Energy loss and theoretical uncertainties in small quark-gluon plasmas

Coleridge Faraday

REVIEW 4 major objections 4 minor 300 references

Energy loss and theoretical uncertainties in small quark-gluon plasmas

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The DGLV energy-loss model for small quark-gluon plasmas violates its own large-formation-time assumption at high parton energy.

desk verdict Solid uncertainty analysis with a robust central finding on LFT violation, but the quantitative small-system thresholds need a signed weighting and a non-circular SPL derivation. read the letter →

arxiv 2506.02056 v1 pith:IKLAPWWG submitted 2025-06-01 hep-ph

Coleridge Faraday This is my paper

classification hep-ph

keywords quark-gluonplasmajetquenchingradiativeenergylossDGLVopacityexpansionshortpathlengthcorrectionlargeformationtimeapproximationnuclearmodificationfactortheoreticaluncertainties

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

The thesis argues that the standard radiative energy loss picture used for jet quenching is internally inconsistent at high momentum once small-system corrections are added. Adding the short pathlength correction to the DGLV model makes the predicted energy loss for gluons large, growing, and sometimes negative, which pushes predicted pion suppression above one at LHC momenta. The paper isolates the culprit with an energy-weighted ratio, $\langle \omega_1/\mu_1\rangle$, which the derivations assume to be much smaller than one; the model's own emission distribution makes it exceed one above about 100 GeV without the correction and above about 30–50 GeV with the correction, depending on parton type and system size. This matters because it means the model is being used in kinematic regions where its derivation is not controlled, and it motivates a rederivation or a kinematic cutoff rather than a simple parameter adjustment. Alongside this, the thesis quantifies other theoretical uncertainties, finding that the Gaussian approximation for elastic energy loss is harmless and that a fitted strong coupling $\alpha_s$ absorbs most—but not all—uncertainty, leaving residual differences in elastic energy loss that affect the $p_T$ and system-size dependence.

What carries the argument

The central diagnostic is the weighted ratio $\langle \omega_1/\mu_1\rangle$, averaged over the radiative energy loss phase space with weight given by the absolute value of the energy loss distribution; it is the direct measure of whether the large formation time assumption is satisfied. The second piece is the short pathlength correction to DGLV (Eq. 3.4), which adds back terms suppressed by $e^{-\mu_1\,\Delta z}$ and breaks color triviality, making the correction much larger for gluons than for quarks and therefore especially important for pion observables. Together these objects convert the question “is the model valid here?” into a concrete numerical condition that the thesis evaluates.

What would settle it

A rederivation of the short pathlength corrected emission kernel that retains finite $\omega_0$ and $\omega_1$ phases instead of expanding them via the large formation time assumption, with the weighted ratio $\langle \omega_1/\mu_1\rangle$ recomputed at $E=100$ GeV and $L=5$ fm, would settle the central claim; if the weighted ratio stays below one once the approximation is relaxed, the reported inconsistency is an artifact of extrapolating the formula.

Watch

Extended reading notes

Core claim

Within the DGLV opacity expansion, the thesis defines the expectation value $\langle R\rangle = \langle \omega_1/\mu_1\rangle$ weighted by the absolute value of the radiative energy loss distribution, where $\omega_1 = (k-q_1)^2/(2xE)$ and $\mu_1 = \sqrt{\mu^2+q_1^2}$; the large formation time approximation requires $\langle R\rangle \ll 1$. For charm quarks and gluons with an exponential scattering-center distribution at $L=5$ fm, $\lambda_g=1$ fm, and $\mu=0.5$ GeV, the uncorrected DGLV result violates this for $E\gtrsim 100$ GeV, and the short pathlength corrected result violates it for $E\gtrsim 35$ GeV (gluons) and $E\gtrsim 50$ GeV (charm), with the breakdown occurring roughly five times earlier in energy for $L=1$ fm systems. The correction itself grows linearly in energy, which is why it dominates at high momentum and produces $R_{AA}(p_T)>1$ for pions. The thesis shows that a kinematic cutoff on the transverse radiated gluon momentum, $|k|_{\rm max} = \min(\sqrt{2xE}\,\mu_1, 2x(1-x)E)$, restores the self-consistency of the large formation time approximation but makes the result sensitive to the exact cutoff value, with factor-of-two variations in the cutoff producing visible bands.

Load-bearing premise

The central diagnostic treats the short pathlength corrected formula as a trustworthy probe of the large formation time approximation even though that correction was derived using the same approximation.

Editorial extensions

If this is right

Standard DGLV predictions for pion and charged-hadron suppression at $p_T \gtrsim 100$ GeV are formally uncontrolled, and with the short pathlength correction the uncontrolled region starts around 30–50 GeV for gluons.
Enforcing the large formation time approximation through a kinematic cutoff on radiated gluon transverse momentum restores self-consistency but adds a new theoretical uncertainty: the result depends on the cutoff multiplier $\kappa$ over a factor-of-two range.
The choice between Gaussian and Poisson distributions for elastic energy loss has almost no effect on $R_{AB}$; what matters is the low-order moments of the loss distribution, so the central limit theorem is not the reason for the insensitivity.
A one-parameter fit of the strong coupling $\alpha_s$ to RHIC and LHC large-system data absorbs most of the radiative and elastic model uncertainties into a shift of the coupling, but residual bands remain and the choice of elastic energy loss kernel changes the $p_T$ and system-size dependence after the fit.
Large-system-constrained model predictions agree with RHIC small-system $p/d/{}^3\mathrm{He}+A$ data but disagree with LHC $p+\mathrm{Pb}$ small-system data.

Reading between the lines

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

Editorial inference: because the short pathlength correction was derived using the same large formation time approximation it is meant to test, the corrected model's violation of that approximation is partially circular; a rederivation without the approximation is needed to know whether the violation is physical or an artifact of extrapolation.
Editorial inference: the same $\langle \omega/\mu\rangle$ diagnostic could be applied to other opacity-expansion based energy loss models to map where their assumptions break at LHC kinematics, not just to DGLV.
Editorial inference: the moment expansion that explains the Gaussian insensitivity suggests a practical uncertainty quantification strategy, namely comparing energy loss models by their first few moments of the loss distribution rather than by their full functional form.
Editorial inference: if the short pathlength correction is as large as reported, LHC small-system data at high $p_T$ (e.g., $p+\mathrm{Pb}$) provide a sharp test, since the corrected model predicts enhancement above unity while the uncorrected model does not.

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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

The thesis does two things worth knowing about. First, it implements a DGLV-based energy loss model with the Kolbe-Horowitz short-pathlength correction and maps how theoretical uncertainties—elastic vs radiative, Gaussian vs Poisson, HTL vs BT, scattering-center distribution, alpha_s—flow through to R_AA. Second, it introduces a self-consistency diagnostic for the large formation time approximation: an energy-weighted average of omega_1/mu_1 over the radiative energy loss kernel. The finding that this ratio exceeds one for E > ~100 GeV in the uncorrected DGLV result is a genuine result, and it is not affected by the circularity worry that applies to the SPL-corrected threshold.

The moment-expansion explanation for the insensitivity to Gaussian vs Poisson elastic energy loss is the cleanest piece of the thesis. The one-parameter alpha_s fit is transparent, and the observation that most uncertainties can be absorbed into a shift of alpha_s while residual bands remain is useful and honestly stated.

The soft spots are real but manageable. The absolute-value weighting in Eq. 4.1 counts phase space where the energy-loss integrand changes sign. The thesis notes this caveat but never quantifies how much of the >1 region contributes to the net Delta E/E or to R_AA. If cancellations make that region unimportant, the claim that the model is being used outside its derivation regime is weaker than it looks. That needs a signed/weighted analysis. Second, the 30-50 GeV thresholds quoted for the SPL-corrected result come from Eq. 3.4, which was derived under the same large-formation-time assumption being tested. Using it to diagnose LFT violation is circular; those specific numbers in the abstract shouldn't be taken at face value. The uncorrected DGLV threshold at ~100 GeV is not circular and stands. The thesis itself flags parts of this in Sec. 4.3, so the issue is incomplete analysis rather than hidden failure.

Also: no code or data released, which makes it hard to check the numerics behind the central diagnostic. The small-system agreement with RHIC data is post-fit, so it's consistency, not a prediction. The exponential scattering-center distribution and the ad hoc magnetic mass are model choices, and the thesis is upfront about them.

Who this is for: jet-quenching phenomenologists who care about uncertainty quantification in energy loss models. It deserves a serious referee. I'd send it out, with the expectation that the author addresses the weighting caveat and the circularity explicitly, and ideally releases the code. The central finding—that the large formation time approximation fails self-consistently in a widely used model—is important enough for the field to engage with.

Referee Report

4 major / 4 minor

Summary. The manuscript presents a pQCD-based energy-loss framework for high-pT hadron suppression in large and small collision systems. It combines the DGLV radiative energy-loss kernel with the Kolbe-Horowitz short-pathlength correction, several elastic energy-loss prescriptions (Gaussian BT, Gaussian HTL, Poisson HTL), realistic IP-Glasma/hydrodynamic geometry, production spectra, and fragmentation. The central claim is a self-consistency check: the energy-weighted emission distribution of the model violates the large formation time approximation, with the ratio <omega_1/mu_1> exceeding unity for E above about 100 GeV in the uncorrected DGLV result and at lower energies when the short-pathlength correction is included. The thesis also argues that a kinematic cutoff on the radiated gluon momentum restores self-consistency at the price of increased cutoff sensitivity, that R_AB is insensitive to Gaussian versus Poisson modeling of elastic energy loss due to a moment expansion, and that a one-parameter fit of alpha_s to large-system data leaves residual model uncertainties and yields small-system predictions that agree with RHIC data but disagree with LHC data.

Significance. If the self-consistency claim survives scrutiny, it is a useful caution for the field: it identifies a kinematic regime in which a widely used opacity-expansion energy-loss model is applied outside the control of its derivation. The systematic treatment of theoretical uncertainties, the explicit comparison of radiative and elastic kernels, and the attempt to separate distributional from mean-energy-loss effects are valuable. The paper is also transparent about many of its own caveats, which is a genuine strength. However, the quantitative thresholds at the center of the claim rest on diagnostics that are not yet fully controlled, and one internal inconsistency about the role of the Gaussian elastic distribution needs reconciliation. The central qualitative finding appears robust, but the small-system-specific numbers in the abstract and in Section 4.1 are not yet reliable as stated.

major comments (4)

[Sec. 4.3 / Eq. (4.1)] The central self-consistency diagnostic is defined with an absolute-value weight, |dE/d{X_i}|. The paper explicitly notes that this is not a standard expectation value and that a violation does not by itself imply a large correction. However, the manuscript never quantifies the net signed contribution of the region where <omega_1/mu_1> > 1 to the actual fractional energy loss Delta E/E (Eq. 3.30) or to R_AA (Eq. 3.37). Because the energy-loss integrand changes sign, the absolute-value-weighted average can be dominated by phase space that largely cancels in the physical observable. The claim that the model is being used in a region where its derivation is uncontrolled needs a quantitative statement that the violating region contributes non-negligibly to the signed integral.
[Sec. 3.2.2 / Eq. (3.4) and Sec. 4.3] The short-pathlength-corrected kernel in Eq. (3.4) is derived while explicitly retaining the large formation time assumption. Using this same kernel to diagnose violation of the large formation time approximation is therefore circular for the corrected result: in the phase space where the diagnostic finds violations, the corrected formula itself is not under control. Consequently, the thresholds quoted for the corrected result (E ~ 30-50 GeV for gluons and charm; small-system thresholds at even lower E) are not robust. The uncorrected DGLV threshold at E ~ 100 GeV does not suffer from this circularity, so the qualitative finding stands, but the quantitative small-system thresholds should be presented only as indicative unless the SPL derivation is redone without the large formation time assumption.
[Sec. 4.2.1 vs. Sec. 5.3] There is a direct tension between two parts of the thesis. Section 4.2.1 attributes the over-suppression of D mesons in p+Pb collisions to the WHDG treatment of elastic energy loss as a Gaussian distribution, which it calls inappropriate for small systems with few scatterings. Section 5.3, however, concludes that R_AB is remarkably insensitive to whether the elastic energy loss is modeled as Gaussian or Poisson, and explains this insensitivity through a moment expansion of R_AB. These claims need to be reconciled. The moment expansion suggests that the sensitivity seen in Chapter 4 is driven by the magnitude of the average elastic energy loss (e.g., BT versus HTL) rather than by the distributional shape. The earlier attribution should be revised or clarified.
[Sec. 4.3 / Fig. 4.5 and Sec. 3.7] The small-system thresholds are obtained from calculations at constant L = 1 fm with an exponential scattering-center distribution and mu = 0.5 GeV. The actual small-system geometry used elsewhere in the paper has a broad distribution of effective pathlengths (Fig. 3.4a), with mean lengths near 1 fm but a substantial tail, and the effective temperatures vary across events. The self-consistency diagnostic should be evaluated with the same geometry averaging used for R_AB, or at least the sensitivity of the reported thresholds to the width of the pathlength distribution should be quantified. As written, the 'E ~ 10 GeV in small systems' claim rests on a single representative brick length.

