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Three-dimensional femtoscopy for proton pairs in heavy-ion collisions

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Adam Kisiel

High Energy Physics - Experiment · Submitted 8 May 2025 · 52 references

Pith's verdict: A genuinely useful methods paper for 3D proton femtoscopy, with a slightly overstated accuracy claim and a closed-loop wave-function test that the paper itself acknowledges.

T0 · AI review

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arXiv ID2505.05276 (version 1)
Pith IDB4NJDDCJ, Pith's permanent record of this paper and its review
CitationAdam Kisiel. "Three-dimensional femtoscopy for proton pairs in heavy-ion collisions." arXiv:2505.05276 (2025). https://pith.science/paper/B4NJDDCJ
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The paper

The paper claims

This paper establishes a complete, model-validated recipe for three-dimensional femtoscopic analysis of proton pairs, based on spherical-harmonics decomposition and a full proton-proton wave function, with fitted radii matching simulated…

The reading

Femtoscopy has long measured the size and dynamics of the fireball created in heavy-ion collisions, but full three-dimensional analyses existed only for pions and kaons. This paper extends that program to proton pairs, where the correlation is shaped as much by Coulomb and strong final-state interactions as by quantum statistics. It proposes storing the correlation function in spherical harmonics—reducing the data to three informative one-dimensional components—and fitting it with a numerical procedure that uses a full proton-proton wave function. On simulated Pb-Pb collisions at collider energies, the fitted source radii match the model input within 5–7 percent, establishing the feasibility of true three-dimensional proton femtoscopy in experiments. The 'outward' radius needs careful reading: in the pair rest frame it is a clean size measurement, while in the longitudinally co-moving frame it mixes source size with emission-time spread.

What carries the argument

The central object is the spherical-harmonics decomposition of the three-dimensional correlation function, $C_l^m(k^*) = \int C(\vec{k}^{\,*}) Y_l^m(\theta_k,\phi_k) \, d\cos\theta_k\, d\phi_k$. For identical protons, symmetry makes all odd-$l$ components vanish and leaves only three components carrying the source-shape information: $C_0^0$ (average size), $C_2^0$ (longitudinal-versus-transverse asymmetry), and $C_2^2$ (out-versus-side asymmetry). The other half of the machinery is the proton-proton wave function, combining (anti)symmetrization of the singlet and triplet spin states with Coulomb and strong final-state interactions in the effective-range approximation. The numerical fitting program evaluates the femtoscopic correlation integral for each grid point in $(R_{\rm out}, R_{\rm side}, R_{\rm long})$ by Monte Carlo sampling of the pair source, builds the correlation directly in spherical harmonics, and minimizes $\chi^2$ over the grid.

Extended reading notes

Core claim

The central claim is that a three-dimensional femtoscopic correlation function for identical protons can be built and fitted without ever forming a three-dimensional histogram. The correlation is decomposed directly into spherical harmonics; for identical protons all odd-$l$ components vanish, and the relevant information is carried by three components: $C_0^0$ (average size), $C_2^0$ (longitudinal versus transverse difference), and $C_2^2$ (out versus side difference). The proton-proton pair wave function includes quantum statistics plus Coulomb and strong final-state interactions, evaluated with the effective-range approximation for singlet and triplet scattering amplitudes. Fitting this wave function through the standard femtoscopic integral against simulated correlations from a hydrodynamic model tuned to Pb-Pb collisions at 2.76 TeV, the method recovers the input source radii in the side and longitudinal directions to within 5% and 7%, and the outward radius in the pair rest frame to within 5%. The outward radius in the longitudinally co-moving frame is an effective quantity, because it necessarily mixes the spatial width with the emission-time difference and space-time correlations.

Load-bearing premise

The whole validation uses the same proton-proton wave-function model to create the data and to fit it; if that wave function is not realistic enough for real protons, the demonstrated accuracy may not carry over to experiment.

Editorial extensions

If this is right

  • Heavy-ion experiments at current and upcoming colliders can plan full three-dimensional proton-proton femtoscopy analyses, since the fitting pipeline runs in hours on a desktop computer.
  • The side and longitudinal radii, and the outward radius defined in the pair rest frame, are directly comparable to model source distributions; only the outward radius in the longitudinally co-moving frame should be read as an effective, time-convoluted quantity.
  • Because the method is fully numerical, non-Gaussian source profiles, alternative reference frames, or more sophisticated wave functions can be substituted without changing the overall analysis workflow.
  • Any comparison of measured three-dimensional radii with model predictions should extract the model radii through the same correlation-function fitting procedure, rather than from single-particle source distributions, to include time-difference and space-time correlation effects.
  • The procedure is ready for application to real data, provided experimental effects such as momentum resolution and particle-identification purity are corrected by the measuring collaboration.

