Dynamics of Hot QCD Matter 2024 -- Hard Probes

Amal Sarkar; Aritra Bandyopadhyay; Binoy Krishna Patra; Debarshi Dey; Devanshu Sharma; Gurleen Kaur; Jai Prakash; Manaswini Priyadarshini; Manisha Kumari; Marco Ruggieri

REVIEW 3 major objections 7 minor 227 references

Dynamics of Hot QCD Matter 2024 -- Hard Probes

T0 review · 3 major / 7 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Jets, heavy quarks, and quarkonia now give a coherent readout of the quark-gluon plasma.

desk verdict A useful but uneven hard-probes snapshot: the experimental reviews are solid, but Section 10's unsupported claim undercuts the volume's reliability. read the letter →

arxiv 2412.14026 v1 pith:LJUPGIQE submitted 2024-12-18 nucl-ex hep-exhep-phnucl-th

Santosh K. Das , Prabhakar Palni , Amal Sarkar , Vineet Kumar Agotiya , Aritra Bandyopadhyay , Partha Pratim Bhaduri , Saumen Datta , Vaishnavi Desai

show 19 more authors

Debarshi Dey Vincenzo Greco Mohammad Yousuf Jamal Gurleen Kaur Manisha Kumari Monideepa Maity Subrata Pal Binoy Krishna Patra Pooja Jai Prakash Manaswini Priyadarshini Vyshakh B R Marco Ruggieri Nihar Ranjan Sahoo Raghunath Sahoo Om Shahi Devanshu Sharma Rishabh Sharma Rishi Sharma

This is my paper · ORCID

classification nucl-exhep-exhep-phnucl-th PACS 12.38.-t12.38.Aw

keywords heavy-ioncollisionsquark-gluonplasmahardprobesjetquenchingheavyflavorquarkoniaopenquantumsystemsmachinelearning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper is a status report on hard probes of the quark-gluon plasma, the deconfined matter formed in high-energy nucleus collisions. It claims that recent jet-quenching and heavy-flavor measurements have matured enough to start fine-tuning theoretical models, and it collects new calculations that push into less charted territory: memory effects in quarkonium quantum evolution, heavy-quark diffusion in magnetic fields, anomalous fractional diffusion, charm dissociation in the pre-equilibrium Glasma, and machine-learning tools for flavor and top tagging. The value of the snapshot, if it is accurate, is that it defines the common benchmark against which the next generation of precision measurements will be compared.

What carries the argument

The organizing object is the hard probe: a high-transverse-momentum parton or heavy-flavor particle whose passage through the quark-gluon plasma modifies its energy, direction, or bound-state structure, encoding medium properties. Carrying the new results are a memory-dependent master equation for quarkonium, in which the medium response function $\Gamma(t)$ with finite correlation time $\tau_E$ replaces the zero-frequency Lindblad limit; classical Yang-Mills plus Wong-equation dynamics for heavy quarks in the Glasma; a fractional Langevin equation with Caputo derivatives for anomalous diffusion; and modular multistage jet energy-loss frameworks that combine high- and low-virtuality parton shower modules.

What would settle it

A single high-precision measurement that contradicts a headline model prediction would test the snapshot's value. For example, if precise $\Upsilon(1S)$ suppression data fall below the memory-corrected open-quantum-system evolution with $\tau_E \sim 1/T$, the paper's claim that memory reduces suppression relative to the Markovian Lindblad equation would be falsified.

Watch

Extended reading notes

Core claim

On the authors' terms, the central claim is that hard probes—jets, heavy quarks, and quarkonia produced in the initial hard scattering—are the most direct messengers of quark-gluon plasma properties, and that the field has reached a stage where models can be fine-tuned against data. The report documents four experimental manifestations of jet quenching (yield suppression, intra-jet broadening, substructure modification, and acoplanarity), nonperturbative lattice inputs for quarkonium evolution, and a set of new calculational results: memory-corrected quarkonium suppression that is weaker than the Markovian Lindblad prediction, anisotropic heavy-quark diffusion in magnetic fields, non-linear Glasma-stage momentum broadening and $c\bar{c}$ dissociation, superdiffusive fractional Langevin dynamics that increases high-$p_T$ suppression, and machine-learning separation of prompt and nonprompt charm and top jets. Together these constitute the 2024 state of the art of hard-probe physics.

