pith. sign in

arxiv: 2607.01783 · v1 · pith:QREP7A6Onew · submitted 2026-07-02 · ✦ hep-ph · hep-ex· hep-th

Subensemble Acceptance Method 3.0: General Corrections to Cumulants from Exact Conservation Constraints

Roman Poberezhnyuk , Volodymyr A. Kuznietsov , Gr\'egoire Pihan , Volodymyr Vovchenko This is my paper

Pith reviewed 2026-07-03 11:14 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-th
keywords subensemble acceptance methodcumulantsexact conservationcanonical ensemblegrand-canonical ensembleBell polynomialsnet-proton cumulantsheavy-ion collisions
0
0 comments X

The pith

SAM-3.0 corrects cumulants for exact global conservation of multiple charges via algebraic recursion.

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

The paper introduces SAM-3.0 to adjust cumulants measured in a subsystem for the effects of exact conservation of multiple global charges in the full system. It takes joint grand-canonical cumulants of the observable with the total charges as input and produces the canonical cumulants through a closed recursion based on multivariate partial exponential Bell polynomials. The method handles any number of observables and conserved charges, including non-conserved quantities like net protons and total energy for the microcanonical case, while recovering SAM-1.0 and SAM-2.0 as special cases and matching the exact binomial acceptance limit. It also supplies leading finite-size corrections from the saddle-point expansion and is applied to refine the hydrodynamics baseline for net-proton cumulants at RHIC-BES energies.

Core claim

The central claim is that the canonical cumulants follow algebraically from the joint grand-canonical cumulants of the acceptance observable with the total event charges through a closed recursion based on multivariate partial exponential Bell polynomials, accommodating any number of conserved charges and observables while reproducing the exact binomial-acceptance limit and containing prior versions as special cases.

What carries the argument

The SAM-3.0 recursion based on multivariate partial exponential Bell polynomials, which maps the required joint grand-canonical cumulants to the canonical cumulants.

If this is right

  • The method applies to any number of observables and any number of simultaneously conserved charges, including total energy.
  • It reproduces the exact binomial-acceptance limit and contains SAM-1.0 and SAM-2.0 as special cases.
  • Leading finite-size corrections follow from the saddle-point expansion.
  • The updated hydrodynamics-based baseline for net-proton cumulants at RHIC-BES energies agrees with direct canonical Monte Carlo sampling.
  • The formalism is validated against Monte Carlo sampling that includes hadronic-afterburner effects.

Where Pith is reading between the lines

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

  • The algebraic structure may allow direct incorporation of exact conservation into existing grand-canonical model calculations without full canonical resampling.
  • Refined baselines from this method could sharpen searches for non-monotonic cumulant behavior in heavy-ion data.
  • The recursion might be combined with other expansion techniques to handle additional dynamical correlations beyond the ensembles considered.

Load-bearing premise

The joint grand-canonical cumulants of the acceptance observable with the total event charges must be accurately known or independently computable as input.

What would settle it

Direct Monte Carlo sampling with exact simultaneous conservation of baryon number, electric charge, and strangeness that produces cumulants differing from the recursion output.

Figures

Figures reproduced from arXiv: 2607.01783 by Gr\'egoire Pihan, Roman Poberezhnyuk, Volodymyr A. Kuznietsov, Volodymyr Vovchenko.

Figure 1
Figure 1. Figure 1: Cumulant ratios of the accepted multiplicity [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Hydro-EV non-critical baseline for net-proton cumulant ratios (top row) and proton factorial cumulant ratios [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between grand-canonical + SAM-3.0 and direct canonical Monte Carlo sampling on the hypersurface [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Hydro-EV calculations of the proton (blue) and antiproton (red) factorial cumulant ratios [PITH_FULL_IMAGE:figures/full_fig_p027_5.png] view at source ↗
read the original abstract