minor comments (4)

[Sec. 4.3 / Eq. (4.3)] The displayed asymptotic expression for <x>_{corr.}^{exp.} appears to be missing a fraction structure; as typeset it reads as an inconsistent quotient. Please correct the formula and check the surrounding derivation.
[Sec. 3.3.1] The opening sentence of the elastic energy-loss section repeats the radiative-section sentence about 'the radiated gluon, the final hard parton, and the exchanged Debye medium quasiparticle'; this is clearly a copy-paste artifact and should be replaced with the appropriate elastic-scattering kinematics.
[Sec. 3.4.2] There is a typo: 'disucssion' should be 'discussion'.
[Fig. 4.6 caption] The caption states 'All curves use constant L=5 fm' even though the bottom panels are computed at L=1 fm; the caption is internally inconsistent and should be corrected.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the LFT self-consistency check and alpha_s calibration are not circular; same-group citations are not load-bearing.

full rationale

The paper's derivation chain is self-contained against external benchmarks. The central self-consistency claim in Sec. 4.3 is obtained by evaluating Eq. 4.1, which weights the kinematic ratio omega_1/mu_1 by the absolute value of the model's own radiative energy-loss integrand, and finding that the large-formation-time assumption is violated for E greater than about 100 GeV (uncorrected DGLV) and E greater than about 30-50 GeV (with the short-pathlength correction). This is a diagnostic of the model's internal consistency, not a parameter fitted to produce the conclusion: no parameter is adjusted to force <omega_1/mu_1> > 1, and the uncorrected threshold is independent of the Kolbe-Horowitz correction. The one-parameter alpha_s fit in Sec. 6.3 is a calibration to RHIC/LHC large-system data, and the small-system predictions are extrapolations, not re-predictions of the fitted data. The Kolbe-Horowitz short-pathlength correction (Eq. 3.4) is an external, parameter-free published derivation with explicitly stated assumptions; although it comes from the same research group (the thesis supervisor is a coauthor of the cited works), it is not invoked as an unverified uniqueness theorem and does not carry the load of the main claim by itself. The paper explicitly flags the limitation that the absolute-value-weighted diagnostic does not quantify the signed contribution to Delta E/E or R_AA (Sec. 4.3), and the LFT-derived form of Eq. 3.4 means the corrected-threshold numbers inherit that derivation assumption; this is a robustness caveat, not a circular reduction. No equation in the paper reduces to its inputs by construction, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The model rests on a set of standard pQCD and hydrodynamic inputs plus a few effective parameters. The main free choices are the strong coupling, the radiative gluon momentum cutoff, the magnetic mass, and the scattering-center distribution. No new particles, forces, or dimensions are introduced.

free parameters (5)

strong coupling alpha_s = fitted to RHIC and LHC large-system data; text uses alpha_s in [0.3,0.5] for scans
A one-parameter fit is performed in Sec. 6.3 to experimental R_AA data; the best-fit value depends on the elastic kernel and the cutoff multiplier.
cutoff multiplier kappa = kappa = 1 for central global fit; varied between 0.5 and 2
The upper bound on the transverse radiated gluon momentum is multiplied by kappa to restore the large formation time approximation; results are sensitive to this choice, and kappa = 1 is selected for the final fit.
magnetic mass mu_M = mu_M = mu
The HTL transverse propagator includes an ad hoc magnetic mass that is not present in standard HTL; the thesis sets it equal to the Debye mass, with lattice results cited as motivation.
scattering center distribution = exponential rho_exp(z) = (2/L) exp(-2z/L); alternative truncated step with a = tau_0
The exponential distribution is adopted for analytic simplicity and is acknowledged to overestimate early-time scattering; the correction is highly sensitive to this distribution, making it an effective free choice.
upper bound k_max for radiated gluon momentum = k_max = 2x(1-x)E (collinear bound); alternative Min(sqrt(2xE mu_1), 2x(1-x)E)
The standard collinear upper bound is used for comparability with prior work, while the alternative bound suppresses contributions that violate the large formation time approximation.

assumptions (6)

domain assumption DGLV opacity expansion is valid to first order in opacity with static Gyulassy-Wang scattering centers
Invoked in Sec. 3.2.1 as the starting point for radiative energy loss; the short-pathlength correction is built on the same expansion.
domain assumption Large formation time approximation, omega_1/mu_1 << 1 and omega_0/mu_1 << 1
Used in the DGLV and short-pathlength derivations (Sec. 3.2.1 and 3.2.2) to neglect certain diagrams; the thesis later shows this assumption is violated in the model's own kinematics.
domain assumption Well-separated scattering centers, lambda_g >> mu^{-1}
Listed in Sec. 3.2.1 as a necessary assumption for the opacity expansion; the thesis notes it is not well founded in small systems.
domain assumption Eikonal, soft radiation, and collinear approximations
These approximations are assumed in the DGLV derivation (Sec. 3.2.1); the thesis tests collinearity and softness and finds them self-consistent.
domain assumption Factorization and binary scaling of hard production spectra, with initial-state effects neglected
Sec. 3.6 assumes dN_AB/dp_i = N_coll * dN_pp/dp_i and neglects nuclear parton distribution function modifications, which could affect small-system comparisons.
domain assumption IP-Glasma initial conditions evolved with the Bjorken approximation for temperature time dependence
Sec. 3.7 uses IP-Glasma initial temperature profiles at tau_0 = 0.4 fm and approximates T(tau) by a Bjorken power law, which is a standard but uncontrolled modeling choice.

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Cite this review

Pith. "Pith review of Energy loss and theoretical uncertainties in small quark-gluon plasmas." pith.science (2026). https://pith.science/paper/IKLAPWWG

@misc{pith2026250602056,
  author       = {Pith},
  title        = {Pith review of: Energy loss and theoretical uncertainties in small quark-gluon plasmas},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IKLAPWWG}},
  note         = {Machine review of arXiv:2506.02056}
}

abstract

We present a perturbative-quantum-chromodynamics-based energy loss model with small system size corrections to both radiative and elastic energy loss, incorporating realistic collision geometry, production spectra, and fragmentation. We use the Djordjevic-Gyulassy-Levai-Vitev (DGLV) radiative energy loss model and add back in previously neglected terms suppressed by system size. This small system size correction, derived by Kolbe and Horowitz, is large for high-momentum pions, raising concerns about key approximations in the radiative energy loss. We analyse the self-consistency of these approximations, finding that a particular approximation - the large formation time approximation - is not satisfied self-consistently within the model. We explore a kinematic cutoff on the transverse radiated gluon momentum, which restores the self-consistency of this approximation, but at the cost of an increased sensitivity to the exact cutoff chosen. We investigate the common application of the central limit theorem to approximate the elastic energy loss as a Gaussian distribution. Our results are insensitive to this approximation - understood not by many scatterings, but rather from an expansion of $R_{AA}$ in terms of moments of the energy loss probability distributions. We also explore uncertainty from the crossover between hard thermal loop and vacuum propagators. We perform a one-parameter fit of the strong coupling $\alpha_s$ to RHIC and LHC large-system data, accounting for two important theoretical uncertainties. Most uncertainties can be absorbed into a shift in $\alpha_s$, but residual uncertainty bands remain. Differences in elastic energy loss persist even after the fit, producing distinct $p_T$ and system size dependencies. We show model predictions for $p / d / {}^3 \text{He} + A$ collisions, finding agreement with RHIC small system data but disagreement with LHC results.

Figures

Figures reproduced from arXiv: 2506.02056 by the authors.

**Figure 1.1.** The Eightfold Way: SU(3) octet of the ground state baryons. Figure taken from [26]. the fact that all hadrons must be color-neutral. The community was initially skeptical of the quark model, as quarks had never been directly observed. The definitive evidence for quarks came from deep inelastic scattering experiments at the Stanford Linear Accelerator Center (SLAC) in the 1960s. These experiments showed that protons… view at source ↗

**Figure 1.2.** Plot of the ratio R = σhadron/σmuon as a function of center of mass energy ECM. Data is shown as indicated in the legend. Solid line is the quark model prediction for 3 colors and 5 quark flavors (energies are not large enough to produce tt¯ pairs). Figure taken from III.80 of [30]. “Confinement” is one of the most unique aspects of QCD [2, 31]. Confinement forces quarks to form color-neutral hadrons which explains … view at source ↗

**Figure 1.3.** Summary plot of the experimental determination of the running of the strong [PITH_FULL_IMAGE:figures/full_fig_p022_1_3.png] view at source ↗

Figures from the paper (79 more)

**Figure 2.1.** Figure 2.1: Illustration of the different phases of matter that the universe was in as a function [PITH_FULL_IMAGE:figures/full_fig_p023_2_1.png]

**Figure 2.2.** Figure 2.2: Possible sketch of the phase diagram of QCD. The vertical axis is the temperature [PITH_FULL_IMAGE:figures/full_fig_p024_2_2.png]

**Figure 2.3.** Figure 2.3: Yields per participant, expressed in units of yields observed in [PITH_FULL_IMAGE:figures/full_fig_p026_2_3.png]

**Figure 2.4.** Figure 2.4: (left) Ξ − + Ξ¯+ and Ω − + Ω¯ + pT spectra in the 0 − 5% multiplicity classes compared to predictions from the BG-BW model (upper panels) with the ratios on a linear scale (lower panels). Figure is taken from [PITH_FULL_IMAGE:figures/full_fig_p026_2_4.png]

**Figure 2.5.** Figure 2.5: Plot of a small subset of posterior hydrodynamic model results for a variety of [PITH_FULL_IMAGE:figures/full_fig_p029_2_5.png]

**Figure 2.6.** Figure 2.6: Elliptic flow v2{2} as a function of pseudorapidity for p + Au (left), d + Au (middle) and 3He + Au (right) collisions at RHIC at √ sNN = 200 GeV. Data from PHENIX experiment is also shown. Figure taken from [81]. 2.3 The Glauber Model The Glauber model is one of the…

**Figure 2.** Figure 2: shows a visualization of a Monte-Carlo implementation of the Glauber model [PITH_FULL_IMAGE:figures/full_fig_p031_2.png]

**Figure 2.7.** Figure 2.7: Illustration of the (Monte-Carlo) Glauber model from two different perspectives [PITH_FULL_IMAGE:figures/full_fig_p031_2_7.png]

**Figure 2.8.** Figure 2.8: Results from Fermilab [84] (left) and LHC [86] and RHIC [85] (right) experiments [PITH_FULL_IMAGE:figures/full_fig_p032_2_8.png]

**Figure 2.9.** Figure 2.9: Illustration of how experiments determine centrality, and how theorists use this [PITH_FULL_IMAGE:figures/full_fig_p033_2_9.png]