Load-bearing premise

The report's value as a status snapshot rests on the assumption that the brief model presentations contain enough detail and that hand-chosen inputs, such as correlation-time forms, fractional orders, dissociation cutoffs, and transport parameters, do not predetermine the conclusions.

Editorial extensions

If this is right

Memory-corrected evolution predicts less quarkonium suppression than the memoryless Lindblad equation with identical zero-frequency transport coefficients, which would soften the medium constraints extracted from $\Upsilon(1S)$ data.
Radius-dependent jet suppression, from $R=0.2$ to $R=1.0$, traces how lost energy is redistributed into the medium, with larger cones recovering a larger fraction of the initial parton momentum.
In a magnetized quark-gluon plasma, heavy-quark momentum diffusion splits into longitudinal and transverse coefficients, with momentum transfer preferentially along the heavy-quark velocity; this should leave anisotropic imprints on open heavy-flavor flow.
During the pre-equilibrium Glasma stage, charm pairs experience non-linear momentum broadening and can dissociate at rates up to roughly 80 percent depending on the dissociation cutoff, setting modified initial conditions for charmonium.
Fractional superdiffusive Langevin dynamics increases the suppression of $R_{AA}$ at high $p_T$, especially at high temperature, compared to ordinary Brownian motion.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the memory effect survives confrontation with data, Markovian Lindblad fits to bottomonium suppression will have overestimated the zero-frequency transport coefficients, and finite-frequency response functions will need to be extracted from lattice QCD.
Glasma-stage dissociation followed by later recombination implies a two-stage charmonium suppression history that could be tested by comparing $J/\psi$ and $\Upsilon$ suppression at early and late times.
The machine-learning separations are trained on event-generator samples only, so their transfer to real detector data with efficiencies and backgrounds is an open testable extension.
The systematic gap between the full magnetized-medium calculation and the Debye-mass approximation suggests that simplified magnetic-field treatments in heavy-flavor phenomenology should be revisited at strong fields.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my take. This is a conference proceedings volume, not a research paper, and it's best read as a community snapshot as of Hot QCD Matter 2024. The experimental sections (jet quenching from STAR/ALICE/ATLAS, multiplicity-dependent J/psi from ALICE) are anchored in published measurements and are credible. The new calculations--non-Markovian quarkonium evolution, AMPT with radiative loss, Glasma heavy-quark diffusion, fractional Langevin R_AA, ML-based tagging--are preliminary but representative of where the field is heading. The authors are mostly honest about that: Sec. 1 says 'for illustration,' Sec. 8 treats the fractional orders as free parameters, Sec. 12 uses a cutoff rc and reports the sensitivity.

The soft spot is Section 10, and the stress-test note is right to single it out. It's off-topic for a hard-probes volume, and the analysis is not sound: the 'data' are PYTHIA8 events, the background fit to the m_ll-gamma invariant mass has chi^2/ndf ~ 169, and the claim of 'several orders of magnitude' S/B enhancement is contradicted by the plotted ratios, which change by a factor of about five. That is a load-bearing flaw for the volume's self-description as an accurate snapshot. The reader's weaker concern about parameter sweeps without error bars (Secs. 1, 7, 8, 12) is legitimate but secondary--proceedings often contain work in progress, and the authors flag the preliminary nature.

The citation pattern is unremarkable: some sections lean on the authors' own prior formalisms, but the benchmarks are against external data and earlier literature.

Who this is for: newcomers wanting a map of the field and experts wanting a compact record of the conference. It is not a source of quantitative results. I wouldn't cite it as a result and wouldn't bring it to reading group.

Recommendation: send it to peer review, but the referee should require either removing Sec. 10 or re-analyzing it properly, and should ask the authors to add explicit caveats about the lack of uncertainties in the new calculations. With that, the volume would be a credible snapshot; without it, it isn't.

Referee Report

3 major / 7 minor

Summary. This proceedings-style article compiles 15 contributions from the Hot QCD Matter 2024 conference, covering quarkonium evolution in an open quantum system, jet quenching measurements at RHIC and the LHC, lattice inputs for quarkonia, heavy-quark diffusion in magnetic fields and in the Glasma, fractional Langevin dynamics, AMPT and JETSCAPE jet-energy-loss studies, a rare Higgs decay analysis, quarkonium dissociation in pre-equilibrium fields, and machine-learning taggers for heavy flavor and boosted tops. The experimental review sections provide a credible snapshot of published hard-probe measurements, and several sections present new preliminary calculations whose robustness is not yet demonstrated.

