Pith. sign in

REVIEW 3 major objections 5 minor 42 references

Systematic analysis of the pp collisions at LHC energies with Tsallis function

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper argues that a single thermodynamically consistent Tsallis function fits the measured transverse momentum spectra of hadrons, strange hadrons, and light nuclei in pp collisions at LHC energies, and that the extracted effective…

desk verdict A broad Tsallis-fit compilation of LHC pp spectra that reconfirms known mass-ordering trends, but the heaviest-nucleus fits anchoring the headline trend have zero or negative degrees of freedom. read the letter →

arxiv 2411.08669 v1 pith:F34QFNGY submitted 2024-11-13 hep-ph

Murad Badshah , Muhammad Waqas , Ahmed M. Khubrani , Muhammad Ajaz This is my paper · ORCID
classification hep-ph
keywords Tsallisfunctiontransversemomentumspectrappcollisionseffectivetemperaturenon-extensivityparameterfreeze-outidentifiedhadronslightnuclei
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 argues that a single thermodynamically consistent Tsallis function, Eq. (4), describes the transverse momentum spectra of identified hadrons, strange hadrons, and light nuclei produced in proton-proton collisions at LHC energies from 0.9 to 13 TeV. From those fits it extracts an effective temperature $T$ and a non-extensivity parameter $q$, and claims that $T$ rises monotonically with particle mass and with collision energy, while $q$ falls with mass. The interpretation offered is that heavier particles, having larger $T$ and $q$ closer to 1, decouple from the system earlier and reach equilibrium faster than lighter ones. If the trend is correct, a single two-parameter form encodes the freeze-out ordering of all produced species across four collision energies.

What carries the argument

The central object is the thermodynamically consistent Tsallis distribution of Eq. (4), $2\pi C p_T m_T [1+(q-1)m_T/T]^{-q/(q-1)}$, with $C=gV/(2\pi)^3$, transverse mass $m_T=\sqrt{p_T^2+m_0^2}$, effective temperature $T$, and non-extensivity parameter $q$. It extends the Boltzmann-Gibbs exponential, recovered at $q=1$, to the power-law tail at high $p_T$, which lets one fit spectra from soft pions to heavy-nucleus data with one expression. The extracted $T$ and $q$ are the carriers of the paper's freeze-out argument.

What would settle it

Re-fit the helium-3 and tritium spectra with the same Tsallis function using data sets with more points than fitted parameters, or with $T$ fixed by an independent measurement; if the best-fit $T$ falls well below 250 MeV, the claimed monotonic mass ordering of effective temperature loses its upper endpoint.

Watch

Extended reading notes

Core claim

Using the thermodynamically consistent form $d^2N/(N_{ev}\,dp_T\,dy)=2\pi C p_T m_T [1+(q-1)m_T/T]^{-q/(q-1)}$, the authors fit the published LHC data for pions, kaons, protons, $K_s^0$, $\Lambda$, $\Xi^-$, deuterons, tritons, and helium-3, together with the corresponding antiparticles, at $\sqrt{s}=0.9$, 2.76, 7, and 13 TeV. The fitted effective temperature $T$ increases from about 55 MeV for pions to roughly 250 MeV for tritons and helium-3, and for each species $T$ grows with collision energy; $q$ decreases from about 1.19 for pions to values near 1.00--1.05 for the heaviest nuclei. The authors take these systematics as evidence of an early, close-to-equilibrium freeze-out of heavier particles, and they also report that $K^+$ has a higher effective temperature than $K^-$ and that particles and antiparticles can freeze out separately. The normalization parameter $N_0$ increases with collision energy.

Load-bearing premise

The monotonic rise of $T$ with mass is anchored by fits of helium-3 and tritium spectra that have fewer data points than fitted parameters, so the about-250 MeV temperatures at the heavy end of the trend are not statistically constrained by those data.

Editorial extensions

If this is right

  • The thermodynamically consistent Tsallis function can serve as a single baseline parametrization for $p_T$ spectra of light and heavy species in $pp$ collisions, removing the need to switch between exponential and power-law forms.
  • The monotonic rise of $T$ with mass implies that heavier particles decouple earlier in the evolution, so measurements of light nuclei and strange baryons probe earlier stages of the collision than pion spectra.
  • The reported $K^+$/$K^-$ split in effective temperature implies that kaon species freeze out at different times, so combined fits should not force equal freeze-out parameters for charge-conjugate pairs.
  • Because $N_0$ grows with collision energy while $q$ shows no reported energy dependence, the increase in multiplicity with energy is carried mainly by the normalization rather than by the shape of the non-extensive distribution.

