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arxiv: 2606.28098 · v1 · pith:XAZBSPIXnew · submitted 2026-06-26 · ⚛️ nucl-ex · hep-ex

Multiplicity dependence of the size of the common hadron emission source in pp collisions at the LHC

ALICE Collaboration This is my paper

Pith reviewed 2026-06-29 01:44 UTC · model grok-4.3

classification ⚛️ nucl-ex hep-ex
keywords femtoscopypp collisionssource radiusmultiplicity dependenceproton correlationsLHChadron emissionALICE
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The pith

The hadron emission source in pp collisions has a multiplicity dependence distinct from that in Pb-Pb collisions.

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

The analysis extracts the spatial size of the common hadron-emitting source in proton-proton collisions at 13.6 TeV by measuring two-proton correlation functions with the upgraded ALICE detector. The source radii are obtained by fitting the data under several models of the nucleon-nucleon interaction, and the extracted values remain consistent across those models. When placed on the same transverse-mass intervals, the multiplicity scaling of the radii differs markedly from the scaling previously measured in Pb-Pb collisions at 5.02 TeV. This contrast supplies direct information on how the emission region grows with the number of produced particles in small versus large collision systems.

Core claim

Femtoscopic radii extracted from pp collisions at 13.6 TeV exhibit a multiplicity dependence that is markedly different from those in Pb-Pb collisions at 5.02 TeV in similar m_T intervals. The radii are determined from measured correlation functions by assuming several state-of-the-art models of nucleon-nucleon interactions; the consistency among the resulting radii demonstrates robustness with respect to interaction-model assumptions. Precise knowledge of the source size in pp collisions is required for subsequent studies of residual strong interactions among hadrons.

What carries the argument

Femtoscopic extraction of source radius from two-proton correlation functions, using nucleon-nucleon interaction models to convert measured correlations into radii.

If this is right

  • The source-size baseline established in pp collisions can be used to interpret femtoscopic studies of residual strong interactions among other hadron pairs.
  • The observed difference in multiplicity dependence between pp and Pb-Pb systems constrains models of how the emission volume scales with collision-system size.
  • The simultaneous measurement of multiplicity and m_T dependence supplies a reference for testing whether hydrodynamic or string-fragmentation pictures correctly describe particle emission in small systems.

Where Pith is reading between the lines

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

  • The different scaling may indicate that initial-state geometry or non-equilibrium effects play a larger role in setting the emission region in pp than in heavy-ion collisions.
  • Extending the same femtoscopic technique to other small systems such as p-Pb could test whether the multiplicity dependence follows a universal curve or depends on the projectile size.
  • The data set could be re-analyzed with additional pair species to check whether the source size is species-independent at fixed multiplicity and m_T.
  • pith_inferences are editorial extensions and not claims made by the paper.

Load-bearing premise

The conversion of measured correlation functions into source radii assumes that the chosen nucleon-nucleon interaction models are accurate enough to separate the source geometry from the final-state interaction.

What would settle it

A measurement in which the extracted radii vary significantly when different nucleon-nucleon interaction models are substituted would indicate that the source-size values are not robust.

Figures

Figures reproduced from arXiv: 2606.28098 by ALICE Collaboration.

Figure 1
Figure 1. Figure 1: Real part of the radial p–p wave functions for Argonne v18 (blue), Norfolk NV2-II A (green), and ChEFT potentials (red) as a function of the relative nucleon-nucleon distance r. The ratio in the lower panels is obtained w.r.t. Argonne v18. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left panel: the real part of the p–p wave functions obtained from the four variations of the Norfolk potential (black and blue lines together with black axis) and the two Gaussian source distributions (red lines with red axis) as a function of the relative nucleon–nucleon distance r. Right panel: the calculated p–p correlation functions for all the potential variations and the two source radii. The correla… view at source ↗
Figure 3
Figure 3. Figure 3: Fits of the measured p–p (upper row) and p–p (lower row) correlation functions in all multiplicity ranges and mT range [1.02,1.14]GeV/c 2 fitted with the RSM. The total fit with uncertainties is indicated by the blue band and the baseline with uncertainties is indicated by the red band. Statistical uncertainties are indicated by the vertical error bars and are smaller than the markers. Systematic uncertain… view at source ↗
Figure 4
Figure 4. Figure 4: Fits of the measured p–p (upper row) and p–p (lower row) correlation functions in all multiplicity ranges and mT range [1.56,1.86]GeV/c 2 fitted with the RSM. For detailed description see [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The mT dependence of the effective radius r0 (left) and the core radius rcore (right) for different multi￾plicity classes. The black data points are from a previous analysis using a high-multiplicity data set collected by ALICE at √ s = 13 TeV [16, 17]. Here, INEL> 0 refers to inelastic pp collisions with at least one charged particle in the event within |η| < 1.0 [2], while 0–0.17% denotes the highest-mul… view at source ↗
Figure 6
Figure 6. Figure 6: The mT dependence of the effective radius r0 (left) and the core radius rcore (right) for two different multiplicity classes. The red data points correspond to the extraction of the radii using this analysis’s full MB data set. The black data points are from a previous analysis using a high-multiplicity data set collected by ALICE at √ s = 13 TeV [16, 17]. The bands correspond to the parametrization of the… view at source ↗
Figure 7
Figure 7. Figure 7: The uncertainties correspond to the 1σ spread obtained by repeating the fit while varying the data points within their uncertainties. mT [GeV/c 2 ] m [fm] t [fm] pp [1.02,1.14) 0.253+0.002 −0.002 0.569+0.024 −0.024 [1.14,1.20) 0.253+0.004 −0.004 0.518+0.028 −0.028 [1.20,1.26) 0.276+0.004 −0.004 0.388+0.030 −0.020 [1.26,1.38) 0.218+0.010 −0.005 0.515+0.045 −0.020 [1.38,1.56) 0.195+0.012 −0.003 0.527+0.050 −… view at source ↗
Figure 7
Figure 7. Figure 7: Multiplicity dependence of the effective radius r0 for various mT intervals measured in pp and Pb– Pb collisions [53]. The bands represent the parametrization for different multiplicity classes, shown with a 1σ uncertainty. Note that the mT intervals differ between the two collision systems. - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Educa￾tion, Culture, Sp… view at source ↗
read the original abstract