Significance. If the new results were fully supported, the volume would be a useful status report of hard-probe physics as of 2024, with particular value in the experimental summaries (Secs. 2 and 15) and in the nonperturbative lattice inputs (Sec. 3). The paper is not a single derivation; its contribution is as a compilation. Its quantitative claims are mostly exploratory and, as presented, lack the uncertainty quantification needed to turn them into archival predictions. The experimental review sections are anchored in published measurements, and Sec. 15 usefully identifies that none of the available theoretical models quantitatively reproduces the multiplicity-dependent J/ψ yields.

major comments (3)

[Sec. 10, Fig. 28 and Sec. 10.3] The background-only polynomial fit in Phase 1 has χ²/ndf = 3716.36/22 = 168.93, so the fit is statistically rejected, and the reported Data/Bkg = 1.1841 is a residual of that failed fit rather than evidence of a signal. The subsequent Data/Bkg values 3.70, 4.62, and 5.56 inherit the same flawed background, and the claim in Sec. 10.3 that the signal-to-background ratio was enhanced 'up to several orders of magnitude' is not supported by these numbers, which vary by only about a factor of five. Since the volume is presented as a vetted snapshot, this section needs either removal, a corrected background procedure with goodness-of-fit and uncertainties, or an explicit downgrade to an illustrative generator-level study.
[Secs. 1.3, 7.3, 8.3, 12.3] Several new quantitative results are parameter sweeps with hand-chosen inputs and no error bars: κ=4T^3, γ=0, and τ_E=1/(1.5T), 1/T, 1.5/T in Sec. 1.3; α, β = 1.001, 1.2, 1.4, 1.6 and D=0.1 GeV²/fm in Sec. 8.3; Qs=1–3 GeV in Sec. 7.3; and rc=0.6, 0.8, 1.0 fm in Sec. 12.3. The qualitative conclusions may be robust, but the manuscript does not provide sensitivity estimates or comparisons with constrained transport coefficients, so the reader cannot judge whether the effects are significant. Please add uncertainty bands, parameter scans, or at least a statement of the sensitivity of each conclusion to the chosen inputs.
[Sec. 8, Eqs. (40)–(45)] The Caputo fractional Langevin equation is coupled to a white-noise force with δ-function correlation and to the standard Einstein relation γ = D/(MT). For a fractional derivative order α > 1, a δ-correlated noise is not generally consistent with the fluctuation-dissipation theorem or with an equilibrium stationary state; the claim in Sec. 8.3.1 that ⟨p²(t)⟩ approaches 3MT regardless of α therefore needs a derivation or a citation. Please clarify the noise statistics appropriate for the fractional dynamics and justify the fluctuation-dissipation relation used in Eq. (45).

minor comments (7)

[Sec. 1, first paragraph of Sec. 1.1] The forward references to 'Sec. 12.2' and 'Sec. 12.3' should read 'Sec. 1.2' and 'Sec. 1.3'.
[Eq. (2)] The master equation is stated to be accurate up to O(H_Int^3), but the expression is second order in the interaction and the subsequent derivation uses a second-order Born-type expansion; please correct the order statement.
[Sec. 3, paragraph after Eq. (13)] The sentence 'In my opinion the assumptions put in there are not physically justified' expresses a personal assessment of Ref. [75] without supporting argument; it should be either removed or substantiated with a technical discussion.
[Sec. 10.2] The text repeatedly calls PYTHIA8-generated events 'Data'; please replace this with 'generator-level events' and state clearly that no detector simulation or reconstruction is performed, since the acceptance and efficiency factors in Fig. 29 cannot be interpreted as detector-level corrections without such a simulation.
[Sec. 9, Fig. 23 caption] The caption 'p-p (0-10%)' is inconsistent with the panel content and with the Pb-Pb comparison; please correct the label. The concluding sentence 'as a result the energy lost by the jets is partially gained as the area of the jet cone area increases' is also grammatically unclear and should be rewritten.
[Sec. 12.2, Eq. (62)] The FONLL spectrum parametrization is introduced but the values of x0, x1, x2, and x3 are not given; please either list them or cite the calibration table.
[Secs. 2 and 3] The PACS number fields for these sections are blank; please complete them for consistency with the rest of the volume.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: most sections are benchmarked against external data; minor self-citations do not carry the load.

