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arxiv: 2604.19585 · v1 · submitted 2026-04-21 · ✦ hep-ph

Recognition: unknown

Centrality Dependence of the Balance Functions for Identified Particles in Pb--Pb Collisions Using Pythia + Angantyr

Rashi Gupta , Ankhi Roy
Authors on Pith no claims yet

Pith reviewed 2026-05-10 02:18 UTC · model grok-4.3

classification ✦ hep-ph
keywords balance functionsidentified particlesPb-Pb collisionsPYTHIA Angantyrcentrality dependenceparticle correlationsresonance decays
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0 comments X

The pith

The balance function for pions narrows in central Pb-Pb collisions while remaining constant for kaons and protons.

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

This paper uses the PYTHIA 8.3 + Angantyr model to compute balance functions from two-particle correlations for pions, kaons, and protons in Pb-Pb collisions at 2.76 TeV. It finds that the pion balance function is narrower overall and its width decreases from peripheral to central collisions, unlike the nearly unchanged widths for kaons and protons. The model matches peripheral collision data reasonably but underpredicts the narrowing seen in central collisions. This indicates that resonance decays and possible collective effects are important but not fully captured by the current tune. Such studies help understand pair production and space-time evolution in the dense matter created in heavy-ion collisions.

Core claim

The results indicate that the balance function for pions is narrower compared to kaons and protons. The pion balance function width decreases from peripheral to central collisions, while the widths for kaons and protons remain nearly unchanged. For the Monash 2013 tune used in this study, PYTHIA 8.3 + Angantyr describes peripheral collisions reasonably well but does not quantitatively reproduce central Pb-Pb data. This suggests that an improved description of central Pb-Pb collisions may require a dedicated heavy-ion tuning of the Angantyr framework. Resonance decays and Bose-Einstein correlations produce a dip at zero for pions and kaons.

What carries the argument

Two-particle azimuthal angular correlations (Δφ, Δη) used to construct balance functions B(Δφ, Δη) for identified particle-antiparticle pairs ππ, KK, and pp.

If this is right

  • The narrowing of the pion balance function in central collisions arises from resonance effects and Bose-Einstein correlations, visible as a dip at zero angular separation.
  • Kaons and protons maintain nearly constant balance function widths across centralities, indicating less sensitivity to collision density.
  • Incorporating multi-parton interactions and color reconnection influences the correlations but does not fully resolve the discrepancy in central events.
  • A dedicated heavy-ion tuning of Angantyr is required to match central Pb-Pb balance function data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If collective flow is the primary missing element, adding it to the model should reproduce the observed pion narrowing in central collisions.
  • Balance functions could serve as a test observable to discriminate between different heavy-ion production models beyond the current framework.
  • Repeating the analysis at other collision energies or in smaller systems like p-Pb would test whether the pion centrality trend is a general feature.

Load-bearing premise

The Angantyr framework with the standard Monash 2013 tune, without heavy-ion-specific adjustments for collective flow or medium effects, can be directly compared to central Pb-Pb data for balance functions.

What would settle it

A measurement showing no decrease in the pion balance function width from peripheral to central collisions, or quantitative agreement between the current model tune and central Pb-Pb data widths, would challenge the reported results.

Figures

Figures reproduced from arXiv: 2604.19585 by Ankhi Roy, Rashi Gupta.

Figure 1
Figure 1. Figure 1: FIG. 1. Charge–anticharge pair production at different times [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Centrality distribution of charged particles in Pb–Pb [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Balance functions ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Balance functions ( [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Balance functions ( [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Balance functions [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Balance functions of pion pairs, projected onto the ∆ [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Balance functions ( [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Balance functions ( [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Balance functions ( [PITH_FULL_IMAGE:figures/full_fig_p006_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Balance functions of kaon pairs, projected onto the ∆ [PITH_FULL_IMAGE:figures/full_fig_p007_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Balance functions of kaon pairs, projected onto the ∆ [PITH_FULL_IMAGE:figures/full_fig_p007_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Balance functions ( [PITH_FULL_IMAGE:figures/full_fig_p008_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Balance functions ( [PITH_FULL_IMAGE:figures/full_fig_p008_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Balance functions ( [PITH_FULL_IMAGE:figures/full_fig_p008_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Balance functions width ( [PITH_FULL_IMAGE:figures/full_fig_p009_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Balance functions width ( [PITH_FULL_IMAGE:figures/full_fig_p009_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Balance functions Integral ( [PITH_FULL_IMAGE:figures/full_fig_p009_18.png] view at source ↗
read the original abstract

