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REVIEW 3 major objections 4 minor 141 references

The paper demonstrates that Pythia's Lund string hadronization, combined with colour reconnection, can be embedded in Herwig 7 and tuned into a general-purpose 'LH Tune' that performs competitively with Herwig's native cluster model and Pyt

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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A Lund string model tune inside Herwig 7, the LH Tune, gives competitive descriptions of many LEP and LHC observables and enables fixed-shower comparison of string vs cluster hadronization.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection A real, citable artifact — the first hadron-collider string tune inside Herwig with colour reconnection — but the abstract oversells it, and the unexplained 73.5% run attrition in the final tuning stage is the main thing to fix. the 3 major comments →

arxiv 2509.02348 v1 pith:E7HVVG33 submitted 2025-09-02 hep-ph hep-ex

Herwig 7 with the Lund String Model: Tuning and Comparative Hadronization Studies

Michaela Divisova , Miroslav Myska , Pratixan Sarmah , Andrzej Si\'odmok This is my paper
classification hep-ph hep-ex
keywords hadronizationLund string modelcluster modelMonte Carlo event generatorsHerwigPythiatuningcolour reconnection
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 makes the case that the Lund string hadronization model, the mechanism Pythia uses to turn coloured partons into hadrons, can be transplanted into Herwig 7 with no loss of descriptive power. By extending the TheP8I interface so that Herwig's angular-ordered parton shower feeds Pythia's string fragmentation and its QCD-based colour reconnection, the authors build a four-stage tune—the Les Houches (LH) Tune—from LEP, Tevatron, and LHC data. They show the resulting tune lands close to the established Herwig cluster default and the Pythia Monash tune across most observables it was tested on, and generalizes to measurements it was not tuned to, including lower-energy data. The payoff is a controlled comparison: with one shower fixed, switching between cluster and string hadronization separates hadronization effects from perturbative-shower effects in systematic-uncertainty estimates.

Core claim

The central claim is that a modern Lund string model, including the QCD-based colour reconnection scheme needed for hadron-collider final states, is fully usable inside Herwig 7 and can be tuned to collider data at the same quality as the generator's native cluster model. The evidence is the LH Tune: fragmentation and final-state-radiation parameters are fit first to LEP event shapes and multiplicities, then flavour parameters to particle multiplicities, then initial-state radiation and intrinsic transverse momentum to Z-boson production at the LHC, and finally multiple-parton-interaction and colour-reconnection parameters to minimum-bias and underlying-event data at 0.9, 1.8, 7, and 13 TeV.

What carries the argument

The load-bearing object is the extended TheP8I interface, which bridges Herwig 7's ThePEG event framework to Pythia 8's hadronization classes. It converts showered Herwig events into Pythia-readable colour singlet systems, then runs Pythia's StringFragmentation, with new access to ColourReconnection and JunctionSplitting parameters so that colour reconnection can be tuned from within Herwig. On top of that, the Professor polynomial-response-surface method supplies the tuning machinery: a weighted chi-squared fit over sampled parameter points, applied in four sequential stages under a decoupling assumption.

Load-bearing premise

The tuning assumes the four groups of parameters—fragmentation, flavour, initial-state radiation/intrinsic kT, and multiple-parton-interaction/colour reconnection—are independent enough that fixing each group in sequence does not bias the result, and that the polynomial response surface interpolates the true generator response accurately.

What would settle it

Take the same data sets and tune all parameters simultaneously, or in a different order, and compare predictions on untuned LHC distributions; if the alternative tune moves by more than the quoted uncertainties or systematically beats the LH Tune on held-out observables such as identified strange-baryon yields at 7 TeV, the decoupling assumption is falsified. A cheaper check is to evaluate the Professor response surface at the LH Tune parameter point against direct generator runs to see whether the polynomial interpolation was accurate there.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Herwig 7.4 ships the LH Tune, so string-model predictions in Herwig become a standard, maintained option rather than a custom patch.
  • With the shower held fixed, differences between cluster and string predictions directly quantify hadronization-model uncertainty for event shapes, multiplicities, underlying event, and beyond.
  • The interface exposes colour-reconnection parameters to Herwig users, making the QCD-based colour reconnection scheme available for studies of top-pair final states and other colour-reconnection-sensitive processes.
  • The LH Tune can be used at energies from 50 GeV up to 13 TeV, covering lower-energy experiments such as STAR as well as LHC analyses.
  • The separately tuned initial- and final-state radiation couplings come out nearly equal, suggesting they could be unified in a future tune.