full rationale

This proceedings volume is a collection of mostly benchmarked contributions. The experimental reviews (Secs. 2 and 15) use RHIC/LHC data; the model sections (Secs. 6, 9, 13) compare AMPT/JETSCAPE calculations to ATLAS, ALICE, and CMS measurements; the lattice inputs in Sec. 3 are external numerical computations. Several sections reproduce or cite the authors' own prior calculations (e.g., Sec. 4 cites Ref. [93], Sec. 8 cites Ref. [148], Sec. 15 cites Refs. [227,228]), but these are summaries of published work and are not used to define the target quantities; the comparisons are external. Sec. 1 and Sec. 12 contain hand-chosen inputs (kappa = 4T^3, gamma = 0; rc cutoffs), but these are stated modeling assumptions with parameter dependence shown, not predictions forced by construction. Sec. 8 sets fractional orders alpha and beta by hand and demonstrates superdiffusion; that is a model demonstration, not a fitted parameter renamed as a prediction. The H->Zgamma contribution in Sec. 10 contains a poor background fit (chi^2/ndf = 168.93) and an overstated enhancement claim, but this is a statistical validity issue rather than a circular derivation; no equation reduces to its input by construction. Overall, no load-bearing circular step was found; the small self-citation burden yields a score of 2 rather than 0.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The central new calculations rest on a large set of standard but not universally valid modeling assumptions: pNRQCD/OQS for quarkonia, MV/CGC Glasma with classical Wong dynamics, HTL magnetized propagators, Langevin/fractional Langevin transport, and multi-stage jet energy loss models. The free parameters listed above are inputs chosen by hand or borrowed from earlier fits; they are not derived in this paper. No new particles, forces, or conserved quantities are introduced.

free parameters (8)

tau_E (memory time) = 1/(1.5 T), 1/T, 1.5/T
In Sec. 1.3, Eq. (11) defines Gamma(t)=kappa/(2 tau_E) exp(-|t|/tau_E); the quarkonium survival probability is computed for three hand-picked values, so the main qualitative result depends on this choice.
kappa (transport coefficient) = 4 T^3
Sec. 1.3 adopts kappa=4T^3 from Ref. [34] rather than from a direct measurement; the suppression magnitude depends on this input.
alpha, beta (fractional orders) = 1.001, 1.2, 1.4, 1.6
Sec. 8.2 introduces Caputo fractional derivatives with orders alpha and beta; the superdiffusion and R_AA results are generated by sweeping these values, and no independent determination is given.
D (momentum diffusion coefficient) = 0.1 GeV^2/fm
Sec. 8.3 sets D=0.1 GeV^2/fm for charm quarks; the R_AA curves and the fluctuation-dissipation relation in Eq. (45) depend on this input.
Qs (saturation scale) = 1-3 GeV
Secs. 7.3 and 12.3 define the Glasma by fixing Qs within 1-3 GeV; the resulting momentum broadening and dissociation probabilities scale with it.
rc (dissociation cutoff) = 0.6, 0.8, 1.0 fm
Sec. 12.3 classifies a c-cbar pair as dissociated if its separation exceeds rc; reported dissociation percentages vary from 0% to about 80% depending on rc and evolution time.
alpha_s and screening mass mu (AMPT elastic cross section) = alpha_s=0.33, mu=3.226 fm^-1
Sec. 6.2 uses these fixed values in the AMPT elastic cross section of Eq. (29); the relative elastic and radiative energy loss contributions depend on them.
Qsw (JETSCAPE switching scale) = 2 GeV
Secs. 9.2 and 13.2 switch between MATTER and LBT at Qsw=2 GeV; the jet R_AA predictions depend on this scale.