We present the subensemble acceptance method 3.0 (SAM-3.0), which corrects cumulants of an observable measured in a subsystem of a large system for the effect of exact global conservation of multiple charges. The required input is the set of joint grand-canonical cumulants of the acceptance observable with the total event charges, from which the canonical cumulants follow algebraically via a closed recursion based on (multivariate) partial exponential Bell polynomials. The framework accommodates any number of observables, including non-conserved quantities such as net protons, and any number of simultaneously conserved charges, including the total energy, which yields the microcanonical ensemble. The mapping contains SAM-1.0 and SAM-2.0 as special cases and, unlike SAM-2.0, reproduces the exact binomial-acceptance limit. We also derive the leading finite-size corrections from the saddle-point expansion. We apply the method to update the hydrodynamics-based non-critical baseline (Hydro-EV) for net-proton cumulants at RHIC-BES energies, finding a refined baseline that agrees with direct canonical Monte Carlo sampling and stays close to the earlier SAM-2.0 result. We further validate the formalism against direct Monte Carlo sampling with exact simultaneous conservation of baryon number, electric charge, and strangeness, including hadronic-afterburner effects.

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 / 2 minor

Summary. The manuscript presents the Subensemble Acceptance Method 3.0 (SAM-3.0) for correcting cumulants of observables measured in a subsystem to account for exact global conservation of multiple charges. The required inputs are the joint grand-canonical cumulants of the acceptance observable with the total event charges; the canonical cumulants are then obtained algebraically via a closed recursion based on multivariate partial exponential Bell polynomials. The framework generalizes SAM-1.0 and SAM-2.0, reproduces the exact binomial-acceptance limit, accommodates arbitrary numbers of observables and charges (including energy for the microcanonical ensemble), derives leading finite-size corrections from the saddle-point expansion, updates the Hydro-EV non-critical baseline for net-proton cumulants at RHIC-BES energies, and validates the results against direct Monte Carlo sampling with exact simultaneous conservation of baryon number, electric charge, and strangeness, including afterburner effects.

Significance. If the algebraic mapping holds, the work supplies an exact, general, and parameter-free tool for conservation corrections in cumulant measurements. This is valuable for establishing reliable non-critical baselines in heavy-ion collision fluctuation studies. The closed recursion on standard combinatorial objects (multivariate partial exponential Bell polynomials) together with direct Monte Carlo validation against exact sampling constitutes a clear methodological advance over prior versions.

minor comments (2)
  1. [Introduction / Methods] The abstract states that the mapping contains SAM-1.0 and SAM-2.0 as special cases; the main text should include an explicit paragraph or appendix showing the reduction conditions for each prior version to aid readers.
  2. [Formalism] Notation for the multivariate partial exponential Bell polynomials should be cross-referenced to a standard reference (e.g., the original Bell or Comtet) at first appearance to ensure reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment, accurate summary of the SAM-3.0 framework, and the recommendation to accept. No major comments were raised that require clarification or revision.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The central derivation is an exact algebraic recursion expressing canonical cumulants in terms of supplied joint grand-canonical cumulants via multivariate partial exponential Bell polynomials. This mapping is self-contained combinatorial mathematics, contains earlier SAM versions only as special cases, reproduces the binomial limit by direct substitution, and is validated by independent Monte Carlo sampling with exact conservation. No parameter is fitted to the target observable, no uniqueness theorem is imported from self-citation to force the result, and the hydrodynamics baseline is an external application rather than an internal input. The derivation therefore stands on its own equations without reduction to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the application of standard combinatorial mathematics (multivariate partial exponential Bell polynomials) to map between ensembles; no free parameters are introduced or fitted in the core method, and no new physical entities are postulated.

axioms (1)
  • standard math Canonical cumulants follow algebraically from grand-canonical joint cumulants via a closed recursion based on multivariate partial exponential Bell polynomials
    Explicitly stated in the abstract as the mechanism for obtaining the corrected cumulants.

pith-pipeline@v0.9.1-grok · 5797 in / 1440 out tokens · 55077 ms · 2026-07-03T11:14:20.344087+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

67 extracted references · 56 canonical work pages · 26 internal anchors

  1. [1]

    Single observable and single conserved charge In the one-dimensional setting of Sec. II (d=1,s=1), with an arbitrary observableXin the acceptance and a single conserved chargeB tot, assumption (ii) impliesκ n,m(Xin, Btot) =κ n,m(Xin, Bin) forn≥1, since all cross- correlations withB out vanish upon expandingB tot =B in +B out. The right-hand side is a pure...