Where Pith is reading between the lines

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

  • If the decoupling assumption holds, the same four-stage strategy could be applied to any hadronization model plugged into Herwig, turning model choice into a tunable dimension of systematic uncertainty.
  • The paper leaves implicit that its interface also opens the door to testing newer Pythia hadronization variants—thermodynamical fragmentation, string shoving, hyperfine-split string breaks—inside Herwig without changing the shower.
  • The identified-particle spectra at 7 TeV, which no tune describes within 50 percent, suggest that flavour parameters tuned at LEP do not fully transfer to the LHC environment; a hadron-collider flavour extension of the LH Tune would be the natural next step.
  • A simultaneous full-dimensional tune, once computationally affordable, would provide both a cross-check of the LH Tune and a Hessian-style error set for it.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper interfaces the Pythia 8 Lund string hadronization model and its QCD-based colour reconnection scheme with Herwig 7's angular-ordered parton shower through an extended TheP8I interface. Using Rivet and Professor, the authors perform a four-stage sequential tune of fragmentation, flavour, ISR/intrinsic-kT, and MPI/CR parameters against LEP, Tevatron, and LHC data, yielding the 'LH Tune'. They compare this tune with Herwig's default cluster tune, Pythia 8's Monash tune, and an earlier string-model autotune across many observables, including some not used in the fit. The abstract and Section 3.1 claim that the LH Tune 'shows good performance across a wide range of observables' and is competitive with existing tunes; the tune will be included in Herwig 7.4.

Significance. If confirmed, this work provides the community with a validated general-purpose string-hadronization tune inside Herwig, enabling controlled comparisons of hadronization models with a fixed parton shower. The paper's strengths are its use of standard, reproducible tuning tools (Rivet/Professor), its explicit reporting of some failures (Section 4.2.2 pseudorapidity, Section 4.2.3 flavour spectra), and the planned public release of the interface patch. The four-stage tuning methodology is conventional and the paper contains a large body of plots that qualitatively support the central claim. However, the central claim rests on the reliability of the Professor interpolation and on the decoupling assumption, both of which receive only limited scrutiny in the manuscript.

major comments (3)
  1. [Section 3.1.2] The final tuning stage samples 1000 parameter vectors but only 265 'valid' runs are used for the Professor interpolation. No explanation is given for the 73.5% attrition. If invalid runs (crashes, timeouts, unphysical events) correlate with parameter values, the surviving points are not a uniform sample of the intended hypercube, and the response surface—and hence the optimum—may be biased. This concern is reinforced by the LH Tune values m0 = 2.87 GeV and junctionCorrection = 4.55, both sitting near the upper edges of their ranges (0.1–3 GeV and 0.05–5, respectively). The authors should quantify the causes of invalid runs, show the parameter-space distribution of valid vs. invalid points, and provide robustness checks such as repeated Professor fits on subsets, direct generator validation at the reported optimum, and sensitivity studies to the parameter ranges.
  2. [Section 3.1.1] The four-stage sequential tuning rests on the assumption, stated as 'we expect this assumption to hold', that fragmentation, flavour, ISR/kT, and MPI/CR parameter groups decouple. No numerical test of this decoupling is presented. Strong cross-group correlations could lead to a biased parameter set and would invalidate the generalization claim. The authors should test the assumption, for example by scanning MPI/CR parameters at fixed fragmentation/flavour values and checking LEP event-shape and multiplicity observables, or by comparing the sequential tune with a joint fit on a representative subset of observables. Without such checks, the 'good performance' claim is not fully supported.
  3. [Sections 4.1–4.2 and Abstract] Many of the plots used to demonstrate good performance (Figs. 4–6, 8–9, 11, 18–23) are exactly the observables included in the Professor fit; these cannot independently validate the tune. The paper does include validation plots (Figs. 7, 10, 12, 13, 15, 24–25) and reasonably discusses them, but it does not provide quantitative goodness-of-fit measures (e.g., chi2/ndf) for either fitted or validation observables. In addition, Section 4.2.3 reports that none of the tunes describes the LHC flavour data well, with discrepancies up to 50%, and Section 4.2.2 reports that the LH Tune is 'farthest from the data' for the pseudorapidity distribution. These limitations should be reconciled with the abstract's 'good performance across a wide range of observables' by an explicit, quantitative summary of validation performance.
minor comments (4)
  1. [Section 4.2.2, near Fig. 12] The text says observables in Fig. 12 use tracks with pT > 500 GeV and the 13 TeV distributions in Fig. 11 use pT > 100 GeV; these should be 500 MeV and 100 MeV. The same unit error appears in the Fig. 12 caption.
  2. [Figure 13 caption] The caption contains a typo: 'ALTAS' should be 'ATLAS'.
  3. [Figure 14 caption (e)] The caption describes the observable as the 'number of Λ and Λbar mesons'; Λ is a baryon, not a meson.
  4. [Fig. 3 and Eq. (4)] The power-law form in Eq. (4) is an assumed parametric form, and the red curve in Fig. 3 is a fit of that form. The statement that this 'demonstrates the intrinsic power law' is too strong, especially because the individual energy tunes share other parameters. Please soften the wording and present parameter uncertainties for the power-law fit.