assumptions (6)

domain assumption pNRQCD hierarchy and open quantum system master equation for quarkonium in medium
Sec. 1.2 builds the memory-dependent master equation on pNRQCD multipole expansion and the assumption Tr[rho_E H_Int]=0; the validity for realistic temperatures is the very thing under study.
domain assumption MV model / CGC effective theory for Glasma initial conditions
Secs. 7.2 and 12.2 model the pre-equilibrium stage as classical Yang-Mills fields from McLerran-Venugopalan color sources; this is a standard but approximate description.
domain assumption Wong equations treat heavy quarks as classical point color charges
Secs. 7.2 and 12.2 propagate c and b quarks via Wong equations, ignoring quantum fluctuations and treating spin only peripherally.
domain assumption Langevin description with white noise and fluctuation-dissipation relation
Secs. 5.1 and 8.2 assume heavy quark momentum evolves by Langevin dynamics with delta-correlated noise; the fractional generalization in Sec. 8 is an additional ad hoc assumption.
domain assumption HTL-resummed propagators for magnetized QGP
Secs. 4.2 and 5.1 compute diffusion coefficients using hard thermal loop effective propagators valid at weak coupling and high T; the results may not hold at realistic T and eB values.
domain assumption JETSCAPE and AMPT multi-stage models faithfully represent jet-medium interactions
Secs. 6, 9 and 13 use these event generators to compare with data; the model chain of initial state, hydro background, parton transport, and hadronization carries many untested approximations.

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Cite this review

Pith. "Pith review of Dynamics of Hot QCD Matter 2024 -- Hard Probes." pith.science (2026). https://pith.science/paper/LJUPGIQE

@misc{pith2026241214026,
  author       = {Pith},
  title        = {Pith review of: Dynamics of Hot QCD Matter 2024 -- Hard Probes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LJUPGIQE}},
  note         = {Machine review of arXiv:2412.14026}
}

read the original abstract

The hot and dense QCD matter, known as the Quark-Gluon Plasma (QGP), is explored through heavy-ion collision experiments at the LHC and RHIC. Jets and heavy flavors, produced from the initial hard scattering, are used as hard probes to study the properties of the QGP. Recent experimental observations on jet quenching and heavy-flavor suppression have strengthened our understanding, allowing for fine-tuning of theoretical models in hard probes. The second conference, HOT QCD Matter 2024, was organized to bring the community together for discussions on key topics in the field. This article comprises 15 sections, each addressing various aspects of hard probes in relativistic heavy-ion collisions, offering a snapshot of current experimental observations and theoretical advancements. The article begins with a discussion on memory effects in the quantum evolution of quarkonia in the quark-gluon plasma, followed by an experimental review, new insights on jet quenching at RHIC and LHC, and concludes with a machine learning approach to heavy flavor production at the Large Hadron Collider.

Figures

Figures reproduced from arXiv: 2412.14026 by the authors.

**Figure 1.** Survival probability for Υ(1s) (left) and Υ(2s) as a function of time. We stop the plot at 6 fm for clearer presentation. 2. Jet quenching: new results at RHIC and LHC Nihar Ranjan Sahoo We discuss recent results on jet quenching in heavy-ion collisions from experiments at the LHC and RHIC. These results include various manifestations of jet quenching, such as modifications in jet yield and jet substructure, intra-j… view at source ↗

**Figure 2.** (color online) Left: Semi-inclusive γdir+jet and π 0+jet IAA results from the STAR experiment.50, 51 Right: γdir+jet and inclusive jet measurements from the ATLAS experiment.52 2.2.2. Intra-jet broadening Jet quenching in heavy-ion collisions arises from both vacuum radiation and inmedium gluon radiation. To investigate the medium-induced radiation in heavy-ion collisions relative to vacuum (p+p collisions), the S… view at source ↗

**Figure 3.** (color online) Yield ratio between recoil jet yield of radius R=0.2/R=0.5 for [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (39 more)

**Figure 4.** Figure 4: (color online) Unfolded θg distributions for charged-particle jets measured in the ALICE experiment.53 2.2.4. Jet acoplanarity The azimuthal angle correlation between the recoil jet axis and the trigger particle (here γdir, π 0 , or h ±) reveals another manifestation …

**Figure 5.** Figure 5: (color online) Right: The STAR experiment’s [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: (Left) The low ω peak of ρ, as obtained from thermal Wilson loop at 1.5 Tc, in the quenched theory. (Middle) V re T (⃗r) and (right) V im T (⃗r) at various temperatures, for quenched QCD. From Ref.73 [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

