Phenomenology of baryon dynamics with directed flow in relativistic heavy-ion collisions

Tribhuban Parida

REVIEW 5 major objections 5 minor 299 references

Phenomenology of baryon dynamics with directed flow in relativistic heavy-ion collisions

T0 review · 5 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This thesis proposes a two-component initial baryon profile which, together with a tilted energy profile and baryon diffusion in a hybrid hydrodynamic calculation, reproduces the rapidity-odd directed flow ($v_1$) of identified hadrons…

desk verdict A plausible two-component baryon stopping model that reproduces v1 splitting across BES energies, but the baseline and diffusion-coefficient claims are undersupported by calibration choices. read the letter →

arxiv 2505.06522 v1 pith:B5N3VFZH submitted 2025-05-10 nucl-th hep-exhep-phnucl-ex

Tribhuban Parida This is my paper · ORCID

classification nucl-thhep-exhep-phnucl-ex

keywords directedflowbaryonstoppingdiffusionrelativistichydrodynamicsquark-gluonplasmabeamenergyscannet-protonheavy-ioncollisions

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that the puzzling rapidity-odd directed flow ($v_1$) of protons, antiprotons, lambdas, and antilambdas in heavy-ion collisions is controlled by how baryon number is initially deposited and then diffuses through the quark-gluon plasma. It proposes a two-component initial net-baryon profile that combines participant-like and binary-collision-like sources, and feeds this profile together with a tilted energy distribution into a hybrid hydrodynamic and hadronic-transport model. With this setup, the model simultaneously describes the $v_1$ data for identified hadrons across beam energies from 7.7 to 200 GeV, including the splitting between baryons and antibaryons and the double sign change in the mid-rapidity slope of net-proton and net-lambda directed flow between 7.7 and 39 GeV. The author further demonstrates that baryon stopping and diffusion create a substantial background for the directed-flow splitting attributed to electromagnetic-field effects, and uses the successful description to extract the baryon diffusion coefficient for the strongly interacting medium for the first time.

What carries the argument

The central object is the two-component initial net-baryon deposition profile of Eq. 4.5, in which participant sources ($N_\pm$) carry a forward-backward asymmetric rapidity envelope and binary-collision sources ($N_{\rm coll}$) carry a symmetric envelope, weighted by a free parameter $\omega$. This profile controls the tilt of the baryon distribution in the reaction plane, while the Bozek-Wyskiel tilted initial condition controls the energy tilt; the relative tilt sets the pressure gradients that drive directed flow. Baryon diffusion is implemented through a relaxation-type current with $\kappa_B = \tau_B n_B (\frac13 \coth(\mu_B/T) - n_B T/(\epsilon+p))$ and $\tau_B = C_B/T$, where $C_B$ is the free parameter extracted from data. The competition between baryon advection and the diffusion current, captured through the estimators $\langle -\partial_x p\rangle_{n_B}$ and $\langle -\partial_x(\mu_B/T)\rangle_{n_B}$, determines the sign and magnitude of the baryon $v_1$ and its splitting from antibaryons.

What would settle it

Run the same initial-baryon-profile model with the baryon diffusion coefficient set to zero but with an equation of state that includes a critical point or a strong first-order transition, and compare the resulting $dv_1/dy$ of net-protons and net-lambdas at 7.7 GeV; if the double sign change survives without baryon diffusion, the claim that baryon dynamics carry the signal is disproved.

Watch

Extended reading notes

Core claim

Using a new ansatz for the initial net-baryon distribution (Eq. 4.5), where baryon charge is deposited both by participant nucleons with forward-backward asymmetric rapidity profiles and by binary-collision sources with a forward-backward symmetric profile, the hybrid hydrodynamic calculation reproduces the rapidity-odd $v_1$ of identified hadrons across $\sqrt{s_{NN}}=7.7$–$200$ GeV. The model captures the elusive baryon-antibaryon $v_1$ splitting, the double sign change of $dv_1/dy$ for net-protons and net-lambdas between 7.7 and 39 GeV, and the centrality trend of the charged-hadron $v_1$ splitting that has been attributed to electromagnetic fields; this establishes a non-critical baryonic baseline for critical-point searches. The same model provides a first estimation of the baryon diffusion coefficient of the strongly interacting matter created in heavy-ion collisions.

Load-bearing premise

The load-bearing premise is that the low-energy sign changes in the directed-flow slope of protons and lambdas come from baryon stopping and diffusion, not from equation-of-state effects; if the equation of state alone can produce the same double sign change, the paper's central attribution collapses.