  2. [2]

    Multiple observables and conserved charges In the multidimensional setting of Sec. III (dobservables,scharges), the SAM-1.0 assumptions generalize, forn̸=0, to κXB n m (Xin,B tot) =α κ XB n m (Xtot,B tot).(77) For a single observableX, the second-order diagonal canonical cumulant (60) becomes κX|B 2 =α β κ Xtot 2 +α 2 κXtot 2 −κ(X tot, Ba) (K−1)ab κ(Xtot,...

  3. [3]

    In the present setup, we assume that the single charge corresponds to a conserved particle number, i.e

    Single conserved particle number A useful analytic benchmark is provided by the binomial acceptance limit, where an observed conserved charge inside the acceptance is obtained by independent Bernoulli sampling from the corresponding total charge carriers in the full event [43]. In the present setup, we assume that the single charge corresponds to a conser...

  4. [4]

    conserved charge

    Multiple conserved charges The multidimensional binomial-acceptance framework, with species-dependent acceptance probabilities and arbi- trary observables, is derived in Appendix C. There we obtain the canonical multi-charge binomial cumulants without deriving the constrained multivariate distribution: we compute the unconstrained grand-canonical binomial...

    2025

  5. [5]

    M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Signatures of the tricritical point in QCD, Phys. Rev. Lett.81, 4816 (1998), arXiv:hep-ph/9806219 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  6. [6]

    M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Event-by-event fluctuations in heavy ion collisions and the QCD critical point, Phys. Rev. D60, 114028 (1999), arXiv:hep-ph/9903292 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  7. [7]

    M. A. Stephanov, Non-Gaussian Fluctuations near the QCD Critical Point, Phys. Rev. Lett.102, 032301 (2009), arXiv:0809.3450 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  8. [8]

    M. A. Stephanov, Sign of Kurtosis near the QCD Critical Point, Phys. Rev. Lett.107, 052301 (2011), arXiv:1104.1627 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  9. [9]

    The QCD Equation of State to $\mathcal{O}(\mu_B^6)$ from Lattice QCD

    A. Bazavovet al., The QCD Equation of State toO(µ 6 B) from Lattice QCD, Phys. Rev. D95, 054504 (2017), arXiv:1701.04325 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  10. [10]

    Higher order fluctuations and correlations of conserved charges from lattice QCD

    S. Borsanyi, Z. Fodor, J. N. Guenther, S. K. Katz, K. K. Szabo, A. Pasztor, I. Portillo, and C. Ratti, Higher order fluctuations and correlations of conserved charges from lattice QCD, JHEP10, 205, arXiv:1805.04445 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv

  11. [11]

    Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC

    L. Adamczyket al.(STAR), Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC, Phys. Rev. Lett.112, 032302 (2014), arXiv:1309.5681 [nucl-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  12. [12]

    Adamet al.(STAR), Nonmonotonic Energy Dependence of Net-Proton Number Fluctuations, Phys

    J. Adamet al.(STAR), Nonmonotonic Energy Dependence of Net-Proton Number Fluctuations, Phys. Rev. Lett.126, 092301 (2021), arXiv:2001.02852 [nucl-ex]

    work page arXiv 2021

  13. [13]

    M. S. Abdallahet al.(STAR), Cumulants and correlation functions of net-proton, proton, and antiproton multiplicity distributions in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider, Phys. Rev. C104, 024902 (2021), arXiv:2101.12413 [nucl-ex]

    work page arXiv 2021

  14. [14]

    B. E. Aboonaet al.(STAR), Precision Measurement of Net-Proton-Number Fluctuations in Au+Au Collisions at RHIC, Phys. Rev. Lett.135, 142301 (2025), arXiv:2504.00817 [nucl-ex]

    work page arXiv 2025

  15. [15]

