (QGP). Based on a linear Boltzmann transport model that incorporates both Yukawa and string types of interactions between heavy quarks and the QGP, we study the production and evolution of heavy quarks and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> mesons within the same framework. A <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> bound state dissociates while one of its constituent heavy quarks scatters with the QGP with momentum transfer greater than its binding energy. The medium-modified charm and bottom quarks can recombine into <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> mesons, and the medium-modified bottom quarks can also fragment to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> mesons. We find that most primordial <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> mesons generated from the initial hard collisions dissociate inside the QGP. The production of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> mesons is primarily driven by the recombination mechanism at low transverse momentum and fragmentation at high transverse momentum. The string interaction dominates over the Yukawa interaction in the nuclear modification of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> mesons. The participant number dependence of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> meson <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mi>AA</mi></msub></math> is determined by the complicated interplay between the heavy quark yield, energy loss, and the QGP volume. We obtain a reasonable description of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mi>AA</mi></msub></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> mesons in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mi>NN</mi></msub></msqrt><mo>=</mo><mn>5.02</mn></mrow></math> TeV, and provide predictions for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Au</mi><mo>+</mo><mi>Au</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mi>NN</mi></msub></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV.

Lejing Zhang

Xiaowen Li

Wen-Jing Xing

Shanshan Cao

Nuclear modification of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>c</mi></msub></math> mesons in relativistic heavy-ion collisions based on a linear Boltzmann transport model

Jet-induced medium excitation is a crucial part of jet interactions with the quark-gluon plasma (QGP) in relativistic heavy-ion collisions, and has recently been confirmed by experiment for the first time. Based on the AMPT model simulation, we propose the strangeness enhancement around quenched jets as a novel signature of jet-induced medium excitation. By applying the jet-particle correlation techniques, we calculate jet-induced particle yields around the jets and find a significant enhancement of the strange-to-non-strange-hadron ratio and the double-to-single-strange-hadron ratio correlated with jets in relativistic nucleus-nucleus collisions relative to proton-proton collisions. This enhancement increases with both the strength of jet-QGP interactions and the radial distance from jet axis. These observations align with the features of jet-induced medium excitation and parton coalescence in hadron formation, and await experimental validation in the future measurements.

Ao Luo

Probing medium response via strangeness enhancement around quenched jets

We have implemented the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math> dimensional CLVisc hydrodynamics model with TrENTo-3D initial conditions to investigate the spin polarization of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Λ</mi></math> hyperons along the beam direction in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">p</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>8.16</mn></mrow></math> TeV. Following our previous theoretical framework based on quantum kinetic theory, we consider three different scenarios: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Λ</mi></math> equilibrium, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math> quark equilibrium, and isothermal equilibrium scenarios. We have computed the second Fourier sine coefficients of spin polarization along the beam direction, denoted as <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>〈</mo><msub><mi>P</mi><mi>z</mi></msub><mo form="prefix">sin</mo><mn>2</mn><mrow><mo>(</mo><msub><mi>ϕ</mi><mi>p</mi></msub><mo>−</mo><msub><mi mathvariant="normal">Ψ</mi><mn>2</mn></msub><mo>)</mo></mrow><mo>〉</mo></mrow></math>, with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>ϕ</mi><mi>p</mi></msub><mo>−</mo><msub><mi mathvariant="normal">Ψ</mi><mn>2</mn></msub></mrow></math> being the azimuthal angle relative to the second-order event plane <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">Ψ</mi><mn>2</mn></msub></math>, as functions of multiplicity, transverse momentum, and pseudorapidity in the three scenarios. Additionally, we have also computed the spin polarization along the beam direction, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mi>z</mi></msub></math>, as a function of the azimuthal angle. We find that the spin polarization induced by thermal vorticity always provides an opposite contribution compared to the shear-induced polarization in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">p</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions. The total spin polarization computed by the current hydrodynamic model disagrees with the data measured by LHC-CMS experiments.

Cong Yi

United States

Canada

Xiang-Yu Wu

Germany

Jie Zhu

Shi Pu

Spin polarization of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Λ</mi></math> hyperons along the beam direction in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>8.16</mn></mrow></math> TeV using hydrodynamic approaches

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

Heavy flavor jets provide ideal tools to probe the mass effect on jet substructure in both vacuum and quark-gluon plasma. An energy-energy correlator (EEC) is an excellent jet substructure observable owning to its strong sensitivity to jet physics at different scales. We perform a complete realistic simulation on medium modification of heavy and light flavor jet EECs in heavy-ion collisions. A clear flavor hierarchy is observed for jet EECs in both vacuum and quark-gluon plasma due to the mass effect. The medium modification of inclusive jet EECs at different angular scales exhibits a very rich structure: suppression at intermediate angles, and enhancement at small and large angles, which can be well explained by the interplay of mass effect, energy loss, medium-induced radiation, and medium response. These unique features of jet EECs are shown to probe the physics of jet-medium interaction at different scales, and can be readily validated by upcoming experiments.

Xin-Nian Wang

Flavor Hierarchy of Jet Energy Correlators inside the Quark-Gluon Plasma

For the Laplacian of an n-Riemannian manifold X, the Weyl law states that the k-th eigenvalue is asymptotically proportional to (k/V)2/n , where V is the volume of X. We show that this result can be derived via physical considerations by demanding that the gravitational potential for a compactification on X behaves in the expected (4+n)-dimensional way at short distances. In simple product compactifications, when particle motion on X is ergodic, for large k the eigenfunctions oscillate around a constant, and the argument is relatively straightforward. The Weyl law thus allows to reconstruct the four-dimensional Planck mass from the asymptotics of the masses of the spin 2 Kaluza-Klein modes. For warped compactifications, a puzzle appears: the Weyl law still depends on the ordinary volume V, while the Planck mass famously depends on a weighted volume obtained as an integral of the warping function. We resolve this tension by arguing that in the ergodic case the eigenfunctions oscillate now around a power of the warping function rather than around a constant, a property that we call weighted quantum ergodicity. This has implications for the problem of gravity localization, which we discuss. We show that for spaces with Dp-brane singularities the spectrum is discrete only for p = 6, 7, 8, and for these cases we rigorously prove the Weyl law by applying modern techniques from RCD theory.