Editorial extensions

If this is right

If the model is right, the baryon-antibaryon $v_1$ splitting observed across the beam energy scan is a direct signal of initial baryon stopping and subsequent baryon diffusion, not primarily a critical-point or equation-of-state effect.
The observed double sign change in $dv_1/dy$ of net-protons and net-lambdas between 7.7 and 39 GeV can be reproduced without invoking a first-order phase transition; baryon dynamics provide a non-critical baseline that critical-point searches must subtract.
The centrality and system-size dependence of the split in directed-flow slope between oppositely charged hadrons, previously read as a clean electromagnetic-field signal, contains a significant baryon-stopping induced background that must be modeled before extracting the field strength.
The rapidity-even $v_1$ splitting between protons and antiprotons, if measured, would constrain the rapidity dependence of the initial baryon deposition profile and thereby discriminate between baryon-junction-inspired stopping pictures.
The first extracted value of the baryon diffusion coefficient, obtained through model-to-data comparison, provides a concrete input for finite-baryon-density hydrodynamic simulations and can be checked against future measurements of $p_T$-differential baryon-antibaryon $v_1$ splitting.

Reading between the lines

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

The same two-component deposition mechanism could be tested directly at future low-energy runs by measuring the rapidity-odd $v_1$ of multi-strange baryons such as $\Xi$ and $\Omega$, whose baryon number and strangeness make them sensitive to the same diffusion current with different quantum-number weights.
Because the baryon diffusion coefficient is extracted with a constant $C_B$ across beam energies, a natural extension is to allow $C_B(T,\mu_B)$ to vary; the double sign change near 7.7 GeV may then serve as a direct sensitivity probe for a temperature- and density-dependent diffusion coefficient.
The claim that electromagnetic-field backgrounds are baryon-dominated could be probed by repeating the analysis in smaller systems, such as Cu+Au or $p$+Au collisions, where the baryon-stopping profile differs; a return of the $\Delta(dv_1/dy)$ centrality trend under such conditions would strengthen the background interpretation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things worth knowing. The thesis is the most serious hydrodynamic attempt I have seen at reproducing the baryon-antibaryon v1 splitting and the net-proton/net-lambda double sign change across BES energies; the two-component baryon deposition ansatz in Eq. 4.5 is a genuine extension of participant-only and junction-motivated profiles. But the headline claims—a non-critical baseline and a first extraction of the baryon diffusion coefficient—outrun what the evidence supports, and the stress-test note is on target.

What is actually new and good: the initial net-baryon profile combines participant sources with asymmetric rapidity envelopes and binary-collision sources with symmetric ones, tied to a single/double junction picture. This is a clean phenomenological idea. The chapter also shows mathematically and numerically that the JYP tilted-source ansatz reduces to Bozek-Wyskiel at large eta_t, which is a useful clarification. Calibration is not sloppy: yields, pT spectra, mean pT, v2, and net-proton rapidity distributions are used to fix the bulk parameters, and the model then describes v1 for pi, p, pbar across 7.7-200 GeV. Some predictions—K+- splitting at 7.7 and 11.5 GeV, phi v1, centrality dependence of proton v1 at low energies—fail or overshoot, and the author says so. That honesty earns credit.

The weak spots are real and load-bearing for the advertised claims. Table 4.1 lists eta_m and omega as calibrated to v1(pi+, p, pbar), and Table 4.2 shows CB=0.5 at 7.7 and 11.5 GeV specifically because CB=1 could not describe proton and antiproton v1 simultaneously. So the famous sign change is accommodated, not predicted. Worse, the author himself flags in Sec 4.9 that the low-energy sign change could come from the EoS rather than baryon diffusion, and no EoS-variation study is presented. Chapter 6's diffusion coefficient is a fit without reported uncertainties or propagation of the CB/EoS ambiguity. As it stands, the paper establishes a plausible tunable model, not a baseline and not a coefficient estimate.

Who should read it: BES phenomenologists and anyone constructing initial conditions for finite-baryon hydro. The math and data handling look standard, and I found no fatal contradiction in the audited part. It deserves a serious referee, not a desk reject. But if it goes to a journal, the revision must reframe the claims, add an EoS scan and CB sensitivity, and separate fitted from predicted observables.