**Figure 2.10.** Figure 2.10: Nuclear density profiles and collision geometry from the optical Glauber model. [PITH_FULL_IMAGE:figures/full_fig_p034_2_10.png]

**Figure 2.11.** Figure 2.11: Summary plot of RAA as a function of pT for various particle species as measured by experiments at LHC and RHIC. Figure is taken from [90]. approximation [103], the choice of potential to model interactions with the plasma, the use of vacuum vs HTL propagators [104,…

**Figure 3.** Figure 3: a shows the fractional energy loss ∆ [PITH_FULL_IMAGE:figures/full_fig_p056_3.png]

**Figure 3.1.** Figure 3.1: a shows the fractional energy loss ∆E/E of light quarks for the various radiative and elastic energy loss kernels discussed in Sec. 3.2 and 3.3, for both a large pathlength of L = 4 fm (top pane) and a small pathlength of L = 1 fm (bottom pane). The fractional energy…

**Figure 3.** Figure 3: shows the fractional energy loss ∆ [PITH_FULL_IMAGE:figures/full_fig_p057_3.png]

**Figure 3.2.** Figure 3.2: Plot of the fractional energy loss ∆E/E as a function of length L for gluons with various elastic and radiative energy loss kernels at pT = 10 GeV (top pane) and pT = 50 GeV (bottom pane). The temperature is kept constant at T = 0.25 GeV [PITH_FULL_IMAGE:figures/ful…

**Figure 3.3.** Figure 3.3: The ratio of the magnitude of the correction to the DGLV radiative energy [PITH_FULL_IMAGE:figures/full_fig_p058_3_3.png]

**Figure 3.** Figure 3: a shows the probability distribution of effective pathlengths for 0–5% most [PITH_FULL_IMAGE:figures/full_fig_p062_3.png]

**Figure 3.** Figure 3: a according to Eq. 3.44 [PITH_FULL_IMAGE:figures/full_fig_p063_3.png]

**Figure 3.4.** Figure 3.4: Distribution of effective pathlengths (left) and effective temperatures (right) for [PITH_FULL_IMAGE:figures/full_fig_p063_3_4.png]

**Figure 3.** Figure 3: compares the temperature of the plasma as a function of proper time in the [PITH_FULL_IMAGE:figures/full_fig_p064_3.png]

**Figure 3.5.** Figure 3.5: Plot of the temperature T as a function of the proper time τ (in the plasma rest frame). The Bjorken expansion approximation (Bjorken) [149] to the τ dependence of temperature, T(τ ) ≈ Teff(τ0)[τ0/τ ] 1/3 , is plotted along with the effective temperature Teff(τ ) cal…

**Figure 4.1.** Figure 4.1: The nuclear modification factor RAA as a function of final transverse momentum pT is calculated for D0 and B mesons with and without the short pathlength correction to the radiative energy loss. Calculations were done for D0 mesons in 0–10% and 30–50% centrality clas…

**Figure 4.2.** Figure 4.2: The nuclear modification factor RpA for D0 mesons as a function of final transverse momentum pT is calculated with and without the short pathlength correction. The RpA is calculated both with collisional and radiative energy loss (el. + rad.), and with radiative ener…

**Figure 4.** Figure 4: shows predictions for the [PITH_FULL_IMAGE:figures/full_fig_p073_4.png]

**Figure 4.** Figure 4: a shows that the short pathlength correction does, in fact, lead to a stronger [PITH_FULL_IMAGE:figures/full_fig_p074_4.png]

**Figure 4.3.** Figure 4.3: The nuclear modification factor RAA and RpA for π mesons as a function of final transverse momentum pT in Pb + Pb and p + Pb collisions at √ s = 5.02 TeV. Predictions are calculated with and without the short pathlength correction to the radiative energy loss, using …

**Figure 4.** Figure 4: investigates the large formation time assumption. The figure shows the expec [PITH_FULL_IMAGE:figures/full_fig_p076_4.png]

**Figure 4.4.** Figure 4.4: Plot of ⟨R⟩ ≡ ⟨ω1/µ1⟩ as a function of parent parton energy E. ⟨R⟩ ≪ 1 implies consistency with the large formation time assumption. ⟨R⟩ is computed without (dashed) and with (solid) the short pathlength correction for charm quarks (dark red) and gluons (orange). All…

**Figure 4.** Figure 4: a and 4.5b show the expectation values of [PITH_FULL_IMAGE:figures/full_fig_p078_4.png]

**Figure 4.5.** Figure 4.5: Plots of ⟨R⟩ as a function of parent parton energy E, where ⟨R⟩ ≪ 1 implies consistency with the large formation time assumption. ⟨R⟩ is computed without (dashed) and with (solid) the short pathlength correction for charm quarks [gluons] with scattering centers distr…

**Figure 4.** Figure 4: b shows [PITH_FULL_IMAGE:figures/full_fig_p080_4.png]

**Figure 4.6.** Figure 4.6: Plots of ⟨R⟩ as a function of parent parton energy E. ⟨R⟩ ≪ 1 implies consistency with the respective approximations (collinear in a, soft in b). ⟨R⟩ is computed without (dashed) and with (solid) the short pathlength correction for charm quarks [gluons] with scatteri…

**Figure 4.** Figure 4: a tests the consistency of the large pathlength assumption with the DGLV [PITH_FULL_IMAGE:figures/full_fig_p081_4.png]

**Figure 4.7.** Figure 4.7: Plots of ⟨R⟩ as a function of parent parton energy E to test the validity of large pathlength assumptions. ⟨R⟩ is computed with and without (solid and dashed, respectively) the short pathlength correction for charm quarks [gluons] with scattering centers distributed …

**Figure 4.** Figure 4: a shows [PITH_FULL_IMAGE:figures/full_fig_p083_4.png]

**Figure 4.** Figure 4: a shows [PITH_FULL_IMAGE:figures/full_fig_p084_4.png]

**Figure 4.8.** Figure 4.8: Plot of the nuclear modification factor RAA as a function of final transverse momentum pT in √ s = 5.02 TeV Pb + Pb collisions. Predictions with (solid) and without (dashed) the short pathlength correction to the radiative energy loss are shown using the exponential …

**Figure 4.** Figure 4: b shows [PITH_FULL_IMAGE:figures/full_fig_p085_4.png]

**Figure 4.9.** Figure 4.9: The nuclear modification factor RpA for D mesons as a function of final transverse momentum pT in 0–10% central p+Pb collisions at √ s = 5.02 TeV. Only radiative energy loss is included; predictions with (solid) and without (dashed) the short pathlength correction ar…

**Figure 4.10.** Figure 4.10: Plot of the nuclear modification factor RAA and RpA for π mesons as a function of final transverse momentum pT in Pb + Pb and p + Pb collisions at √ s = 5.02 TeV. Predictions with (solid) and without (dashed) the short pathlength correction to the radiative energy l…

**Figure 3.** Figure 3: a and 3.1b in the energy loss model.) Thus, since [PITH_FULL_IMAGE:figures/full_fig_p090_3.png]

**Figure 5.1.** Figure 5.1: Nuclear modification factor RAA as a function of pT for D mesons produced in 0–10% most central Pb + Pb collisions at √ sNN = 5.02 TeV. We produce theoretical results through our convolved radiative and elastic energy loss model by varying the elastic model between G…

**Figure 5.2.** Figure 5.2: Comparison of the nuclear modification factor [PITH_FULL_IMAGE:figures/full_fig_p097_5_2.png]

**Figure 5.3.** Figure 5.3: Nuclear modification factor RAA as a function of pT for B mesons produced in 0–100% most central Pb+Pb collisions at √ sNN = 5.02 TeV. Theoretical results are produced through our convolved radiative and elastic energy loss model, by varying the elastic model between…

**Figure 5.4.** Figure 5.4: Nuclear modification factor RAA for pions in 0–5% central Pb + Pb collisions. Theoretical results include variations in elastic models (Gaussian BT, Gaussian HTL, Poisson HTL) and radiative models (DGLV, DGLV + SPL). 5.2.2 Large system suppression at RHIC Figures 5.6…

**Figure 5.5.** Figure 5.5: Comparison of the nuclear modification factor [PITH_FULL_IMAGE:figures/full_fig_p100_5_5.png]

**Figure 5.6.** Figure 5.6: Nuclear modification factor [PITH_FULL_IMAGE:figures/full_fig_p100_5_6.png]

**Figure 5.7.** Figure 5.7: Nuclear modification factor RAA as a function of transverse momentum pT for pions produced in Au + Au collisions at √ sNN = 200 GeV. Theoretical results are obtained using different combinations of elastic and radiative energy loss models. The impact of the short pat…

**Figure 5.8.** Figure 5.8: Nuclear modification factor RAA as a function of pT for D mesons produced in 0–10% most central Au + Au collisions at √ sNN = 200 GeV. Theoretical results are produced for pions through our convolved radiative and elastic energy loss model, by varying the elastic mod…

**Figure 5.** Figure 5: a shows the nuclear modification factor [PITH_FULL_IMAGE:figures/full_fig_p102_5.png]

**Figure 5.9.** Figure 5.9: Nuclear modification factor RAB as a function of transverse momentum pT for D and B mesons produced in p + Pb collisions at √ sNN = 5.02 TeV. Theoretical results are obtained using different combinations of elastic and radiative energy loss models [PITH_FULL_IMAGE:f…

**Figure 5.10.** Figure 5.10: Nuclear modification factor RAB as a function of pT for pions produced in 0–100% most central Pb + Pb collisions at √ sNN = 5.02 TeV. Theoretical results for pions are produced through our convolved radiative and elastic energy loss model, by varying the elastic mod…

**Figure 5.11.** Figure 5.11: Nuclear modification factor for pions as a function of transverse momentum [PITH_FULL_IMAGE:figures/full_fig_p105_5_11.png]

**Figure 5.12.** Figure 5.12: Nuclear modification factor R3HeA as a function of pT for 0–5% most central 3He + Au collisions at √ sNN = 200 GeV. Theoretical results are produced through our convolved radiative and elastic energy loss model, by varying the elastic model between Gaussian BT [147,…

**Figure 5.13.** Figure 5.13: Comparison of realistic Poisson distribution to Gaussian approximation for [PITH_FULL_IMAGE:figures/full_fig_p106_5_13.png]

**Figure 5.14.** Figure 5.14: Plot of the double ratio RPG ≡ RPois. AB /RGauss. AB , where the RAB is calculated with the DGLV radiative energy loss [106] convolved with the HTL Poisson elastic energy loss for RPois. AB , and HTL Gaussian elastic energy loss for RGauss. AB . The ratio RPG AB is …

**Figure 5.** Figure 5: plots the ratio (∆ [PITH_FULL_IMAGE:figures/full_fig_p109_5.png]

**Figure 5.15.** Figure 5.15: Plot of the ratio ∆E el./∆E rad. eff. ≡ (1 − Rel. AB)/(1 − Rrad. AB ), where Rel. AB is the nuclear modification factor calculated with the radiative energy loss turned off, and similarly Rrad. AB has the elastic energy loss turned off. The ratio (∆E el./∆E rad.)ef…

**Figure 5.** Figure 5: shows the order-by-order contributions to [PITH_FULL_IMAGE:figures/full_fig_p111_5.png]

**Figure 5.16.** Figure 5.16: Figure showing the breakdown of the RAB in terms of the moments ⟨ϵ i ⟩ ≡ R dϵϵiPtot.(ϵ) of the total energy loss probability distribution as a function of pT for a gluon at constant temperature T = 0.25 GeV. The top pane is calculated at constant pathlength L = 4 fm…

**Figure 5.17.** Figure 5.17: Plot of the average important moment ⟨n⟩ as a function of pT for gluons and light quarks produced in 0–5% most central p+ Pb, d+ Au, Au + Au, and Pb + Pb collisions. All curves are computed with Poisson HTL elastic energy loss and DGLV radiative energy loss [PITH_F…

