pith. sign in

arxiv: 2606.30164 · v1 · pith:IQJP4FQWnew · submitted 2026-06-29 · ✦ hep-lat · hep-ph· nucl-ex· nucl-th

Isospin-Driven Splitting of Chemical Potentials in Isobar Collisions from Lattice QCD

Heng-Tong Ding , Jin-Biao Gu , Arpith Kumar , Jia Ni This is my paper

Pith reviewed 2026-06-30 03:39 UTC · model grok-4.3

classification ✦ hep-lat hep-phnucl-exnucl-th
keywords lattice QCDisobar collisionschemical potentialsisospin splittingmagnetic fieldsheavy-ion collisionsQCD crossoverstrangeness neutrality
0
0 comments X

The pith

Lattice QCD maps isospin differences between Ru and Zr nuclei to chemical potential splittings dominated by the electric charge sector.

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

The paper presents first-principles (2+1)-flavor lattice QCD results for isospin-driven splittings of conserved-charge chemical potentials between the isobar collision systems Ru+Ru and Zr+Zr in the QCD crossover region. It outlines a framework that, under strangeness neutrality and a fixed charge-to-baryon ratio, translates the isospin difference encoded in the two nuclei's charge-to-baryon ratios into splitting ratios of the chemical potentials. Using continuum-estimated leading-order lattice coefficients, the calculated ratios at vanishing magnetic field match the magnitude of Bayesian extractions from STAR data and give a negative splitting for the electric-charge chemical potential and a positive one for strangeness, with the charge sector larger. The dependence on magnetic field strength along the pseudo-critical line remains moderate, although Ru-Zr differences in the normalized magnetic response of certain chemical-potential ratios show clear enhancement.

Core claim

Using continuum-estimated lattice results for the leading-order coefficients q1 ≡ (μ_Q/μ_B)_LO and s1 ≡ (μ_S/μ_B)_LO, the splitting ratios at vanishing magnetic field are of similar magnitude to recent Bayesian extractions from STAR isobar data and yield Δμ_Q < 0 and Δμ_S > 0, with the electric-charge sector dominating; at nonzero magnetic fields the splitting ratios show only moderate eB dependence while Ru-Zr differences in the normalized magnetic-field response of chemical-potential ratios display a pronounced enhancement.

What carries the argument

The mapping framework that, under strangeness neutrality and charge-to-baryon ratio r ≡ n_Q/n_B, converts the isospin difference between the nuclei (encoded in r_Zr and r_Ru) into the splitting ratios Δμ_Q/Δμ_B, Δμ_S/Δμ_B and Δμ_S/Δμ_Q as functions of μ_B(r_Ru)/Δμ_B, using the lattice coefficients q1 and s1.

If this is right

  • The electric-charge sector dominates the isospin-driven chemical-potential splitting between the two isobar systems.
  • Δμ_Q is negative while Δμ_S is positive at vanishing magnetic field.
  • The splitting ratios exhibit only moderate dependence on magnetic-field strength along the pseudo-critical line.
  • Ru-Zr differences in the normalized magnetic-field response of ratios involving μ_Q/μ_B are pronouncedly enhanced.

Where Pith is reading between the lines

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

  • The lattice baseline can be used to test or refine Bayesian extractions of chemical potentials from existing or future isobar data.
  • Extension of the calculation to next-to-leading order in the chemical-potential expansion would test whether the reported ratios remain stable.
  • The enhanced magnetic response may produce measurable effects in fluctuation observables once strong fields are included in hydrodynamic modeling.

Load-bearing premise

The leading-order lattice coefficients together with the mapping under strangeness neutrality and fixed charge-to-baryon ratio capture the full isospin-driven splittings without sizable higher-order corrections in the chemical potentials.

What would settle it

An extraction from isobar collision data that finds splitting ratios with the opposite sign for Δμ_Q or magnitudes differing by more than roughly a factor of two from the lattice values at zero magnetic field would falsify the central result.

Figures

Figures reproduced from arXiv: 2606.30164 by Arpith Kumar, Heng-Tong Ding, Jia Ni, Jin-Biao Gu.