Referee Report

5 major / 5 minor

Summary. This thesis-style manuscript proposes a two-component initial net-baryon deposition profile (Eq. 4.5), combining participant and binary-collision sources with forward/backward Gaussian rapidity envelopes, and uses it as input to a hybrid MUSIC+iSS+UrQMD framework with a tilted energy-density profile. The central claim is that this setup reproduces the rapidity-odd directed flow v1 of identified hadrons, including the baryon-antibaryon splitting, across sqrt(s_NN) = 7.7–200 GeV, and the double sign change in dv1/dy for net-protons and net-lambdas between 7.7 and 39 GeV (Secs. 4.6–4.7, 4.9, Figs. 4.16–4.19). The manuscript also claims to establish a non-critical baryonic baseline for critical-point searches, to show that baryon stopping and diffusion constitute a significant background to electromagnetic-field interpretations of v1 splitting, and to provide the first estimation of the baryon diffusion coefficient of the strongly interacting medium (Ch. 6).

Significance. If the central claims survive closer scrutiny, the paper would be a useful phenomenological step: it identifies an initial-condition ansatz that correlates several v1 observables, makes falsifiable predictions (e.g., rapidity-even v1 splitting between p and pbar, K± and phi v1 at low energies), and proposes a concrete mechanism for baryon-antibaryon v1 splitting. The use of public codes (MUSIC, iSS, UrQMD) and the detailed parameter tables aid reproducibility, and the gradient-based estimators of Sec. 4.5 provide an instructive decomposition of baryon flow into advection and diffusion. The paper is also honest in listing several of its own limitations. The significance is, however, conditional: the main v1 comparisons are partly fits rather than independent predictions, and the separation of baryon-dynamics effects from equation-of-state effects is not established.

major comments (5)

[Sec. 4.6 and Table 4.1] The parameters eta_m and omega are explicitly calibrated to the rapidity dependence of v1 of pi+, p, and pbar, so the agreement shown in Figs. 4.16–4.18 for those species is partly a fit rather than an independent description. This is especially consequential for the baryon-antibaryon splitting: Table 4.2 sets C_B = 0.5 at sqrt(s_NN) = 7.7 and 11.5 GeV specifically because C_B = 1 could not simultaneously explain the v1 of protons and antiprotons, and this is exactly the energy range where the claimed double sign change of dv1/dy for net-protons and net-lambdas occurs. The paper should label fitted observables as fitted, distinguish them from genuinely predicted observables, and either demonstrate the double sign change with a single fixed C_B or with an independently motivated energy dependence of C_B, or downgrade the wording from reproduction to accommodation.
[Sec. 4.9] The manuscript itself leaves open whether the low-energy sign change in dv1/dy for p and Lambda comes from baryon stopping and diffusion or from the equation of state. Since all simulations use the single crossover EoS NEoS-BQS (Sec. 2.2), and since the pressure enters baryon flow through both the equilibrium and diffusion terms, the model cannot currently separate these two effects. Consequently, the abstract's claim that the model establishes a non-critical baryonic baseline is not yet supported. A concrete test would be to repeat the 7.7 and 11.5 GeV calculations with a different EoS (e.g., one with a first-order transition or a stronger density dependence) while keeping C_B and the initial profiles fixed, and to show that the double sign change persists. Without such a study, the baseline claim should be presented as conditional on EoS assumptions.
[Chapter 6] The claimed first estimation of the baryon diffusion coefficient is presented as a single numerical value without propagating the C_B ambiguity from Table 4.2 or the EoS uncertainty noted in Sec. 4.9. The chapter should provide a scan over C_B (including the 0.5 vs 1.0 values used at different energies) and over EoS variants, and should present the extracted coefficient with a model-systematic uncertainty band. As written, the extraction inherits the circularity of the v1 calibration and is therefore not yet a robust transport-coefficient determination.
[Sec. 4.7.2 and Fig. 4.16] At 0–10% centrality and sqrt(s_NN) < 19.6 GeV, the model fails to describe v1(p) while describing v1(pi+), a failure that the text attributes to centrality-independent tau0 and omega and to the absence of pre-equilibrium dynamics. Because the central object of the paper is the initial baryon deposition mechanism, this failure indicates that the two-component profile is not yet a closed model of baryon stopping across centrality. The domain of the central claim should be restricted to 10–40% centrality unless a centrality-dependent parameterization of the baryon profile is provided.
[Abstract and Fig. 4.16] The phrase 'identified hadrons' overstates the validated scope. The paper itself reports that the model overestimates the K+ - K- v1 splitting at sqrt(s_NN) = 7.7 and 11.5 GeV and fails to capture phi v1 at those energies, attributing this to the lack of independent evolution of net strangeness and electric charge (Eqs. 4.10–4.11). The summary should therefore claim validated description for pi±, p, Lambda, and their antiparticles in the 10–40% centrality class, and present K and phi results as predictions of a model with simplified charge and strangeness dynamics.