**Figure 5.** Figure 5: shows a strong [PITH_FULL_IMAGE:figures/full_fig_p114_5.png]

**Figure 5.** Figure 5: shows the [PITH_FULL_IMAGE:figures/full_fig_p115_5.png]

**Figure 5.18.** Figure 5.18: Production spectrum power n(pT ) as a function of pT for gluons, light quarks, charm quarks, and bottom quarks produced at RHIC and LHC. agreement at the level of the RAB shown in [PITH_FULL_IMAGE:figures/full_fig_p116_5_18.png]

**Figure 5.19.** Figure 5.19: Plot of the ratio of the full RAB to the slowly-varying power law approximation to the full RAB, R power law AB /Rfull AB as a function of pT . Curves are produced for 0–5% most central p + Pb, d + Au, Au + Au, and Pb + Pb collisions. In order to understand why the …

**Figure 5.20.** Figure 5.20: Comparison of the production spectra dσ/dpT to the slowly-varying power law approximation in Eq. 5.10 as a function of pT for gluons produced at √ sNN = 200 GeV and √ sNN = 5.5 TeV. ϵ. We will perform the expansion presented in Eq. 5.3 explicitly for the full spectr…

**Figure 5.21.** Figure 5.21: Order-by-order ratio of the O(⟨ϵ i ⟩) contribution to the RAB for the full result, to the same order contribution for the power law approximation. The order-by-order ratio is shown for the 0th − −4 th order contributions for light quarks produced at both √ sNN = 200…

**Figure 6.** Figure 6: plots the ∆ [PITH_FULL_IMAGE:figures/full_fig_p127_6.png]

**Figure 6.1.** Figure 6.1: The fractional radiative energy loss calculated according to DGLV and short [PITH_FULL_IMAGE:figures/full_fig_p127_6_1.png]

**Figure 6.** Figure 6: plots the ratio [PITH_FULL_IMAGE:figures/full_fig_p128_6.png]

**Figure 6.2.** Figure 6.2: plots the ratio RAB/Rκ=1 AB , where Rκ=1 AB represents the RAB calculated with κ = 1. The left column shows the ratio plotted for the HTL elastic energy loss convolved with DGLV radiative energy loss, while the right column shows the ratio plotted for HTL elastic ene…

**Figure 6.** Figure 6: plots the [PITH_FULL_IMAGE:figures/full_fig_p133_6.png]

**Figure 6.3.** Figure 6.3: Plot of the nuclear modification factor RAA as a function of transverse momentum pT for strong coupling αs in the range [0.3, 0.5] (from large RAA to small large RAA). Top panels show results for charged hadrons (h ±) produced in 0–5% centrality Pb + Pb collisions an…

**Figure 6.4.** Figure 6.4: (left) Nuclear modification factor RAA as a function of transverse momentum pT for Pb + Pb collisions at √ sNN = 5.02 TeV. Theoretical curves are produced by varying the elastic energy loss between HTL and BT and the multiplier κ of cutoff for transverse radiated glu…

**Figure 6.** Figure 6: plots the [PITH_FULL_IMAGE:figures/full_fig_p136_6.png]

**Figure 6.5.** Figure 6.5: Plot of the χ 2 as a function of αs. Theoretical curves are generated from the HTL (blue) [104] as well as BT (green) [147, 148] elastic energy loss convolved with DGLV + SPL [184, 185] radiative energy loss with the large formation time + collinear cutoff and κ = 1.…

**Figure 6.6.** Figure 6.6: Plot of the χ 2 for global fit to data with fixed κ = 1 (multiplier of |k|max) in central Pb + Pb and Au + Au collisions. All data for collision Pb + Pb and Au + Au collisions for centrality classes less than 60% was included. The pT range considered was 5 GeV ≤ pT ≤…

**Figure 6.7.** Figure 6.7: Model results for the nuclear modification factor [PITH_FULL_IMAGE:figures/full_fig_p139_6_7.png]

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Works this paper leans on

300 extracted references · 27 canonical work pages

[1]

S. L. Glashow, Nucl. Phys.22, 579 (1961)

1961
[2]

D. J. Gross and F. Wilczek, Phys. Rev. Lett.30, 1343 (1973)

1973
[3]

P. W. Higgs, Phys. Rev. Lett.13, 508 (1964)

1964
[4]

Weinberg, Phys

S. Weinberg, Phys. Rev. Lett.19, 1264 (1967)

1967
[5]

Einstein, Annalen Phys.49, 769 (1916)

A. Einstein, Annalen Phys.49, 769 (1916)

1916
[6]

Wilczek,A Beautiful Question: Finding Nature’s Deep Design(Penguin Press, 2015)

F. Wilczek,A Beautiful Question: Finding Nature’s Deep Design(Penguin Press, 2015)

2015
[7]

Carroll,The Biggest Ideas in the Universe: Space, Time, and Motion(Penguin Random House, 2022)

S. Carroll,The Biggest Ideas in the Universe: Space, Time, and Motion(Penguin Random House, 2022)

2022
[8]

R. P. Feynman, R. B. Leighton, and M. Sands,The Feynman Lectures on Physics (1963)

1963

Show all 300 references

[9]

Dalton,A New System of Chemical Philosophy(R

J. Dalton,A New System of Chemical Philosophy(R. Bickerstaff, Manchester, 1808)
[10]

J. J. Thomson, The London, Edinburgh, and Dublin Philosophical Magazine and Jour- nal of Science44, 293 (1897)
[11]

Bohr, Philosophical Magazine26, 1 (1913)

N. Bohr, Philosophical Magazine26, 1 (1913)

1913
[12]

Heisenberg, Zeitschrift f¨ ur Physik33, 879 (1925)

W. Heisenberg, Zeitschrift f¨ ur Physik33, 879 (1925)

1925
[13]

Schr¨ odinger, Annalen der Physik79, 361 (1926)

E. Schr¨ odinger, Annalen der Physik79, 361 (1926)

1926
[14]

Planck, Annalen der Physik309, 553 (1901)

M. Planck, Annalen der Physik309, 553 (1901)

1901
[15]

Einstein, Annalen der Physik322, 132 (1905)

A. Einstein, Annalen der Physik322, 132 (1905)

1905
[16]

de Broglie, Annales de Physique3, 22 (1924), phD Thesis

L. de Broglie, Annales de Physique3, 22 (1924), phD Thesis

1924
[17]

Chadwick, Nature129, 312 (1932)

J. Chadwick, Nature129, 312 (1932)

1932
[18]

R. P. Feynman, Reviews of Modern Physics20, 367 (1948)

1948
[19]

Schwinger, Physical Review73, 416 (1948)

J. Schwinger, Physical Review73, 416 (1948). 133 Chapter 7 134

1948
[20]

Tomonaga, Progress of Theoretical Physics3, 1 (1948)

S.-I. Tomonaga, Progress of Theoretical Physics3, 1 (1948)

1948
[21]

H. D. Politzer, Phys. Rev. Lett.30, 1346 (1973)

1973
[22]

G. D. Rochester and C. C. Butler, Nature160, 855 (1947)

1947
[23]

C. M. G. Lattes, G. P. S. Occhialini, and C. F. Powell, Nature160, 486 (1947)

1947
[24]

Gell-Mann, Physics1, 63 (1961)

M. Gell-Mann, Physics1, 63 (1961)

1961
[25]

Ne’eman, Nucl

Y. Ne’eman, Nucl. Phys.26, 222 (1961)

1961
[26]

The history of qcd,

“The history of qcd,” CERN Courier (2023), accessed: 2024-08-30

2023
[27]

Gell-Mann, Phys

M. Gell-Mann, Phys. Lett.8, 214 (1964)

1964
[28]

Zweig, CERN-TH-401 (1964)

G. Zweig, CERN-TH-401 (1964)

1964
[29]

Fritzsch, M

H. Fritzsch, M. Gell-Mann, and H. Leutwyler, Phys. Lett. B47, 365 (1973)

1973
[30]

Hikasaet al.(Particle Data Group), Phys

K. Hikasaet al.(Particle Data Group), Phys. Rev. D45, S1 (1992), [Erratum: Phys.Rev.D 46, 5210 (1992)]

1992
[31]

D. J. Gross and F. Wilczek, Phys. Rev. D8, 3633 (1973)

1973
[32]

D. J. Gross and F. Wilczek, Phys. Rev. D9, 980 (1974)

1974
[33]

R. L. Workmanet al.(Particle Data Group), PTEP2022, 083C01 (2022)

2022
[34]

Adcoxet al.(PHENIX), Nucl

K. Adcoxet al.(PHENIX), Nucl. Phys. A757, 184 (2005), arXiv:nucl-ex/0410003

2005 arXiv
[35]

B. B. Backet al.(PHOBOS), Nucl. Phys. A757, 28 (2005), arXiv:nucl-ex/0410022

2005 arXiv
[36]

Adamset al.(STAR), Nucl

J. Adamset al.(STAR), Nucl. Phys. A757, 102 (2005), arXiv:nucl-ex/0501009

2005 arXiv
[37]

Arseneet al.(BRAHMS), Nucl

I. Arseneet al.(BRAHMS), Nucl. Phys. A757, 1 (2005), arXiv:nucl-ex/0410020

2005 arXiv
[38]

Acharyaet al.(ALICE), Eur

S. Acharyaet al.(ALICE), Eur. Phys. J. C84, 813 (2024), arXiv:2211.04384 [nucl-ex]

2024 arXiv
[39]

Recreating the big bang on earth,

Phys.org, “Recreating the big bang on earth,” (2020), accessed: 2024-08-28

2020
[40]

E. W. Kolb,The Early Universe, Vol. 69 (Taylor and Francis, 2019)

2019
[41]

J. C. Collins and M. J. Perry, Phys. Rev. Lett.34, 1353 (1975)

1975
[42]

Busza, K

W. Busza, K. Rajagopal, and W. van der Schee, Ann. Rev. Nucl. Part. Sci.68, 339 (2018), arXiv:1802.04801 [hep-ph]

2018 arXiv
[43]

Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, Nature443, 675 (2006), arXiv:hep-lat/0611014

2006 arXiv
[44]

Bzdak, S

A. Bzdak, S. Esumi, V. Koch, J. Liao, M. Stephanov, and N. Xu, Phys. Rept.853, 1 (2020), arXiv:1906.00936 [nucl-th]. Chapter 7 135

2020 arXiv
[45]

Aarts, F

G. Aarts, F. Attanasio, B. J¨ ager, E. Seiler, D. Sexty, and I.-O. Stamatescu, AIP Conf. Proc.1701, 020001 (2016), arXiv:1412.0847 [hep-lat]

2016 arXiv
[46]

K. J. Eskola, Nucl. Phys. A910-911, 163 (2013), arXiv:1209.1546 [hep-ph]

2013 arXiv
[47]

Giacaloneet al., (2024), arXiv:2405.20210 [nucl-th]

G. Giacaloneet al., (2024), arXiv:2405.20210 [nucl-th]

2024 arXiv
[48]

Giacaloneet al., (2024), arXiv:2402.05995 [nucl-th]

G. Giacaloneet al., (2024), arXiv:2402.05995 [nucl-th]

2024 arXiv
[49]

Pasechnik and M

R. Pasechnik and M. ˇSumbera, Universe3, 7 (2017), arXiv:1611.01533 [hep-ph]

2017 arXiv
[50]

Qin and X.-N

G.-Y. Qin and X.-N. Wang, Int. J. Mod. Phys. E24, 1530014 (2015), arXiv:1511.00790 [hep-ph]

2015 arXiv
[51]

C. Gale, S. Jeon, and B. Schenke, Int. J. Mod. Phys. A28, 1340011 (2013), arXiv:1301.5893 [nucl-th]

2013 arXiv
[52]