Reading between the lines

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

  • The upper endpoint of the $T$-versus-mass ordering is set by helium-3 and tritium fits whose $\chi^2$/NDF values are quoted with a dash, meaning fewer data points than fitted parameters; the roughly 250 MeV temperatures at that endpoint are therefore not statistically pinned by the data, and the smoothness of the claimed trend depends on those points.
  • The same framework, applied to proton-nucleus or nucleus-nucleus spectra, would test whether the mass-ordering pattern persists in larger systems or is specific to small $pp$ collisions.
  • One could directly test the freeze-out interpretation by comparing the extracted effective temperature for a species to the kinetic freeze-out temperature obtained from femtoscopic correlation measurements; the gap would quantify the flow contribution.
  • Because $q$ for helium-3 and tritium is nearly 1, those fits essentially sit at the Boltzmann-Gibbs limit, suggesting that the mass dependence of $q$ may be saturating at the heavy end, a point the paper does not discuss.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper fits the thermodynamically consistent Tsallis function (Eq. 4) to transverse momentum spectra of identified hadrons (π±, K±, p/p̄), strange hadrons (K_s^0, Λ, Ξ−), and light nuclei (d, d̄, t, t̄, 3He, 3Hē) in pp collisions at 0.9, 2.76, 7, and 13 TeV using CMS and ALICE data. The fits are used to extract the effective temperature T, the non-extensivity parameter q, and a normalization/multiplicity parameter N0. The central conclusions are that T increases monotonically with particle mass and collision energy, q decreases with particle mass, heavier particles decouple earlier and approach equilibrium faster, and N0 increases with collision energy. The paper reports that the model fits the data very well, and it presents the extracted parameters in Table 1 and the trends in Figs. 2–5.

Significance. The paper assembles a broad set of identified, strange, and nuclear species over four LHC energies and shows that a single compact functional form can describe most of the mid-pT spectra. If the extracted parameter trends were statistically robust, the mass ordering of T and the anti-correlation between T and q would provide a useful systematic benchmark for thermal-model studies of small collision systems, extending previous Tsallis analyses to light nuclei. The data/fit ratio panels and the tabulated parameters are helpful for reproducibility, although no fit code or machine-readable data tables are included. However, the highest-mass points that anchor the mass-ordering claim (3He, t, t̄) are not statistically constrained, and the N0-versus-energy claim is internally inconsistent with the paper's own table; these issues must be resolved before the central conclusions can be accepted.