minor comments (5)

[Throughout] There are numerous typographical and grammatical slips, including 'it's' for 'its', 'collsion', 'diffsusion', 'afterbuner', 'represnted', 'claculations', and 'constraint' used as a verb; a careful proofreading pass is needed.
[Fig. 4.16] The figure is very dense, with five particle species across seven collision energies in a single layout; the small panels and overlapping uncertainty bands make it hard to assess the claimed agreement. Larger panels or separate figures for each energy would substantially improve readability.
[Eq. 4.9] The normalization condition for the initial net-baryon density should spell out the integration domain and the role of tau0; as written the equation is dimensionally non-transparent and the connection to Npart is not immediately clear.
[Sec. 2.2] The equation of state is referred to interchangeably as 'NEoSB', 'NEoS-B', and 'NEoS-BQS'; the notation should be standardized in one place and used consistently.
[Sec. 4.2] The phrase 'rapidity envelop profiles' should be 'rapidity envelope profiles', and the parameters eta_nB0, sigma_B+ and sigma_B- should be defined in a single table for easy reference, rather than only in the text and Fig. 4.2.

Circularity Check

2 steps flagged · score 6.0 of 10

The baryon-antibaryon v1 splitting and the low-energy sign change are partly fits: the tilt parameters (ηm, ω) and the baryon diffusion parameter CB are calibrated to the v1 of p, p̄, and π+, so the central 'reproduction' is not an independent prediction, although yields, spectra, v2, and the v1 of K, Λ, and φ remain unfitted content.

fitted input called prediction [Sec. 4.6 (Table 4.1) and Sec. 4.7.2]
"The parameters present in the expression of initial energy and net-baryon distribution and the corresponding experimental data used for their calibration is provided in Table 4.1. ... [Table row:] ηm, ω | Rapidity dependence of the v1 of π+, p and ¯p. ... Therefore, by suitably choosing (ηm, ω) at each √sNN, we are able to describe the rapidity dependence of v1 for π+, p, and ¯p simultaneously in the 10-40% centrality range. However, the v1 of other hadrons are our model predictions."

The parameters ηm and ω control the relative tilt between the energy and net-baryon density profiles, which is the mechanism that generates the proton-antiproton v1 splitting in this model. The paper's own calibration table states that these parameters are fitted to the rapidity-dependent v1 of π+, p, and p̄. The subsequent 'description' of p and p̄ v1, and of the net-proton/net-Lambda double sign change built from those fitted v1 curves, is therefore an accommodation of the fitted inputs rather than a genuinely predicted outcome. Only the other species (K, Λ, φ) are explicitly labeled as predictions.
fitted input called prediction [Sec. 4.6 (parameter selection) and Table 4.2]
"For collisions at √sNN ≥ 19.6 GeV, we set CB = 1.0. However, for √sNN = 11.5 and 7.7 GeV, we opt for CB = 0.5, as we did not find a suitable parameter set for CB = 1 to concurrently explain the v1 of protons and anti-protons at these lower energies."

CB is the proportionality constant fixing the baryon diffusion coefficient, and the paper's central nontrivial claim is the double sign change in dv1/dy of net-protons and net-lambdas between 7.7 and 39 GeV. CB is changed exactly at 7.7 and 11.5 GeV, with the stated reason being that CB = 1 could not reproduce the proton and anti-proton v1 at those energies. Thus the low-energy v1 behavior, including the sign change, is accommodated by an energy-dependent retuning of the diffusion parameter rather than predicted from a fixed transport coefficient. The Chapter 6 'first estimation' of the baryon diffusion coefficient inherits these energy-dependent CB choices, so the quoted coefficient is not independent of the v1 fits.