Muller, Acta Phys

B. Muller, Acta Phys. Polon. B43, 761 (2012), arXiv:1112.5382 [nucl-th]

2012 arXiv
[53]

Herrmann, J

N. Herrmann, J. P. Wessels, and T. Wienold, Ann. Rev. Nucl. Part. Sci.49, 581 (1999)

1999
[54]

Rafelski and R

J. Rafelski and R. Hagedorn, inInternational Symposium on Statistical Mechanics of Quarks and Hadrons(1980)

1980
[55]

Rafelski and B

J. Rafelski and B. Muller, Phys. Rev. Lett.48, 1066 (1982), [Erratum: Phys.Rev.Lett. 56, 2334 (1986)]

1982
[56]

Andersenet al.(W A97), Phys

E. Andersenet al.(W A97), Phys. Lett. B449, 401 (1999)

1999
[57]

Adamet al.(ALICE), Phys

J. Adamet al.(ALICE), Phys. Lett. B758, 389 (2016), arXiv:1512.07227 [nucl-ex]

2016 arXiv
[58]

B. B. Abelevet al.(ALICE), Phys. Lett. B728, 216 (2014), [Erratum: Phys.Lett.B 734, 409–410 (2014)], arXiv:1307.5543 [nucl-ex]

2014 arXiv
[59]

New State of Matter created at CERN,

CERN, “New State of Matter created at CERN,” https://home.cern/news/press- release/cern/new-state-matter-created-cern (2000)

2000
[60]

Adamet al.(ALICE), Nature Phys.13, 535 (2017), arXiv:1606.07424 [nucl-ex]

J. Adamet al.(ALICE), Nature Phys.13, 535 (2017), arXiv:1606.07424 [nucl-ex]

2017 arXiv
[61]

B. B. Abelevet al.(ALICE), Phys. Lett. B728, 25 (2014), arXiv:1307.6796 [nucl-ex]

2014 arXiv
[62]

K. H. Ackermannet al.(STAR), Phys. Rev. Lett.86, 402 (2001), arXiv:nucl- ex/0009011

2001
[63]

Jacobs and G

P. Jacobs and G. Cooper, (2000), arXiv:nucl-ex/0008015

2000 arXiv
[64]

Huovinen, P

P. Huovinen, P. F. Kolb, U. W. Heinz, P. V. Ruuskanen, and S. A. Voloshin, Phys. Lett. B503, 58 (2001), arXiv:hep-ph/0101136

2001 arXiv
[65]

Luzum and P

M. Luzum and P. Romatschke, Phys. Rev. C78, 034915 (2008), [Erratum: Phys.Rev.C 79, 039903 (2009)], arXiv:0804.4015 [nucl-th]. Chapter 7 136

2008 arXiv
[66]

Romatschke and U

P. Romatschke and U. Romatschke, Phys. Rev. Lett.99, 172301 (2007), arXiv:0706.1522 [nucl-th]

2007 arXiv
[67]

A. K. Chaudhuri, (2007), arXiv:0708.1252 [nucl-th]

2007 arXiv
[68]

C. Gale, S. Jeon, B. Schenke, P. Tribedy, and R. Venugopalan, Phys. Rev. Lett.110, 012302 (2013), arXiv:1209.6330 [nucl-th]

2013 arXiv
[69]

Schenke, P

B. Schenke, P. Tribedy, and R. Venugopalan, Phys. Rev. Lett.108, 252301 (2012), arXiv:1202.6646 [nucl-th]

2012 arXiv
[70]

Alveret al.(PHOBOS), Phys

B. Alveret al.(PHOBOS), Phys. Rev. Lett.98, 242302 (2007), arXiv:nucl-ex/0610037

2007 arXiv
[71]

Schenke, C

B. Schenke, C. Shen, and P. Tribedy, Phys. Rev. C102, 044905 (2020), arXiv:2005.14682 [nucl-th]

2020 arXiv
[72]

G. Nijs, W. van der Schee, U. G¨ ursoy, and R. Snellings, Phys. Rev. C103, 054909 (2021), arXiv:2010.15134 [nucl-th]

2021 arXiv
[73]

J. E. Bernhard, J. S. Moreland, and S. A. Bass, Nature Phys.15, 1113 (2019)

2019
[74]

Aadet al.(ATLAS), Phys

G. Aadet al.(ATLAS), Phys. Rev. C90, 044906 (2014), arXiv:1409.1792 [hep-ex]

2014 arXiv
[75]

Khachatryanet al.(CMS), JHEP09, 091 (2010), arXiv:1009.4122 [hep-ex]

V. Khachatryanet al.(CMS), JHEP09, 091 (2010), arXiv:1009.4122 [hep-ex]

2010 arXiv
[76]

Chatrchyanet al.(CMS), Phys

S. Chatrchyanet al.(CMS), Phys. Lett. B718, 795 (2013), arXiv:1210.5482 [nucl-ex]

2013 arXiv
[77]

Chatrchyanet al.(CMS), Phys

S. Chatrchyanet al.(CMS), Phys. Lett. B724, 213 (2013), arXiv:1305.0609 [nucl-ex]

2013 arXiv
[78]

Khachatryanet al.(CMS), Phys

V. Khachatryanet al.(CMS), Phys. Rev. Lett.115, 012301 (2015), arXiv:1502.05382 [nucl-ex]

2015 arXiv
[79]

Adareet al.(PHENIX), Phys

A. Adareet al.(PHENIX), Phys. Rev. Lett.111, 212301 (2013), arXiv:1303.1794 [nucl- ex]

2013
[80]

R. D. Weller and P. Romatschke, Phys. Lett. B774, 351 (2017), arXiv:1701.07145 [nucl-th]

2017 arXiv
[81]

W. Zhao, S. Ryu, C. Shen, and B. Schenke, Phys. Rev. C107, 014904 (2023), arXiv:2211.16376 [nucl-th]

2023 arXiv
[82]

M. L. Miller, K. Reygers, S. J. Sanders, and P. Steinberg, Ann. Rev. Nucl. Part. Sci. 57, 205 (2007), arXiv:nucl-ex/0701025

2007 arXiv
[83]

R. J. Glauber, inLectures in Theoretical Physics, Vol. 1, edited by W. E. Brittin and L. G. Dunham (Interscience, New York, 1959) p. 315

1959
[84]

J. E. Elias, W. Busza, C. Halliwell, D. Luckey, L. Votta, and C. Young, Phys. Rev. Lett.41, 285 (1978)

1978
[85]

B. B. Backet al.(PHOBOS), Phys. Rev. C74, 021901 (2006), arXiv:nucl-ex/0509034. Chapter 7 137

2006 arXiv
[86]

Abbaset al.(ALICE), Phys

E. Abbaset al.(ALICE), Phys. Lett. B726, 610 (2013), arXiv:1304.0347 [nucl-ex]

2013 arXiv
[87]

J. C. Collins, D. E. Soper, and G. F. Sterman, Adv. Ser. Direct. High Energy Phys. 5, 1 (1989), arXiv:hep-ph/0409313

1989 arXiv
[88]

Collins,Foundations of Perturbative QCD, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology, Vol

J. Collins,Foundations of Perturbative QCD, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology, Vol. 32 (Cambridge University Press, 2023)

2023
[89]

Mayet al., Phys

M. Mayet al., Phys. Rev. Lett.35, 407 (1975)

1975
[90]

Connors, C

M. Connors, C. Nattrass, R. Reed, and S. Salur, Rev. Mod. Phys.90, 025005 (2018), arXiv:1705.01974 [nucl-ex]

2018 arXiv
[91]

Cao and X.-N

S. Cao and X.-N. Wang, Rept. Prog. Phys.84, 024301 (2021), arXiv:2002.04028 [hep- ph]

2021 arXiv
[92]

R. J. Glauber and G. Matthiae, Nucl. Phys. B21, 135 (1970)

1970
[93]

Ehlerset al.(JETSCAPE), (2024), arXiv:2408.08247 [hep-ph]

R. Ehlerset al.(JETSCAPE), (2024), arXiv:2408.08247 [hep-ph]

2024
[94]

K. M. Burkeet al.(JET), Phys. Rev. C90, 014909 (2014), arXiv:1312.5003 [nucl-th]

2014 arXiv
[95]

Caoet al.(JETSCAPE), Phys

S. Caoet al.(JETSCAPE), Phys. Rev. C104, 024905 (2021), arXiv:2102.11337 [nucl- th]

2021 arXiv
[96]

S. A. Bass, C. Gale, A. Majumder, C. Nonaka, G.-Y. Qin, T. Renk, and J. Ruppert, Phys. Rev. C79, 024901 (2009), arXiv:0808.0908 [nucl-th]

2009 arXiv
[97]

Armesto, M

N. Armesto, M. Cacciari, T. Hirano, J. L. Nagle, and C. A. Salgado, J. Phys. G37, 025104 (2010), arXiv:0907.0667 [hep-ph]

2010 arXiv
[98]

X.-F. Chen, C. Greiner, E. Wang, X.-N. Wang, and Z. Xu, Phys. Rev. C81, 064908 (2010), arXiv:1002.1165 [nucl-th]

2010 arXiv
[99]

G.-Y. Qin, J. Ruppert, C. Gale, S. Jeon, and G. D. Moore, Phys. Rev. C80, 054909 (2009), arXiv:0906.3280 [hep-ph]

2009 arXiv
[100]

Z.-B. Kang, R. Lashof-Regas, G. Ovanesyan, P. Saad, and I. Vitev, Phys. Rev. Lett. 114, 092002 (2015), arXiv:1405.2612 [hep-ph]

2015 arXiv
[101]

Karmakar, D

B. Karmakar, D. Zigic, M. Djordjevic, P. Huovinen, M. Djordjevic, and J. Auvinen, Phys. Rev. C110, 044906 (2024), arXiv:2403.17817 [hep-ph]

2024 arXiv
[102]

Karmakar, D

B. Karmakar, D. Zigic, I. Salom, J. Auvinen, P. Huovinen, M. Djordjevic, and M. Djordjevic, Phys. Rev. C108, 044907 (2023), arXiv:2305.11318 [hep-ph]

2023 arXiv
[103]

W. A. Horowitz and B. A. Cole, Phys. Rev. C81, 024909 (2010), arXiv:0910.1823 [hep-ph]

2010 arXiv
[104]

Wicks,Fluctuations with small numbers: Developing the perturbative paradigm for jet physics in the QGP at RHIC and LHC, PhD thesis (2008)

S. Wicks,Fluctuations with small numbers: Developing the perturbative paradigm for jet physics in the QGP at RHIC and LHC, PhD thesis (2008). Chapter 7 138

2008
[105]

Romatschke and M

P. Romatschke and M. Strickland, Phys. Rev. D71, 125008 (2005), arXiv:hep- ph/0408275

2005
[106]

Djordjevic and M

M. Djordjevic and M. Gyulassy, Nucl. Phys. A733, 265 (2004), arXiv:nucl-th/0310076

2004 arXiv
[107]

Wicks, W

S. Wicks, W. Horowitz, M. Djordjevic, and M. Gyulassy, Nucl. Phys. A784, 426 (2007), arXiv:nucl-th/0512076

2007 arXiv
[108]

Y. L. Dokshitzer and D. E. Kharzeev, Phys. Lett. B519, 199 (2001), arXiv:hep- ph/0106202

2001
[109]

L. D. Landau and I. Pomeranchuk, Dokl. Akad. Nauk Ser. Fiz.92, 535 (1953)

1953
[110]

A. B. Migdal, Phys. Rev.103, 1811 (1956)

1956
[111]

Armestoet al., Phys

N. Armestoet al., Phys. Rev. C86, 064904 (2012), arXiv:1106.1106 [hep-ph]

2012 arXiv
[112]

Baier, Y

R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne, and D. Schiff, Nucl. Phys. B 483, 291 (1997), arXiv:hep-ph/9607355

1997 arXiv
[113]

