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REVIEW 4 major objections 6 minor 39 references

On the Square Speed of Sound in High-Energy Collisions: Range of Values and How to Understand It

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper argues that the square speed of sound in hadronic matter decoupled from high-energy collisions, extracted from Gaussian rapidity distributions via the Landau relation, lies between 0 and 1/3 for most collision energies.

desk verdict A well-organized parametric study that overclaims: the 0-to-1/3 range is a consequence of the assumed sigma = L/6, not an extraction from data. read the letter →

arxiv 2412.01467 v3 pith:5UPVNCPM submitted 2024-12-02 hep-ph hep-ex

Ting-Ting Duan , Fu-Hu Liu , Khusniddin K. Olimov This is my paper · ORCID
classification hep-phhep-ex PACS 12.40.Ee13.85.Ni13.87.Ce
keywords squarespeedofsoundenergylossrapidityshiftGaussiandistributionLandauhydrodynamicmodelhadronicmatterconformalboundhigh-energycollisions
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 paper offers a simple way to extract the square speed of sound, $c_s^2$, of the hadronic matter that freezes out in high-energy collisions. It treats the produced particles' rapidity distribution as one Gaussian, computes the rapidity gap $L$ between leading target and projectile nucleons after an assumed energy-loss fraction $k$ between 0.5 and 0.9, and sets the Gaussian width to $\sigma = L/6$, the six-$\sigma$ range of a Gaussian. Plugging this width into the Landau hydrodynamic relation converts it into $c_s^2$, which the paper finds stays between 0 and 1/3 for most nucleon-nucleon center-of-mass energies, with values above 1/3 appearing only near $\sqrt{s_{NN}}\sim 10$ TeV. Values above 1/3 are interpreted as early, not-yet-expanded cylindrical geometries that later cool down below 1/3. If the extraction works, a rapidity-width measurement plus an energy-loss assumption reproduces the conformal bound without lattice or equation-of-state input.

What carries the argument

The load-bearing object is the Landau relation between the Gaussian width $\sigma$ of the rapidity spectrum and the square speed of sound, $\sigma^2 = \frac{8}{3}\frac{c_s^2}{1-c_s^4}\ln\left(\frac{\sqrt{s_{NN}}}{2m_N}\right)$, together with the inversion that yields $c_s^2$ from $\sigma$ and $\sqrt{s_{NN}}$. To use this relation, the paper sets $\sigma \approx L/6$ via the 99.7% containment of a Gaussian, where $L$ is the rapidity shift between leading target and projectile nucleons computed from Eqs. (1)-(8) with an assumed energy-loss fraction $k$ between 0.5 and 0.9. The six-$\sigma$ identification is what turns a kinematic statement about leading nucleons into a width for produced hadrons, and the assumed $k$ window sets how large $L$ is at each energy.

What would settle it

Measure the full rapidity distribution in proton-proton collisions at, say, 200 GeV and 13 TeV, fit it to a single Gaussian, and compute $L$ from leading-nucleon energies using Eqs. (1)-(8). If the fitted $\sigma/L$ differs from $1/6$ by more than experimental uncertainty, or if the $c_s^2$ extracted from Eq. (12) disagrees with the value obtained from lattice-QCD equation-of-state calculations under the same conditions, the central claim fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that the square speed of sound, $c_s^2$, of hadronic matter that has decoupled in high-energy collisions can be read off from the width of a single Gaussian rapidity distribution through the Landau relation, and that when the width is fixed to one sixth of the total rapidity shift between leading target and projectile nucleons, the extracted values fall in the range $0 \le c_s^2 \le 1/3$ for most collision energies. The extraction chain is explicit: beam energies and an assumed energy-loss fraction $k$ in the interval 0.5 to 0.9 give the leading-nucleon rapidities, their difference gives $L$, the 99.7% containment rule of a Gaussian sets $\sigma = L/6$, and the Landau relation converts $\sigma$ into $c_s^2$. Below roughly ten TeV the curves stay under $1/3$; around and above that scale some cases cross $1/3$. The paper attributes values from $1/3$ to $1/2$ to non-central collision cylinders with transverse flow, values from $1/2$ to $1$ to central cylinders, and states that all such values fall below $1/3$ once the system expands. It also states that the larger-width curves in Figure 3 are not physically realizable, and that at very high energies a single Gaussian may give way to two or three Gaussian sources, each with its own $c_s^2$.