major comments (3)
  1. [Table 1, 7 TeV rows] The entries for 3He, t, and t̄ report χ2/NDF as '0.3471/-', '1.1596e-04/-', and '4.3612e-04/-'. A dash in the denominator leaves the number of degrees of freedom unspecified, and in the standard reading of χ2/NDF it is zero or negative; for a three-parameter fit (T, q, N0) this implies that the data contain fewer independent points than fitted parameters. The extracted values T≈250 MeV and q≈1.003–1.004 for these species are therefore not statistically constrained by the measured pT spectra. These three species are the heaviest points in Figs. 2 and 3, so the claimed monotonic growth of T and decrease of q with mass rest precisely on statistically unsupported entries. The same concern applies in milder form to d and d̄ at 0.9 TeV, which have only one degree of freedom. The authors should report the actual number of data points for every fit and either remove the unconstrained high-mass points from the trend plots or refit them with a reduced number of free parameters (e.g., fixing q) so that the degrees of freedom are positive.
  2. [Abstract and Section 4, N0 claim] The abstract and conclusion state that the multiplicity parameter N0 increases with collision energy, but Table 1 shows non-monotonic behavior: for π+ N0 is 46.95 at 7 TeV and 41.85 at 13 TeV; the same drop between 7 and 13 TeV is visible for K+ (6.13 to 5.55) and p (2.71 to 2.45). If N0 is claimed as a function of collision energy, the paper must either restrict the statement to 0.9–7 TeV, explain the 13 TeV values quantitatively, or redefine N0 so that the claim matches the table. As written, a central abstract claim is contradicted by the paper's own fitted values.
  3. [Section 3 and Table 1, fit quality] The statement repeated in the abstract and Section 3 that the Tsallis model 'fits the experimental data very well' is not supported by all entries in Table 1. For example, π+ at 7 TeV has χ2/NDF = 56.1243/20 ≈ 2.8, and several other species have χ2/NDF above 2. With roughly 20 degrees of freedom, a χ2/NDF of 2.8 is a relatively poor fit by conventional criteria. The paper should report fit quality more quantitatively (p-values or χ2 per data point) and temper the blanket 'very well' wording where the fits are marginal.
minor comments (5)
  1. [Conclusion and Table 1] The abstract and conclusion list Λ̄ and Ξ+ among the analyzed strange hadrons, but Table 1 contains only K_s^0, Λ, and Ξ−. Please align the species list with the actual tabulated fits and state explicitly where no data are available.
  2. [Section 2, Eq. (4)] The text introduces C = gV/(2π)^3 as a normalization constant in Eqs. (2)–(3), but Eq. (4) is used with N0 as an additional fitted normalization, and the kinetic freezeout volume V promised in the Introduction is never extracted. The relation between C and N0 should be clarified.
  3. [Section 3, Figs. 2–3] The figure captions and text refer to several species (e.g., Λ̄, Ξ+) that are not shown in the figures, and the legends are difficult to read after scaling. Please ensure that every symbol in each legend is defined and that the plotted species match Table 1.
  4. [Section 3, K± asymmetry] The statement that K+ has a larger T than K− and the interpretation via coalescence is speculative and is not tested against any coalescence model; it should be presented as a qualitative suggestion or supported by a dedicated calculation.
  5. [Throughout] There are numerous typographical and grammatical errors (e.g., 'differnt', 'distribtions', 'Moreovere', 'subordination of the effective temperature'), and the notation for 3He and anti-3He is rendered inconsistently. A careful language and notation edit is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the trends are summaries of independently fitted parameters, not predictions forced by construction.

full rationale

The paper's analysis is a direct fit of the thermodynamically consistent Tsallis form, Eq. (4), to published pT spectra from CMS and ALICE. The words 'extracted' and 'obtained from the Tsallis model' describe T, q, and N0 as fit outputs, and the mass and energy trends are read off Table 1 and Figs. 2-5 rather than used as constraints in the fit. No equation defines T or q in terms of the claimed monotonicity, and no fitted parameter is relabeled as a prediction of independent data. The two self-citations ([18], [42]) occur in a side comment about separate freezeout of particles and antiparticles and are not load-bearing: the current data in Table 1 themselves show K+ T above K- T. Equation (4) is attributed to the cited literature [37]; the paper does not establish that this citation shares authors, and even if it did, adopting a published functional form is an ansatz, not a circular derivation. The zero- or negative-NDF entries for 3He and t at 7 TeV (e.g., 0.3471/- and 1.1596e-04/-) are a legitimate statistical robustness concern because the high-mass end of the T-mass trend rests on very few data points, but that is a weakness of evidence rather than a circularity; the paper does not claim these points were predicted from the lighter species. Accordingly, no circular step is exhibited.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The analysis introduces no new theoretical entities or conserved quantities. It relies entirely on the assumed Tsallis functional form, the published experimental data, and the standard interpretations of T and q. The only free inputs are the three fit parameters per spectrum and the choice of fit ranges and scaling factors, which are not documented in full detail.

free parameters (3)
  • Effective temperature T per species per energy = 55.68 to 250.71 MeV across Table 1
    Fitted from each pT spectrum; the paper's main trend (T increases with mass and energy) is a direct statement about these fitted values.
  • Non-extensivity parameter q per species per energy = 1.003 to 1.191 in Table 1
    Fitted from the power-law tail of each spectrum; the conclusion that q decreases with mass restates these fitted values.
  • Multiplicity/normalization parameter N0 per species per energy = 0.0000019 to 46.95 in Table 1
    Normalization constant of each fit; used for the reported N0 versus collision energy trend.
assumptions (4)
  • domain assumption The thermodynamically consistent Tsallis form (Eq. 4) is the correct underlying distribution for all pT regimes of the analyzed spectra
    The model is imposed before fitting, and the paper does not test alternative Tsallis variants (e.g., Refs [30,31]) or quantify the model uncertainty.
  • domain assumption The published CMS and ALICE spectra are accurate and mutually consistent across detectors and energies
    The analysis uses experimental data from Refs [32-35] without independent cross-checks of those measurements.
  • domain assumption The extracted T is an effective temperature that includes flow, with T = T0 + m0 <beta_T>^2 as in Ref [13], but the flow velocity is not independently constrained
    The paper invokes this relation in the Introduction and then interprets T as a freezeout indicator without separating thermal and flow contributions.
  • domain assumption The interpretation that smaller q means closer to equilibrium and faster thermalization is taken from the non-extensive statistics literature cited in Refs [27-31]
    The paper applies this standard interpretation to the fitted q values without additional justification.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Systematic analysis of the pp collisions at LHC energies with Tsallis function." pith.science (2026). https://pith.science/paper/F34QFNGY