Baier, Y

R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne, and D. Schiff, Nucl. Phys. B 484, 265 (1997), arXiv:hep-ph/9608322

1997 arXiv
[114]

B. G. Zakharov, JETP Lett.65, 615 (1997), arXiv:hep-ph/9704255

1997 arXiv
[115]

Baier, Y

R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne, and D. Schiff, Nucl. Phys. B 478, 577 (1996), arXiv:hep-ph/9604327

1996 arXiv
[116]

B. G. Zakharov, JETP Lett.63, 952 (1996), arXiv:hep-ph/9607440

1996 arXiv
[117]

Gyulassy and X.-n

M. Gyulassy and X.-n. Wang, Nucl. Phys. B420, 583 (1994), arXiv:nucl-th/9306003

1994 arXiv
[118]

U. A. Wiedemann, Nucl. Phys. B588, 303 (2000), arXiv:hep-ph/0005129

2000 arXiv
[119]

C. A. Salgado and U. A. Wiedemann, Phys. Rev. D68, 014008 (2003), arXiv:hep- ph/0302184

2003
[120]

Armesto, C

N. Armesto, C. A. Salgado, and U. A. Wiedemann, Phys. Rev. D69, 114003 (2004), arXiv:hep-ph/0312106

2004 arXiv
[121]

Gyulassy, P

M. Gyulassy, P. Levai, and I. Vitev, Nucl. Phys. B594, 371 (2001), arXiv:nucl- th/0006010

2001
[122]

U. A. Wiedemann, Nucl. Phys. A690, 731 (2001), arXiv:hep-ph/0008241

2001 arXiv
[123]

Wicks, (2008), arXiv:0804.4704 [nucl-th]

S. Wicks, (2008), arXiv:0804.4704 [nucl-th]

2008 arXiv
[124]

Gyulassy, P

M. Gyulassy, P. Levai, and I. Vitev, Phys. Lett. B538, 282 (2002), arXiv:nucl- th/0112071

2002
[125]

Djordjevic and U

M. Djordjevic and U. Heinz, Phys. Rev. C77, 024905 (2008), arXiv:0705.3439 [nucl-th]. Chapter 7 139

2008 arXiv
[126]

Djordjevic and U

M. Djordjevic and U. W. Heinz, Phys. Rev. Lett.101, 022302 (2008), arXiv:0802.1230 [nucl-th]

2008 arXiv
[127]

Djordjevic, Phys

M. Djordjevic, Phys. Rev. C80, 064909 (2009), arXiv:0903.4591 [nucl-th]

2009 arXiv
[128]

Braaten and R

E. Braaten and R. D. Pisarski, Nucl. Phys. B337, 569 (1990)

1990
[129]

V. V. Klimov, Sov. Phys. JETP55, 199 (1982)

1982
[130]

R. D. Pisarski, Phys. Rev. Lett.63, 1129 (1989)

1989
[131]

H. A. Weldon, Phys. Rev. D26, 1394 (1982)

1982
[132]

H. A. Weldon, Phys. Rev. D26, 2789 (1982)

1982
[133]

Mehtar-Tani and K

Y. Mehtar-Tani and K. Tywoniuk, JHEP06, 187 (2020), arXiv:1910.02032 [hep-ph]

2020 arXiv
[134]

Mehtar-Tani, JHEP07, 057 (2019), arXiv:1903.00506 [hep-ph]

Y. Mehtar-Tani, JHEP07, 057 (2019), arXiv:1903.00506 [hep-ph]

2019 arXiv
[135]

P. B. Arnold, G. D. Moore, and L. G. Yaffe, JHEP12, 009 (2001), arXiv:hep- ph/0111107

2001
[136]

P. B. Arnold, G. D. Moore, and L. G. Yaffe, JHEP06, 030 (2002), arXiv:hep- ph/0204343

2002
[137]

P. B. Arnold, G. D. Moore, and L. G. Yaffe, JHEP11, 057 (2001), arXiv:hep- ph/0109064

2001
[138]

Majumder and M

A. Majumder and M. Van Leeuwen, Prog. Part. Nucl. Phys.66, 41 (2011), arXiv:1002.2206 [hep-ph]

2011 arXiv
[139]

Caron-Huot and C

S. Caron-Huot and C. Gale, Phys. Rev. C82, 064902 (2010), arXiv:1006.2379 [hep-ph]

2010 arXiv
[140]

Guo and X.-N

X.-f. Guo and X.-N. Wang, Phys. Rev. Lett.85, 3591 (2000), arXiv:hep-ph/0005044

2000 arXiv
[141]

Wang and X.-f

X.-N. Wang and X.-f. Guo, Nucl. Phys. A696, 788 (2001), arXiv:hep-ph/0102230

2001 arXiv
[142]

M. E. Peskin and D. V. Schroeder,An Introduction to quantum field theory(Addison- Wesley, Reading, USA, 1995)

1995
[143]

Gyulassy, P

M. Gyulassy, P. Levai, and I. Vitev, Phys. Rev. Lett.85, 5535 (2000), arXiv:nucl- th/0005032

2000
[144]

W. A. Horowitz,Probing the Frontiers of QCD, PhD thesis (2010), arXiv:1011.4316 [nucl-th]

2010 arXiv
[145]

J. D. Bjorken, (1982)

1982
[146]

M. H. Thoma and M. Gyulassy, Nucl. Phys. B351, 491 (1991)

1991
[147]

Braaten and M

E. Braaten and M. H. Thoma, Phys. Rev. D44, R2625 (1991). Chapter 7 140

1991
[148]

Braaten and M

E. Braaten and M. H. Thoma, Phys. Rev. D44, 1298 (1991)

1991
[149]

J. D. Bjorken, Phys. Rev. D27, 140 (1983)

1983
[150]

Djordjevic, Phys

M. Djordjevic, Phys. Rev. C74, 064907 (2006), arXiv:nucl-th/0603066

2006 arXiv
[151]

Casalderrey-Solana, H

J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, and U. A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions(Cambridge University Press, 2014) arXiv:1101.0618 [hep-th]

2014 arXiv
[152]

D’Hoker and D

E. D’Hoker and D. Z. Freedman, inTheoretical Advanced Study Institute in Elementary Particle Physics (TASI 2001): Strings, Branes and EXTRA Dimensions(2002) pp. 3– 158, arXiv:hep-th/0201253

2002 arXiv
[153]

I. R. Klebanov, inTheoretical Advanced Study Institute in Elementary Particle Physics (TASI 99): Strings, Branes, and Gravity(2000) pp. 615–650, arXiv:hep-th/0009139

2000 arXiv
[154]

S. S. Gubser, Phys. Rev. D74, 126005 (2006), arXiv:hep-th/0605182

2006 arXiv
[155]

C. P. Herzog, A. Karch, P. Kovtun, C. Kozcaz, and L. G. Yaffe, JHEP07, 013 (2006), arXiv:hep-th/0605158

2006 arXiv
[156]

Casalderrey-Solana and D

J. Casalderrey-Solana and D. Teaney, JHEP04, 039 (2007), arXiv:hep-th/0701123

2007 arXiv
[157]

Bitaghsir Fadafan, H

K. Bitaghsir Fadafan, H. Liu, K. Rajagopal, and U. A. Wiedemann, Eur. Phys. J. C 61, 553 (2009), arXiv:0809.2869 [hep-ph]

2009 arXiv
[158]

Mikhailov, (2003), arXiv:hep-th/0305196

A. Mikhailov, (2003), arXiv:hep-th/0305196

2003 arXiv
[159]

P. M. Chesler, K. Jensen, A. Karch, and L. G. Yaffe, Phys. Rev. D79, 125015 (2009), arXiv:0810.1985 [hep-th]

2009 arXiv
[160]

P. M. Chesler, K. Jensen, and A. Karch, Phys. Rev. D79, 025021 (2009), arXiv:0804.3110 [hep-th]

2009 arXiv
[161]

S. S. Gubser, D. R. Gulotta, S. S. Pufu, and F. D. Rocha, JHEP10, 052 (2008), arXiv:0803.1470 [hep-th]

2008 arXiv
[162]

H. Liu, K. Rajagopal, and U. A. Wiedemann, Phys. Rev. Lett.97, 182301 (2006), arXiv:hep-ph/0605178

2006 arXiv
[163]

Casalderrey-Solana, D

J. Casalderrey-Solana, D. C. Gulhan, J. G. Milhano, D. Pablos, and K. Rajagopal, JHEP10, 019 (2014), [Erratum: JHEP 09, 175 (2015)], arXiv:1405.3864 [hep-ph]

2014 arXiv
[164]

Morad and W

R. Morad and W. A. Horowitz, JHEP11, 017 (2014), arXiv:1409.7545 [hep-th]

2014 arXiv
[165]

W. A. Horowitz, Phys. Rev. D91, 085019 (2015), arXiv:1501.04693 [hep-ph]

2015 arXiv
[166]

A. K. Mes, R. W. Moerman, J. P. Shock, and W. A. Horowitz, Annals Phys.436, 168675 (2022), arXiv:2008.09196 [hep-th]. Chapter 7 141

2022 arXiv
[167]

Sjostrand, S

T. Sjostrand, S. Mrenna, and P. Z. Skands, Comput. Phys. Commun.178, 852 (2008), arXiv:0710.3820 [hep-ph]

2008 arXiv
[168]

Schenke, C

B. Schenke, C. Gale, and S. Jeon, Phys. Rev. C80, 054913 (2009), arXiv:0909.2037 [hep-ph]

2009 arXiv
[169]

C. Park, S. Jeon, and C. Gale, Nucl. Phys. A982, 643 (2019), arXiv:1807.06550 [nucl-th]

2019 arXiv
[170]

Cao and A

S. Cao and A. Majumder, Phys. Rev. C101, 024903 (2020), arXiv:1712.10055 [nucl-th]

2020 arXiv
[171]

Majumder, Phys

A. Majumder, Phys. Rev. C88, 014909 (2013), arXiv:1301.5323 [nucl-th]

2013 arXiv
[172]

Armesto, L

N. Armesto, L. Cunqueiro, and C. A. Salgado, Eur. Phys. J. C63, 679 (2009), arXiv:0907.1014 [hep-ph]

2009 arXiv
[173]

Renk, Phys

T. Renk, Phys. Rev. C83, 024908 (2011), arXiv:1010.4116 [hep-ph]

2011 arXiv
[174]

Renk, Phys

T. Renk, Phys. Rev. C88, 044905 (2013), arXiv:1306.2739 [hep-ph]

2013 arXiv
[175]

K. C. Zapp, J. Stachel, and U. A. Wiedemann, JHEP07, 118 (2011), arXiv:1103.6252 [hep-ph]

2011 arXiv
[176]

K. C. Zapp, F. Krauss, and U. A. Wiedemann, JHEP03, 080 (2013), arXiv:1212.1599 [hep-ph]

2013 arXiv
[177]

Casalderrey-Solana, D

J. Casalderrey-Solana, D. Gulhan, G. Milhano, D. Pablos, and K. Rajagopal, JHEP 03, 135 (2017), arXiv:1609.05842 [hep-ph]

2017 arXiv
[178]

Hulcher, D

Z. Hulcher, D. Pablos, and K. Rajagopal, JHEP03, 010 (2018), arXiv:1707.05245 [hep-ph]

2018 arXiv
[179]

Renk, Phys

T. Renk, Phys. Rev. C78, 034908 (2008), arXiv:0806.0305 [hep-ph]

2008 arXiv
[180]

Renk, Phys

T. Renk, Phys. Rev. C79, 054906 (2009), arXiv:0901.2818 [hep-ph]

2009 arXiv
[181]

Faraday, A

C. Faraday, A. Grindrod, and W. A. Horowitz, Eur. Phys. J. C83, 1060 (2023), arXiv:2305.13182 [hep-ph]

2023 arXiv
[182]

