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)

This paper presents a phenomenological study on the angle between the standard and winner-take-all (WTA) jet axes <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mi mathvariant="normal">Δ</mi><msubsup><mi>R</mi><mrow><mi>axis</mi></mrow><mrow><mi>WTA</mi><mtext>–</mtext><mi>Std</mi></mrow></msubsup><mo>)</mo></mrow></math> in high-energy nuclear collisions. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math> baseline is provided by the Pythia8 event generator. The in-medium jet propagation is simulated by the linear Boltzmann transport (Lbt) model, which considers both the elastic and inelastic jet-medium interactions. Our theoretical results calculated by the Lbt model show that the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>R</mi><mrow><mi>axis</mi></mrow><mrow><mi>WTA</mi><mtext>–</mtext><mi>Std</mi></mrow></msubsup></mrow></math> distribution in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</mi></mrow></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>5.02</mn><mspace width="0.16em"></mspace><mi>TeV</mi></mrow></math> is narrower than that in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math>, which agrees well with the recent ALICE measurements. The narrowing of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>R</mi><mrow><mi>axis</mi></mrow><mrow><mi>WTA</mi><mtext>–</mtext><mi>Std</mi></mrow></msubsup></mrow></math>, which seems to violate the nature of intrajet broadening due to jet quenching, may be attributed to the influence of “selection bias.” However, the physical details still need to be fully understood. Utilizing a matching-jet method to track the jet evolution in the QGP to remove the selection bias in the Monte Carlo simulations, we observe that the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>R</mi><mrow><mi>axis</mi></mrow><mrow><mi>WTA</mi><mtext>–</mtext><mi>Std</mi></mrow></msubsup></mrow></math> distribution becomes broader due to the jet-medium interactions. At the same time, by rescaling the quark- and gluon-jet fractions in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions to be the same as that in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math>, we find that the fraction change may not significantly influence the modification pattern of jet <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>R</mi><mrow><mi>axis</mi></mrow><mrow><mi>WTA</mi><mtext>–</mtext><mi>Std</mi></mrow></msubsup></mrow></math>. On the other hand, the selected jet sample in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">A</mi><mo>+</mo><mi mathvariant="normal">A</mi></mrow></math> collisions has a significantly narrower initial <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>R</mi><mrow><mi>axis</mi></mrow><mrow><mi>WTA</mi><mtext>–</mtext><mi>Std</mi></mrow></msubsup></mrow></math> distribution than the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math> baseline, and such a biased comparison between <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">A</mi><mo>+</mo><mi mathvariant="normal">A</mi></mrow></math> conceals the actual intrajet broadening effect in the experimental measurements. The investigations presented in this paper will deepen our understanding of the relationship between the actual intrajet modifications in the QGP and the experimental observations.

Jin-Wen Kang

Lei Wang

Phenomenological study of the angle between jet axes in heavy-ion collisions

When an energetic parton traverses the hot QCD medium, it may suffer from multiple scattering and lose its energy. The medium-induced gluon radiation for a massive quark will be suppressed relative to that of a light quark due to the dead-cone effect. The development of new declustering techniques of jet evolution makes a direct study of the dead-cone effect in the QCD medium possible for the first time. In this work, we compute the emission angle distribution of the charm-quark-initiated splittings in $\textit{D}$ $^{0}$ meson tagged jet and that of the light parton-initiated splittings in an inclusive jet in $\textit{p}$+$\textit{p}$ and Pb+Pb at 5.02 TeV by utilizing the declustering techniques of jet evolution. The heavy quark propagation and induced energy loss in the QCD medium are simulated with the SHELL model based on the Langevin equation. By directly comparing the emission angle distributions of charm-quark-initiated splittings with those of light parton-initiated splittings at the same energy intervals of the initial parton, we provide insights into the fundamental splitting structure in $\textit{A}$+$\textit{A}$ collisions, thereby exploring the possible observation of the dead-cone effect in medium-induced radiation. We further investigate the case of the emission angle distributions normalized to the number of splittings and find the dead-cone effect will broaden the emission angle of the splitting and reduce the possibility for such splitting to occur, leading the massive parton to lose less energy. We also find that the collisional energy loss mechanism has a negligible impact on the medium modification to the emission angle distribution of the charm-quark-initiated splittings for $\textit{D}$ $^{0 }$meson-tagged jets.