@misc{pith2026241108669,
  author       = {Pith},
  title        = {Pith review of: Systematic analysis of the pp collisions at LHC energies with Tsallis function},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F34QFNGY}},
  note         = {Machine review of arXiv:2411.08669}
}
read the original abstract

This work focuses on the study of identified hadrons and strange hadrons, recorded by CMS, and light nuclei and their anti-nuclei, recorded by ALICE, at 0.9 TeV, 2.76 TeV, 7 TeV and 13 TeV centre of mass energies in pp collision at mid rapidities. The transverse momentum distributions of these particles are analyzed using the Tsallis model, which fits the experimental data very well. Several important parameters for studying the characteristics of the medium produced during such collisions are extracted. The effective temperature (T) increases monotonically with increasing particle mass and also with increasing collision energy. The non-extensivity parameter (q) decreases with the mass of the particle. For heavier particles, greater T and smaller q mean that they decouple early from the system and attain equilibrium quickly compared to lighter ones. Furthermore, with an increase in collision energy, the multiplicity parameter N0 increases.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 37 canonical work pages

  1. [1]

    Bass S. A. et al., Journal of Physics G: Nuclear and Particle Physics, 25 (1999) R1

    work page 1999

  2. [2]

    and Satz H., Physics Letters B, 178 (1986) 416

    Matsui T. and Satz H., Physics Letters B, 178 (1986) 416. 10

    work page 1986

  3. [3]

    and Hwa R

    Bialas A. and Hwa R. C., Physics Letters B, 253 (1991) 436

    work page 1991

  4. [4]

    and Stachel J., Nature, 448 (2007) 302

    Braun-Munzinger P. and Stachel J., Nature, 448 (2007) 302

    work page 2007

  5. [5]

    Liu F. M. et al., Physical Review C, 89 (2014) 034906

    work page 2014

  6. [6]

    et al., The European Physical Journal Plus, 137 (2022) 592

    Ajaz M. et al., The European Physical Journal Plus, 137 (2022) 592

    work page 2022

  7. [7]

    Extraction of freezeout parameters and their dependence on collision energy and collision cross-section

    Waqas M. et al., arXiv preprint arXiv:2112.00975 (2021)

    work page Pith review arXiv 2021

  8. [8]

    et al., arXiv preprint arXiv:1011.1940 (2010)

    Alver B. et al., arXiv preprint arXiv:1011.1940 (2010)

    arXiv 2010

Show all 42 references
  1. [9]

    et al., Scientific Reports, 12 (2022) 1

    Ajaz M. et al., Scientific Reports, 12 (2022) 1

    2022

  2. [10]

    et al., Entropy, 23 (2021) 1363

    Waqas M. et al., Entropy, 23 (2021) 1363

    2021

  3. [11]

    et al., Journal of Physics G: Nuclear and Particle Physics, 48 (2021) 075108

    Waqas M. et al., Journal of Physics G: Nuclear and Particle Physics, 48 (2021) 075108

    2021

  4. [12]

    D., Physical review D, 27 (1983) 140

    Bjorken J. D., Physical review D, 27 (1983) 140

    1983

  5. [13]