Load-bearing premise

The load-bearing premise is that the spread of produced particles is exactly six times the rapidity gap between the leading nucleons after an assumed energy loss of 50 to 90 percent; neither the proportionality nor the loss window is measured in this paper.

Editorial extensions

If this is right

  • If the extraction holds, a single Gaussian fit to rapidity spectra plus a 50-90% energy-loss assumption reproduces $c_s^2 \le 1/3$ for most collision energies without any equation-of-state input.
  • The predicted crossing of $1/3$ near $\sqrt{s_{NN}}\sim 10$ TeV gives a specific energy where forward-rapidity data can test the scheme.
  • At very high energies the single Gaussian is expected to fail, so two- or three-source decompositions replace it; the central source has the largest $c_s^2$, and no fourth source is needed at currently accessible energies.
  • Values above $1/3$ are not violations but early-time cylindrical geometries, $c_s^2=1/d$ with $d=2$ or $d=1$, which later expansion reduces below $1/3$.

Reading between the lines

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

  • Not addressed by the paper: the 0-to-1/3 window is tied to the six-sigma convention; choosing a different containment range would shift all extracted values and change the crossing energy.
  • Not addressed by the paper: direct measurement of leading-baryon energy loss would replace the assumed $k$ window with data, and an energy-dependent $k$ would move the predicted $\sim 10$ TeV crossing point.
  • Not addressed by the paper: applying the same width-based extraction separately to pions, kaons, and protons could reveal species-dependent $c_s^2$, since each species has its own rapidity width.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The manuscript reviews the square speed of sound c_s^2 across different forms of matter and then proposes a method to extract c_s^2 for hadronic matter decoupled from the hot, dense system in high-energy collisions. Assuming an energy-loss rate k for incident nucleons (Eqs. 1-4), the authors compute the total rapidity shift L between the leading target and projectile nucleons (Eq. 8). They then equate L with the 6-sigma span of a Gaussian rapidity distribution of produced hadrons (Eq. 9), set sigma = L/6, insert this into the Landau-model relation between sigma and c_s^2 (Eq. 10), and solve for c_s^2 (Eqs. 11-12). Scanning k over 0.5-0.9 and sqrt(s_NN) over a wide range, they find that c_s^2 lies between 0 and 1/3 in most cases (Fig. 2); larger sigma values (Fig. 3) produce c_s^2 above 1/3, which the authors disclaim as lacking physical justification. The paper closes with qualitative explanations for c_s^2 = 1/d based on the dimensionality of expansion and dilution of the produced matter.

Significance. If the central claim were established, the paper would offer a simple kinematical route to c_s^2 from the measured width of rapidity distributions, connecting the conformal bound c_s^2 <= 1/3 to a Gaussian-width convention. The algebraic inversion of Eq. (10) in Eqs. (11)-(12) is correct, and the manuscript is commendably candid about its failure modes: it explicitly states that the Figure 3 scenarios lack physical justification and that Eq. (9) cannot be used when the rapidity distribution is a superposition of multiple Gaussians. The literature survey across neutron stars, dark matter, and dark energy is informative. However, the headline claim is not an extraction: no experimental rapidity distribution is fitted, and the 0-to-1/3 range is a direct consequence of the asserted normalization sigma = L/6 rather than of measured data.

