Analysis Note: Directed flow $v_1$ of protons in the Xe+Cs(I) collisions at 3.8 AGeV

Alexander Demanov; Arkadiy Taranenko; Mikhail Mamamev; Petr Parfenov; Valery Troshin

REVIEW 4 major objections 7 minor 1 cited by

Analysis Note: Directed flow $v_1$ of protons in the Xe+Cs(I) collisions at 3.8 AGeV

T0 review · 4 major / 7 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper reports the first measurement of the directed flow $v_1$ of protons in 10-30% central Xe+Cs(I) collisions at 3.8 AGeV, showing that the rapidity dependence is roughly described by the JAM model with a momentum-dependent mean…

desk verdict A genuine first proton v1 point for Xe+Cs at 3.8 AGeV, using solid methods and transparent systematics, but with a self-declared preliminary centrality calibration and no numerical tables; worth refereeing conditionally. read the letter →

arxiv 2412.08570 v2 pith:P3TEEHQ4 submitted 2024-12-11 nucl-ex hep-ex

Mikhail Mamamev , Arkadiy Taranenko , Alexander Demanov , Petr Parfenov , Valery Troshin This is my paper · ORCID

classification nucl-exhep-ex

keywords directedflowprotonv1Xe+CscollisionsBM@NNICAeventplanenuclearequationofstateJAMtransportmodel

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

This analysis note reports the first measurement of the directed flow of protons ($v_1$) in Xe+Cs(I) collisions at 3.8 AGeV, for the 10-30% centrality class, using data from the BM@N run8. The authors extract $v_1$ as a function of center-of-mass rapidity and transverse momentum with the event-plane method, using spectator fragments registered in the forward hadron calorimeter (FHCal) as the symmetry plane. They find that the measured $v_1(y_{cm})$ is roughly described by the JAM transport model with a momentum-dependent mean field, and that the midrapidity slope $dv_1/dy_{cm}|_{y_{cm}=0}$ is consistent with the published energy dependence of proton directed flow from other experiments. The centrality estimate is explicitly preliminary: the note states that the CCT2 trigger efficiency, run-by-run FSD+GEM multiplicity changes, and the systematic uncertainties of the MC-Glauber and Gamma-Fit methods still need evaluation. The result extends flow measurements, a probe of the nuclear equation of state, to a new reaction system at NICA energies.

What carries the argument

The central object is the first-order event plane vector $Q_1$ reconstructed from the energy deposition of spectator fragments in the forward hadron calorimeter (FHCal). The method uses three (and sometimes four) sub-events defined by FHCal pseudorapidity ranges F1, F2, F3 and by charged-track groups $T^+$ and $T^-$, with the resolution correction factor $R_1^y$ computed from the $Y$-component correlations. Because the BM@N magnetic field deflects charged particles along $x$, the directed flow is extracted only from $Y$ components: $v_1 = 2\langle y_1 Y_1^a\rangle / R_1^y$. Non-uniform azimuthal acceptance is handled by recentering, twist, and rescaling corrections from the QnTools framework. The midrapidity slope is obtained by fitting $v_1(y_{cm})$ with $v_1 = a + b y_{cm} + c y_{cm}^3$.

What would settle it

Recompute the centrality boundaries after measuring the CCT2 trigger efficiency and the run-by-run FSD+GEM multiplicity drift, then re-extract $v_1(y_{cm})$ and its midrapidity slope for the revised 10-30% bin. If the slope moves outside the band of published values, or the JAM comparison degrades by more than the quoted uncertainties, the paper's central quantitative claim is falsified.

Watch

Extended reading notes

Core claim

The paper claims that the first directed-flow ($v_1$) measurement of protons from Xe+Cs(I) collisions at 3.8 AGeV has been obtained, for the 10-30% centrality bin. Using the first-order event plane reconstructed from spectator energy deposition in the FHCal, with three- and four-sub-event resolution corrections and acceptance corrections applied to both the flow vectors and the proton $u_1$ vectors, the authors measure $v_1$ as a function of rapidity and $p_T$. The resulting $v_1(y_{cm})$ is roughly reproduced by JAM in the mean-field mode with a momentum-dependent potential, while the extracted midrapidity slope $dv_1/dy_{cm}|_{y_{cm}=0}$ agrees within uncertainties with the published trend from STAR, HADES, and FOPI. The paper states these are first results and that the centrality estimate is very preliminary, so the final quantitative conclusions await the pending corrections.

Load-bearing premise

The load-bearing premise is that the 10-30% centrality selection is correct, because the measured $v_1$ is quoted for that bin and the note itself says the centrality estimate is very preliminary.

Editorial extensions

If this is right

BM@N can produce differential flow measurements of identified protons in the $\sqrt{s_{NN}} \approx 2$--$3.5$ GeV range, adding a new data point to the energy and system-size dependence of $v_1$.
The measured $v_1(y_{cm})$ provides a benchmark for JAM with a momentum-dependent mean field in the Xe+Cs system, extending model tests beyond Au+Au.
The midrapidity slope of proton $v_1$ at $\sqrt{s_{NN}} = 3.26$ GeV can be added to the existing compilation of $dv_1/dy$ versus collision energy, and it is consistent with the published trend.
The agreement among resolution factors and $v_1$ values from different FHCal sub-event planes indicates that the spectator-based event plane works reliably despite the beam-hole leakage.
The final quantitative results require the pending centrality corrections, as the note states that the centrality estimate is very preliminary.