Faraday and W

C. Faraday and W. A. Horowitz, (2024), arXiv:2408.14426 [nucl-th]

2024 arXiv
[183]

Shen, private communication

C. Shen, private communication
[184]

Kolbe and W

I. Kolbe and W. A. Horowitz, Phys. Rev. C100, 024913 (2019), arXiv:1511.09313 [hep-ph]

2019 arXiv
[185]

Kolbe,Short path length pQCD corrections to energy loss in the quark gluon plasma, Master’s thesis, Cape Town U

I. Kolbe,Short path length pQCD corrections to energy loss in the quark gluon plasma, Master’s thesis, Cape Town U. (2015), arXiv:1509.06122 [hep-ph]

2015 arXiv
[186]

Gyulassy, P

M. Gyulassy, P. Levai, and I. Vitev, Nucl. Phys. B571, 197 (2000), arXiv:hep- ph/9907461. Chapter 7 142

2000
[187]

Vitev and M

I. Vitev and M. Gyulassy, Phys. Rev. Lett.89, 252301 (2002), arXiv:hep-ph/0209161

2002 arXiv
[188]

Baier, Y

R. Baier, Y. L. Dokshitzer, A. H. Mueller, and D. Schiff, Nucl. Phys. B531, 403 (1998), arXiv:hep-ph/9804212

1998 arXiv
[189]

Mehtar-Tani, C

Y. Mehtar-Tani, C. A. Salgado, and K. Tywoniuk, Phys. Rev. Lett.106, 122002 (2011), arXiv:1009.2965 [hep-ph]

2011 arXiv
[190]

Mehtar-Tani, C

Y. Mehtar-Tani, C. A. Salgado, and K. Tywoniuk, Phys. Lett. B707, 156 (2012), arXiv:1102.4317 [hep-ph]

2012 arXiv
[191]

Mehtar-Tani and K

Y. Mehtar-Tani and K. Tywoniuk, JHEP01, 031 (2013), arXiv:1105.1346 [hep-ph]

2013 arXiv
[192]

Armesto, H

N. Armesto, H. Ma, Y. Mehtar-Tani, C. A. Salgado, and K. Tywoniuk, JHEP01, 109 (2012), arXiv:1110.4343 [hep-ph]

2012 arXiv
[193]

Mehtar-Tani, C

Y. Mehtar-Tani, C. A. Salgado, and K. Tywoniuk, JHEP04, 064 (2012), arXiv:1112.5031 [hep-ph]

2012 arXiv
[194]

Mehtar-Tani, C

Y. Mehtar-Tani, C. A. Salgado, and K. Tywoniuk, JHEP10, 197 (2012), arXiv:1205.5739 [hep-ph]

2012 arXiv
[195]

Blaizot and Y

J.-P. Blaizot and Y. Mehtar-Tani, Nucl. Phys. A929, 202 (2014), arXiv:1403.2323 [hep-ph]

2014 arXiv
[196]

Blaizot, F

J.-P. Blaizot, F. Dominguez, E. Iancu, and Y. Mehtar-Tani, JHEP06, 075 (2014), arXiv:1311.5823 [hep-ph]

2014 arXiv
[197]

Iancu, JHEP10, 095 (2014), arXiv:1403.1996 [hep-ph]

E. Iancu, JHEP10, 095 (2014), arXiv:1403.1996 [hep-ph]

2014 arXiv
[198]

Iancu and D

E. Iancu and D. N. Triantafyllopoulos, Phys. Rev. D90, 074002 (2014), arXiv:1405.3525 [hep-ph]

2014 arXiv
[199]

Mehtar-Tani and K

Y. Mehtar-Tani and K. Tywoniuk, Nucl. Phys. A979, 165 (2018), arXiv:1706.06047 [hep-ph]

2018 arXiv
[200]

M. D. Sievert and I. Vitev, Phys. Rev. D98, 094010 (2018), arXiv:1807.03799 [hep-ph]

2018 arXiv
[201]

A. V. Sadofyev, M. D. Sievert, and I. Vitev, Phys. Rev. D104, 094044 (2021), arXiv:2104.09513 [hep-ph]

2021 arXiv
[202]

Majumder and B

A. Majumder and B. Muller, Phys. Rev. C77, 054903 (2008), arXiv:0705.1147 [nucl-th]

2008 arXiv
[203]

He, L.-G

Y. He, L.-G. Pang, and X.-N. Wang, Phys. Rev. Lett.125, 122301 (2020), arXiv:2001.08273 [hep-ph]

2020 arXiv
[204]

Y. Fu, J. Casalderrey-Solana, and X.-N. Wang, Phys. Rev. D107, 054038 (2023), arXiv:2204.05323 [hep-ph]

2023 arXiv
[205]

Casalderrey-Solana and C

J. Casalderrey-Solana and C. A. Salgado, Acta Phys. Polon. B38, 3731 (2007), arXiv:0712.3443 [hep-ph]. Chapter 7 143

2007 arXiv
[206]

P. B. Gossiaux and J. Aichelin, Phys. Rev. C78, 014904 (2008), arXiv:0802.2525 [hep- ph]

2008 arXiv
[207]

Blaizot and E

J.-P. Blaizot and E. Iancu, Phys. Rept.359, 355 (2002), arXiv:hep-ph/0101103

2002 arXiv
[208]

M. L. Bellac,Thermal Field Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2011)

2011
[209]

Nakamura, T

A. Nakamura, T. Saito, and S. Sakai, Phys. Rev. D69, 014506 (2004), arXiv:hep- lat/0311024

2004
[210]

A. Hart, M. Laine, and O. Philipsen, Nucl. Phys. B586, 443 (2000), arXiv:hep- ph/0004060

2000
[211]

G. D. Moore and D. Teaney, Phys. Rev. C71, 064904 (2005), arXiv:hep-ph/0412346

2005 arXiv
[212]

J. Xu, A. Buzzatti, and M. Gyulassy, JHEP08, 063 (2014), arXiv:1402.2956 [hep-ph]

2014 arXiv
[213]

J. G. Skellam, Journal of the Royal Statistical Society109, 296 (1946)

1946
[214]

W. A. Horowitz and M. Gyulassy, Nucl. Phys. A872, 265 (2011), arXiv:1104.4958 [hep-ph]

2011 arXiv
[215]

Djordjevic and M

M. Djordjevic and M. Gyulassy, Phys. Rev. C68, 034914 (2003), arXiv:nucl- th/0305062

2003
[216]

Faraday and W

C. Faraday and W. A. Horowitz, in67th Annual Conference of the South African Institute of Physics(2023) arXiv:2309.06246 [hep-ph]

2023 arXiv
[217]

Chatrchyanet al.(CMS), Phys

S. Chatrchyanet al.(CMS), Phys. Lett. B710, 256 (2012), arXiv:1201.3093 [nucl-ex]

2012 arXiv
[218]

Chatrchyanet al.(CMS), Phys

S. Chatrchyanet al.(CMS), Phys. Rev. Lett.106, 212301 (2011), arXiv:1102.5435 [nucl-ex]

2011 arXiv
[219]

Cacciari, S

M. Cacciari, S. Frixione, and P. Nason, JHEP03, 006 (2001), arXiv:hep-ph/0102134

2001 arXiv
[220]

X. N. Wang, private communication
[221]

Cacciari, P

M. Cacciari, P. Nason, and C. Oleari, JHEP04, 006 (2006), arXiv:hep-ph/0510032

2006 arXiv
[222]

de Florian, R

D. de Florian, R. Sassot, and M. Stratmann, Phys. Rev. D75, 114010 (2007), arXiv:hep-ph/0703242

2007 arXiv
[223]

Schenke, P

B. Schenke, P. Tribedy, and R. Venugopalan, Phys. Rev. C86, 034908 (2012), arXiv:1206.6805 [hep-ph]

2012 arXiv
[224]

Schenke, S

B. Schenke, S. Jeon, and C. Gale, Phys. Rev. Lett.106, 042301 (2011), arXiv:1009.3244 [hep-ph]

2011 arXiv
[225]

Schenke, S

B. Schenke, S. Jeon, and C. Gale, Phys. Rev. C85, 024901 (2012), arXiv:1109.6289 [hep-ph]. Chapter 7 144

2012 arXiv
[226]

Schenke, S

B. Schenke, S. Jeon, and C. Gale, Phys. Rev. C82, 014903 (2010), arXiv:1004.1408 [hep-ph]

2010 arXiv
[227]

S. A. Basset al., Prog. Part. Nucl. Phys.41, 255 (1998), arXiv:nucl-th/9803035

1998 arXiv
[228]

Bleicheret al., J

M. Bleicheret al., J. Phys. G25, 1859 (1999), arXiv:hep-ph/9909407

1999 arXiv
[229]

B. Bert, C. Faraday, and W. A. Horowitz, (2024), work in preparation

2024
[230]

Djordjevic, M

M. Djordjevic, M. Gyulassy, R. Vogt, and S. Wicks, Phys. Lett. B632, 81 (2006), arXiv:nucl-th/0507019

2006 arXiv
[231]

Djordjevic, M

M. Djordjevic, M. Gyulassy, and S. Wicks, Phys. Rev. Lett.94, 112301 (2005), arXiv:hep-ph/0410372

2005 arXiv
[232]

Borsanyi, Z

S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP01, 138 (2012), arXiv:1112.4416 [hep-lat]

2012 arXiv
[233]

Gyulassy and L

M. Gyulassy and L. McLerran, Nucl. Phys. A750, 30 (2005), arXiv:nucl-th/0405013

2005 arXiv
[234]

U. A. Wiedemann, , 521 (2010), arXiv:0908.2306 [hep-ph]

2010 arXiv
[235]

Adcoxet al.(PHENIX), Phys

K. Adcoxet al.(PHENIX), Phys. Rev. Lett.88, 022301 (2002), arXiv:nucl-ex/0109003

2002 arXiv
[236]

Adamset al.(STAR), Phys

J. Adamset al.(STAR), Phys. Rev. Lett.91, 072304 (2003), arXiv:nucl-ex/0306024

2003 arXiv
[237]

S. S. Adleret al.(PHENIX), Phys. Rev. Lett.96, 202301 (2006), arXiv:nucl- ex/0601037

2006
[238]

S. S. Adleret al.(PHENIX), Phys. Rev. Lett.94, 232301 (2005), arXiv:nucl- ex/0503003

2005
[239]

S. S. Adleret al.(PHENIX), Phys. Rev. Lett.98, 172302 (2007), arXiv:nucl- ex/0610036

2007
[240]

Dainese, C

A. Dainese, C. Loizides, and G. Paic, Eur. Phys. J. C38, 461 (2005), arXiv:hep- ph/0406201

2005
[241]

W. A. Horowitz, Nucl. Phys. A904-905, 186c (2013), arXiv:1210.8330 [nucl-th]

2013 arXiv
[242]

Song and U

H. Song and U. W. Heinz, Phys. Rev. C77, 064901 (2008), arXiv:0712.3715 [nucl-th]

2008 arXiv
[243]

Adamet al.(ALICE), JHEP06, 050 (2016), arXiv:1603.02816 [nucl-ex]

J. Adamet al.(ALICE), JHEP06, 050 (2016), arXiv:1603.02816 [nucl-ex]

2016 arXiv
[244]

Aadet al.(ATLAS), Phys

G. Aadet al.(ATLAS), Phys. Rev. Lett.116, 172301 (2016), arXiv:1509.04776 [hep- ex]

2016 arXiv
[245]

Arleo and S

F. Arleo and S. Peign´ e, Phys. Rev. Lett.125, 032301 (2020), arXiv:2003.01987 [hep-ph]

2020 arXiv
[246]

Arleo, G

F. Arleo, G. Jackson, and S. Peign´ e, JHEP01, 164 (2022), arXiv:2107.05871 [hep-ph]

2022 arXiv
[247]

Aadet al.(ATLAS), Phys

G. Aadet al.(ATLAS), Phys. Lett. B748, 392 (2015), arXiv:1412.4092 [hep-ex]. Chapter 7 145

2015 arXiv
[248]