Circularity Check

1 steps flagged

One power-law 'demonstration' reduces to its own fitted ansatz; the central tuning claim retains independent validation.

specific steps
  1. fitted input called prediction [Section 3.1.2, Eq. (4), Fig. 3]
    "This parameter has been removed from the list of free parameters in [119] and set to follow a power law governed by the three parameters. ... Fig. 3 shows a red curve for the new LH Tune along with the individual pmin⊥(s) points obtained from fully independent tunes at four different energies. ... the individual points lie very close to the curve obtained from the LH Tune, thus demonstrating the intrinsic power law that it obeys."

    Eq. (4) defines pmin⊥(s) as a power law with fitted parameters c, b, and pmin⊥,0. The 'points' in Fig. 3 are not direct measurements but evaluations of the same assumed power-law form using each single-energy tune's fitted parameters. The red curve is likewise the LH Tune's own power-law parametrization. The agreement between points and curve is therefore a consistency check of the imposed ansatz, not an independent demonstration that the energy evolution obeys a power law. The claimed 'intrinsic power law' is an input assumption (taken from [119]) rather than a derived result.

full rationale

This is a tuning paper, so many successful comparisons against LEP and LHC data are expected to reproduce the fitted observables. The paper is transparent about this: Figs. 5, 6, 8, 9, 11 and the appendix figures are explicitly described as included in the tuning interpolation, while Figs. 7, 10, 12, 13 and 15 are presented as unweighted validation observables. Those held-out comparisons provide genuine independent evidence for the LH Tune's generalization, so the central claim is not circular. The only concrete reduction found is the pmin⊥(s) power-law discussion in Section 3.1.2, where the power-law form is imposed in Eq. (4), fitted to each tune, and then presented as 'demonstrating the intrinsic power law.' That step is circular by construction but does not affect the main comparative hadronization conclusions. There are no load-bearing self-citation chains or imported uniqueness theorems; the cited previous work supplies tuning strategies and parametrizations but the validation is external to the fitted values.

Axiom & Free-Parameter Ledger

31 free parameters · 7 axioms · 0 invented entities

Everything the central claim rests on: 31 tuned parameters (Tables 1-4) plus imported phenomenological models (Lund string, AOPS, cluster comparison, QCD-based CR) and tuning-infrastructure assumptions (decoupling, Professor interpolation). The paper adds no new physical entities; its deliverable is a parameter set and a software patch, so the ledger counts parameters and imported-model assumptions rather than invented physics.