major comments (4)
  1. [Sec. 2, Eq. (9)] The identification sigma ≈ L/6 is asserted on the basis of the Gaussian 99.7% rule, but this is a statistical convention rather than a physical relation. Equating the kinematic rapidity separation of the leading nucleons with the 6-sigma span of the produced-hadron distribution is neither derived nor tested against any measured rapidity distribution in this paper. Because Eq. (10) gives c_s^2 proportional to sigma^2 at small c_s^2, changing the coefficient from 1/6 to 1/4 changes c_s^2 by a factor of about 2.25; the paper's own Fig. 3 shows that such a change pushes most values above 1/3. The range 0 to 1/3 in Fig. 2 is therefore a property of the chosen normalization, not an empirical result, and the abstract's phrase 'The extracted square speed of sound lies within a range from 0 to 1/3' overstates the support the analysis provides.
  2. [Sec. 3, Figs. 1-2 and Data Availability Statement] The energy-loss parameter k is scanned over 0.5-0.9 on the basis of proton-nucleus studies [23-26], but no comparison is made with measured leading-nucleon spectra or with measured rapidity widths at the energies considered, and the Data Availability Statement confirms that no data sets were used. Since L and hence sigma are determined by k through Eqs. (1)-(9), both the magnitude of c_s^2 and the energy at which c_s^2 crosses 1/3 depend on the assumed k interval. The statement that c_s^2 lies in 0 to 1/3 'in most cases' is consequently a statement about the model's parameter space rather than about collisions, unless the k range is anchored to data.
  3. [Sec. 3, discussion of refs. [39,40]] The manuscript states that the connection between L and c_s^2 is established via L = 6 sigma using the authors' previous works [39,40]. Those works fitted (pseudo)rapidity distributions and already assumed the Landau relation Eq. (10); the fits are not reproduced here. The only genuinely new step in the present paper is Eq. (9), and that is precisely the step that fixes the claimed 0-to-1/3 range. The central claim is therefore not independently validated in this manuscript, and the reliance on the self-cited earlier analyses makes the argument appear self-referential.
  4. [Sec. 3, paragraphs after Fig. 3 and Sec. 4 Summary] The text concedes that the sigma > L/6 scenarios 'lack physical justification' and that, once the rapidity distribution is a superposition of two or three Gaussians, 'each sigma can no longer be obtained from the relationship with L' via Eq. (9). These concessions directly limit the claimed universality of the 0-to-1/3 range, yet the Summary restates the range as a robust extracted result with only qualitative caveats. The manuscript should either restrict its claims to the conditional statement 'under the assumptions of Eq. (9),' or supply direct fits to measured rapidity distributions that support the range as an extraction.
minor comments (6)
  1. [Sec. 2, Eqs. (1)-(5)] The notation uses awkward double-letter subscripts (E_TT_beam, E_LT, etc.) throughout, apparently from the original formatting; this harms readability and should be replaced with standard single-letter subscripts. The beam frame (laboratory vs. center-of-mass) should also be defined explicitly before Eq. (5).
  2. [Sec. 3, paragraph before Fig. 1] The binary-collision number nu is introduced with quoted fractions from [23] to motivate the k range, but nu is never used quantitatively; the connection between the nu distributions and the chosen values k = 0.5-0.9 should be made explicit.
  3. [Sec. 2, discussion of ref. [22]] The claim that the non-conformal viscous solution of [22] yields 'a marginally larger sigma^2' compared with the conformal solution is stated without the relevant formula or quantitative comparison; please provide the relationship or the numerical values.
  4. [Sec. 2, Eq. (10)] Eq. (10) is presented as the Landau-model relation without derivation; a brief derivation or a precise pointer to the expression in refs. [16,21] would clarify the origin of the factor (8/3) c_s^2 / (1 - c_s^4) and the model's domain of validity.
  5. [Sec. 4, Summary] The final paragraph interprets values between 1/3 and 1/2 as indicating non-central collisions and values between 1/2 and 1 as indicating central collisions, but no quantitative argument is given for these thresholds; given that Fig. 3 values above 1/3 are disclaimed as physically unjustified, this explanatory scheme appears to be in tension with the rest of the paper.
  6. [Throughout] There are many typographical and grammatical errors (e.g., 'leadings to', 'slowly decelerate', inconsistent use of 'square speed of sound' instead of the more standard 'squared speed of sound'); a thorough copy-edit is needed.

Circularity Check

2 steps flagged · score 8.0 of 10

The central 0-to-1/3 range is imposed by the asserted identification sigma = L/6 (Eq. 9), backed by self-citations [39,40]; the result reduces to its own input assumption.

  1. self definitional [Section 2, Eq. (9) and surrounding text; Section 3, Fig. 2 and Fig. 3 discussion]
    "The total rapidity shift represents the distribution range of particles in one-dimensional rapidity y space. According to the Landau hydrodynamic model for hadron production in high-energy collisions [11–14], y follows an approximate Gaussian distribution characterized by a width or standard deviation σ [14, 15]. Based on properties of Gaussian distributions, it can be expected that approximately 99.7% of particles will fall within the rapidity range of [−3σ, 3σ]. If one considers a range of 6σ as representing the total rapidity shift L, then one has σ ≈ 1/6 L."

