Exploring Event-by-Event $\it{p}_{\rm T}$ Fluctuations in pp Collisions at $\sqrt{s} = 13$ TeV: An Insight from ALICE

Bushra Ali (for the ALICE Collaboration)

REVIEW 4 major objections 6 minor 21 references

Exploring Event-by-Event $\it{p}_{\rm T}$ Fluctuations in pp Collisions at $\sqrt{s} = 13$ TeV: An Insight from ALICE

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Event-by-event mean-transverse-momentum correlations in 13 TeV pp collisions decrease as a power of charged multiplicity, with an exponent that deviates from statistical independence and varies with the transverse-momentum window…

desk verdict New ALICE preliminary data on pT fluctuations at 13 TeV, but the claimed dynamical signal rests on an unjustified -0.5 baseline that likely breaks down for fixed pT windows. read the letter →

arxiv 2505.15161 v1 pith:H4C4BNRI submitted 2025-05-21 hep-ex nucl-ex

Bushra Ali (for the ALICE Collaboration) This is my paper · ORCID

classification hep-exnucl-ex

keywords event-by-eventfluctuationsmeantransversemomentumtwo-particlepTcorrelatormultiplicitydependencepower-lawscalingsoft-hardQCDcrossoverproton-protoncollisionsLHC

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports that event-by-event fluctuations of the mean transverse momentum in proton-proton collisions at 13 TeV shrink as the charged-particle multiplicity grows, and that the shrinkage follows a power law whose exponent differs from the pure-statistics value of -0.5. By moving the transverse-momentum acceptance upward, the correlation strength drops sharply and approaches zero, which the authors read as a crossover from soft processes (collective flow, resonance decays) to uncorrelated hard scatterings (jets, parton fragmentation). The fitted power-law index also depends on the width of the $p_{\rm T}$ window in a non-monotonic way. The paper's conclusion is that mean-$p_{\rm T}$ correlations in pp collisions are mostly driven by semi-hard and hard QCD processes, especially at high $p_{\rm T}$. This matters because pp collisions are the baseline against which heavy-ion data are judged, and non-monotonic $p_{\rm T}$ correlations across energies could be a signature of quark-gluon plasma formation.

What carries the argument

The central object is the two-particle $p_{\rm T}$ correlator $C_m$, defined for a multiplicity class $m$ as the average over events and over particle pairs of the product of each particle's deviation from the class-average mean $p_{\rm T}$, normalized as $\sqrt{C_m}/M(p_{\rm T})_m$. The argument is carried by fitting this normalized correlator to $a\cdot N_{\rm ch}^{b}$ and comparing the exponent $b$ to the statistical superposition value $-0.5$; the systematic change of $b$ and of the correlation magnitude with the width and position of the $p_{\rm T}$ window is what maps the soft-to-hard transition.

What would settle it

Recompute $\sqrt{C_m}/M(p_{\rm T})_m$ from mixed events—formed by drawing particles randomly from different events in the same multiplicity class so that single-particle spectra are preserved but inter-particle correlations are destroyed—and fit the same power law; if the measured index $b$ equals the mixed-event index (expected $-0.5$), then the dynamical deviations claimed in the paper are absent.

Watch

Extended reading notes

Core claim

The paper's central claim is that the normalized two-particle correlator $\sqrt{C_m}/M(p_{\rm T})_m$—the event-by-event fluctuation of the mean transverse momentum expressed in units of the average $p_{\rm T}$—decreases with charged-particle multiplicity $N_{\rm ch}$ in 13 TeV pp collisions, and that this decrease is described by a power law $a\cdot N_{\rm ch}^{b}$ over the range $10<N_{\rm ch}<70$. The fitted index $b$ deviates from the expectation of $-0.5$ that would hold if particles were statistically independent, and the deviation depends on the position and width of the $p_{\rm T}$ acceptance window: widening the window from 0.15–1.0 up to 0.15–6.0 GeV/$c$ raises the correlation strength, while shifting a fixed-width window from soft to hard $p_{\rm T}$ suppresses it toward zero. The paper interprets this pattern as a crossover between soft and hard sources, and notes that a pQCD-based Monte Carlo model captures the high-$p_{\rm T}$ behavior better than a core-corona model. The conclusion asserts that mean-$p_{\rm T}$ correlations in pp collisions are mainly driven by semi-hard and hard QCD processes, particularly at high $p_{\rm T}$.