Figure 1
Figure 1. Figure 1: FIG. 1. Isospin parameter [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Magnetic field [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Isospin-driven conserved charge splitting ratios, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: Since the Λ carries strangeness S = −1, it enters the net-strangeness proxy with the opposite sign to the kaon, i.e. net-S → K˜ + − Λ; for simplicity, we set the ˜ subscript K + Λ in the corresponding STAR-cut proxy σ 2,kcut-STAR p+Λ, QPID, K+Λ. The relevant chemical-potential observ￾ables are then constructed from these proxy fluctuations. The proxy observables with kinematic cuts lead to visible deviatio… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Isospin-driven conserved charge splitting ratios, [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Ratio observables [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Lattice-QCD continuum estimates for isospin-driven [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Isospin-driven conserved charge splitting ratios, [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

Strong magnetic fields produced in relativistic heavy-ion collisions can modify fluctuations of conserved charges and, consequently, their associated chemical potentials. We present first-principles $(2+1)$-flavor lattice-QCD results for isospin-driven splittings of conserved-charge chemical potentials between the isobar systems $^{96}_{44}\mathrm{Ru}+^{96}_{44}\mathrm{Ru}$ and $^{96}_{40}\mathrm{Zr}+^{96}_{40}\mathrm{Zr}$ in the QCD crossover region, both at vanishing and nonzero magnetic fields along the pseudo-critical line $T_{pc}(eB)$. We outline a framework that, under strangeness neutrality and charge-to-baryon ratio $r\equiv n_{\rm Q}/n_{\rm B}$, maps the isospin difference between two nuclei, as encoded in $r_{\rm Zr}$ and $r_{\rm Ru}$, onto splitting ratios $\Delta\mu_{\rm Q}/\Delta\mu_{\rm B}$, $\Delta\mu_{\rm S}/\Delta\mu_{\rm B}$, and $\Delta\mu_{\rm S}/\Delta\mu_{\rm Q}$ as functions of $\mu_{\rm B}(r_{\rm Ru})/\Delta\mu_{\rm B}$. Using continuum-estimated lattice results for the leading-order coefficients $q_1\equiv(\mu_{\rm Q}/\mu_{\rm B})_{\rm LO}$ and $s_1\equiv(\mu_{\rm S}/\mu_{\rm B})_{\rm LO}$, we find that, at vanishing magnetic field, the splitting ratios are of similar magnitude to recent Bayesian extractions from STAR isobar data and yield $\Delta\mu_{\rm Q}<0$ and $\Delta\mu_{\rm S}>0$, with the electric-charge sector dominating. At nonzero magnetic fields, the splitting ratios show only moderate $eB$ dependence. We therefore further examine Ru--Zr differences in the normalized magnetic-field response of chemical-potential ratios, particularly those involving $\mu_{\rm Q}/\mu_{\rm B}$, which display a pronounced enhancement in lattice QCD. We also present hadron resonance gas (HRG) results and experimentally motivated proxy observables with kinematic cuts to facilitate contact with experiment.

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

2 major / 2 minor

Summary. The manuscript computes (2+1)-flavor lattice QCD results for isospin-driven splittings of conserved-charge chemical potentials between ^{96}Ru+^{96}Ru and ^{96}Zr+^{96}Zr collisions in the crossover region. It outlines a framework under strangeness neutrality and fixed charge-to-baryon ratio r that maps the nuclear isospin difference (via r_Zr and r_Ru) onto the splitting ratios Δμ_Q/Δμ_B, Δμ_S/Δμ_B, and Δμ_S/Δμ_Q expressed as functions of μ_B(r_Ru)/Δμ_B. Using continuum-estimated leading-order coefficients q1 ≡ (μ_Q/μ_B)_LO and s1 ≡ (μ_S/μ_B)_LO, the work reports that at vanishing magnetic field the ratios have magnitudes similar to STAR Bayesian extractions, with Δμ_Q < 0, Δμ_S > 0 and the electric-charge sector dominating; moderate eB dependence is found along T_pc(eB), together with an enhanced magnetic response in certain normalized ratios. HRG results and kinematic-cut proxy observables are also presented.

Significance. If the central results hold, the paper supplies first-principles lattice input that directly connects isospin asymmetry in isobar systems to observable chemical-potential splittings, enabling quantitative comparison with STAR data and offering a controlled way to assess magnetic-field effects. The continuum estimation of the LO coefficients, the explicit inclusion of nonzero eB along the pseudo-critical line, and the provision of HRG benchmarks for experimental contact are concrete strengths that increase the utility of the work for the heavy-ion community.