    L is defined from the kinematic rapidity separation of the leading nucleons (Eq. 8), not from a measured width of the produced-hadron rapidity distribution. Equating L to the 6σ span of a Gaussian converts a statistical convention into the physical input for Eq. (10). Since c_s^2 is then obtained by inverting Eq. (10), the quoted 0–1/3 range is a property of the chosen coefficient 1/6. The paper's own Fig. 3 shows that σ = 0.2L, 0.4L, 0.6L, and 0.8L push c_s^2 > 1/3 while being dismissed as 'not physically realizable under standard conditions'; only σ = L/6 keeps the result in the claimed band. No measured rapidity distribution is fitted anywhere in the paper, so σ is not extracted but imposed.

  2. self citation load bearing [Section 3, paragraph citing [39,40]]
    "Both the works [39, 40] gave σ and c_s^2 each to each, then the connection between L and c_s^2 is established due to L = 6σ."

    The cited works [39,40] are by the same research group (Gao and Liu, with Liu a co-author of the present paper), and the relation L = 6σ is exactly Eq. (9) restated. The paper presents this self-citation as the empirical anchor for the relation, but those prior works themselves rely on the same Landau-Gaussian ansatz and are not independent, machine-checked, or externally benchmarked evidence. The central 0-to-1/3 result therefore rests on a self-referential chain rather than on independent validation, a fragility the paper itself concedes when noting that Eq. (9) no longer holds for multi-Gaussian rapidity distributions.

full rationale

The Landau relation in Eq. (10), connecting σ to c_s^2, is an external result and is not itself circular. However, the paper's central output is not extracted from measured rapidity widths: σ is defined as L/6, with L computed from an assumed energy-loss parameter k (taken in 0.5–0.9) and the kinematic formulas Eqs. (1)–(8). Inverting Eq. (10) then returns c_s^2 as a function of that imposed σ. The paper's own Fig. 3 demonstrates that σ values larger than L/6 (0.2L to 0.8L) give c_s^2 > 1/3 for most energies, and these scenarios are dismissed as lacking physical justification. Thus the advertised 0 ≤ c_s^2 ≤ 1/3 range is a consequence of the chosen normalization, not an empirical finding. The appeal to previous works [39,40] for L = 6σ is self-citational and is not an independent verification. Acknowledging caveats about non-Gaussian or multi-source rapidity distributions does not remove the definitional circularity in the main claim; it confirms that the numerical range is an artifact of the single-Gaussian 6σ convention.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The ledger shows the central range result depends on the arbitrary sigma = L/6 normalization, the assumed energy-loss interval, and the Landau model, with no new data or independent constraint.

free parameters (2)
  • energy loss rate k = 0.5, 0.6, 0.7, 0.8, 0.9 (scanned)
    Section 3: 'it is advisable to consider as many values as possible within the range 0.5 < k < 1.' The value of L, and therefore sigma via sigma = L/6, depends directly on k.
  • Gaussian width-to-rapidity-shift ratio n in sigma = L/n = 6
    Eq. (9): sigma is approximately L/6. Chosen from the 3-sigma rule applied to the assumed Gaussian; not derived from data. Fig. 3 varies this choice implicitly via sigma = 0.2-0.8 L.
assumptions (4)
  • domain assumption The Landau hydrodynamic model gives a Gaussian rapidity distribution and the relation sigma = sqrt(8/3 c_s^2 / (1 - c_s^4) ln(sqrt(s_NN) / 2 m_N)).
    Section 2, Eqs. (10)-(12), citing refs [11-21]. This is the backbone of the extraction.
  • ad hoc to paper The total rapidity shift L equals the 6-sigma span of the produced-hadron Gaussian distribution.
    Section 3, Eq. (9): 'If one considers a range of 6 sigma as representing the total rapidity shift L'. This links leading-nucleon kinematics to the width of produced particles without direct evidence.
  • domain assumption Leading nucleons lose a fraction k of energy with 0.5 < k < 1.
    Section 3, based on refs [23-26] from 1984-2001. No measurement is reported in this paper.
  • domain assumption The conformal equation of state with constant c_s^2 underlies Eq. (10).
    Eq. (10) is the conformal Landau result; the paper does not use the non-conformal generalization from ref [22] in the main calculation.