In this paper, we study the balance functions for pions, kaons, and protons in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 2.76$ TeV using the PYTHIA 8.3 + Angantyr model. The balance function is evaluated through two-particle azimuthal angular correlations $(\Delta \phi, \Delta \eta)$ between particle and antiparticle. Correlations are constructed for $\pi\pi$, $KK$, and $pp$, and their dependence on collision centrality is investigated. The results indicate that the balance function for pions is narrower compared to kaons and protons. Notably, the pion balance function width decreases from peripheral to central collisions, while the widths for kaons and protons remain nearly unchanged. For the Monash 2013 tune used in this study, PYTHIA 8.3 + Angantyr describes peripheral collisions reasonably well but does not quantitatively reproduce central Pb--Pb data. This suggests that an improved description of central Pb--Pb collisions may require a dedicated heavy-ion tuning of the Angantyr framework. We further explore the influence of resonance decays and collective effects by incorporating multi-parton interactions and color reconnection into the analysis. Owing to resonance effects and Bose--Einstein correlations, a dip at $\Delta \eta = 0$ and $\Delta \phi = 0$ is observed for pions and kaons.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper studies balance functions for identified particles (pions, kaons, protons) in Pb-Pb collisions at √s_NN = 2.76 TeV using PYTHIA 8.3 + Angantyr with the Monash 2013 tune. Balance functions are obtained from two-particle azimuthal correlations in (Δφ, Δη) for ππ, KK, and pp pairs. The results show narrower balance functions for pions than for kaons and protons; the pion width decreases from peripheral to central collisions while kaon and proton widths stay nearly constant. The model reproduces peripheral data reasonably well but does not quantitatively match central Pb-Pb data. A dip at (Δη, Δφ) = (0,0) for pions and kaons is attributed to resonance decays and Bose-Einstein correlations. The authors suggest that dedicated heavy-ion tuning of Angantyr is needed for central collisions and explore the role of multi-parton interactions and color reconnection.

Significance. If the reported trends hold, the work supplies a useful baseline for charge-balance observables in a string-based Monte Carlo framework that lacks explicit hydrodynamic or medium effects. The explicit statement that the untuned Angantyr setup succeeds for peripheral but fails for central collisions, together with the identification of resonance and Bose-Einstein contributions to the zero-angle dip, provides concrete guidance for future model development. The study thereby helps delineate the physics ingredients still missing in current Angantyr implementations for heavy-ion balance-function studies.

major comments (1)
  1. The central claim that the model 'does not quantitatively reproduce central Pb-Pb data' is load-bearing for the motivation to pursue dedicated tuning, yet the manuscript provides no numerical measure (e.g., integrated difference, χ², or width ratios) of the discrepancy in the results section. Without such quantification, it is difficult to judge how severe the mismatch is or whether it is uniform across all centralities.
minor comments (2)
  1. The abstract and introduction refer to 'collective effects' via MPI and color reconnection, but the text does not specify which parameters were varied or whether the default Monash settings were retained; a short table or sentence clarifying the exact settings used would improve reproducibility.
  2. Figure captions and axis labels should explicitly state the centrality classes (e.g., 0-5 %, 70-80 %) and the normalization convention for the balance functions so that readers can directly compare the plotted widths to experimental publications.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment. We appreciate the positive assessment of the work's significance as a baseline for charge-balance studies in a string-based Monte Carlo framework. We address the major comment below and will revise the manuscript to incorporate the suggested quantification.

read point-by-point responses

  1. Referee: The central claim that the model 'does not quantitatively reproduce central Pb-Pb data' is load-bearing for the motivation to pursue dedicated tuning, yet the manuscript provides no numerical measure (e.g., integrated difference, χ², or width ratios) of the discrepancy in the results section. Without such quantification, it is difficult to judge how severe the mismatch is or whether it is uniform across all centralities.

    Authors: We agree that an explicit numerical quantification of the discrepancy would strengthen the central claim and better support the motivation for dedicated heavy-ion tuning of Angantyr. While the figures in the results section visually demonstrate that the model reproduces peripheral data reasonably well but deviates in central collisions (particularly the narrowing of the pion balance function), we did not provide metrics such as width ratios or χ² values. In the revised manuscript, we will add quantitative measures: specifically, we will report the root-mean-square widths of the balance functions for model and data in each centrality class, compute the ratio of these widths (model/data) to illustrate the trend with centrality, and include a simple χ² per degree of freedom for the central (0-10%) collisions to quantify the overall mismatch. These additions will allow readers to assess the severity and uniformity of the discrepancy more rigorously without altering the qualitative conclusions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; direct simulation outputs with fixed tune

full rationale

The paper computes balance functions directly from PYTHIA 8.3 + Angantyr events generated with the fixed Monash 2013 tune, without any parameter adjustment or fitting to the target balance-function widths, shapes, or centrality trends. Results for pion, kaon, and proton pairs are obtained by constructing two-particle correlations in the generated sample and binning by centrality; the reported narrowing of the pion balance function with increasing centrality (while kaon/proton widths stay flat) follows immediately from the event generator output. The explicit statement that the untuned model reproduces peripheral data but fails to match central Pb-Pb data is a qualitative comparison, not a prediction derived from the data itself. No self-definitional equations, fitted-input-as-prediction steps, or load-bearing self-citations appear in the derivation chain. The analysis remains self-contained against external benchmarks because the Monte Carlo pipeline is independent of the measured balance functions.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The analysis rests on the validity of PYTHIA's standard QCD modeling and the Angantyr extension, plus the pre-tuned Monash 2013 parameters that were fitted in earlier works.

free parameters (1)
  • Monash 2013 tune parameters
    Multiple parameters in the tune were fitted to prior data; used here without refitting to balance functions.
axioms (2)
  • domain assumption PYTHIA parton shower, hadronization, and resonance decay models are sufficiently accurate for this observable
    Invoked throughout the simulation of particle production and correlations.
  • domain assumption Angantyr correctly extends PYTHIA to heavy-ion geometry and multiple interactions
    Required to generate Pb-Pb events from the proton-proton base model.

pith-pipeline@v0.9.0 · 5559 in / 1489 out tokens · 55641 ms · 2026-05-10T02:18:15.959583+00:00 · methodology

discussion (0)

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Reference graph

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