    Physical Review C, 106 (2022) 014910

    Cao et al,. Physical Review C, 106 (2022) 014910

    2022

  6. [14]

    et al., Physical Review C, 92 (2015) 024917

    Chatterjee S. et al., Physical Review C, 92 (2015) 024917

    2015

  7. [15]

    et al., Chinese Journal of Physics, 77 (2022) 1713

    Waqas M. et al., Chinese Journal of Physics, 77 (2022) 1713

    2022

  8. [16]

    et al., Nuclear Physics A, 931 (2014) 1114

    Kumar L. et al., Nuclear Physics A, 931 (2014) 1114

    2014

  9. [17]

    et al., Universe, 8 (2022) 138

    Waqas M. et al., Universe, 8 (2022) 138

    2022

  10. [18]

    et al., Scientific Reports, 11 (2021) 1

    Waqas M. et al., Scientific Reports, 11 (2021) 1

    2021

  11. [19]

    et al., Nature Physics, 13 (2017) 535

    Adam J. et al., Nature Physics, 13 (2017) 535

    2017

  12. [20]

    and Nayak T

    Sahoo R. and Nayak T. K., arXiv preprint arXiv:2201.00202 (2022)

    2022 arXiv

  13. [21]

    Sahoo R., arXiv preprint arXiv:1908.10566 (2019)

    2019 arXiv

  14. [22]

    Collaboration A. L. I. C. E., Eur. Phys. J. C, 80 (2020) 693

    2020

  15. [23]

    et al., Physical review letters, 116 (2016) 172302

    Khachatryan V. et al., Physical review letters, 116 (2016) 172302

    2016

  16. [24]

    N., Physics Letters B, 579 (2004), 299

    Wang X. N., Physics Letters B, 579 (2004), 299

    2004

  17. [25]

    and Wong C

    Gatoff G. and Wong C. Y., Physical Review D, 46 (1992) 997

    1992

  18. [26]

    Fries, et al., Annu

    R. Fries, et al., Annu. Rev. Nucl. Part. Sci., 58 (2008) 177

    2008

  19. [27]

    Wong C. Y. and Wilk G., arXiv preprint arXiv:1210.3661 (2012)

    2012 arXiv

  20. [28]

    et al., Physical Review C, 79 (2009) 051901

    Tang Z. et al., Physical Review C, 79 (2009) 051901

    2009

  21. [29]

    Zheng and Lilin Zhu, Advances in High Energy Physics, 2016 (2016) 9632126

    H. Zheng and Lilin Zhu, Advances in High Energy Physics, 2016 (2016) 9632126

    2016

  22. [30]

    Cleymans et al., J

    J. Cleymans et al., J. Phys.: Conf. Ser., 779 (2017) 012079

    2017

  23. [31]

    Cleymans and D

    J. Cleymans and D. Worku, J. Phys. G 39 (2012) 025006

    2012

  24. [32]

    et al., The European Physical Journal C, 72 (2012) 1-37

    Chatrchyan S. et al., The European Physical Journal C, 72 (2012) 1-37

    2012

  25. [33]

    Sirunyan A. M. et al., Physical Review D, 96 (2017) 112003. 11

    2017

  26. [34]

    CMS collaboration, arXiv preprint arXiv:1102.4282 (2011)

    2011 arXiv

  27. [35]

    ALICE Collaboration, arXiv preprint arXiv:1709.08522 (2017)

    2017 arXiv

  28. [36]

    et al., Journal of Physics G: Nuclear and Particle Physics, 47 (2020) 105002

    Bíró G. et al., Journal of Physics G: Nuclear and Particle Physics, 47 (2020) 105002

    2020

  29. [37]

    K et al., International Journal of Modern Physics A, 36 (2021) 2150149

    Olimov K. K et al., International Journal of Modern Physics A, 36 (2021) 2150149

    2021

  30. [38]

    U., and Uddin S., Journal of Experimental and Theoretical Physics, 124 (2017) 429

    Bashir I. U., and Uddin S., Journal of Experimental and Theoretical Physics, 124 (2017) 429

    2017

  31. [39]

    Lao H. L. et al., The European Physical Journal A, 52 (2016) 1

    2016

  32. [40]

    et al., Advances in High Energy Physics, 2016 (2016)

    Thakur D. et al., Advances in High Energy Physics, 2016 (2016)

    2016

  33. [41]

    and Mohanty B., Physical Review C, 90 (2014) 034908

    Chatterjee S. and Mohanty B., Physical Review C, 90 (2014) 034908

    2014

  34. [42]

    et al., The European Physical Journal Plus, 136 (2021) 1

    Waqas M. et al., The European Physical Journal Plus, 136 (2021) 1

    2021

Pith tools

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