major comments (2)
  1. [Abstract (framework paragraph)] Abstract, paragraph beginning 'We outline a framework': the splitting ratios are presented as functions of μ_B(r_Ru)/Δμ_B, yet they are obtained from the μ_B-independent LO coefficients q1 and s1 solved at μ=0. At the finite μ_B/T ≳ 1 values probed by the collisions, NLO terms involving fourth-order susceptibilities (χ_4^B, χ_3^{BQ}, χ_2^{BQS}) enter the full solution for μ_Q and μ_S; because r_Ru ≠ r_Zr these corrections need not cancel in Δμ_Q and Δμ_S, so the reported signs, the claimed similarity to STAR values, and the dominance of the electric-charge sector could shift. This approximation is load-bearing for the headline comparison and requires either an explicit NLO calculation or a quantitative justification that the corrections remain negligible.
  2. [Abstract] Abstract, sentence on vanishing-B results: the statement that the splitting ratios 'are of similar magnitude to recent Bayesian extractions from STAR isobar data' is made without reference to the specific μ_B range or to any error budget on the lattice side. Because the LO coefficients are external inputs and the framework does not reduce the splittings to quantities obtained from the authors' own fits, it is unclear whether the similarity survives once the μ_B dependence implicit in the STAR extraction is folded in.
minor comments (2)
  1. [Abstract] The notation r_Zr and r_Ru is introduced without an explicit definition or numerical values; adding a short table or sentence giving the charge-to-baryon ratios for the two nuclei would improve readability.
  2. [Abstract] The phrase 'continuum-estimated lattice results' for q1 and s1 appears without a citation to the underlying lattice ensembles or to the reference that performed the continuum extrapolation; a pointer to that work is needed for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major point below and agree that revisions will strengthen the presentation of the LO framework and the comparison to STAR data.

read point-by-point responses

  1. Referee: [Abstract (framework paragraph)] Abstract, paragraph beginning 'We outline a framework': the splitting ratios are presented as functions of μ_B(r_Ru)/Δμ_B, yet they are obtained from the μ_B-independent LO coefficients q1 and s1 solved at μ=0. At the finite μ_B/T ≳ 1 values probed by the collisions, NLO terms involving fourth-order susceptibilities (χ_4^B, χ_3^{BQ}, χ_2^{BQS}) enter the full solution for μ_Q and μ_S; because r_Ru ≠ r_Zr these corrections need not cancel in Δμ_Q and Δμ_S, so the reported signs, the claimed similarity to STAR values, and the dominance of the electric-charge sector could shift. This approximation is load-bearing for the headline comparison and requires either an explicit NLO calculation or a quantitative justification that the corrections remain negligible.

    Authors: We agree that the framework relies on LO coefficients and that NLO contributions from fourth-order susceptibilities could in principle modify the splitting ratios at finite μ_B. However, the isospin-driven splittings Δμ_Q and Δμ_S are generated at leading order by the difference in r between the two nuclei; higher-order terms enter as corrections whose relative size can be estimated from existing lattice results on χ_4^B, χ_3^{BQ} and χ_2^{BQS}. Published values indicate that these corrections remain below ~15% for μ_B/T ≲ 2 in the crossover region. We will add a dedicated paragraph in the revised manuscript that (i) recalls the NLO expansion, (ii) quotes the relevant lattice susceptibilities, and (iii) shows that the signs, the dominance of the electric-charge sector, and the order-of-magnitude agreement with STAR survive after inclusion of these estimates. This supplies the quantitative justification requested without requiring a full NLO re-calculation of the entire isobar mapping. revision: yes

  2. Referee: [Abstract] Abstract, sentence on vanishing-B results: the statement that the splitting ratios 'are of similar magnitude to recent Bayesian extractions from STAR isobar data' is made without reference to the specific μ_B range or to any error budget on the lattice side. Because the LO coefficients are external inputs and the framework does not reduce the splittings to quantities obtained from the authors' own fits, it is unclear whether the similarity survives once the μ_B dependence implicit in the STAR extraction is folded in.

    Authors: We will revise the abstract and the main text to (i) state the μ_B range corresponding to the QCD crossover region explored (μ_B/T ≲ 2–3), (ii) quote the numerical values and uncertainties of the continuum-estimated q1 and s1, and (iii) compare the resulting splitting ratios directly with the μ_B-dependent STAR Bayesian bands. The similarity in magnitude is preserved within these ranges; the revised wording will make the comparison transparent and will clarify that the lattice coefficients carry their own (small) systematic errors. revision: yes

Circularity Check

0 steps flagged

No significant circularity; lattice inputs independent of target ratios

full rationale

The paper computes leading-order coefficients q1 ≡ (μ_Q/μ_B)_LO and s1 ≡ (μ_S/μ_B)_LO from second-order susceptibilities on the lattice at vanishing chemical potential under strangeness neutrality and fixed r. These serve as external first-principles inputs to map isospin differences (r_Zr vs r_Ru) onto splitting ratios. The framework and resulting Δμ_Q < 0, Δμ_S > 0 are not obtained by fitting to the target splittings or to STAR data; the comparison to Bayesian extractions is external. No self-definitional reduction, fitted-input-as-prediction, or load-bearing self-citation chain is present. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the mapping framework under strangeness neutrality and fixed r, plus the leading-order truncation in chemical potentials; these are domain assumptions rather than derived results.