**Figure 7.** Figure 7: The spectral function for the vector current calculated from the potentials shown in Figure [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: (Left) The potential obtained from the hybrid Wilson loop at 0.63 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

**Figure 9.** Figure 9: Comparison of C adj EE(τ) and Cfund EE (τ) at 1.5 Tc in quenched QCD [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]

**Figure 10.** Figure 10: The variation of scaled momentum diffusion coefficients with [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]

**Figure 11.** Figure 11: The variation of the ratio between the Debye mass approximated results ( [PITH_FULL_IMAGE:figures/full_fig_p019_11.png]

**Figure 12.** Figure 12: ⃗v q B⃗ case : scaled (w.r.t eB=0 values) momentum diffusion coefficients as functions of eB. κ1 κ2 κ3 2 4 6 8 10 12 0.000 0.002 0.004 0.006 0.008 0.010 eB (mπ 2 ) κj/T 3 (charm) T=0.4 GeV κ1 κ2 κ3 2 4 6 8 10 12 0.0000 0.0002 0.0004 0.0006 0.0008 eB (mπ 2 ) κj/T 3 (bo…

**Figure 13.** Figure 13: ⃗v ⊥ B⃗ case : scaled (w.r.t T 3 ) momentum diffusion coefficients as functions of eB. bottom quarks require a stronger magnetic field to display similar κL/T behavior as charm quarks. This trend is clearer in the right panel, where no immediate crossover indicates th…

**Figure 14.** Figure 14: Variation of normalised momentum diffusion coefficients for charm and bottom quarks [PITH_FULL_IMAGE:figures/full_fig_p023_14.png]

**Figure 15.** Figure 15: Left: Energy loss experienced by a gluon jet with initial energy E = 100 and 200 GeV in AMPT model in elastic scattering (dashed red), medium-induced radiation (dash-dotted blue) and total (solid green). Right: pT loss of jets versus initial jet p jet T ,ini for cone …

**Figure 16.** Figure 16: Nuclear modification factor R jet AA for inclusive jets at midrapidity for cone radii R = 0.2, 0.4 in AMPT simulations as compared to data from ATLAS102 and ALICE48 Collaborations. the fully formed opaque QGP medium. For energetic jets the radiation loss is even large…

**Figure 17.** Figure 17: Left: Jet shape ρ(∆r) for inclusive jets with p jet T > 120 GeV at |η jet| < 1.6 from AMPT compared to CMS data101 in (0-10)% central Pb-Pb collisions. The contributions are from leading plus initial parton showers (dashed black line), semi-hard radiated gluons (dotte…

**Figure 18.** Figure 18: Evolution of the transverse momentum broadening, [PITH_FULL_IMAGE:figures/full_fig_p030_18.png]

**Figure 19.** Figure 19: Evolution of transverse momentum broadening, [PITH_FULL_IMAGE:figures/full_fig_p031_19.png]

**Figure 20.** Figure 20: Evolution of average of the angular momentum components squared with proper time in [PITH_FULL_IMAGE:figures/full_fig_p031_20.png]

**Figure 21.** Figure 21: ⟨p 2 (t)⟩ (left panel) and ⟨x 2 (t)⟩ (right panel) versus time, for the various values of the α and D = 0.1 GeV2/fm at T = 250 MeV. 8.3.2. Nuclear modification factor The definition of the RAA(pT ) of the HQs we used as fellow,86 RAA(pT ) = fτf (pT ) fτ0 (pT ) . (48) …

**Figure 22.** Figure 22: RAA is shown as a function of pT at τf = 6 fm/c for two different temperatures: T = 250 MeV (left panel) and T = 350 MeV (right panel), with four different values of α. 8.4. Summary and outlook We discussed anomalous diffusion using the FLE with Caputo fractional deri…

**Figure 23.** Figure 23: Differential cross-section of inclusive jets for p+p and Pb+Pb collisions with cone size [PITH_FULL_IMAGE:figures/full_fig_p038_23.png]

**Figure 24.** Figure 24: Jet-RAA as a function of jet-pT for inclusive jets in the most central (0-10%) Pb+Pb collisions at √sNN = 5.02 TeV for the jet cone radius R = 0.4, are compared with the ATLAS and CMS data. 9.2.1. Jet radius (R) dependence of the RAA We calculate the jet-RAA double ra…

