REVIEW
Simulating the emission source function in very peripheral relativistic heavy-ion collisions
High Energy Physics - Phenomenology · Submitted 23 Sep 2026 · 57 references
Pith's verdict: A competent, genuinely new hybrid-model source-reconstruction study whose headline m_T-scaling claim is under-pinned by fits with no reported uncertainties or ranges; worth a serious referee, but the trend needs to be re-grounded before it is publishable as stated.
T0 · AI review
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Referee report
The paper
The paper claims
In the most peripheral Pb-Pb collisions, a hybrid transport simulation reconstructs the hadron emission source and shows that a single Gaussian fit is inadequate: a Gaussian-plus-exponential form isolates a compact core whose radii…
The reading
What carries the argument
The central tool is emission-coordinate reconstruction from the afterburner record: each particle's final four-momentum is propagated back along a straight line to the time of its last interaction or decay, so every pair in the pair rest frame (PRF) carries a relative separation r* that is histogrammed into a radial source function. The source is fitted with the Gaussian-plus-exponential form S_G+E(r*) = A[f_core exp(-r*^2/(4 $R_core^{2}$)) + (1-f_core) exp(-|r*|/R_tail)], whose Gaussian part isolates the compact core radius R_core while the exponential term absorbs the long-range tail. The LCMS-to-PRF boost, which mixes the emission-time difference with the out component and visibly widens the out profile, together with the Cooper-Frye sampling of the e_crit = 0.5 GeV/$fm^{3}$ particlization hypersurface, sets the scale of the reported R_core values.
Extended reading notes
Core claim
The paper claims that in 80–90% centrality Pb–Pb collisions at sqrt(s_NN) = 5.02 TeV, the emission source function, reconstructed microscopically from the SMASH–vHLLE–SMASH afterburner record, is non-Gaussian: a compact core carries most pairs, but long-range tails generated mainly by long-lived resonance decays extend the source far beyond any single Gaussian fit. Fitting the radial source function in the pair rest frame with a Gaussian-plus-exponential form, the Gaussian core radii R_core for pion, kaon, proton, and cross-species pairs decrease monotonically with transverse mass and lie approximately on one common curve. The authors read this common trend as the m_T-scaling already seen in pp collisions, extended to the most peripheral Pb–Pb collisions, with radii somewhat larger than in pp as expected for a bigger system. They infer that the compact part of the freeze-out source in these very peripheral collisions is set by the same common m_T-dependent kinematic scale seen in small systems.
Load-bearing premise
The load-bearing premise is that the SMASH–vHLLE–SMASH chain with eta/s = 0.08, tau_0 = 0.5 fm/c, and particlization at e_crit = 0.5 GeV/$fm^{3}$ reproduces the true space-time emission geometry of very peripheral Pb–Pb collisions, and since the primordial core radii come directly from that particlization hypersurface, an unpinned freeze-out criterion would contaminate the reported R_core(m_T) trend.
Editorial extensions
If this is right
- Precision femtoscopy in peripheral heavy-ion collisions needs a two-component source parametrization, because a single Gaussian systematically misses the extended tails in all OSL components and in the radial source.
- The compact freeze-out core in 80–90% centrality Pb–Pb appears to be governed by a common m_T-dependent scale shared across pion, kaon, proton, and cross-species pairs, extending the pp m_T-scaling picture to very peripheral heavy-ion collisions.
- Resonance decays, not hadronic rescattering, drive the long-range non-Gaussian structure: rescattering barely changes the emission geometry, while decay products emitted deep inside the light cone at large time delays populate the tails.
- The LCMS-to-PRF boost couples the emission-time difference to the out direction, so the choice of reference frame materially reshapes the extracted source size and must be handled explicitly in source analyses.
- Future high-precision femtoscopy and source-imaging analyses must adopt core-plus-tail decompositions rather than assuming Gaussian sources.
Reading between the lines
- If the common m_T-scaling holds, the difference between very peripheral Pb–Pb and pp may reduce to a single overall size scale, implying that hydrodynamic flow in the freeze-out layer sets the core size even at this low multiplicity.
- Because the reported trend rests on a single particlization criterion, rerunning the chain at different e_crit values and checking whether the common R_core(m_T) curve survives would separate a kinematic origin of the scaling from a freeze-out-model artifact.