Femtoscopic analysis can shed light on hadron production in pp collisions. In this paper, proton-proton correlations measured in collisions at $\sqrt{s}=13.6$ TeV recorded with the ALICE detector at the LHC are presented. The analysis is based on the minimum bias dataset collected in 2022 following the upgrade of the ALICE detector and corresponds to an integrated luminosity of $19.3$ pb$^{-1}$. The increased integrated luminosity allows us, for the first time, to simultaneously measure the multiplicity and transverse-mass ($m_{\rm T}$) dependence of the size of the hadron-emitting source. Precise knowledge of the femtoscopic source size in pp collisions is a crucial ingredient for using femtoscopy to study the residual strong interaction among stable and unstable hadrons at the LHC. In this light, the source radius was determined from the measured correlation functions by assuming several state-of-the-art models of the nucleon$-$nucleon interactions. The consistency among the extracted radii demonstrates the robustness of the measurement with respect to interaction model assumptions. A comparison to femtoscopic radii measured in Pb$-$Pb collisions at $\sqrt{s}=5.02$ TeV reveals a markedly different multiplicity dependence in similar $m_{\rm T}$ intervals, providing new insight into the system-size dependence of particle emission dynamics.

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

0 major / 1 minor

Summary. The manuscript reports proton-proton femtoscopic correlation functions measured in minimum-bias pp collisions at √s=13.6 TeV with the upgraded ALICE detector, using an integrated luminosity of 19.3 pb^{-1}. The source radius is extracted simultaneously as a function of charged-particle multiplicity and transverse mass m_T by fitting the measured correlation functions with several state-of-the-art nucleon-nucleon interaction models; the extracted radii are shown to be consistent across models. A direct comparison to femtoscopic radii from Pb-Pb collisions at √s=5.02 TeV in similar m_T intervals reveals a qualitatively different multiplicity dependence, interpreted as new insight into system-size dependence of particle emission dynamics.

Significance. If the central extraction and comparison hold, the result supplies a data-driven benchmark for the multiplicity and m_T evolution of the emission source in small collision systems. This benchmark is directly relevant to ongoing femtoscopic analyses of residual strong interactions among stable and unstable hadrons at the LHC. The use of multiple external interaction models together with a large dataset and explicit cross-checks of model dependence strengthens the robustness of the reported radii.

minor comments (1)
  1. [Abstract] Abstract: the abstract provides no details on systematic uncertainties, error bars, or data-selection criteria, which would allow full verification of the extracted radii and the multiplicity dependence claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript, the recognition of its robustness through the use of multiple interaction models and large dataset, and the recommendation to accept.

Circularity Check

0 steps flagged

No significant circularity; derivation is data-driven from external models

full rationale

The paper measures p-p correlation functions directly from LHC data, then converts them to source radii using NN interaction models taken from external literature (not fitted or derived inside this work). Radii are reported as consistent across several such models, and the multiplicity dependence is compared to independent Pb-Pb measurements. No equation reduces a claimed prediction to a fitted parameter or self-citation by construction; the central claim rests on external benchmarks and direct data comparison.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that femtoscopic correlation functions can be inverted to source radii once nucleon-nucleon interaction models are supplied; no new free parameters or invented entities are introduced.

axioms (1)
  • domain assumption Femtoscopic correlations measured in momentum space can be used to extract the spatial size of the hadron emission source when nucleon-nucleon interaction potentials are known.
    Invoked to determine the source radius from the measured correlation functions.

pith-pipeline@v0.9.1-grok · 5761 in / 1251 out tokens · 28529 ms · 2026-06-29T01:44:30.268943+00:00 · methodology

discussion (0)

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Reference graph

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