Yun-Fan Liu

Wei Dai

Exposing the dead-cone effect of jet quenching in QCD medium * Supported by the Major Project of Basic and Applied Basic Research of Guangdong Province, China (2020B0301030008), and the Natural Science Foundation of China (1935007, 11805167)

This paper presents a theoretical study on the production of leptons from decay of heavy-flavor hadrons (denoted as HFLs) in high-energy nuclear collisions at the CERN Large Hadron Collider. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">pp</mi></math> baseline is calculated by the fonll program, which matches the next-to-leading order perturbative QCD (pQCD) calculation with the next-to-leading-logarithm large-<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math> resummation. The in-medium propagation of heavy quarks is driven by the modified Langevin equations, which consider both the elastic and inelastic partonic interactions. We propose a method to separate the respective influence of the six factors, i.e., <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">pp</mi></math> spectra, cold nuclear matter (CNM) effects, in-medium energy loss (E-loss), fragmentation functions (FFs), coalescence (Coal), and decay channels, which may contribute to the larger <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> of HFL <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>←</mo><mi>b</mi></mrow></math> compared to that of HFL <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>←</mo><mi>c</mi></mrow></math> in nucleus-nucleus collisions. Based on quantitative analysis, we demonstrate that both coalescence hadronization decay channels and the mass-dependent E-loss play an essential role at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>p</mi><mi>T</mi></msub><mo>&lt;</mo><mn>5</mn><mspace width="0.16em"></mspace><mi>GeV</mi></mrow></math>, while the latter dominates the higher <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math> region. It is also found that the influences of the CNM effects and FFs are insignificant. At the same time, different initial <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">pp</mi></math> spectra of charm and bottom quarks have a considerable impact at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>p</mi><mi>T</mi></msub><mo>&gt;</mo><mn>5</mn><mspace width="0.16em"></mspace><mi>GeV</mi></mrow></math>. Furthermore, we explore the path-length dependence of jet quenching by comparing the HFL <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> in two different collision systems. Our investigations show smaller HFL <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</mi></mrow></math> than in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Xe</mi><mo>+</mo><mi>Xe</mi></mrow></math> within the same centrality bin, consistent with the ALICE data. The longer propagation time and more effective energy loss of heavy quarks in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions play critical roles in the stronger yield suppression of the HFLs compared to that in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Xe</mi><mo>+</mo><mi>Xe</mi></mrow></math>. In addition, we observe a scaling behavior of the HFL <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Xe</mi><mo>+</mo><mi>Xe</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions.

Shuwan Shen

Production of leptons from decay of heavy-flavor hadrons in high-energy nuclear collisions

The effect of finite coupling corrections to the Langevin diffusion coefficients on a moving heavy quark in the Super Yang-Mills plasma was investigated. These corrections are related to curvature squared corrections in the corresponding gravity sector. We compared the results of both longitudinal and perpendicular Langevin diffusion coefficients with those for   $\mathcal{N}$  =4 Super Yang-Mills plasma. It was observed that the curvature-squared corrections influence the Langevin diffusion coefficients, and the corrections for both Langevin diffusion coefficients demonstrate the dependence on the velocity of the moving heavy quark and the specifics of the higher derivative correction. In addition, we conducted calculations for the Langevin diffusion coefficients of a moving heavy quark within the Gauss-Bonnet background.