Load-bearing premise

The argument rests on the assumption that the chosen power-law form $aN_{\rm ch}^b$ and the fit range $10<N_{\rm ch}<70$ describe the data, and that $p_{\rm T}$ cleanly separates soft from hard particle production; if either fails, the reported exponent and its physical interpretation do not follow.

Editorial extensions

If this is right

If the conclusion is right, the low-$p_{\rm T}$ window (0.15–1.0 GeV/$c$) carries most of the dynamical correlation, so future measurements comparing pp with heavy-ion collisions must match the acceptance window before interpreting differences as collective effects.
The deviation of $b$ from $-0.5$ gives a quantitative, multiplicity-dependent observable that any Monte Carlo generator must reproduce; the better agreement of the pQCD model at wide $p_{\rm T}$ windows makes hard QCD the likely driver in that regime.
High-multiplicity pp events cannot serve as a purely soft baseline; their mean-$p_{\rm T}$ correlations already contain a jet-induced component that grows with the $p_{\rm T}$ acceptance.
If $b$ indeed approaches the statistical value at very high $p_{\rm T}$, then the high-$p_{\rm T}$ window isolates approximately independent hard scatterings, providing a practical way to measure the hard component separately.

Reading between the lines

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

A sharper test of the claimed crossover would be to map $b$ as a function of the upper edge of the $p_{\rm T}$ window in fine steps; a sharp transition at some characteristic $p_{\rm T}$ would locate the momentum scale where jet contributions overcome soft ones.
The same analysis could be run with mixed events that preserve single-particle spectra but destroy inter-particle correlations; any measured deviation of $b$ from the mixed-event value would then quantify the dynamical-correlation fraction directly, which the paper does not subtract.
The model comparison would be more decisive if the power-law index $b$ were extracted from the Monte Carlo predictions in the same $10<N_{\rm ch}<70$ fit range and compared numerically, rather than only by eye.
If the soft-to-hard crossover is real, the normalized correlator for identified particles of different masses might separate decay-driven correlations from genuine flow-like correlations in the low-$p_{\rm T}$ window.

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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 thing to know: this is a conference proceedings that extends the ALICE two-particle pT correlator measurement to 13 TeV pp and to wider and shifted pT windows (up to 6 GeV/c, and fixed-width windows from 1–2 through 4–5 GeV/c). The data are new and the figures are clear. The comparison with PYTHIA8 and EPOS LHC is useful and honestly presented. For that, credit is due. It is also plainly labeled ALICE Preliminary, which is the right framing for this format.

The soft spot is load-bearing. The paper claims that in the absence of dynamical correlations the correlator should scale as Nch^{-0.5}, and that fitted indices deviating from -0.5 are therefore evidence of dynamical correlations and a soft-to-hard crossover. That baseline is only valid if the number of accepted particles in the pT window is proportional to Nch with a constant fraction, and if the single-particle pT distribution inside the window does not change shape with multiplicity. Neither is established here. In pp at 13 TeV the spectrum hardens with multiplicity, so for windows like 0.15–1.0 GeV/c the selected fraction and the pT variance inside the window will vary with Nch. A trivial superposition would then produce an apparent power index different from -0.5, and the observed b ≈ -0.41 for the lowest window and the non-monotonic pattern across windows could be a phase-space artifact rather than a dynamical signal. The PYTHIA and EPOS comparisons do not rescue this, because both models also contain multiplicity-dependent pT spectra; they are not a superposition baseline. This needs to be controlled before the crossover interpretation can stand.