free parameters (1)
  • charge-to-baryon ratio r
    Fixed input value used to map isospin differences onto splitting ratios; concrete numerical value not stated in abstract.
axioms (2)
  • domain assumption strangeness neutrality
    Invoked to close the mapping from isospin difference to chemical-potential splittings (abstract, 'We outline a framework').
  • domain assumption leading-order truncation in chemical potentials
    Only q1 and s1 coefficients are used; higher-order terms are not included.

pith-pipeline@v0.9.1-grok · 5958 in / 1592 out tokens · 67256 ms · 2026-06-30T03:39:44.299068+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

74 extracted references · 73 canonical work pages · 36 internal anchors

  1. [1]

    The effects of topological charge change in heavy ion collisions: "Event by event P and CP violation"

    D.E. Kharzeev, L.D. McLerran and H.J. Warringa,The Effects of topological charge change in heavy ion collisions: ’Event by event P and CP violation’,Nucl. Phys.A803(2008) 227 [0711.0950]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  2. [2]

    Estimate of the magnetic field strength in heavy-ion collisions

    V. Skokov, A.Y. Illarionov and V. Toneev,Estimate of the magnetic field strength in heavy-ion collisions,Int. J. Mod. Phys.A24(2009) 5925 [0907.1396]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  3. [3]

    Event-by-event generation of electromagnetic fields in heavy-ion collisions

    W.-T. Deng and X.-G. Huang,Event-by-event generation of electromagnetic fields in heavy-ion collisions,Phys. Rev.C85(2012) 044907 [1201.5108]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  4. [4]

    Astrakhantsev, V.V

    N. Astrakhantsev, V.V. Braguta, M. D’Elia, A.Y. Kotov, A.A. Nikolaev and F. Sanfilippo,Lattice study of the electromagnetic conductivity of the quark-gluon plasma in an external magnetic field,Phys. Rev. D102(2020) 054516 [1910.08516]

    work page arXiv 2020

  5. [5]

    G.S. Bali, G. Endr˝ odi and S. Piemonte,Magnetic susceptibility of QCD matter and its decomposition from the lattice,JHEP07(2020) 183 [2004.08778]

    work page arXiv 2020

  6. [6]

    H.-T. Ding, O. Kaczmarek and F. Meyer,Thermal dilepton rates and electrical conductivity of the QGP from the lattice,Phys. Rev. D94(2016) 034504 [1604.06712]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  7. [7]

    Huang, D

    A. Huang, D. She, S. Shi, M. Huang and J. Liao, Dynamical magnetic fields in heavy-ion collisions,Phys. Rev. C107(2023) 034901 [2212.08579]

    work page arXiv 2023

  8. [8]

    The Chiral Magnetic Effect

    K. Fukushima, D.E. Kharzeev and H.J. Warringa,The Chiral Magnetic Effect,Phys. Rev. D78(2008) 074033 [0808.3382]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  9. [9]

    "Strongly interacting matter in magnetic fields": an overview

    D.E. Kharzeev, K. Landsteiner, A. Schmitt and H.-U. Yee,’Strongly interacting matter in magnetic fields’: an overview,Lect. Notes Phys.871(2013) 1 [1211.6245]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  10. [10]

    Kharzeev and J

    D.E. Kharzeev and J. Liao,Chiral magnetic effect reveals the topology of gauge fields in heavy-ion collisions,Nature Rev. Phys.3(2021) 55 [2102.06623]

    work page arXiv 2021

  11. [11]

    Electric-current Susceptibility and the Chiral Magnetic Effect

    K. Fukushima, D.E. Kharzeev and H.J. Warringa, Electric-current Susceptibility and the Chiral Magnetic Effect,Nucl. Phys. A836(2010) 311 [0912.2961]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  12. [12]

    Fluctuations and correlations of hot QCD matter in an external magnetic field

    W.-j. Fu,Fluctuations and correlations of hot QCD matter in an external magnetic field,Phys. Rev. D88 (2013) 014009 [1306.5804]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  13. [13]

    Magnetic shift of the chemical freezeout and electric charge fluctuations

    K. Fukushima and Y. Hidaka,Magnetic Shift of the Chemical Freeze-out and Electric Charge Fluctuations, Phys. Rev. Lett.117(2016) 102301 [1605.01912]. [14]STARcollaboration,Search for the chiral magnetic effect with isobar collisions at √sN N=200 GeV by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider,Phys. Rev. C105(2022) 014901 [2109.00131]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  14. [14]

    Kharzeev, J

    D.E. Kharzeev, J. Liao and S. Shi,Implications of the isobar-run results for the chiral magnetic effect in heavy-ion collisions,Phys. Rev. C106(2022) L051903 [2205.00120]

    work page arXiv 2022

  15. [15]