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Cite this review

Pith. "Pith review of On the Square Speed of Sound in High-Energy Collisions: Range of Values and How to Understand It." pith.science (2026). https://pith.science/paper/5UPVNCPM

@misc{pith2026241201467,
  author       = {Pith},
  title        = {Pith review of: On the Square Speed of Sound in High-Energy Collisions: Range of Values and How to Understand It},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5UPVNCPM}},
  note         = {Machine review of arXiv:2412.01467}
}
read the original abstract

After reviewing the sound speeds in various forms and conditions of matter, we investigate the sound speed of hadronic matter that has decoupled from the hot and dense system formed during high-energy collisions. We comprehensively consider factors such as energy loss of the incident beam, rapidity shift of leading nucleons, and the Landau hydrodynamic model for hadron production. The sound speed is related to the width or standard deviation of the Gaussian rapidity distribution of hadrons. The extracted square speed of sound lies within a range from 0 to 1/3 in most cases. For scenarios exceeding this limit, we also provide an explanation.

Figures

Figures reproduced from arXiv: 2412.01467 by the authors.

Figure 2
Figure 2. Dependence of 𝑐𝑐𝑠𝑠 2 on √𝑠𝑠𝑁𝑁𝑁𝑁 at 𝜎𝜎 = 𝐿𝐿⁄6, in which 𝑘𝑘 = 0.5, 0.6, 0.7, 0.8, and 0.9 which corresponds to various curves with different colors marked in the panel. The dependence of 𝑐𝑐𝑠𝑠 2 on √𝑠𝑠𝑁𝑁𝑁𝑁 is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

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Works this paper leans on

39 extracted references · 39 canonical work pages

  1. [1]

    The speed of sound and specific heat in the QCD plasma: hydrodynamics, fluctuations and conformal symmetry,

    R. V . Gavai, S. Gupta, and S. Mukherjee, “The speed of sound and specific heat in the QCD plasma: hydrodynamics, fluctuations and conformal symmetry,” Physical Review D , vol. 71, article 074013, 2005

    work page 2005

  2. [2]

    QCD equations of state and speed of sound in neutron stars,

    T. Kojo, “QCD equations of state and speed of sound in neutron stars,” AAPPS Bulletin, vol. 31, p. 11, 2021

    work page 2021

  3. [3]

    Inference of the sound speed and related properties of neutron stars,

    L. Brandes, W. Weise, and N. Kaiser, “Inference of the sound speed and related properties of neutron stars,” Physical Review D, vol. 107, article 014011, 2023

    work page 2023

  4. [4]

    Constraints on the dark matter sound speed from galactic scales: the cases of the modified and extended Chaplygin gas,

    P. P. Avelino and V . M. C. Ferreira, “Constraints on the dark matter sound speed from galactic scales: the cases of the modified and extended Chaplygin gas,” Physical Review D, vol. 91, article 083508, 2015

    work page 2015

  5. [5]

    Dark energy with non- adiabatic sound speed: initial conditions and detectability,

    G. Ballesteros and J. Lesgourgues, “Dark energy with non- adiabatic sound speed: initial conditions and detectability,” Journal of Cosmology and Astroparticle Physics, vol. 2010, no. 10, p. 014, 2010

    work page 2010

  6. [6]

    Constraints on the s ound speed of dynamical dark energy,

    J.-Q. Xia, Y.-F. Cai, T.-T. Qiu, G.-B. Zhao, and X. M. Zhang , “Constraints on the s ound speed of dynamical dark energy,” International Journal of Modern Physics D, vol. 17, pp. 1229–1243, 2008

    work page 2008

  7. [7]

    Constraints on the sound speed of dark energy,

    S. Hannestad, “Constraints on the sound speed of dark energy,” Physical Review D, vol. 71, article 103519, 2005

    work page 2005

  8. [8]

    Speed of Sound in Magnetized Nuclear Matter

    R. Mondal, N. Chaudhuri, P. Roy, and S. Sarkar, “Speed of s ound in m agnetized nuclear matter,” 2023, https://arxiv.org/abs/2312.03310

    work page Pith review arXiv 2023

Show all 39 references
  1. [9]

    Speed of sound in string gas cosmology,

    N. Lashkari and R. H. Brandenberger, “Speed of sound in string gas cosmology,” Journal of High Energy Physics, vol. 2008, no. 09, p. 082, 2008

    2008

  2. [10]

    Heavy fields, reduced speeds of sound and decoupling during inflation,

    A. Achúcarro, V . Atal, S. Céspedes, J.-O. Gong, G. A. Palma, and S. P. Patil, “Heavy fields, reduced speeds of sound and decoupling during inflation,” Physical Review D , vol. 86, article 121301(R), 2012