Other issues are more minor. There are no systematic uncertainties, no data tables, no event-selection or track-efficiency details, and no fit-quality information – acceptable for a proceedings but it makes the numbers hard to evaluate. The abstract's phrase about "signature of QGP formation" overreaches for a single-energy pp measurement. Also, the text says the comparison to ref [1] was previously reported for pp at 13 TeV, but ref [1] is the 7 TeV measurement; the later sentence comparing 7 to 13 TeV contradicts the earlier mislabeling.

Who is this for? Heavy-ion and QCD phenomenologists who want early look at ALICE's extended pT-fluctuation data. They will get some useful qualitative pictures, not a final result. A serious referee could help by forcing the acceptance-correction analysis and full systematics. For a conference proceedings, I would accept it with caveats; for a journal, major revision is needed. My recommendation: send it to peer review, but only if the referee insists on addressing the baseline issue.

Referee Report

4 major / 6 minor

Summary. This proceedings-style paper reports an ALICE measurement of the event-by-event mean transverse momentum correlator sqrt(C_m)/M(pT)_m in pp collisions at sqrt(s)=13 TeV, studied as a function of charged-particle multiplicity and of the position/width of the pT selection window. The authors fit the multiplicity dependence with a power law a*Nch^b, quote values of b for several pT windows, interpret deviations from b=-0.5 as evidence for dynamical correlations, and compare the data with PYTHIA8 (Monash) and EPOS LHC. They conclude that the correlator is driven mainly by semi-hard and hard QCD processes, especially at high pT.

Significance. If the quantitative claims survive scrutiny, the paper would provide a useful differential extension of the earlier ALICE pp measurement, with new information on how the pT-correlation strength depends on the pT window. The comparison to PYTHIA8 and EPOS LHC is a sensible first step, and the power-law parametrization is a pragmatic way to summarize the trends. The paper is, however, built on a statistical baseline statement that is not derived and is, as written, not valid for fixed pT windows; this directly affects the central interpretation of the fitted index b. The absence of systematic uncertainties, fit-quality metrics, and experimental-selection details further prevents the reader from assessing the claimed deviations. The qualitative trends and the qualitative model comparison are valuable, but the quantitative conclusions are presently not supported.

major comments (4)

[Section 2 (after Fig. 2)] The statement 'In the absence of dynamical correlations, the correlator is expected to follow statistical scaling, yielding a power index of b=-0.5' is not generally valid for the fixed pT windows used here. For independent particles, sqrt(C_m)/M(pT)_m scales as sqrt(sigma^2(Nch)/N_acc(Nch))/mu(Nch), where sigma and mu are the single-particle pT variance and mean inside the acceptance and N_acc is the number of accepted particles. If the pT spectrum hardens with multiplicity, the accepted fraction N_acc/N_ch and the within-window ratio sigma/mu can both depend on Nch; a pure superposition can then produce a power index different from -0.5, with a window-dependent deviation. The observed b≈-0.41 in the 0.15-1.0 GeV/c window and the non-monotonic dependence of b on window width may therefore be, at least in part, acceptance and spectral-shape effects rather than genuine event-by-event dynamical correlations. Please provide a derivation of the statistical baseline including these effects, or demonstrate quantitatively that they are negligible.
[Section 2 (power-law fits)] The power-law fits are performed in the range 10<Nch<70 with the functional form a*Nch^b, but the paper gives no justification for this range or form and reports no goodness-of-fit (chi^2/ndf), number of fitted points, or systematic uncertainty on a and b. Since the central quantitative claim is the deviation of b from -0.5 and its variation with pT window, the manuscript should report the fit quality, stability with respect to the fit range, and the full uncertainty budget for b.
[Section 2 (experimental details)] The paper does not state the event-selection or track-selection criteria, trigger definitions, efficiency corrections, or the number of events used; the data points in Figures 1-4 are shown without systematic uncertainties. Without this information, the deviations of b and the quantitative agreement with PYTHIA and EPOS cannot be evaluated. At minimum, the authors should give the relevant ALICE analysis details and quote systematic uncertainties on the correlator values and on the fitted indices.
[Section 2 (Figs. 3 and 4)] The comparison with PYTHIA8 and EPOS LHC is made only by visual inspection; the text states that agreement 'may be noticed to be rather better' at higher pT without any quantitative metric. Because both models themselves contain multiplicity-dependent pT spectra and are not a superposition baseline, they do not by themselves resolve the concern raised above about the b=-0.5 expectation. Please add a quantitative comparison (for example, ratio plots or chi^2 per point) and clarify what the model comparison demonstrates beyond the corrected statistical baseline.

