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REVIEW 4 major objections 4 minor 49 references

Two-particle number and transverse momentum balance function with event-topology in pp collisions at $\sqrt{s}=13$ TeV

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read By sorting proton-proton collisions by transverse spherocity—jet-like versus isotropic—this paper shows that charge-balance function widths narrow with multiplicity, more strongly in jet-like events, while momentum balance correlations stay

desk verdict Useful first MC look at balance functions vs spherocity in pp, but the EPOS core on/off comparison does not isolate radial flow, and uncertainty bars are missing. read the letter →

arxiv 2508.20198 v1 pith:YZJTRORR submitted 2025-08-27 hep-ex hep-ph

Subash Chandra Behera , Arvind Khuntia This is my paper
classification hep-exhep-ph
keywords balancefunctiontransversespherocityevent-shapeanalysischargeconservationradialflowsmallcollisionsystemsPYTHIA8EPOS-LHC
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 works out what charge balance functions can reveal about proton-proton collisions when events are separated not just by multiplicity but by event shape. Using the PYTHIA8 and EPOS-LHC event generators at 13 TeV, it finds that the width of the balance function in relative pseudorapidity and relative azimuthal angle narrows as multiplicity rises, and that jet-like (low-spherocity) events produce narrower balance functions than isotropic ones. The momentum balance function's width, by contrast, stays nearly flat with multiplicity. By switching EPOS-LHC's hydrodynamic core on and off, the paper isolates the contribution of radial flow and argues that the extra narrowing seen with the core is a quantitative signature of flow-induced localization of charge-balancing pairs. If this is right, balance functions become a charge-sensitive observable that can distinguish collective expansion from plain fragmentation in small collision systems.

What carries the argument

The analysis is carried by three ingredients: the charge balance function B(Δη,Δϕ), which measures how close opposite-sign charge-balancing pairs sit in relative pseudorapidity and azimuthal angle; the charge-dependent transverse momentum correlator P2^CD, which measures covariance of transverse momentum deviations for unlike-sign pairs; and transverse spherocity S0, an event-shape variable between 0 (pencil-like, jet-dominated) and 1 (isotropic). The isolating device is the EPOS-LHC core on/off toggle: with the hydrodynamic core on, a dense core expands and generates radial flow; with the core off, the same event generator hadronizes without collective expansion, providing the counterfactua

What would settle it

Run EPOS-LHC with the core enabled but with the collective radial-flow velocity set to zero while keeping hadronization identical; if the Δϕ width still narrows with multiplicity, the narrowing is not caused by flow. On the data side, if high-multiplicity isotropic pp events measured at the LHC Run 3 show widths that track the no-core curve rather than the core curve, the flow-localization claim would be contradicted.

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Extended reading notes

Core claim

The paper's central claim is that the charge-dependent number balance function B(Δη,Δϕ) and the charge-dependent transverse momentum correlator P2^CD, when binned in transverse spherocity classes and charged-particle multiplicity, separate two regimes of charge balancing in pp collisions. The widths of B in both Δη and Δϕ decrease systematically with multiplicity, with the decrease most pronounced in low-spherocity (jet-like) events; isotropic high-spherocity events show wider balance functions. The momentum correlator P2^CD, however, shows a nearly flat multiplicity dependence. The paper's decisive comparison is EPOS-LHC with its hydrodynamic core enabled versus disabled: the core-enabled v

Load-bearing premise

The load-bearing premise is that turning the EPOS-LHC hydrodynamic core off removes radial flow without changing anything else, such as hadronization, the core-corona partition, or which events fall into which spherocity class.

Editorial extensions

If this is right

  • Multiplicity narrowing of B(Δη) and B(Δϕ) can be read as localization of charge-balancing pairs in denser events.
  • Jet-like low-spherocity events give the narrowest widths, so local charge conservation within jet fragmentation dominates that event class.
  • Isotropic high-spherocity events give broader widths, pointing to soft multi-parton interactions and color-reconnection effects rather than hard jets.
  • Switching off the EPOS-LHC hydrodynamic core removes most of the multiplicity dependence in Δϕ widths, indicating that radial flow is the quantitative driver of azimuthal localization in the model.
  • The nearly flat P2^CD widths imply momentum correlations are less sensitive to flow than number correlations, so the two observables probe different aspects of charge conservation.