    Ding, J.-B

    H.-T. Ding, J.-B. Gu, A. Kumar, S.-T. Li and J.-H. Liu, Baryon Electric Charge Correlation as a Magnetometer of QCD,Phys. Rev. Lett.132(2024) 201903 [2312.08860]

    work page arXiv 2024

  16. [16]

    Brandt, G

    B.B. Brandt, G. Endr˝ odi, E. Garnacho-Velasco, G. Mark´ o and A.D.M. Valois,Localized chiral magnetic effect in equilibrium QCD,Phys. Rev. D112(2025) 034508 [2409.17616]. [18]ALICEcollaboration,Measurement of correlations among net-charge, net-proton, and net-kaon multiplicity distributions in Pb-Pb collisions at √sN N = 5.02 TeV, JHEP08(2025) 210 [2503....

    work page arXiv 2025

  17. [17]

    Endrodi, Prog

    G. Endrodi,QCD with background electromagnetic fields on the lattice: A review,Prog. Part. Nucl. Phys.141 (2025) 104153 [2406.19780]

    work page arXiv 2025

  18. [18]

    Strongly interacting matter in extreme magnetic fields

    P. Adhikari et al.,Strongly interacting matter in extreme magnetic fields,Prog. Part. Nucl. Phys.146 (2026) 104199 [2412.18632]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  19. [19]

    Lattice QCD at finite temperature and density

    H.-T. Ding,Lattice QCD at finite temperature and density, in42th International Symposium on Lattice Field Theory, 3, 2026 [2603.16230]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  20. [20]

    Thermodynamics of magnetized matter in hot and dense QCD

    B.B. Brandt and G. Endrodi,Thermodynamics of magnetized matter in hot and dense QCD,2604.26715

    work page internal anchor Pith review Pith/arXiv arXiv

  21. [21]

    G.S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S.D. Katz, S. Krieg et al.,The QCD phase diagram for external magnetic fields,JHEP02(2012) 044 [1111.4956]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  22. [22]

    G.S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S.D. Katz and A. Schafer,QCD quark condensate in external magnetic fields,Phys. Rev.D86(2012) 071502 [1206.4205]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  23. [23]

    Chiral Properties of Strong Interactions in a Magnetic Background

    M. D’Elia and F. Negro,Chiral Properties of Strong Interactions in a Magnetic Background,Phys. Rev. D 83(2011) 114028 [1103.2080]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  24. [24]

    D’Elia, L

    M. D’Elia, L. Maio, F. Sanfilippo and A. Stanzione, Phase diagram of QCD in a magnetic background,Phys. Rev. D105(2022) 034511 [2111.11237]

    work page arXiv 2022

  25. [25]

    G.S. Bali, F. Bruckmann, G. Endr¨ odi, S.D. Katz and A. Sch¨ afer,The QCD equation of state in background magnetic fields,JHEP08(2014) 177 [1406.0269]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  26. [26]

    D’Elia, L

    M. D’Elia, L. Maio, F. Sanfilippo and A. Stanzione, Confining and chiral properties of QCD in extremely strong magnetic fields,Phys. Rev. D104(2021) 114512 [2109.07456]

    work page arXiv 2021

  27. [27]

    Endrodi, M

    G. Endrodi, M. Giordano, S.D. Katz, T.G. Kov´ acs and F. Pittler,Magnetic catalysis and inverse catalysis for heavy pions,JHEP07(2019) 007 [1904.10296]

    work page arXiv 2019

  28. [28]

    Ding, S.T

    H.T. Ding, S.T. Li, J.H. Liu and X.D. Wang,Chiral condensates and screening masses of neutral pseudoscalar mesons in thermomagnetic QCD medium, Phys. Rev. D105(2022) 034514 [2201.02349]

    work page arXiv 2022

  29. [29]

    Ding, J.-B

    H.-T. Ding, J.-B. Gu, S.-T. Li and R. Thakkar,Chiral condensates and screening masses of neutral pseudoscalar mesons from lattice QCD at physical quark masses,Phys. Rev. D111(2025) 074513 [2501.11262]. [32]HotQCDcollaboration,Fluctuations and Correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the ...

    work page arXiv 2025

  30. [30]

    Fluctuations of conserved charges at finite temperature from lattice QCD

    S. Borsanyi, Z. Fodor, S.D. Katz, S. Krieg, C. Ratti and K. Szabo,Fluctuations of conserved charges at finite temperature from lattice QCD,JHEP01(2012) 138 [1112.4416]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  31. [31]

    H.-T. Ding, F. Karsch and S. Mukherjee, Thermodynamics of strong-interaction matter from Lattice QCD,Int. J. Mod. Phys.E24(2015) 1530007 [1504.05274]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  32. [32]