minor comments (6)

[Abstract] The phrase 'minimum bias and and high-multiplicity' contains a duplicated 'and'; please correct.
[Section 2 (paragraph after Fig. 1)] The sentence 'In the case of widening pT windows, the strength of the correlator increases with multiplicity' appears to be a typo: the increase is with pT-window width, not with multiplicity, and the figure shows the correlator decreasing with Nch for each window.
[Equation (1)] The equation is not typeset cleanly; the denominator 'Sigma_{nev,m} k N_pairs^k' is garbled and should be rewritten so that the pair-count normalization is unambiguous.
[Figure 2 right panel] The earlier ALICE points at sqrt(s)=7 TeV and Pb-Pb at 2.76 TeV are shown without uncertainties, and the quoted '~11% increase' from 7 to 13 TeV is not accompanied by a significance statement.
[Section 1] Reference [8] is a proceedings contribution by the author; the claim that a 'dedicated analysis' of high-multiplicity pp events revealed the decreasing trend should also cite the published ALICE paper [1].
[Abstract] The sentence about 'non-monotonic variations in pT correlations with changing energy could serve as a signature of QGP formation' is not connected to any result in the paper; please either elaborate or remove it.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the correlator is measured, fitted empirically, and compared with independent MC models and an external superposition baseline.

full rationale

The paper's derivation chain is self-contained in the sense required by this review. The two-particle correlator sqrt(C_m)/M(pT)_m is defined directly from measured per-event pT values (Eqs. 1-2), and the multiplicity dependence is characterized by a power-law fit a*(Nch)^b with a and b as free parameters. The fitted index b is presented as an empirical result, not as a prediction derived from the fit input. The b=-0.5 superposition expectation is an external benchmark imported from the earlier ALICE publication [1], not fitted in this paper, and the comparison with PYTHIA8 and EPOS LHC provides independent model predictions. The only self-citation, [8], appears in the introduction to support the peripheral claim that high-multiplicity pp events show a similar decreasing trend with multiplicity; this observation is not load-bearing for the central power-law-index comparison or the soft-to-hard interpretation. To the extent that the fixed-pT-window validity of the b=-0.5 baseline is questionable because Nch acceptance and pT variance may change with multiplicity, that is a physics-validity concern about the interpretation, not circularity in the derivation. No step in the paper reduces by construction to its own input, and no fitted parameter is renamed as a prediction.

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

The analysis rests on two fitted power-law parameters (amplitude a and index b) per pT window, a hand-chosen fit interval 10<Nch<70, and physics assumptions about the soft/hard pT separation and the validity of the statistical and MC baselines. No new entities are introduced.

free parameters (3)

power-law amplitude a = not reported
Free parameter in the fit a*(Nch)^b used to describe the correlator versus Nch; the paper does not quote a for each pT window.
power-law index b = -0.41 +/- 0.031 (0.15-1.0 GeV/c), -0.48 +/- 0.03 (0.15-2.0 GeV/c), others not tabulated
Fitted separately for each pT window; the variation of b is the main quantitative result, but only statistical uncertainties are reported.
power-law fit range = 10 < N_ch < 70
Chosen by hand in Section 2; no justification is given and the restricted range affects the extracted index b.