    Adamczewski-Muschet al.(HADES), Proton-number fluctuations in √sNN = 2.4 GeV Au+Au collisions studied with the High-Acceptance DiElectron Spectrometer (HADES), Phys

    J. Adamczewski-Muschet al.(HADES), Proton-number fluctuations in √sNN = 2.4 GeV Au+Au collisions studied with the High-Acceptance DiElectron Spectrometer (HADES), Phys. Rev. C102, 024914 (2020), arXiv:2002.08701 [nucl-ex]

    work page arXiv 2020

  16. [16]

    Acharyaet al.(ALICE), Global baryon number conservation encoded in net-proton fluctuations measured in Pb-Pb collisions at √sNN = 2.76 TeV, Phys

    S. Acharyaet al.(ALICE), Global baryon number conservation encoded in net-proton fluctuations measured in Pb-Pb collisions at √sNN = 2.76 TeV, Phys. Lett. B807, 135564 (2020), arXiv:1910.14396 [nucl-ex]

    work page arXiv 2020

  17. [17]

    Acharyaet al.(ALICE), Closing in on critical net-baryon fluctuations at LHC energies: cumulants up to third order in Pb-Pb collisions, Phys

    S. Acharyaet al.(ALICE), Closing in on critical net-baryon fluctuations at LHC energies: cumulants up to third order in Pb-Pb collisions, Phys. Lett. B844, 137545 (2023), arXiv:2206.03343 [nucl-ex]

    work page arXiv 2023

  18. [18]

    Isserstedt, M

    P. Isserstedt, M. Buballa, C. S. Fischer, and P. J. Gunkel, Baryon number fluctuations in the QCD phase diagram from Dyson-Schwinger equations, Phys. Rev. D100, 074011 (2019), arXiv:1906.11644 [hep-ph]

    work page arXiv 2019

  19. [19]

    W.-j. Fu, J. M. Pawlowski, and F. Rennecke, QCD phase structure at finite temperature and density, Phys. Rev. D101, 054032 (2020), arXiv:1909.02991 [hep-ph]

    work page arXiv 2020

  20. [20]

    Gao and J

    F. Gao and J. M. Pawlowski, QCD phase structure from functional methods, Phys. Rev. D102, 034027 (2020), arXiv:2002.07500 [hep-ph]

    work page arXiv 2020

  21. [21]

    M. P. Pradeep, J. Karthein, K. Rajagopal, M. Stephanov, and Y. Yin, Freezing out fluctuations in Hydro+ near the QCD critical point, Phys. Rev. Lett.130, 162301 (2023), arXiv:2211.09142 [hep-ph]

    work page arXiv 2023

  22. [22]

    J. M. Karthein, M. S. Pradeep, K. Rajagopal, M. Stephanov, and Y. Yin, Quantifying fluctuation signatures of the QCD critical point using maximum entropy freeze-out, Phys. Rev. D113, 074010 (2026), arXiv:2508.19237 [nucl-th]

    work page arXiv 2026

  23. [23]

    Different Realizations of Cooper-Frye Sampling with Conservation Laws

    C. Schwarz, D. Oliinychenko, L. G. Pang, S. Ryu, and H. Petersen, Different realizations of Cooper–Frye sampling with conservation laws, J. Phys. G45, 015001 (2018), arXiv:1707.07026 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  24. [24]

    Oliinychenko and V

    D. Oliinychenko and V. Koch, Microcanonical Particlization with Local Conservation Laws, Phys. Rev. Lett.123, 182302 (2019), arXiv:1902.09775 [hep-ph]

    work page arXiv 2019

  25. [25]

    Vovchenko and V

    V. Vovchenko and V. Koch, Particlization of an interacting hadron resonance gas with global conservation laws for event- by-event fluctuations in heavy-ion collisions, Phys. Rev. C103, 044903 (2021), arXiv:2012.09954 [hep-ph]. 23

    work page arXiv 2021

  26. [26]

    Hadronic Fluctuations and Correlations

    V. Koch, Hadronic Fluctuations and Correlations, inRelativistic Heavy Ion Physics, edited by R. Stock (2010) pp. 626–652, arXiv:0810.2520 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  27. [27]