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

    A. Bazavov, H.-T. Ding, P. Hegde et al.,The QCD Equation of State toO(µ 6 B)from Lattice QCD,Phys. Rev.D95(2017) 054504 [1701.04325]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  33. [33]

    Bollweg, H.T

    D. Bollweg, H.T. Ding, J. Goswami, F. Karsch, S. Mukherjee, P. Petreczky et al., Strangeness-correlations on the pseudocritical line in (2+1)-flavor QCD,Phys. Rev. D110(2024) 054519 [2407.09335]

    work page arXiv 2024

  34. [34]

    Clarke, P

    D.A. Clarke, P. Dimopoulos, F. Di Renzo, J. Goswami, C. Schmidt, S. Singh et al.,Searching for the QCD critical end point using multipoint Pad´ e approximations, Phys. Rev. D112(2025) L091504 [2405.10196]

    work page arXiv 2025

  35. [35]

    Bors´ anyi, Z

    S. Bors´ anyi, Z. Fodor, J.N. Guenther, P. Kumar, P. Parotto, A. P´ asztor et al.,Finite density QCD phase structure from strangeness fluctuations,Phys. Rev. D 113(2026) 054507 [2510.26455]

    work page arXiv 2026

  36. [36]

    A. Adam, S. Bors´ anyi, Z. Fodor, J.N. Guenther, L. Pirelli, P. Parotto et al.,Finite density lattice QCD without extrapolation: Bulk thermodynamics with physical quark masses from the canonical ensemble, 2604.14117

    work page internal anchor Pith review Pith/arXiv arXiv

  37. [37]

    Clarke, J

    D.A. Clarke, J. Goswami, F. Karsch and P. Petreczky, Generalized definition of the isothermal compressibility in (2+1)-flavor QCD,Phys. Rev. D113(2026) 034502 [2506.22816]. [41]JLQCDcollaboration,Quark Number Susceptibilities and Conserved Charge Fluctuations in(2 + 1)-flavor QCD with M¨ obius domain-wall fermions (MDWF), 2604.22514

    work page arXiv 2026

  38. [38]

    Probing freeze-out conditions in heavy ion collisions with moments of charge fluctuations

    F. Karsch and K. Redlich,Probing freeze-out conditions in heavy ion collisions with moments of charge fluctuations,Phys. Lett. B695(2011) 136 [1007.2581]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  39. [39]

    Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC : An Overview

    X. Luo and N. Xu,Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC : An Overview,Nucl. Sci. Tech.28(2017) 112 [1701.02105]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  40. [40]

    Rustamov,Deciphering the phases of QCD matter with fluctuations and correlations of conserved charges, EPJ Web Conf.276(2023) 01007 [2210.14810]

    A. Rustamov,Deciphering the phases of QCD matter with fluctuations and correlations of conserved charges, EPJ Web Conf.276(2023) 01007 [2210.14810]

    work page arXiv 2023

  41. [41]

    Pandav, D

    A. Pandav, D. Mallick and B. Mohanty,Search for the QCD critical point in high energy nuclear collisions, Prog. Part. Nucl. Phys.125(2022) 103960 [2203.07817]. [46]STARcollaboration,Recent Results and Methods on Higher Order and Off-diagonal Cumulants of Identified Net-particle Multiplicity Distributions in Au+Au Collisions at STAR,Nucl. Phys. A982(2019) 863

    work page arXiv 2022

  42. [42]

    Nonaka,Experimental Overview on Fluctuations of Conserved Charges,Acta Phys

    T. Nonaka,Experimental Overview on Fluctuations of Conserved Charges,Acta Phys. Polon. Supp.16(2023) 1

    2023

  43. [43]

    Ding, S.T

    H.T. Ding, S.T. Li, Q. Shi and X.D. Wang,Fluctuations and correlations of net baryon number, electric charge and strangeness in a background magnetic field,Eur. Phys. J. A57(2021) 202 [2104.06843]

    work page arXiv 2021

  44. [44]

    Ding, J.-B

    H.-T. Ding, J.-B. Gu, A. Kumar and S.-T. Li,Second order fluctuations of conserved charges in external magnetic fields,Phys. Rev. D111(2025) 114522 [2503.18467]

    work page arXiv 2025

  45. [45]

    Kadam, S

    G. Kadam, S. Pal and A. Bhattacharyya,Interacting hadron resonance gas model in magnetic field and the fluctuations of conserved charges,J. Phys. G47(2020) 125106 [1908.10618]

    work page arXiv 2020

  46. [46]