assumptions (4)

domain assumption In the absence of dynamical correlations, the normalized correlator should scale as Nch^{-0.5}, i.e., power index b=-0.5.
Invoked in Section 2 (after Fig. 2) as the statistical baseline; deviations are interpreted as dynamical correlations. This is a theoretical expectation, not derived in the paper.
domain assumption Low-pT particles are dominated by soft processes (collective flow, resonance decays) and high-pT particles by hard scatterings and jet fragmentation.
Used throughout Section 1 and Section 2 to interpret the pT-window dependence as a soft-to-hard crossover. It is a modeling assumption about the physics, not tested here.
domain assumption Charged-particle multiplicity Nch is a suitable estimator of event size or source size in pp collisions for classifying events.
Assumed in all multiplicity-binned analyses; the paper does not discuss multiplicity fluctuations, event-class selection, or their biases.
domain assumption The MC generators PYTHIA8 and EPOS LHC provide valid physical baselines for comparison.
Used in Figs. 3 and 4; the paper gives a qualitative agreement but no validation or uncertainties for the models.

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Cite this review

Pith. "Pith review of Exploring Event-by-Event $\it{p}_{\rm T}$ Fluctuations in pp Collisions at $\sqrt{s} = 13$ TeV: An Insight from ALICE." pith.science (2026). https://pith.science/paper/H4C4BNRI

@misc{pith2026250515161,
  author       = {Pith},
  title        = {Pith review of: Exploring Event-by-Event $\itp_\rm T$ Fluctuations in pp Collisions at $\sqrts = 13$ TeV: An Insight from ALICE},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H4C4BNRI}},
  note         = {Machine review of arXiv:2505.15161}
}

abstract

Event-by-event fluctuations of the mean transverse momentum ($p_{\rm T}$) of relativistic charged particles are analyzed using the two-particle correlator $\sqrt{C_m}/M(p_{\rm T})_m$, which quantifies the correlations strength in units of the mean $p_{\rm T}$ in proton-proton collision at $\sqrt{s} = 13$ TeV in ALICE both for minimum bias and and high-multiplicity triggered events. The non-monotonic variations in $p_{\rm T}$ correlations with changing energy could serve as a signature of QGP formation. A comprehensive investigation across soft-, intermediate-, and hard-$p_{\rm T}$ regions could provide crucial insights into both equilibrium (e.g., thermal radial flow) and non-equilibrium (e.g., jet/minijet) contributions to $p_{\rm T}$ fluctuations. The dependence of the correlator on particle multiplicity for different $p_{\rm T}$ window widths and positions is explored. The correlator values are found to decrease with increasing charged particle density, following a power-law behavior similar to observations in both small and large systems at lower energies. Additionally, the influence of $p_{\rm T}$ range on the power-law coefficient is studied and results are compared with predictions from Monte Carlo models, such as PYTHIA (pQCD string model) and EPOS (core-corona model), to enhance understanding of the underlying mechanisms driving $p_{\rm T}$ fluctuations.

Figures

Figures reproduced from arXiv: 2505.15161 by the authors.

**Figure 1.** Variations of √ Cm/M(pT)m with Nch for varying pT window widths on the left and varying pT window positions on the right [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** A power-law fit to the normalized correlator for pro [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Experimentally observed normalized correlator v [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Comparison of the experimentally observed normal [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

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

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[2] [2]

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[3] [3]

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work page 2019

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Khachatryan et al, (CMS Collaboration) Phys

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Adler et al, (STAR Collaboration) Phys

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Acharya et al., (ALICE Collaboration) Phys

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Adams et al, (STAR Collaboration) Phys

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Bushra Ali, PoS(ICHEP2024) 476 (2024) 571. 10.22323/1. 476.0571

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