Germany

Qi Zhou

 curvature-squared corrections on Langevin diffusion coefficients  

We investigate the flavor dependence of jet quenching, by performing a systematic analysis of medium modifications on the inclusive jet, γ+jet, and b-jet in Pb+Pb collisions at the LHC. Our results from MadGraph+PYTHIA exhibit excellent agreement with experimental measurements of the inclusive jet, γ+jet and b-jet simultaneously in p+p collisions. We then utilize a Bayesian data-driven method to extract systematically the flavor-dependent jet energy loss distributions from experimental data, where the gluon, light quark and b-quark initiated energy loss distributions are well constrained and satisfy the predicted flavor hierarchy of jet quenching, i.e. <math><mo>〈</mo><mi>Δ</mi><msub><mrow><mi>E</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>〉</mo><mo>&gt;</mo><mo>〈</mo><mi>Δ</mi><msub><mrow><mi>E</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>〉</mo><mo>&gt;</mo><mo>〈</mo><mi>Δ</mi><msub><mrow><mi>E</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>〉</mo></math>. It is shown that the quark-initiated jet energy loss distribution shows weaker centrality and <math><msub><mrow><mi>p</mi></mrow><mrow><mtext>T</mtext></mrow></msub></math> dependence than the gluon-initiated one. We demonstrate the impacts of the slope of initial spectra, color-charge as well as parton mass dependent jet energy attenuation on the <math><mi>γ</mi><mo>/</mo><mi>b</mi></math>-jet suppression observed in heavy-ion collisions.

Shan-Liang Zhang

Hongxi Xing

Flavor dependence of jet quenching in heavy-ion collisions from a Bayesian analysis

Heavy-flavor jets are powerful tools to gain insight into the in-medium partonic energy-loss mechanisms and the quark-gluon plasma's (QGP) transport properties in high-energy nuclear collisions. In this work we present the first theoretical study of the longitudinal momentum fraction <math><msub><mi>z</mi><mrow><mo>|</mo><mo>|</mo></mrow></msub></math> carried by heavy-flavor mesons in jets in <math><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions at <math><mrow><msqrt><msub><mi>s</mi><mi>NN</mi></msub></msqrt><mo>=</mo><mn>5.02</mn><mspace width="0.16em"></mspace><mi>TeV</mi></mrow></math>. The <math><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math> baseline is provided by powheg<math><mrow><mo>+</mo><mi>p</mi></mrow></math>ythia8, which matches the next-to-leading-order hard processes with the parton shower. We employ a Monte Carlo transport model, which considers the collisional and radiative partonic energy loss, to simulate the evolution of heavy-flavor jets in the expanding QGP medium. We observe steeper <math><msub><mi>z</mi><mrow><mo>|</mo><mo>|</mo></mrow></msub></math> distributions of <math><msup><mi>B</mi><mn>0</mn></msup></math> jets compared to those of <math><msup><mi>D</mi><mn>0</mn></msup></math> jets at the same kinematics region in <math><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math> collisions, which may be a hint of the harder jet fragmentation function of b jets compared to c jets in vacuum. In <math><mrow><mi>A</mi><mo>+</mo><mi>A</mi></mrow></math> collisions, it is shown that the jet quenching effect would generally decrease the values of <math><msub><mi>z</mi><mrow><mo>|</mo><mo>|</mo></mrow></msub></math>. We have made a systematical study on how several factors, including jet <math><msub><mi>p</mi><mi>T</mi></msub></math>, jet radius <math><mi>R</mi></math>, and collision centrality, would influence the medium modification of <math><msub><mi>z</mi><mrow><mo>|</mo><mo>|</mo></mrow></msub></math> distributions of a <math><msup><mi>D</mi><mn>0</mn></msup></math> jet. In addition, we predict visibly stronger nuclear modifications of <math><msup><mi>B</mi><mn>0</mn></msup></math>-jet <math><msub><mi>z</mi><mrow><mo>|</mo><mo>|</mo></mrow></msub></math> distributions compared to a <math><msup><mi>D</mi><mn>0</mn></msup></math> jet within the same <math><msub><mi>p</mi><mi>T</mi></msub></math> windows as a result of the much steeper initial <math><msub><mi>z</mi><mrow><mo>|</mo><mo>|</mo></mrow></msub></math> distribution of the <math><msup><mi>B</mi><mn>0</mn></msup></math> jet in vacuum.