    2012

  3. [12]

    Some questions of the relativistic hydrodynamics,

    I. M. Khalatnikov , “Some questions of the relativistic hydrodynamics,” Journal of Experimental and Theoretical Physics, vol. 27, pp. 529–541, 1954

    1954

  4. [13]

    Hydrodynamic theory of multiple production of particles,

    S. Z. Belen ’kji and L. D. Landau, “ Hydrodynamic theory of multiple production of particles,” Il Nuovo Cimento, vol. 3, pp. 15–31, 1956

    1956

  5. [14]

    Bulk dynamics in heavy ion collisions,

    P. A. Steinberg, “Bulk dynamics in heavy ion collisions,” Nuclear Physics A, vol. 752, pp. 423–432, 2005

    2005

  6. [15]

    Unified descriptions of Hwa-Bjorken and Landau relativistic hydrodynamics and the pseudorapidity distributions in high energy heavy ion collisions,

    Z. J. Jiang, H. P. Deng, Y . Zhang, and H. L. Zhang, “Unified descriptions of Hwa-Bjorken and Landau relativistic hydrodynamics and the pseudorapidity distributions in high energy heavy ion collisions,” Nuclear Physics Review, vol. 32, pp. 398–404, 2015

    2015

  7. [16]

    Landau hydrodynamics reexamined,

    C.-Y . Wong, “Landau hydrodynamics reexamined,” Physical Review C , vol. 78, a rticle 054902, 2008

    2008

  8. [17]

    Multiparticle production in high energy particle collisions,

    E. V . Shuryak, “Multiparticle production in high energy particle collisions,” Yadernaya Fizika, vol. 16, pp. 395–405, 1972

    1972

  9. [18]

    Multiple production of hadrons and predictions of the Landau theory,

    O. V . Zhirov and E. V . Shuryak, “Multiple production of hadrons and predictions of the Landau theory,” Yadernaya Fizika, vol. 21, pp. 861–867, 1975

    1975

  10. [19]

    Rapidity and angular distributions of charged secondaries according to the hydrodynamical model of particle production,

    P. Carruthers and M. Duong -Van, “Rapidity and angular distributions of charged secondaries according to the hydrodynamical model of particle production,” Physical Review D, vol. 8, pp. 859–874, 1973

    1973

  11. [20]

    Heretical models of particle production,

    P. Carruthers, “Heretical models of particle production,” Annals of the New York Academy of Sciences, vol. 229, pp. 91–123, 1974

    1974

  12. [21]

    Onset of deconfinement in nucleus - nucleus collisions: review for pedestrians and experts,

    M. Gazdzickia, M. Gorensteinc, and P. Seybothe, “Onset of deconfinement in nucleus - nucleus collisions: review for pedestrians and experts,” Acta Physica Polonica B, vol. 42, pp. 307–352, 2011

    2011

  13. [22]

    Viscosity, non- conformal equation of state and sound velocity in Landau hydrodynamics,

    D. Biswas, K. Deka, A. Jaiswal, and S. Roy, “Viscosity, non- conformal equation of state and sound velocity in Landau hydrodynamics,” Physical Review C , vol. 102, article 014912, 2020

    2020

  14. [23]

    Multiplicity distributions of produced particles and energy loss in proton-nucleus collisions at 200 GeV/ c,

    B. Liu and Y . C. Wang, “Multiplicity distributions of produced particles and energy loss in proton-nucleus collisions at 200 GeV/ c,” High Energy Physics and Nuclear Physics (successor Chinese Physics C), vol. 11, pp. 231–237, 1987

    1987

  15. [24]

    Nuclear stopping power for ultrarelativistic protons,

    J. Hüfner and A. Klar, “Nuclear stopping power for ultrarelativistic protons,” Phys ics Letters B, vol. 145, pp. 167–170, 1984

    1984

  16. [25]

    Nuclear stopping power at high energies,

    S. Da té, M. Gyulassy, and H. Sumiyoshi , “Nuclear stopping power at high energies,” Physical Review D, vol. 32, pp. 619–636 (1985)

    1985

  17. [26]

    Transverse-energy distribution in proton–nucleus collisions at high energy,

    F.-H. Liu, “ Transverse-energy distribution in proton–nucleus collisions at high energy,” Canadian Journal of Physics, vol. 79, pp. 739–748, 2001