Reading between the lines

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

  • The same spherical-harmonics pipeline should transfer to other baryon pairs with strong final-state interactions, such as Lambda-Lambda pairs, provided their wave functions are known; the paper validates only protons but the machinery is pair-type agnostic.
  • The demonstration that the outward radius in the longitudinally co-moving frame mixes spatial and temporal widths implies that past comparisons of pion and kaon outward radii with models may need revisiting if they did not account for emission-time differences.
  • At lower collision energies where protons are the most abundant particles, this method could make three-dimensional proton femtoscopy a practical baryon-sector probe of phase-transition signatures, not just an average-size measurement.
  • A concrete next test would be applying the same pipeline to high-multiplicity small systems, such as proton-proton or proton-nucleus collisions, where source sizes fall below the tested lower bound and the Gaussian source assumption may be strained.
Original abstract

Femtoscopy, a technique of measuring the size and the dynamics of the system created in heavy-ion collisions is used extensively in experiments at RHIC, LHC, SPS, and the FAIR/GSI. Analysis for pairs of pions is most common, due to their large abundance in the collisions, as well as well-understood theoretical formalism and advanced experimental methodology. It is usually performed in three dimensions in longitudinally co-moving reference frame of the pair, to maximize the amount of information obtained about the source. Similar three-dimensional analysis has also been performed for charged and neutral kaons. In contrast analyses for all other pair types -- either for pairs of identical protons, or for pairs of non-identical particles are only one-dimensional. The abundance of heavier particles is lower than for pions, while the theoretical formalism for such correlations, as well as practical experimental methodology is limited to one-dimensional case up to now. This work identifies specific challenges arising in the analysis of three-dimensional proton-proton femtoscopy and proposes a theoretical formalism to analyze them, as well as specific experimental methods to extract and fit correlations. A test and validation of these methods is performed on correlations simulated in the LHyquid+Therminator2 model, and demonstrates the feasibility of such analysis. The caveats in the theoretical interpretation of the results are discussed, by comparing the fitted values of femtscopic radii with the true characteristics of the source extracted directly from the model.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,011 input tokens.

What the abstract itself states, as probabilities: claims first 0.26 · states limitation 0.88 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.54 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Femtoscopy, a technique of measuring the size and the dynamics of the system created in heavy-ion collisions is used extensively in experiments at RHIC, LHC, SPS, and the FAIR/GSI. Analysis for pairs of pions is most common, due to their large abundance in the collisions, as well as well-understood theoretical formalism and advanced experimental methodology. It is usually performed in three dimensions in longitudinally co-moving reference frame of the pair, to maximize the amount of information obtained about the source. Similar three-dimensional analysis has also been performed for charged and neutral kaons. In contrast analyses for all other pair types -- either for pairs of identical protons, or for pairs of non-identical particles are only one-dimensional. The abundance of heavier particles is lower than for pions, while the theoretical formalism for such correlations, as well as practical experimental methodology is limited to one-dimensional case up to now. This work identifies specific challenges arising in the analysis of three-dimensional proton-proton femtoscopy and proposes a theoretical formalism to analyze them, as well as specific experimental methods to extract and fit correlations. A test and validation of these methods is performed on correlations simulated in the LHyquid+Therminator2 model, and demonstrates the feasibility of such analysis. The caveats in the theoretical interpretation of the results are discussed, by comparing the fitted values of femtscopic radii with the true characteristics of the source extracted directly from the model.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Femtoscopy, a technique of measuring the size and the dynamics of the system created in heavy-ion collisions is used extensively in experiments at RHIC, LHC, SPS, and the FAIR/GSI. background 1.00 0.04 0.02 asserted 1.00
s1 Analysis for pairs of pions is most common, due to their large abundance in the collisions, as well as well-understood theoretical formalism and advanced experimental methodology. background 1.00 0.04 0.02 asserted 1.00
s2 It is usually performed in three dimensions in longitudinally co-moving reference frame of the pair, to maximize the amount of information obtained about the source. background 0.97 0.07 0.02 asserted 1.00
s3 Similar three-dimensional analysis has also been performed for charged and neutral kaons. background 0.99 0.08 0.02 asserted 1.00
s4 In contrast analyses for all other pair types -- either for pairs of identical protons, or for pairs of non-identical particles are only one-dimensional. gap 0.79 0.07 0.05 asserted 1.00
s5 The abundance of heavier particles is lower than for pions, while the theoretical formalism for such correlations, as well as practical experimental methodology is limited to one-dimensional case up to now. gap 0.83 0.05 0.03 asserted 1.00
s6 This work identifies specific challenges arising in the analysis of three-dimensional proton-proton femtoscopy and proposes a theoretical formalism to analyze them, as well as specific experimental methods to extract and fit correlations. contribution 1.00 0.95 0.35 asserted 1.00
s7 A test and validation of these methods is performed on correlations simulated in the LHyquid+Therminator2 model, and demonstrates the feasibility of such analysis. method 0.43 0.95 0.39 asserted 1.00
s8 The caveats in the theoretical interpretation of the results are discussed, by comparing the fitted values of femtscopic radii with the true characteristics of the source extracted directly from the model. limitation 0.79 0.87 0.09 asserted 0.87

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1. Proton-proton femtoscopic correlation function fo
Figure 2. FIG. 2. Proton-proton correlation functions for example
Figure 3. FIG. 3. Proton-proton correlation functions for example
Figure 4. FIG. 4. Results of the three-dimensional LCMS
Figure 5. FIG. 5. Results of the one-dimensional PRF fits
Figure 6. FIG. 6. Comparison of the input model source distributions
Figure 7. FIG. 7. Comparison of input model radii estimated directly
Figure 9. FIG. 9. Comparison of input model radii estimated directly
Figure 10. FIG. 10. Distributions of
Figure 11. FIG. 11. Comparison of the width of the

Showing 10 of the paper's 11 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2505.05276 by the authors.

References

Discussion

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