Reading between the lines

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

  • Applying this spherocity-binned balance-function analysis to LHC Run 3 pp data would directly test whether measured widths track the core-on or core-off EPOS-LHC curve.
  • Because the core on/off toggle changes the whole hadronization environment, a model variant that removes only the collective velocity field would isolate radial flow more cleanly and is a natural follow-up calculation.
  • The near-flat P2^CD widths hint that momentum balancing is dominated by short-range jet and resonance correlations; removing resonance decays from the analysis may expose a weaker but cleaner flow signal in momentum space.
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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 / 4 minor

Summary. This paper presents a generator-level study of charge-dependent two-particle number balance functions B and transverse-momentum balance functions P_2^CD in pp collisions at sqrt(s)=13 TeV, as a function of charged-particle multiplicity and transverse spherocity. Using PYTHIA8 and EPOS-LHC (both with and without the hydrodynamic core), the authors report narrowing of B widths in Delta eta and Delta phi with increasing multiplicity, wider B in isotropic (high-spherocity) events than in jet-like (low-spherocity) events, and a weaker multiplicity dependence for the P_2^CD widths. The main interpretive claim is that comparing EPOS-LHC with its hydrodynamic core enabled versus disabled provides a quantitative handle on radial-flow-induced localization of charge-balancing pairs.

Significance. If the central claims are supported, this would be the first differential application of balance functions to event-topology classes in small systems and could provide a useful generator-level benchmark for LHC Run 3 measurements. The analysis uses standard definitions (Eqs. 1-10), large MC samples, and a controlled model comparison that is, in principle, informative about how different hadronization/collectivity mechanisms affect charge correlations. The main added value is the spherocity classification, which sharpens the sensitivity to jet-like versus isotropic event populations. However, the paper's interpretive strength is currently limited by the lack of uncertainties on all plotted quantities and by an overreach in the claim that the EPOS core on/off comparison isolates radial flow.

major comments (4)
  1. [Abstract; Sec. III; Sec. IV.C, Figs. 9-10] The statement in Sec. III that the core on/off comparison 'explicitly isolates radial flow contributions' is not supported. Disabling the core in EPOS-LHC also changes the hadronization mechanism (statistical/microcanonical hadronization of the core versus string fragmentation), the core-corona partition, and the event selection. Figure 1 shows that the spherocity distributions differ between the core-on and core-off configurations, so the top/bottom 20% spherocity classes select different event populations. String fragmentation itself enforces local charge conservation and produces resonance decays, both of which directly shape B and P_2^CD widths. The differences in Figs. 9 and 10 cannot therefore be uniquely attributed to radial flow. Please either provide a control that varies radial-flow strength while keeping the core-corona decomposition and hadronization fixed, or soften the inte
  2. [Figs. 3-10; Sec. IV.C] No statistical or systematic uncertainties are shown on any correlation function or width. The conclusions rest on comparisons of widths across multiplicity and spherocity classes (e.g., 'nearly flat' vs. 'clear narrowing' in Fig. 10). Without propagated MC statistical errors and at least a discussion of systematic choices (spherocity percentile, pT range, width integration range, generator tune), the quantitative statements are not fully testable. The 500M events make random errors small, but they are not zero, and the significance of the core on/off differences is not quantified.
  3. [Sec. II; Fig. 9 and Fig. 10 captions] The width extraction ranges are stated inconsistently. The text says the P_2^CD widths are estimated in the region |Delta eta, Delta phi| <=1.0, but the Fig. 10 captions use the same projection cuts as for B (|Delta phi|<=pi/2 for sigma(Delta eta), |Delta eta|<=1.0 for sigma(Delta phi)). In addition, the Delta eta integration range for sigma(Delta eta) is not explicitly stated in the captions; the text says |Delta eta|<=3.0 for B. Since the widths are the quantitative outputs of the paper, these ranges must be unambiguous and consistent.
  4. [Abstract; Sec. IV.C, Fig. 10] The abstract's claim that 'for the momentum correlations, a nearly flat dependence is observed with Nch' is inconsistent with the body. In Sec. IV.C the P_2^CD widths are described as showing a 'mild decrease' for PYTHIA8 and, for EPOS-LHC with the core enabled, 'clear narrowing at high multiplicities' (Fig. 10c,d). Please reconcile the abstract with the shown trends, or qualify the claim as e.g. 'weaker multiplicity dependence than B.'
minor comments (4)
  1. [Sec. V] Typo: 'summerizes' should be 'summarizes'.
  2. [Figure captions 3-8] The phrase 'are take in' should be 'are taken in', and the inconsistent 'right panel'/'right column' wording should be unified.
  3. [Sec. II / references] Reference [38] is cited for 'multiplicity classes', but the listed ref ([38], CMS arXiv:2410.04578) is about azimuthal anisotropy correlations and appears unrelated. Please replace with an appropriate multiplicity-class reference.
  4. [Sec. III] The statement '500M MC events' should specify whether this total is per generator and per core configuration; the sample sizes affect the statistical assessment.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the balance functions are direct generator outputs, not fitted to the target observables, and the core on/off comparison is a controlled model variation.