free parameters (31)
  • alphaS_FSR (Herwig FSR coupling at MZ) = 0.126
    Fitted to LEP event shapes and multiplicity data in stage 1 (Table 1).
  • pmin_perp (FSR infrared cutoff) = 1.03 GeV
    Fitted jointly with alphaS_FSR; strongly anti-correlated with the coupling (Table 1, Section 3.1.1).
  • aLund (Lund fragmentation a) = 0.75
    Fitted to LEP event shapes and scaled momentum spectra (Table 1).
  • bLund (Lund fragmentation b) = 0.90 GeV^-2
    Fitted to LEP data in stage 1 (Table 1).
  • sigma (Gaussian pT kick width) = 0.31 GeV
    Fitted to LEP transverse momentum distributions (Table 1).
  • aExtraSQuark = 0.18
    Fitted, increases a for s quarks (Table 1).
  • aExtraDiquark = 0.05
    Fitted, increases a for diquarks (Table 1).
  • rFactC = 0.68
    Bowler modification exponent for charm, fitted to LEP flavour data (Table 1).
  • rFactB = 1.27
    Bowler exponent for bottom, fitted to LEP b-quark fragmentation (Table 1).
  • probStoUD = 0.19
    Strangeness suppression, fitted to particle multiplicity ratios (Table 2).
  • probQQtoQ = 0.08
    Diquark suppression, fitted to baryon multiplicities (Table 2).
  • probSQtoQQ = 0.99
    Strange diquark suppression, fitted (Table 2).
  • probQQ1toQQ0 = 0.02
    Spin-1 vs spin-0 diquark suppression, fitted (Table 2).
  • etaSup = 0.51
    Eta suppression, fitted to meson multiplicities (Table 2).
  • etaPrimeSup = 0.18
    Eta-prime suppression, fitted (Table 2).
  • popcornRate = 0.73
    Baryon-meson-antibaryon production rate, fitted to baryon data (Table 2).
  • mesonUDvector = 0.33
    Vector/pseudoscalar ratio for u,d mesons, fitted (Table 2).
  • mesonSvector = 0.68
    Vector/pseudoscalar ratio for s mesons, fitted (Table 2).
  • mesonCvector = 1.07
    Ratio for charm mesons, fitted (Table 2).
  • mesonBvector = 1.85
    Ratio for bottom mesons, fitted (Table 2).
  • alphaS_ISR (Herwig ISR coupling at MZ) = 0.124
    Fitted to ATLAS/CMS Z pT and phi* data at 7 TeV (Table 3).
  • kT (intrinsic primordial kT) = 1.304 GeV
    Fitted to Drell-Yan Z pT data (Table 3).
  • Power c (MPI pmin exponent) = 0.23
    Fitted to MB/UE data across 0.9-13 TeV; enters Eq. (4) power law (Table 4).
  • pmin_perp_0 (MPI threshold scale) = 3.13 GeV
    Fitted, base scale of the pmin(s) power law (Table 4).
  • Offset b (MPI energy offset) = 530.5 GeV
    Fitted, offset in the pmin(s) power law (Table 4).
  • mu2 (MPI regularization) = 1.14 GeV^-2
    Fitted to MB/UE data (Table 4).
  • ladderMult = 0.57
    Fitted MPI ladder multiplicity parameter (Table 4).
  • ladderbFactor = 0.97
    Fitted MPI ladder parameter (Table 4).
  • Rdiff = 0.21
    Diffraction fraction, fitted to MB data (Table 4).
  • m0 (CR lower mass bound) = 2.87 GeV
    Colour reconnection parameter from Pythia via TheP8I, fitted to MB/UE data (Table 4).
  • junctionCorrection (CR junction mass scale) = 4.55
    Scales junction string mass, fitted (Table 4).
axioms (7)
  • domain assumption Lund string model and its Pythia 8 implementation are a valid description of hadronization
    The paper imports the model wholesale from [76] and [4,5] (Sections 2-3); any deficiency in the model propagates into the tune.
  • domain assumption Herwig 7 AOPS correctly generates the perturbative initial and final state
    Takes the angular-ordered shower [14] as given; differences from Pythia's pT-ordered shower are attributed to the models.
  • ad hoc to paper Fragmentation and flavour parameter groups decouple from each other and from MPI/CR parameters
    Section 3.1.1: 'we adopt the same assumption as other Pythia tunes... that these sets of parameters decouple and can be tuned separately... We expect this assumption to hold for our setup without introducing significant correlations.'
  • domain assumption Professor polynomial response surfaces interpolate the true generator response over the sampled hypercubes
    Section 3.1: the optimal tune is the minimum of fitted polynomials; with 575-950 samples in 9-11 dimensions (and only 265 valid multi-energy runs), interpolation error is unquantified.
  • domain assumption Pythia QCD-based colour reconnection [81] is needed and valid inside Herwig
    CR is switched on through TheP8I and tuned; the scheme is taken from [81] without independent validation in this setup.
  • domain assumption CT14LO PDFs are adequate for the LO event generation
    Section 3.1.2 uses Herwig's default CT14LO [101] without PDF uncertainty assessment.
  • domain assumption Linear confinement V(r) = kappa*r with kappa ~ 1 GeV/fm anchors the string picture
    Section 2, Eq. (1); the string tension is implicitly related to fragmentation parameters but not explicitly tunable.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Herwig 7 with the Lund String Model: Tuning and Comparative Hadronization Studies." pith.science (2026). https://pith.science/paper/E7HVVG33

@misc{pith2026250902348,
  author       = {Pith},
  title        = {Pith review of: Herwig 7 with the Lund String Model: Tuning and Comparative Hadronization Studies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E7HVVG33}},
  note         = {Machine review of arXiv:2509.02348}
}
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read the original abstract