- The mechanism implies m_T-scaling should degrade progressively as centrality moves inward; mapping where the common trend breaks against the more central Pb–Pb radii would sharpen the boundary of the small-system-like regime.
- A direct experimental check is available: high-precision source imaging of 80–90% centrality Pb–Pb should show both the two-component structure and the pp-like common m_T-scaling curve.
Original abstract
We present a microscopic femtoscopic investigation of the space-time emission source in low-multiplicity (80--90\% centrality) $\text{Pb}-\text{Pb}$ collisions at $\sqrt{s_{NN}} = 5.02~\text{TeV}$, using a hybrid transport framework coupling SMASH initial conditions, 3+1D viscous hydrodynamics (vHLLE), and a SMASH hadronic cascade afterburner. Access to the full space-time evolution of the produced particles allows for the direct reconstruction of emission source functions in both the Longitudinally Comoving System and the Pair Rest Frame. We study identical pairs of mesons ($\pi\pi$, $KK$) and baryons ($pp$), as well as cross-species combinations, while explicitly isolating the contributions from primordial particles, hadronic rescattering, and long-lived resonance decays. Our analysis shows that simple Gaussian fits are inadequate for precision source analyses, whereas a combined Gaussian plus exponential parametrization better captures the compact core and the extended tail. Finally, the extracted Gaussian core radii, $R_{\text{core}}$, for our very peripheral collisions demonstrate an approximate $m_T$-scaling behavior rather similar to the one observed in pp reactions.
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.
The abstract, sentence by sentence
We present a microscopic femtoscopic investigation of the space-time emission source in low-multiplicity (80--90\% centrality) $\text{Pb}-\text{Pb}$ collisions at $\sqrt{s_{NN}} = 5.02~\text{TeV}$, using a hybrid transport framework coupling SMASH initial conditions, 3+1D viscous hydrodynamics (vHLLE), and a SMASH hadronic cascade afterburner. Access to the full space-time evolution of the produced particles allows for the direct reconstruction of emission source functions in both the Longitudinally Comoving System and the Pair Rest Frame. We study identical pairs of mesons ($\pi\pi$, $KK$) and baryons ($pp$), as well as cross-species combinations, while explicitly isolating the contributions from primordial particles, hadronic rescattering, and long-lived resonance decays. Our analysis shows that simple Gaussian fits are inadequate for precision source analyses, whereas a combined Gaussian plus exponential parametrization better captures the compact core and the extended tail. Finally, the extracted Gaussian core radii, $R_{\text{core}}$, for our very peripheral collisions demonstrate an approximate $m_T$-scaling behavior rather similar to the one observed in pp reactions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a microscopic femtoscopic investigation of the space-time emission source in low-multiplicity (80--90\% centrality) $\text{Pb}-\text{Pb}$ collisions at $\sqrt{s_{NN}} = 5.02~\text{TeV}$, using a hybrid transport framework coupling SMASH initial conditions, 3+1D viscous hydrodynamics (vHLLE), and a SMASH hadronic cascade afterburner. | contribution 0.60 | 0.94 | 0.04 | asserted 0.96 |
| s1 | Access to the full space-time evolution of the produced particles allows for the direct reconstruction of emission source functions in both the Longitudinally Comoving System and the Pair Rest Frame. | method 0.81 | 0.57 | 0.04 | asserted 0.85 |
| s2 | We study identical pairs of mesons ($\pi\pi$, $KK$) and baryons ($pp$), as well as cross-species combinations, while explicitly isolating the contributions from primordial particles, hadronic rescattering, and long-lived resonance decays. | contribution 0.56 | 0.93 | 0.04 | asserted 0.93 |
| s3 | Our analysis shows that simple Gaussian fits are inadequate for precision source analyses, whereas a combined Gaussian plus exponential parametrization better captures the compact core and the extended tail. | result 0.98 | 0.94 | 0.27 | asserted 1.00 |
| s4 | Finally, the extracted Gaussian core radii, $R_{\text{core}}$, for our very peripheral collisions demonstrate an approximate $m_T$-scaling behavior rather similar to the one observed in pp reactions. | result 0.98 | 0.96 | 0.49 | asserted 0.98 |
What was examined, and what was not
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Figures
Showing 8 of the paper's 10 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2609.28394 by the authors.
References
Discussion
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