full rationale

The derivation chain is mostly self-contained with respect to the computational framework: MUSIC hydrodynamics, the Bozek-Wyskiel tilted energy profile, the NEoS-BQS equation of state, and the UrQMD afterburner are external inputs and are not derived from the thesis's claims. The two-component net-baryon deposition ansatz is new, and many comparisons are genuinely predictive after calibration, including charged-particle yields, net-proton rapidity distributions, pT spectra, mean pT, v2, and the directed flow of K, Λ, and φ. However, the central baryon-antibaryon v1 claim is partially circular by the paper's own calibration tables. Table 4.1 explicitly lists ηm and ω as calibrated to the rapidity dependence of v1 of π+, p, and p̄, and Sec. 4.7.2 states these parameters are 'suitably chosen' to reproduce p and p̄ v1; the claimed reproduction of the p-p̄ splitting is therefore a fit, not an independent test. Separately, Table 4.2 retunes CB to 0.5 at √sNN = 7.7 and 11.5 GeV because CB = 1 could not explain proton and anti-proton v1, so the double sign change in net-proton and net-Lambda dv1/dy cited as the key success is accommodated exactly in the energy region where it occurs. The Chapter 6 baryon diffusion coefficient extraction inherits these same CB values and hence is not independent of the v1 fits. A limitation is also flagged in the text after Fig. 4.17: the author writes that it is 'essential to find out whether such a sign change primarily arises from initial baryon stopping and it's diffusion or reflects the equation of state (EoS) effect,' and no EoS-variation study is presented; that is a correctness risk rather than circularity, but it weakens the 'non-critical baryonic baseline' claim. Because substantial independent content exists (unfitted species predictions, centrality and system-size dependence, yields and spectra), the circularity is partial rather than total, giving a score of 6.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The central success of the model is achieved through a parametric ansatz for initial baryon deposition with per-energy shape parameters, plus a baryon diffusion coefficient whose magnitude is tuned to the same v1 data. The physics input is the two-component deposition with a baryon-junction motivation, but no first-principles constraint fixes the Gaussian envelopes or the CB value. There are no new particles, forces, or dimensions.

free parameters (8)

omega (baryon two-component weight) = 0.25, 0.25, 0.20, 0.11, 0.15, 0.22, 0.35 for 200, 62.4, 39, 27, 19.6, 11.5, 7.7 GeV
Sets the relative contribution of binary collisions to participant sources in the initial baryon distribution (Eq. 4.5). Tuned to the v1 data of pi+, p, and pbar as stated in Table 4.1.
eta_m (energy tilt parameter) = 2.2, 1.4, 1.1, 1.1, 0.8, 0.4, 0.3 for 200 to 7.7 GeV
Controls the tilt of the initial energy density in the Bozek-Wyskiel model (Eqs. 3.3-3.7). Calibrated to the rapidity dependence of v1 of pi+ (Table 4.1).
eta_0^{nB}, sigma_B,+, sigma_B,- (initial baryon peak and widths) = Table 4.2 per energy, e.g., 200 GeV: 4.6, 1.6, 0.1
Fix the rapidity envelope of the initial net-baryon distribution (Eqs. 4.6-4.7). These are constrained by net-proton rapidity yields, but the split between peak and widths is a modeling choice that trades off against the diffusion coefficient.
CB (baryon diffusion coefficient scaling) = 1.0 for sqrt(sNN) >= 19.6 GeV; 0.5 for 7.7 and 11.5 GeV
Sets the magnitude of the baryon diffusion current through tau_B = CB/T (Eq. 2.21). Chosen per energy so that the v1 of protons and antiprotons are described, as stated in Sec. 4.6.
epsilon_0, alpha, eta_0, sigma_eta (energy profile parameters) = Table 4.2 per energy
Set the normalization and longitudinal shape of the initial energy density. Calibrated to charged-particle or pi+ yields at midrapidity and to the pseudorapidity distribution of charged particles.
tau_0 (initial hydro time) = 0.6, 0.6, 1.0, 1.2, 1.8, 2.6, 3.6 fm for 200 to 7.7 GeV
Initial proper time for hydrodynamics, chosen larger than the nuclear passage time at each energy (Sec. 4.6).
epsilon_f (particlization energy density) = 0.26 GeV/fm3
Freeze-out energy density used in the Cooper-Frye prescription. Selected to reproduce the proton-to-antiproton ratio and particle yields, as described in Sec. 4.6.
eta/s (shear viscosity to entropy ratio) = 0.08
Kept fixed at 0.08 for all energies. The authors state that a temperature- and baryon-chemical-potential-dependent eta/s could improve quantitative agreement.