full rationale

This is a Monte Carlo model-comparison study, not a derivation in which an output is constructed from the input it claims to predict. The number and momentum balance functions B and P2^CD are computed directly from final-state particles via the standard definitions in Eqs. (1)-(10); no parameter is fitted to the widths or shapes that are later reported. The EPOS-LHC core-on vs core-off comparison is a controlled model variation: the paper states that the difference 'explicitly isolates radial flow contributions,' but even if this assertion is physically oversimplified (because the toggle also changes hadronization and event selection), that is a validity concern about model interpretation, not a circular reduction of the result to its input. The only self-citation is Ref. [30], an author's earlier spherocity paper, but it is used only to define the spherocity variable and the Nch >= 5 requirement, and it is corroborated by independent ALICE references [31,32,48,49]. Thus the central claims remain independent of any self-citation chain, and no prediction is equivalent to its input by construction.

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

The paper introduces no new free parameters fitted to the target observables; it uses standard event-generator tunes as inputs. The axioms are the modeling assumptions of the generators, the event-shape classification, and the standard correlation methodology. No new particles, forces, or conserved quantities are postulated.

assumptions (5)
  • domain assumption Event generators (PYTHIA8 with CP5 tune, EPOS-LHC) reproduce the relevant features of pp collisions
    All results are model outputs; the generators rely on previously tuned parameters that are not validated against data within this paper (Section III).
  • domain assumption Transverse spherocity separates jet-like and isotropic events
    Eq. (9) defines S0; the top/bottom 20% selections assume this classification captures distinct event topologies (Section II, Section IV).
  • standard math Local charge conservation implies opposite-charge pairs are produced locally
    Section II motivates the balance function via local charge conservation; this is a physical assumption underlying the observable.
  • standard math Mixed-event normalization corrects pair acceptance
    Eq. (5) uses the ratio M(0,0)/M(Delta-eta,Delta-phi) to account for acceptance effects; this is a standard technique in two-particle correlations.
  • standard math RMS width over stated ranges measures the separation scale of balancing pairs
    Eq. (10) defines the width as an RMS over the measured balance function; this assumes the balance function can be treated as a distribution over the chosen range.

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Cite this review

Pith. "Pith review of Two-particle number and transverse momentum balance function with event-topology in pp collisions at $\sqrt{s}=13$ TeV." pith.science (2026). https://pith.science/paper/YZJTRORR

@misc{pith2026250820198,
  author       = {Pith},
  title        = {Pith review of: Two-particle number and transverse momentum balance function with event-topology in pp collisions at $\sqrts=13$ TeV},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YZJTRORR}},
  note         = {Machine review of arXiv:2508.20198}
}
abstract

The first study of charge-dependent two-particle differential number ($B$) and momentum balance functions ($P_{2}^{CD}$) with respect to an event shape variable, transverse spherocity, is reported. Results are presented from PYTHIA8 and EPOS-LHC model calculations in proton-proton (pp) collisions at $\sqrt{s} = 13$ TeV. To distinguish between back-to-back jet-like topologies and isotropic events, low and high transverse spherocity values are chosen. The correlation functions are measured as a function of averaged charged-particle multiplicity ($\langle N_{ch}\rangle$) in relative pseudorapidity ($\Delta\eta$) and relative azimuthal angle ($\Delta\phi$) with $|\eta| < 2.4$ and $0.2 < p_{T} < 2.0$ GeV. A narrowing of the balance function width is observed in $\Delta\eta$ and $\Delta\phi$ from low- to high-multiplicity collisions. Wider balance functions are found in isotropic events as compared to jet-like events. However, for the momentum correlations, a nearly flat dependence is observed with $\langle N_{ch}\rangle$. This study investigates charge conservation mechanisms and their correlations for events classified with jet-like and isotropic topologies. To isolate medium-driven effects, we compare EPOS-LHC with its hydrodynamic core enabled and disabled and observed narrowing patterns in $B$ and $P_{2}^{CD}$ as a quantitative handle on radial-flow-induced localization of charge-balancing pairs.

Figures

Figures reproduced from arXiv: 2508.20198 by the authors.

Figure 1
Figure 1. FIG. 1. The colored lines show the spherocity distributions [30–32] for different multiplicity classes [38] in pp [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Two-dimensional balance function for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. One-dimensional [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. One-dimensional projections of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. One-dimensional projections of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: , 7 and 8 present the one-dimensional projection of P CD 2 along ∆η and ∆ϕ for differ￾ent multiplicity classes with ⟨Nch⟩ ≈ 8, 58, and 106 in pythia8 and epos-lhc without and with core model. Each column corresponds to a dif￾ferent spherocity class: the left column sho…
Figure 7
Figure 7. Figure 7: FIG. 7. One-dimensional projections of [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. One-dimensional projections of [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. The width of [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. The width of [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.