Adareet al.(PHENIX), Phys

A. Adareet al.(PHENIX), Phys. Rev. Lett.116, 122301 (2016), arXiv:1509.04657 [nucl-ex]

2016
[249]

Acharyaet al.(ALICE), Phys

S. Acharyaet al.(ALICE), Phys. Lett. B783, 95 (2018), arXiv:1712.05603 [nucl-ex]

2018 arXiv
[250]

Acharyaet al.(ALICE), Phys

S. Acharyaet al.(ALICE), Phys. Rev. C99, 024906 (2019), arXiv:1807.11321 [nucl-ex]

2019 arXiv
[251]

J. I. Kapusta and C. Gale,Finite-temperature field theory: Principles and applications, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2011)

2011
[252]

Balek (ATLAS), Nucl

P. Balek (ATLAS), Nucl. Part. Phys. Proc.289-290, 281 (2017), arXiv:1802.02071 [hep-ex]

2017 arXiv
[253]

Acharyaet al.(ALICE), JHEP10, 174 (2018), arXiv:1804.09083 [nucl-ex]

S. Acharyaet al.(ALICE), JHEP10, 174 (2018), arXiv:1804.09083 [nucl-ex]

2018 arXiv
[254]

Andronicet al., Eur

A. Andronicet al., Eur. Phys. J. C76, 107 (2016), arXiv:1506.03981 [nucl-ex]

2016 arXiv
[255]

A. M. Sirunyanet al.(CMS), Phys. Lett. B782, 474 (2018), arXiv:1708.04962 [nucl-ex]

2018 arXiv
[256]

A. M. Sirunyanet al.(CMS), Phys. Rev. Lett.119, 152301 (2017), arXiv:1705.04727 [hep-ex]

2017 arXiv
[257]

Acharyaet al.(ALICE), JHEP12, 092 (2019), arXiv:1906.03425 [nucl-ex]

S. Acharyaet al.(ALICE), JHEP12, 092 (2019), arXiv:1906.03425 [nucl-ex]

2019 arXiv
[258]

Aadet al.(ATLAS), JHEP07, 074 (2023), arXiv:2211.15257 [hep-ex]

G. Aadet al.(ATLAS), JHEP07, 074 (2023), arXiv:2211.15257 [hep-ex]

2023 arXiv
[259]

Khachatryanet al.(CMS), JHEP04, 039 (2017), arXiv:1611.01664 [nucl-ex]

V. Khachatryanet al.(CMS), JHEP04, 039 (2017), arXiv:1611.01664 [nucl-ex]

2017 arXiv
[260]

Sekihata (ALICE), Nucl

D. Sekihata (ALICE), Nucl. Phys. A982, 567 (2019), arXiv:1807.11240 [hep-ex]

2019 arXiv
[261]

Buzzatti and M

A. Buzzatti and M. Gyulassy, Phys. Rev. Lett.108, 022301 (2012), arXiv:1106.3061 [hep-ph]

2012 arXiv
[262]

Buzzatti and M

A. Buzzatti and M. Gyulassy, Nucl. Phys. A904-905, 779c (2013), arXiv:1210.6417 [hep-ph]

2013 arXiv
[263]

Adleret al.(STAR), Phys

C. Adleret al.(STAR), Phys. Rev. Lett.89, 202301 (2002), arXiv:nucl-ex/0206011

2002 arXiv
[264]

S. S. Adleret al.(PHENIX), Phys. Rev. Lett.91, 072303 (2003), arXiv:nucl- ex/0306021

2003
[265]

Aamodtet al.(ALICE), Phys

K. Aamodtet al.(ALICE), Phys. Rev. Lett.106, 032301 (2011), arXiv:1012.1657 [nucl-ex]

2011 arXiv
[266]

Abelevet al.(ALICE), JHEP09, 112 (2012), arXiv:1203.2160 [nucl-ex]

B. Abelevet al.(ALICE), JHEP09, 112 (2012), arXiv:1203.2160 [nucl-ex]

2012 arXiv
[267]

Adamet al.(ALICE), JHEP03, 081 (2016), arXiv:1509.06888 [nucl-ex]

J. Adamet al.(ALICE), JHEP03, 081 (2016), arXiv:1509.06888 [nucl-ex]

2016 arXiv
[268]

S. S. Adleret al.(PHENIX), Phys. Rev. Lett.91, 182301 (2003), arXiv:nucl- ex/0305013. Chapter 7 146

2003
[269]

Aamodtet al.(ALICE), Phys

K. Aamodtet al.(ALICE), Phys. Rev. Lett.105, 252302 (2010), arXiv:1011.3914 [nucl-ex]

2010 arXiv
[270]

Acharyaet al.(ALICE), Phys

S. Acharyaet al.(ALICE), Phys. Rev. Lett.132, 172302 (2024), arXiv:2311.14357 [nucl-ex]

2024 arXiv
[271]

Aadet al.(ATLAS), Phys

G. Aadet al.(ATLAS), Phys. Lett. B725, 60 (2013), arXiv:1303.2084 [hep-ex]

2013 arXiv
[272]

B. B. Abelevet al.(ALICE), Phys. Rev. C90, 054901 (2014), arXiv:1406.2474 [nucl- ex]

2014 arXiv
[273]

Adareet al.(PHENIX), Phys

A. Adareet al.(PHENIX), Phys. Rev. Lett.114, 192301 (2015), arXiv:1404.7461 [nucl- ex]

2015
[274]

Adareet al.(PHENIX), Phys

A. Adareet al.(PHENIX), Phys. Rev. Lett.115, 142301 (2015), arXiv:1507.06273 [nucl-ex]

2015
[275]

Aidalaet al.(PHENIX), Phys

C. Aidalaet al.(PHENIX), Phys. Rev. C95, 034910 (2017), arXiv:1609.02894 [nucl-ex]

2017
[276]

Aidalaet al.(PHENIX), Phys

C. Aidalaet al.(PHENIX), Phys. Rev. Lett.120, 062302 (2018), arXiv:1707.06108 [nucl-ex]

2018
[277]

Adamet al.(ALICE), Phys

J. Adamet al.(ALICE), Phys. Rev. C94, 054908 (2016), arXiv:1605.07569 [nucl-ex]

2016 arXiv
[278]

U. A. Acharyaet al.(PHENIX), Phys. Rev. C105, 064902 (2022), arXiv:2111.05756 [nucl-ex]

2022
[279]

Adamet al.(ALICE), Phys

J. Adamet al.(ALICE), Phys. Rev. C91, 064905 (2015), arXiv:1412.6828 [nucl-ex]

2015 arXiv
[280]

Adareet al.(PHENIX), Phys

A. Adareet al.(PHENIX), Phys. Rev. C90, 034902 (2014), arXiv:1310.4793 [nucl-ex]

2014
[281]

Kordell and A

M. Kordell and A. Majumder, Phys. Rev. C97, 054904 (2018), arXiv:1601.02595 [nucl- th]

2018 arXiv
[282]

N. J. Abdulameeret al.(PHENIX), (2023), arXiv:2303.12899 [nucl-ex]

2023
[283]

Bzdak, V

A. Bzdak, V. Skokov, and S. Bathe, Phys. Rev. C93, 044901 (2016), arXiv:1408.3156 [hep-ph]

2016 arXiv
[284]

Aadet al.(ATLAS), Phys

G. Aadet al.(ATLAS), Phys. Rev. Lett.131, 072301 (2023), arXiv:2206.01138 [nucl- ex]

2023 arXiv
[285]

Aadet al.(ATLAS), Eur

G. Aadet al.(ATLAS), Eur. Phys. J. C80, 73 (2020), arXiv:1910.13978 [nucl-ex]

2020 arXiv
[286]

A. Huss, A. Kurkela, A. Mazeliauskas, R. Paatelainen, W. van der Schee, and U. A. Wiedemann, Phys. Rev. C103, 054903 (2021), arXiv:2007.13758 [hep-ph]

2021 arXiv
[287]

A. Huss, A. Kurkela, A. Mazeliauskas, R. Paatelainen, W. van der Schee, and U. A. Wiedemann, Phys. Rev. Lett.126, 192301 (2021), arXiv:2007.13754 [hep-ph]. Chapter 7 147

2021 arXiv
[288]

Zigic, I

D. Zigic, I. Salom, J. Auvinen, P. Huovinen, and M. Djordjevic, Front. in Phys.10, 957019 (2022), arXiv:2110.01544 [nucl-th]

2022 arXiv
[289]

Djordjevic and M

M. Djordjevic and M. Djordjevic, Phys. Lett. B734, 286 (2014), arXiv:1307.4098 [hep- ph]

2014 arXiv
[290]

Faraday and W

C. Faraday and W. A. Horowitz, (2024), work in preparation

2024
[291]

Arleo, Phys

F. Arleo, Phys. Rev. Lett.119, 062302 (2017), arXiv:1703.10852 [hep-ph]

2017 arXiv
[292]

Baier, Nucl

R. Baier, Nucl. Phys. A715, 209 (2003), arXiv:hep-ph/0209038

2003 arXiv
[293]

Adareet al.(PHENIX), Phys

A. Adareet al.(PHENIX), Phys. Rev. C77, 064907 (2008), arXiv:0801.1665 [nucl-ex]

2008 arXiv
[294]

Adareet al.(PHENIX), Phys

A. Adareet al.(PHENIX), Phys. Rev. Lett.101, 232301 (2008), arXiv:0801.4020 [nucl- ex]

2008 arXiv
[295]

Caoet al.(JETSCAPE), Phys

S. Caoet al.(JETSCAPE), Phys. Rev. C96, 024909 (2017), arXiv:1705.00050 [nucl-th]

2017 arXiv
[296]

Kumaret al.(JETSCAPE), Phys

A. Kumaret al.(JETSCAPE), Phys. Rev. C107, 034911 (2023), arXiv:2204.01163 [hep-ph]

2023 arXiv
[297]

S. Shi, J. Liao, and M. Gyulassy, Chin. Phys. C43, 044101 (2019), arXiv:1808.05461 [hep-ph]

2019 arXiv
[298]

Stojku, B

S. Stojku, B. Ilic, M. Djordjevic, and M. Djordjevic, Phys. Rev. C103, 024908 (2021), arXiv:2007.07851 [nucl-th]

2021 arXiv
[299]

Peigne and A

S. Peigne and A. Peshier, Phys. Rev. D77, 114017 (2008), arXiv:0802.4364 [hep-ph]

2008 arXiv
[300]

Buzzatti and M

A. Buzzatti and M. Gyulassy, Nucl. Phys. A910-911, 490 (2013), arXiv:1207.6020 [hep-ph]

2013 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

S. L. Glashow, Nucl. Phys.22, 579 (1961)

1961

[2] [2]

D. J. Gross and F. Wilczek, Phys. Rev. Lett.30, 1343 (1973)

1973

[3] [3]

P. W. Higgs, Phys. Rev. Lett.13, 508 (1964)

1964

[4] [4]

Weinberg, Phys

S. Weinberg, Phys. Rev. Lett.19, 1264 (1967)

1967

[5] [5]

Einstein, Annalen Phys.49, 769 (1916)

A. Einstein, Annalen Phys.49, 769 (1916)

1916

[6] [6]

Wilczek,A Beautiful Question: Finding Nature’s Deep Design(Penguin Press, 2015)

F. Wilczek,A Beautiful Question: Finding Nature’s Deep Design(Penguin Press, 2015)

2015

[7] [7]

Carroll,The Biggest Ideas in the Universe: Space, Time, and Motion(Penguin Random House, 2022)

S. Carroll,The Biggest Ideas in the Universe: Space, Time, and Motion(Penguin Random House, 2022)

2022

[8] [8]

R. P. Feynman, R. B. Leighton, and M. Sands,The Feynman Lectures on Physics (1963)

1963