assumptions (7)

domain assumption The tilted initial energy density profile of Bozek-Wyskiel (Eqs. 3.3-3.7) is an adequate description of initial energy deposition.
Used as an input for all hydrodynamic simulations; the parametrization is not derived from first principles but is a standard phenomenological assumption.
ad hoc to paper The two-component initial baryon profile (Eq. 4.5) with Gaussian rapidity envelopes (Eqs. 4.6-4.7) faithfully represents baryon stopping.
This is the central new ansatz of the thesis. It is motivated by baryon-junction picture and LEXUS, but the specific functional form and per-energy parameters are not derived from a deeper theory.
domain assumption Bjorken flow initial velocity profile u = (cosh eta_s, 0, 0, sinh eta_s) at tau_0 (Eq. 4.12).
Assumes longitudinal boost invariance at initialization even at low energies where boost invariance is broken; the thesis discusses deviations from Bjorken flow as a systematic check in Sec. 4.9.2.
standard math The baryon diffusion current takes the relaxation-time form of Eqs. (2.20)-(2.21) with tau_B = CB/T.
Adopted from kinetic theory as implemented in MUSIC (Ref [187]). The magnitude is controlled by the free parameter CB, which is fitted to data.
domain assumption The NEoS-BQS equation of state with strangeness neutrality and charge-to-baryon ratio nQ = 0.4 nB (Eqs. 4.10-4.11) is valid for the collision energies considered.
The equation of state is from Monnai et al. [201]. The local constraints on strangeness and electric charge evolution are modeling assumptions that affect Kaon and pion directed flow splitting.
domain assumption Event-averaged smooth initial conditions are sufficient for rapidity-odd v1.
Single-shot hydrodynamic evolution from averaged MC Glauber profiles is used for the main results. Event-by-event fluctuation effects on v1 are only checked in Chapter 7 for the rapidity-even component.
domain assumption The freeze-out hypersurface is defined by a constant energy density epsilon_f = 0.26 GeV/fm3.
This is a standard prescription, but the value is tuned to reproduce particle ratios, and the choice affects the extracted baryon diffusion coefficient.

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Cite this review

Pith. "Pith review of Phenomenology of baryon dynamics with directed flow in relativistic heavy-ion collisions." pith.science (2026). https://pith.science/paper/B5N3VFZH

@misc{pith2026250506522,
  author       = {Pith},
  title        = {Pith review of: Phenomenology of baryon dynamics with directed flow in relativistic heavy-ion collisions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B5N3VFZH}},
  note         = {Machine review of arXiv:2505.06522}
}

abstract

This thesis aims to elucidate the role of initial baryon stopping and its diffusion in heavy-ion collisions (HIC) using hydrodynamic model. In this regard, we have studied the observable-directed flow ($v_1$) of identified hadrons, particularly the $v_1$ of baryons and antibaryons, as well as the splitting observed between them in detail. We propose a new ansatz for the initial baryon distribution. By employing this initial baryon deposition model alongside a tilted energy distribution as inputs to a hybrid framework, we successfully describe the rapidity-odd $v_1$ of identified hadrons, including the elusive baryon-antibaryon splitting of $v_1$ across a wide range of $\sqrt{s_{NN}}$. Our model, incorporating baryon stopping and it's subsequent diffusion within a relativistic hydrodynamic framework and employing a crossover equation of state derived from lattice QCD calculations, establishes a non-critical baryonic baseline. Moreover, we demonstrate that recent STAR measurements of the centrality and system-size dependence of $v_1$ splitting between oppositely charged hadrons-attributed to electromagnetic field effects-are significantly influenced by background contributions from baryon stopping and its diffusion. Furthermore, we show that the rapidity dependence of the splitting of the rapidity-even component of $v_1$ between $p$ and $\bar{p}$ is highly sensitive to the initial baryon deposition scheme. If measured experimentally, this could constraint the rapidity dependence of the initial baryon deposition profile. Moreover, it could offer valuable phenomenological insights into the baryon junction picture and help refine constraints on the baryon diffusion coefficient of the medium. Notably, utilizing this phenomenologically successful baryon deposition model, we present the first estimation of the baryon diffusion coefficient for the strongly interacting QCD matter created in HIC.

Figures

Figures reproduced from arXiv: 2505.06522 by the authors.

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**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p097_5.png]

**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p098_5.png]

**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p099_5.png]

**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p100_5.png]

**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p101_5.png]

**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p102_5.png]

**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p103_5.png]

**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p104_5.png]

**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p106_5.png]

**Figure 6.** Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p109_6.png]

**Figure 6.** Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p111_6.png]

**Figure 6.** Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p112_6.png]

**Figure 7.** Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p116_7.png]

**Figure 7.** Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p118_7.png]

**Figure 7.** Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p119_7.png]

**Figure 7.** Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p120_7.png]

**Figure 7.** Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p122_7.png]

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Reviewed August 15, 2026 · model on record in the stance chip above.

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