    V. V. Begun, M. Gazdzicki, M. I. Gorenstein, and O. S. Zozulya, Particle number fluctuations in canonical ensemble, Phys. Rev. C70, 034901 (2004), arXiv:nucl-th/0404056

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  28. [28]

    Baryon number conservation and the cumulants of the net proton distribution

    A. Bzdak, V. Koch, and V. Skokov, Baryon number conservation and the cumulants of the net proton distribution, Phys. Rev. C87, 014901 (2013), arXiv:1203.4529 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  29. [29]

    Bridging the gap between event-by-event fluctuation measurements and theory predictions in relativistic nuclear collisions

    P. Braun-Munzinger, A. Rustamov, and J. Stachel, Bridging the gap between event-by-event fluctuation measurements and theory predictions in relativistic nuclear collisions, Nucl. Phys. A960, 114 (2017), arXiv:1612.00702 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  30. [30]

    Braun-Munzinger, B

    P. Braun-Munzinger, B. Friman, K. Redlich, A. Rustamov, and J. Stachel, Relativistic nuclear collisions: Establishing a non-critical baseline for fluctuation measurements, Nucl. Phys. A1008, 122141 (2021), arXiv:2007.02463 [nucl-th]

    work page arXiv 2021

  31. [31]

    Savchuk and S

    O. Savchuk and S. Pratt, Correlations of conserved quantities at finite baryon density, Phys. Rev. C109, 024910 (2024), arXiv:2311.02046 [nucl-th]

    work page arXiv 2024

  32. [32]

    Equilibrium Statistics as Conditional Laws and Conservation-Induced Correlations

    S. Jaiswal and A. Jaiswal, Equilibrium Statistics as Conditional Laws and Conservation-Induced Correlations, (2026), arXiv:2606.29050 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  33. [33]

    Vovchenko, O

    V. Vovchenko, O. Savchuk, R. V. Poberezhnyuk, M. I. Gorenstein, and V. Koch, Connecting fluctuation measurements in heavy-ion collisions with the grand-canonical susceptibilities, Phys. Lett. B811, 135868 (2020), arXiv:2003.13905 [hep-ph]

    work page arXiv 2020

  34. [34]

    R. V. Poberezhnyuk, O. Savchuk, M. I. Gorenstein, V. Vovchenko, K. Taradiy, V. V. Begun, L. Satarov, J. Steinheimer, and H. Stoecker, Critical point fluctuations: Finite size and global charge conservation effects, Phys. Rev. C102, 024908 (2020), arXiv:2004.14358 [nucl-th]

    work page arXiv 2020

  35. [35]

    Vovchenko, R

    V. Vovchenko, R. V. Poberezhnyuk, and V. Koch, Cumulants of multiple conserved charges and global conservation laws, JHEP10, 089, arXiv:2007.03850 [hep-ph]

    work page arXiv 2007

  36. [36]

    Barej and A

    M. Barej and A. Bzdak, Factorial cumulants from short-range correlations and global baryon number conservation, Phys. Rev. C106, 024904 (2022), arXiv:2205.05497 [hep-ph]

    work page arXiv 2022

  37. [37]

    Barej and A

    M. Barej and A. Bzdak, Cumulants from short-range correlations and baryon number conservation at next-to-leading order, Phys. Rev. C107, 034914 (2023), arXiv:2210.15394 [hep-ph]

    work page arXiv 2023

  38. [38]

    Vovchenko, Correcting event-by-event fluctuations in heavy-ion collisions for exact global conservation laws with the generalized subensemble acceptance method, Phys

    V. Vovchenko, Correcting event-by-event fluctuations in heavy-ion collisions for exact global conservation laws with the generalized subensemble acceptance method, Phys. Rev. C105, 014903 (2022), arXiv:2106.13775 [hep-ph]

    work page arXiv 2022

  39. [39]