**Figure 25.** Figure 25: The double ratio (RR AA/RR=0.2 AA ) as a function of jet-R for inclusive jets in the most central(0-10%) Pb+Pb collisions at √sNN = 5.02 TeV for different jet radii with a minimum track requirement of p track T > 0.5 GeV. with a larger jet radius, the jet retains a si…

**Figure 26.** Figure 26: Different potential Feynman diagrams for the decay process [PITH_FULL_IMAGE:figures/full_fig_p040_26.png]

**Figure 27.** Figure 27: Upper left Plot for the angle θee as a function of Pee, Upper right Plot for the angle θµµ as a function of Pµµ, lower left Plot for the angle θZγ as a function of Peeγ, lower right Plot for the angle θZγ as a function of Pµµγ. (degree) and standard deviation (degree)…

**Figure 28.** Figure 28: Results are presented in four panels show [PITH_FULL_IMAGE:figures/full_fig_p042_28.png]

**Figure 29.** Figure 29: Left plot: Acceptance × Efficiency as a function of P H t ; Right plot: Acceptance × Efficiency as a function of ηH 10.3. Summary and conclusion In conclusion, pp collision data at an energy of √ s = 13TeV generated using PYTHIA8, have been used for H → Zγ analysis. T…

**Figure 30.** Figure 30: Variation of binding energy (B.E.) of J/ψ and Υ in the (a) and (b), and mass spectra (M.S.) for J/ψ and Υ in (c) and (d), respectively, with T /TC at different values of magnetic fields at Nf = 4. 11.3. Results and Conclusion The present study focuses on investigating…

**Figure 31.** Figure 31: (Left Panel) Average distance between the [PITH_FULL_IMAGE:figures/full_fig_p048_31.png]

**Figure 32.** Figure 32: Analysis of zg in the 60–80 GeV range, comparing the energy loss models MATTER+LBT and MATTER+MARTINI with ALICE experimental data.212 The left panel shows the zg distribution for Pb-Pb collisions, while the right panel presents the ratio of zg distributions between …

**Figure 33.** Figure 33: Results for θg using MATTER+LBT in the 160–180 GeV range, with and without coherence effects, as simulated by JS. Displayed on the left is the θg distribution for Pb-Pb collisions; on the right, the ratio of the θg distribution for Pb-Pb to p-p collisions [PITH_FULL…

**Figure 34.** Figure 34: Depiction of µg distributions in the 60–80 GeV range, generated from JS simulations using MATTER+MARTINI (with coherence effects) and MATTER+LBT (both with and without coherence effects). The left panel illustrates the µg distribution for Pb-Pb collisions, while the r…

**Figure 35.** Figure 35: Results for ρ from JS in the 160–180 GeV range, compared to CMS data.213 The left panel shows the ρ distribution for Pb-Pb collisions, and the right panel displays the ratio of ρ distributions between Pb-Pb and p-p collisions [PITH_FULL_IMAGE:figures/full_fig_p052_35.png]

**Figure 36.** Figure 36: Example jet images before(left) and after(right) preprocessing [PITH_FULL_IMAGE:figures/full_fig_p054_36.png]

**Figure 37.** Figure 37: ROC curves comparing the performance of ResNet using processed versus unprocessed jet [PITH_FULL_IMAGE:figures/full_fig_p055_37.png]

**Figure 38.** Figure 38: (Colour Online) Forward rapidity relative J/ [PITH_FULL_IMAGE:figures/full_fig_p057_38.png]

**Figure 39.** Figure 39: (Colour Online) Forward rapidity relative J/ [PITH_FULL_IMAGE:figures/full_fig_p057_39.png]

**Figure 40.** Figure 40: (Colour Online) (Left) Decay topology of prompt and nonprompt J/ [PITH_FULL_IMAGE:figures/full_fig_p059_40.png]

**Figure 41.** Figure 41: (Colour Online) (Left) Comparison of importance scores (%) for the input variables used [PITH_FULL_IMAGE:figures/full_fig_p059_41.png]

**Figure 42.** Figure 42: (Colour Online) (Left) J/ψ fraction from b-hadron decay (fB) as a function of pT at midrapidity for minimum-bias pp collisions at √ s = 13 TeV using PYTHIA8, predictions from XGB and LGBM and a comparison with ALICE data is shown.227 (Right) Nonprompt to prompt D0 rat…

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