The modelling of the formation of colour-singlet hadrons from coloured partons, known as Hadronization, is crucial for generating realistic events in Monte Carlo Event Generators. Due to limited understanding of the non-perturbative regime, physically motivated phenomenological hadronization models with tunable parameters are used and later tuned to the experimental data. Modern Monte Carlo generators primarily employ one of two hadronization models: the Lund string model, which is the default in Pythia, and the cluster model, which is the default in Herwig and Sherpa. In this work, we combine the Lund string hadronization model, as implemented in Pythia 8, with Herwig 7 using TheP8I interface. We tune the string model with Herwig 7's Angular Ordered Parton Shower (AOPS) to lepton and hadron collision data, resulting in the Les Houches Tune (LH Tune), which shows good performance across a wide range of observables. The LH Tune will be included in the Herwig 7.4 release. This development enables a direct comparative study of the two hadronization models within Herwig, both interfaced with the Angular Ordered Parton Shower, which serves as the main motivation behind this work.

Figures

Figures reproduced from arXiv: 2509.02348 by Andrzej Si\'odmok, Michaela Divisova, Miroslav Myska, Pratixan Sarmah.

Figure 1
Figure 1. Figure 1: b. Such a distribution indicates that there is a wide space for finding the optimal values of other pa￾rameters. Subsequently, in the second stage of tuning, eleven flavour parameters listed in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of perturbative threshold p min ⊥ with the centre-of-mass energies for individual tunes and the energy extrapolated LH Tune along with a dedicated fit obtained from [119]. With the combination of these two tuning strate￾gies, we can also study the energy evolution of the min￾imal transverse momentum threshold p min ⊥ (s) separat￾ing semi-hard and soft parts of MPI modelling in [PITH_FULL_IMAGE:f… view at source ↗
Figure 2
Figure 2. Figure 2: Normalized differential cross section of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Multiplicities of identified particles: (a) mean number of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Event Shape observables measured by DELPHI experiment at LEP [ [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Inclusive single particle momentum distributions measured by DELPHI experiment at LEP [ [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Observables measured by (a) SLD [120], (b-d) L3 [121], (e-f) DELPHI [97] and (g-i) ALEPH [122] exper￾iments at LEP and SLC. These observables are not assigned any weights in the tuning procedure, which do not bias the tunes directly. The LH Tune (in red) lies within the bandwidth of other tunes and does reasonably well compared to data in these observables as well, as a test of robustness without overtunin… view at source ↗
Figure 8
Figure 8. Figure 8: Underlying Event particle multiplicity distributions in azimuthal plane relative to the leading object direc [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Underlying Event observables measured by the ATLAS experiment at 13 TeV proton collisions [ [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Underlying Event observables measured by the ATLAS experiment at 13 TeV proton collisions [ [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Minimum Bias observables measured by the ATLAS experiment at 0.9 and 7 TeV [ [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Minimum Bias observables measured by the ATLAS experiment at 13 TeV [ [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Forward rapidity gaps as measured at ALTAS [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Identified particle transverse momentum spectra for proton-proton collisions at 7 TeV. Individual plots [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Observables measured at STAR [130, 131] and SppS (using UA1-UA5 detectors) [132–134] experiments at √ s = 200 GeV. Individual plots are: Transverse momentum spectrum of (a) π + pions, (b) K+ kaons, (c) Ratio of anti-protons (p¯) to pions (π −) as a function of p⊥, (d) multiplicity distribution, (e) charged multiplicity distribution and (f) pseudorapidity distribution for NSD. matter through frontier techn… view at source ↗
Figure 16
Figure 16. Figure 16: Underlying Event measurements for charged particle multiplicity as a function of azimuthal angle related to the [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Minimum Bias measurements for the three different views on distributions of charged particle multiplicity and their [PITH_FULL_IMAGE:figures/full_fig_p026_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Underlying Event observables for proton collisions at [PITH_FULL_IMAGE:figures/full_fig_p027_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Underlying Event observables for proton anti-proton collisions at [PITH_FULL_IMAGE:figures/full_fig_p028_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Underlying Event observables for proton collisions at [PITH_FULL_IMAGE:figures/full_fig_p029_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Minimum Bias observables for proton collisions at [PITH_FULL_IMAGE:figures/full_fig_p030_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Minimum Bias observables for proton anti-proton collisions at [PITH_FULL_IMAGE:figures/full_fig_p030_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Minimum Bias observables for proton collisions at [PITH_FULL_IMAGE:figures/full_fig_p031_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: A selection of Underlying Event and Minimum Bias observables for proton collisions at [PITH_FULL_IMAGE:figures/full_fig_p032_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: A selection of Underlying Event and Minimum Bias observables for proton collisions at [PITH_FULL_IMAGE:figures/full_fig_p032_25.png] view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 5, 2026.