Longitudinal momentum fraction of heavy-flavor mesons in jets in high-energy nuclear collisions

The production of vector boson tagged heavy quark jets potentially provides new tools to probe the jet quenching effect. In this paper, we present the first theoretical study on the angular correlations (  $ \Delta\phi_{bZ} $  ), transverse momentum imbalance (  $ \Delta\phi_{bZ} $  ), and nuclear modification factor (  $ \Delta\phi_{bZ} $  ) of   $ \Delta\phi_{bZ} $   boson tagged b-jets in heavy-ion collisions, which was performed using a Monte Carlo transport model. We find that the medium modification of the   $ \Delta\phi_{bZ} $   for   $ \Delta\phi_{bZ} $   + b-jet has a weaker dependence on   $ \Delta\phi_{bZ} $   than that for   $ \Delta\phi_{bZ} $   + jet, and the modification patterns are sensitive to the initial jet   $ \Delta\phi_{bZ} $   distribution. Additionally, with the high purity of the quark jet in   $ \Delta\phi_{bZ} $   + (b-) jet production, we calculate the momentum imbalance   $ \Delta\phi_{bZ} $   and the nuclear modification factor   $ \Delta\phi_{bZ} $   of   $ \Delta\phi_{bZ} $   + b-jet in Pb+Pb collisions. We observe a smaller   $ \Delta\phi_{bZ} $   and larger   $ \Delta\phi_{bZ} $   of   $ \Delta\phi_{bZ} $   + b-jet in Pb+Pb collisions relative to those of   $ \Delta\phi_{bZ} $   + jet, which may be an indication of the mass effect of jet quenching and can be tested in future measurements.

  Boson Associated -jet Production in High-energy Nuclear Collisions  

The production of   $ \pi^0 $  , η, and ϕ in the most central (0%–5%) Xe+Xe collisions at   $ \pi^0 $   = 5.44 TeV is investigated in the framework of the perturbative QCD (pQCD) improved parton model at an accuracy of next-to-leading order (NLO). The jet quenching effect is effectively incorporated by medium-modified fragmentation functions via the higher-twist approach. Predictions of the nuclear modification factors of   $ \pi^0 $  , η, and ϕ as functions of the transverse momentum   $ \pi^0 $   are made with the jet transport parameter   $ \pi^0 $  , which is extracted from the available experimental data of charged hadrons provided by ALICE and CMS. The particle ratios   $ \pi^0 $   as functions of   $ \pi^0 $   in Xe+Xe collisions at   $ \pi^0 $   = 5.44 TeV as well as in 0%–5% Pb + Pb collisions at   $ \pi^0 $   = 5.02 TeV are also presented. The numerical simulations of the scaled ratios of charged hadron production in the Xe+Xe 5.44 TeV system over those in the Pb+Pb 5.02 TeV system give a good description of the CMS data, and the scaled ratios of   $ \pi^0 $  , η, and ϕ production coincide with the curve of charged hadron production.

Qing Zhang

Particle production at large  in Xe+Xe collisions with jet quenching using the higher twist approach  

In this study, we investigate the impact of jet quenching on the   $ p_{T} $   dispersion (  $ p_{T} $  ) of inclusive jets (  $ p_{T} $  ) in central Pb+Pb (0%–10%) collisions at   $ p_{T} $   TeV. The partonic spectrum in the initial hard scattering of elementary collisions is obtained by an event generator POWHEG+PYTHIA, which matches the next-to-leading order (NLO) matrix elements with parton showering, and the energy loss of a fast parton traversing through hot/dense QCD medium is calculated using Monte Carlo simulation within the Higher-Twist formalism of jet quenching in heavy-ion collisions. We present model calculations of the normalized   $ p_{T} $   distributions of inclusive jets in p+p and central Pb+Pb collisions at   $ p_{T} $   TeV, which offer good descriptions of ALICE measurements. It is shown that the   $ p_{T} $   distributions of inclusive jets in central Pb+Pb collisions shift significantly to a higher   $ p_{T} $   region relative to those in p+p collisions. Thus, the nuclear modification ratio of the   $ p_{T} $   distributions of inclusive jets is smaller than unity in the small   $ p_{T} $   region and larger than one in the large   $ p_{T} $   region. This behavior is caused by a more uneven   $ p_{T} $   distribution for jet constituents as well as the fraction alteration of quark/gluon initiated jets in heavy-ion collisions. The difference in   $ p_{T} $   distribution between groomed and ungroomed jets in Pb+Pb collisions is also discussed.