    2001

  18. [27]

    Baryonic response of dense holographic QCD,

    K.-Y . Kim and I. Zahed, “Baryonic response of dense holographic QCD,” Journal of High Energy Physics, vol. 2008, no. 12, p. 075, 2008

    2008

  19. [28]

    Sound w aves in (2+1) dimensional arXiv:2412.01467v3 [hep-ph] 12 holographic magnetic fluids,

    E. I. Buchbinder, A. Buchel, and S. E. Vázquez, “Sound w aves in (2+1) dimensional arXiv:2412.01467v3 [hep-ph] 12 holographic magnetic fluids,” Journal of High Energy Physics, vol. 2008, no. 12, p. 090, 2008

    2008 arXiv

  20. [29]

    The equation of state in (2+1)-flavor QCD,

    A. Bazavov, T. Bhattacharya, C. DeTar et al., “The equation of state in (2+1)-flavor QCD,” Physical Review D, vol. 90, article 094503, 2014

    2014

  21. [30]

    Exploring the properties of the phases of QCD matter – research opportunities and priorities for the next decade,

    U. Heinz, P. Sorensen, A. Deshpande et al., “Exploring the properties of the phases of QCD matter – research opportunities and priorities for the next decade,” 2015, https://arxiv.org/abs/1501.06477

    2015 arXiv

  22. [31]

    Jet propagation and Mach- cone formation in (3+1) -dimensional ideal hydrodynamics,

    B. Betz, “Jet propagation and Mach- cone formation in (3+1) -dimensional ideal hydrodynamics,” 2009, https://arxiv.org/abs/ 0910.4114, Ph.D. Thesis, University Frankfurt, Germany, 2009

    2009 arXiv

  23. [32]

    The speed of sound in hadronic matter,

    P. Castorina, J. Cleymans, D. E. Miller, and H. Satz, “The speed of sound in hadronic matter,” The European Physical Journal C, vol. 66, pp. 207–213, 2010

    2010

  24. [33]

    Equation of state dependence of Mach cone like structures in Au+Au collisions,

    V . Roy and A. K. Chaudhuri, “Equation of state dependence of Mach cone like structures in Au+Au collisions,” Journal of Physics G, vol. 37, article 035105, 2010

    2010

  25. [34]

    A bound on the speed of sound from holography,

    A. Cherman and T. D. Cohen, “A bound on the speed of sound from holography,” Physical Review D, vol. 80, article 066003, 2009

    2009

  26. [35]

    Holography and the speed of sound at high temperatures,

    P. M. Hohler and M. A. Stephanov, “Holography and the speed of sound at high temperatures,” Physical Review D, vol. 80, article 066002, 2009

    2009

  27. [36]

    The second sound of SU(2),

    C. P. Herzog and S. S. Pufu, “The second sound of SU(2),” Journal of High Energy Physics, vol. 2009, no. 04, p. 126, 2009

    2009

  28. [37]

    QGP susceptibilities from PNJL model,

    S. K. Ghosh, T. K. Mukherjee, M. G. Mustafa, and R. Ray, “QGP susceptibilities from PNJL model,” Indian Journal of Physics, vol. 85, pp. 87–91, 2011

    2011

  29. [38]

    Deconfinement and gluon plasma dynamics in improved holographic QCD,

    U. Gürsoy, E. Kiritsis, L. Mazzanti, and F. Nitti, “Deconfinement and gluon plasma dynamics in improved holographic QCD,” Physical Review Letters, vol. 101, article 181601, 2008

    2008

  30. [39]

    On pseudorapidity distribution and speed of sound in high energy heavy ion collisions based on a new revised Landau hydrodynamic model,

    L. -N. Gao and F.- H. Liu, “On pseudorapidity distribution and speed of sound in high energy heavy ion collisions based on a new revised Landau hydrodynamic model,” Advances in High Energy Physics, vol. 2015, Article ID 184713, 23 pages, 2015

    2015

  31. [40]

    On distributions of emission sources and speed of sound in proton-proton (proton- antiproton) collisions,

    L.-N. Gao and F.- H. Liu, “ On distributions of emission sources and speed of sound in proton-proton (proton- antiproton) collisions,” Advances in High Energy Physics, vol. 2015, Article ID 641906, 10 pages, 2015

    2015

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Reviewed August 12, 2026 · model on record in the stance chip above.