    Vovchenko, V

    V. Vovchenko, V. Koch, and C. Shen, Proton number cumulants and correlation functions in Au-Au collisions at sNN=7.7–200 GeV from hydrodynamics, Phys. Rev. C105, 014904 (2022), arXiv:2107.00163 [hep-ph]

    work page arXiv 2022

  40. [40]

    R. B. Leipnik and C. E. Pearce, The multivariate faa di bruno formula and multivariate taylor expansions with explicit integral remainder term, The ANZIAM Journal48, 327 (2007)

    2007

  41. [41]

    Poberezhniuk, V

    R. Poberezhniuk, V. A. Kuznietsov, G. Pihan, and V. Vovchenko, SAM-3.0:Mathematicaand C++ implementation, https://github.com/UH-Physics-NuclearTheory/SAM3(2026)

    2026

  42. [42]

    Constantine and T

    G. Constantine and T. Savits, A multivariate faa di bruno formula with applications, Transactions of the American Mathematical Society348, 503 (1996)

    1996

  43. [43]

    Comtet,Advanced Combinatorics(D

    L. Comtet,Advanced Combinatorics(D. Reidel Publishing Company, Dordrecht, 1974)

    1974

  44. [44]

    C. S. Withers and S. Nadarajah, Multivariate Bell polynomials and their applications to powers and fractionary iterates of vector power series and to partial derivatives of composite vector functions, Appl. Math. Comput.206, 997 (2008)

    2008

  45. [45]

    Multivariate Bell Polynomials and Derivatives of Composed Functions

    A. Schumann, Multivariate Bell Polynomials and Derivatives of Composed Functions, (2019), arXiv:1903.03899 [math.CA]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  46. [46]

    Haiman and W

    M. Haiman and W. Schmitt, Incidence algebra antipodes and lagrange inversion in one and several variables, Journal of Combinatorial Theory, Series A50, 172 (1989)

    1989

  47. [47]

    Savchuk, R

    O. Savchuk, R. V. Poberezhnyuk, V. Vovchenko, and M. I. Gorenstein, Binomial acceptance corrections for particle number distributions in high-energy reactions, Phys. Rev. C101, 024917 (2020), arXiv:1911.03426 [nucl-th]

    work page arXiv 2020

  48. [48]

    V. A. Kuznietsov, O. Savchuk, M. I. Gorenstein, V. Koch, and V. Vovchenko, Critical point particle number fluctuations from molecular dynamics, Phys. Rev. C105, 044903 (2022), arXiv:2201.08486 [hep-ph]

    work page arXiv 2022

  49. [49]

    V. A. Kuznietsov, R. Poberezhniuk, M. I. Gorenstein, V. Koch, and V. Vovchenko, High-order cumulants and correlation functions near the critical point from molecular dynamics, Phys. Rev. C113, 045209 (2026), arXiv:2511.00755 [nucl-th]

    work page arXiv 2026

  50. [50]

    Efficient formulas for efficiency correction of cumulants

    M. Kitazawa, Efficient formulas for efficiency correction of cumulants, Phys. Rev. C93, 044911 (2016), arXiv:1602.01234 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  51. [51]

    Revealing baryon number fluctuations from proton number fluctuations in relativistic heavy ion collisions

    M. Kitazawa and M. Asakawa, Revealing baryon number fluctuations from proton number fluctuations in relativistic heavy ion collisions, Phys. Rev. C85, 021901 (2012), arXiv:1107.2755 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  52. [52]

    Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions

    M. Kitazawa and M. Asakawa, Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions, Phys. Rev. C86, 024904 (2012), arXiv:1205.3292 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  53. [53]

    Savchuk, R

    O. Savchuk, R. V. Poberezhnyuk, and M. I. Gorenstein, Possible origin of HADES data on proton number fluctuations in Au+Au collisions, Phys. Lett. B835, 137540 (2022), arXiv:2209.01883 [nucl-th]

    work page arXiv 2022

  54. [54]

    Vovchenko and H

    V. Vovchenko and H. Stoecker, Thermal-FIST: A package for heavy-ion collisions and hadronic equation of state, Comput. Phys. Commun.244, 295 (2019), arXiv:1901.05249 [nucl-th]

    work page arXiv 2019

  55. [55]