    Chahal, S

    N. Chahal, S. Dutt and A. Kumar,Effects of finite volume and magnetic fields on thermodynamic properties of quark matter and fluctuations of conserved charges,Phys. Rev. C107(2023) 045203 [2303.16840]

    work page arXiv 2023

  47. [47]

    Mao,Correlations and fluctuations in a magnetized PNJL model with and without the inverse magnetic catalysis effect*,Chin

    S. Mao,Correlations and fluctuations in a magnetized PNJL model with and without the inverse magnetic catalysis effect*,Chin. Phys. C49(2025) 063106 [2410.10217]

    work page arXiv 2025

  48. [48]

    Mao and S

    S. Mao and S. Yang,Correlations and fluctuations in a magnetized three-flavor PNJL model with and without 14 inverse magnetic catalysis effect,Phys. Rev. D112 (2025) 014026 [2504.14532]

    work page arXiv 2025

  49. [49]

    S. Mao, S. Yang, S. Lin, X. Yang, G. Shao and W.-C. Zhang,Fourth order correlation of baryon number and electric charge as a better magnetometer of QCD,2605.14674

    work page internal anchor Pith review Pith/arXiv arXiv

  50. [50]

    Samanta and W

    R. Samanta and W. Broniowski,Magnetic properties of the hadron resonance gas with physical magnetic moments,Phys. Rev. C112(2025) 045202 [2505.14484]

    work page arXiv 2025

  51. [51]

    Vovchenko,Magnetic field effect on hadron yield ratios and fluctuations in a hadron resonance gas,Phys

    V. Vovchenko,Magnetic field effect on hadron yield ratios and fluctuations in a hadron resonance gas,Phys. Rev. C110(2024) 034914 [2405.16306]

    work page arXiv 2024

  52. [52]

    Ding, J.-B

    H.-T. Ding, J.-B. Gu, A. Kumar and S.-T. Li, Leading-order QCD equation of state in strong magnetic fields at nonzero baryon chemical potential,Phys. Rev. D112(2025) 094508 [2508.07532]

    work page arXiv 2025

  53. [53]

    Testing the Chiral Magnetic Effect with Central U+U collisions

    S.A. Voloshin,Testing the Chiral Magnetic Effect with Central U+U collisions,Phys. Rev. Lett.105(2010) 172301 [1006.1020]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  54. [54]

    Chiral magnetic effect in isobaric collisions

    X.-G. Huang, W.-T. Deng, G.-L. Ma and G. Wang, Chiral magnetic effect in isobaric collisions,Nucl. Phys. A967(2017) 736 [1704.04382]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  55. [55]

    Predictions for isobaric collisions at $\sqrt{s_{_{\rm NN}}}$ = 200 GeV from a multiphase transport model

    W.-T. Deng, X.-G. Huang, G.-L. Ma and G. Wang, Predictions for isobaric collisions at √sNN = 200 GeV from a multiphase transport model,Phys. Rev. C97 (2018) 044901 [1802.02292]. [61]STARcollaboration,Methods for a blind analysis of isobar data collected by the STAR collaboration,Nucl. Sci. Tech.32(2021) 48 [1911.00596]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  56. [56]

    Li, H.-j

    H. Li, H.-j. Xu, Y. Zhou, X. Wang, J. Zhao, L.-W. Chen et al.,Probing the neutron skin with ultrarelativistic isobaric collisions,Phys. Rev. Lett.125(2020) 222301 [1910.06170]

    work page arXiv 2020

  57. [57]

    H.-j. Xu, H. Li, X. Wang, C. Shen and F. Wang, Determine the neutron skin type by relativistic isobaric collisions,Phys. Lett. B819(2021) 136453 [2103.05595]

    work page arXiv 2021

  58. [58]

    Pihan, A

    G. Pihan, A. Monnai, B. Schenke and C. Shen,Tracing baryon and electric charge transport in isobar collisions, EPJ Web Conf.296(2024) 05005 [2312.12376]

    work page arXiv 2024

  59. [59]

    Chiral kinetic approach to the chiral magnetic effect in isobaric collisions

    Y. Sun and C.M. Ko,Chiral kinetic approach to the chiral magnetic effect in isobaric collisions,Phys. Rev. C98(2018) 014911 [1803.06043]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  60. [60]

    Z. Yuan, A. Huang, G. Xie, W.-H. Zhou, G.-L. Ma and M. Huang,Exploring the chiral magnetic effect in isobar collisions through chiral anomaly transport,Phys. Rev. C111(2025) 044913 [2412.09130]

    work page arXiv 2025

  61. [61]

    Grefa, C.Y

    J. Grefa, C.Y. Tsang, R. Kumar, V. Dexheimer, C. Ratti and Z. Xu,Chemical potential differentials in the QCD phase diagram from heavy-ion isobar collisions,2601.21232. [68]STARcollaboration,Tracking the baryon number with nuclear collisions,2408.15441

    work page arXiv

  62. [62]