    Vovchenko, Cooper-Frye sampling with short-range repulsion, Phys

    V. Vovchenko, Cooper-Frye sampling with short-range repulsion, Phys. Rev. C106, 064906 (2022), arXiv:2208.13693 [nucl-th]

    work page arXiv 2022

  56. [56]

    3+1D hydrodynamic simulation of relativistic heavy-ion collisions

    B. Schenke, S. Jeon, and C. Gale, (3+1)D hydrodynamic simulation of relativistic heavy-ion collisions, Phys. Rev. C82, 014903 (2010), arXiv:1004.1408 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  57. [57]

    Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics

    B. Schenke, S. Jeon, and C. Gale, Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics, Phys. Rev. Lett.106, 042301 (2011), arXiv:1009.3244 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  58. [58]

    The production of photons in relativistic heavy-ion collisions

    J.-F. Paquet, C. Shen, G. S. Denicol, M. Luzum, B. Schenke, S. Jeon, and C. Gale, Production of photons in relativistic 24 heavy-ion collisions, Phys. Rev. C93, 044906 (2016), arXiv:1509.06738 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  59. [59]

    Particlization in hybrid models

    P. Huovinen and H. Petersen, Particlization in hybrid models, Eur. Phys. J. A48, 171 (2012), arXiv:1206.3371 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  60. [60]

    S. A. Basset al., Microscopic models for ultrarelativistic heavy ion collisions, Prog. Part. Nucl. Phys.41, 255 (1998), arXiv:nucl-th/9803035

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  61. [61]

    Relativistic Hadron-Hadron Collisions in the Ultra-Relativistic Quantum Molecular Dynamics Model (UrQMD)

    M. Bleicheret al., Relativistic hadron hadron collisions in the ultrarelativistic quantum molecular dynamics model, J. Phys. G25, 1859 (1999), arXiv:hep-ph/9909407

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  62. [62]

    Bernhard, UrQMD tailored for use as a hadronic afterburner (2020), https://github.com/jbernhard/urqmd-afterburner [Online; accessed 09-May-2021]

    J. Bernhard, UrQMD tailored for use as a hadronic afterburner (2020), https://github.com/jbernhard/urqmd-afterburner [Online; accessed 09-May-2021]

    2020

  63. [63]

    Charge conservation and the shape of the ridge of two-particle correlations in relativistic heavy-ion collisions

    P. Bozek and W. Broniowski, Charge conservation and the shape of the ridge of two-particle correlations in relativistic heavy-ion collisions, Phys. Rev. Lett.109, 062301 (2012), arXiv:1204.3580 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  64. [64]

    Effects of global charge conservation on time evolution of cumulants of conserved charges in relativistic heavy ion collisions

    M. Sakaida, M. Asakawa, and M. Kitazawa, Effects of global charge conservation on time evolution of cumulants of conserved charges in relativistic heavy ion collisions, Phys. Rev. C90, 064911 (2014), arXiv:1409.6866 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  65. [65]

    Vovchenko, Density correlations under global and local charge conservation, Phys

    V. Vovchenko, Density correlations under global and local charge conservation, Phys. Rev. C110, L061902 (2024), arXiv:2409.01397 [hep-ph]

    work page arXiv 2024

  66. [66]

    Canonical statistical hadronization with local baryon conservation for higher-order cumulants

    M. Ciacco, S. Kundu, V. A. Kuznietsov, M. Puccio, and V. Vovchenko, Canonical statistical hadronization with local baryon conservation for higher-order cumulants, (2026), arXiv:2605.30710 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  67. [67]

    Basar, M

    G. Basar, M. Pradeep, and M. Stephanov, Equation of state and cumulants of proton multiplicity in equilibrium near critical point from Pade estimates, (2026), arXiv:2603.23635 [nucl-th]. Appendix A: Finite-size effects In Sec. II we approximated lnI(t)≃F 0(t) by neglecting the Gaussian prefactor of the saddle-point integration. Restoring the prefactor pro...

    work page arXiv 2026