    QCD Phase Transition in a Strong Magnetic Background

    M. D’Elia, S. Mukherjee and F. Sanfilippo,QCD Phase Transition in a Strong Magnetic Background,Phys. Rev.D82(2010) 051501 [1005.5365]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  63. [63]

    Lattice QCD at non-zero temperature

    P. Petreczky,Lattice QCD at non-zero temperature,J. Phys. G39(2012) 093002 [1203.5320]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  64. [64]

    Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics

    A. Bazavov, H.-T. Ding, P. Hegde, O. Kaczmarek, F. Karsch et al.,Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics,Phys.Rev.Lett. 109(2012) 192302 [1208.1220]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  65. [65]

    Additional Strange Hadrons from QCD Thermodynamics and Strangeness Freeze-out in Heavy Ion Collisions

    A. Bazavov, H.T. Ding, P. Hegde, O. Kaczmarek, F. Karsch et al.,Additional Strange Hadrons from QCD Thermodynamics and Strangeness Freezeout in Heavy Ion Collisions,Phys.Rev.Lett.113(2014) 072001 [1404.6511]. [73]HotQCDcollaboration,Second order cumulants of conserved charge fluctuations revisited: Vanishing chemical potentials,Phys. Rev. D104(2021) [2107.10011]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  66. [66]

    Ding, J.-B

    H.-T. Ding, J.-B. Gu, A. Kumar and S.-T. Li,QCD in strong magnetic fields: Fluctuations of conserved charges and EoS,J. Subatomic Part. Cosmol.5(2026) 100277 [2510.21731]

    work page arXiv 2026

  67. [67]

    Hadron production in central nucleus-nucleus collisions at chemical freeze-out

    A. Andronic, P. Braun-Munzinger and J. Stachel, Hadron production in central nucleus-nucleus collisions at chemical freeze-out,Nucl. Phys. A772(2006) 167 [nucl-th/0511071]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  68. [68]

    Comparison of Chemical Freeze-Out Criteria in Heavy-Ion Collisions

    J. Cleymans, H. Oeschler, K. Redlich and S. Wheaton, Comparison of chemical freeze-out criteria in heavy-ion collisions,Phys. Rev. C73(2006) 034905 [hep-ph/0511094]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  69. [69]

    Decoding the phase structure of QCD via particle production at high energy

    A. Andronic, P. Braun-Munzinger, K. Redlich and J. Stachel,Decoding the phase structure of QCD via particle production at high energy,Nature561(2018) 321 [1710.09425]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  70. [70]

    Effects of kinematic cuts on net-electric charge fluctuations

    F. Karsch, K. Morita and K. Redlich,Effects of kinematic cuts on net-electric charge fluctuations,Phys. Rev. C93(2016) 034907 [1508.02614]. [79]HPQCD, UKQCDcollaboration,Highly improved staggered quarks on the lattice, with applications to charm physics,Phys. Rev.D75(2007) 054502 [hep-lat/0610092]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  71. [71]

    Bazavov, S

    A. Bazavov, S. Dentinger, H.-T. Ding et al.,Meson screening masses in (2+1)-flavor QCD,Phys. Rev. D100(2019) 094510 [1908.09552]. [81]HotQCDcollaboration,Taylor expansions and Pad´ e approximants for cumulants of conserved charge fluctuations at nonvanishing chemical potentials,Phys. Rev. D105(2022) 074511 [2202.09184]

    work page arXiv 2019

  72. [72]

    Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field on a Torus

    M.H. Al-Hashimi and U.J. Wiese,Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field on a Torus,Annals Phys.324(2009) 343 [0807.0630]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  73. [73]

    Ding, S.T

    H.T. Ding, S.T. Li, A. Tomiya, X.D. Wang and Y. Zhang,Chiral properties of (2+1)-flavor QCD in strong magnetic fields at zero temperature,Phys. Rev. D 104(2021) 014505 [2008.00493]. [84]Particle Data Groupcollaboration,Review of Particle Physics,PTEP2020(2020) 083C01

    work page arXiv 2021

  74. [74]

    Bellwied, S

    R. Bellwied, S. Borsanyi, Z. Fodor, J.N. Guenther, J. Noronha-Hostler, P. Parotto et al.,Off-diagonal correlators of conserved charges from lattice QCD and how to relate them to experiment,Phys. Rev. D101 (2020) 034506 [1910.14592]. Appendix A: Next-to-leading-order correction to chemical potential splitting ratios The isospin-driven chemical-potential sp...

    work page arXiv 2020