Reading between the lines

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

One testable extension is to apply the same analysis chain to $v_2$ and to pions and kaons in the same dataset; such multi-differential data would constrain the equation of state more strongly than $v_1$ alone.
If the preliminary centrality is later shifted by the trigger-efficiency and multiplicity corrections, the quantitative comparison with JAM could change, but the qualitative $v_1(y)$ trend is likely stable because the directed-flow slope has only weak centrality dependence except for the most central bin.
A direct comparison of Xe+Cs with Au+Au at matched center-of-mass energy would isolate the system-size dependence of spectator shadowing, a question the paper motivates but does not quantify.
One could also cross-check the spectator-plane resolution with a larger rapidity gap or a different sub-event grouping; if the extracted $v_1$ changed by more than the estimated non-flow contribution, the event-plane assumption would need revision.

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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

First thing to know: this is a real first measurement, not a rehash. The proton v1 for Xe+Cs(I) at 3.8 AGeV from BM@N run8 does not exist anywhere else in the literature, and the note uses standard scalar-product/event-plane methods with a careful sub-event resolution treatment. The systematic section is honest and itemized: track quality, DCA, PID, vertex position, TOF systems, run periods, efficiency weighting. The JAM-with-mean-field comparison is stated as "roughly" capturing the data, which is the right level of claim.

The main soft spot is exactly the one the note itself flags. Section 3.4 says the centrality estimate is "very preliminary" and lists the missing pieces: CCT2 trigger efficiency, run8 drift in FSD+GEM multiplicity, and MC-Glauber vs Gamma-Fit systematics. The physics comparison with JAM and the published dv1/dy energy dependence both use the 10-30% bin. Since v1 is known to vary with centrality, a miscalibrated bin could shift the comparison. Note that the v1 slope is reported to be only weakly centrality dependent except for very central collisions, so the effect might be modest, but it has to be demonstrated, not assumed.

Second soft spot: no numbers. The final v1(y) and v1(pT) points and the extracted slope dv1/dy are shown only in figures. The reader cannot fit the polynomial or compare with the literature without digitizing. For an analysis note this is a real deficiency, and it is easily fixed.

The reader's circularity concern is minor and I mostly disagree with it as a burden. The v1 signal is measured; the model comparison is downstream. There is some reliance on self-cited simulation work [17,21] from the same group, but those are public performance/model studies used as benchmarks, and the calibration methods are standard. Self-citation here is not a smoking gun.

Who is this for: the BM@N/NICA flow community and people doing system-size dependence of flow at 2-5 GeV. It is a within-subfield data point, not a field reorganization. It deserves a serious referee. I would send it to review with the condition that the authors add numerical tables, state the centrality systematics as a caveat or update the calibration, and show the fit parameters for the slope.

Referee Report

4 major / 7 minor

Summary. This analysis note reports the first measurement of the directed flow v1 of protons in 10-30% central Xe+Cs(I) collisions at a beam energy of 3.8 AGeV (BM@N run8). The authors describe the run-by-run quality assurance, event and track selection, proton identification via TOF, centrality determination with MC-Glauber and Gamma-fit methods, event-plane reconstruction using the FHCal spectator calorimeter, and the scalar-product extraction of v1 as a function of rapidity and transverse momentum. The measured v1(y_cm) is compared with JAM transport model calculations with a momentum-dependent mean field, and the midrapidity slope dv1/dy is compared with published proton directed-flow slopes from other experiments. The paper is written as an internal analysis note and includes extensive figures, systematic checks, and links to analysis code and data paths.

Significance. If validated, this is a genuinely new observable: the first directed-flow measurement for the intermediate-mass, asymmetric Xe+Cs(I) system at NICA energies, and it can serve as a system-size and asymmetry benchmark for transport-model comparisons in the 2-5 GeV energy range. The note has real strengths: a very detailed run-by-run QA section, explicit event-selection statistics, a realistic GEANT4-based correction framework, public code repositories for the QA and centrality frameworks, and a systematic-uncertainty study covering tracking, PID, DCA, off-target collisions, acceptance/efficiency, and run-period stability. The main caveats are that the centrality calibration is explicitly labeled preliminary, the final v1 points and slopes are not quoted numerically, and there is an inconsistency in the resolution-correction formulas that directly affects the absolute normalization of v1.

major comments (4)

[Section 3.4, final paragraph] The centrality estimate is explicitly stated to be 'very preliminary', and the text lists the missing ingredients: CCT2 trigger efficiency, run-dependent changes in average FSD+GEM multiplicity, and systematics from the MC-Glauber versus Gamma-fit choices. Since the entire physics claim is made for the 10-30% centrality bin, the comparison with the JAM 10-30% curve in Figure 47 and with the published slope systematics in Figure 48 is conditional on this calibration. If the true centrality of the analyzed sample is shifted, the model comparison and the energy-dependent slope comparison are not apples-to-apples. This is the single most load-bearing limitation and must be resolved before the result can be considered final.
[Section 5, Figures 47-48] The paper never gives the numerical values of the v1(y_cm) and v1(pT) points, the fitted polynomial coefficients a, b, c from v1 = a + b y_cm + c y_cm^3, the extracted slope dv1/dy|y=0, or the corresponding statistical and systematic uncertainties. The claims of 'roughly captures' the JAM trend and 'reasonable agreement' with published slopes cannot be quantitatively checked from the text alone. A table with the binned v1 values, their uncertainties, the fit parameters, and the fit quality (e.g., chi2/ndf) should be added.
[Section 4.1, Eq. (25) and Section 4.3, Eq. (28)] The resolution-correction formulas are inconsistent as printed. Equation (25), R^y_1{a(b,c)} = sqrt( 2<Y_b Y_c> / (2<Y_a Y_b> 2<Y_a Y_c>) ), is dimensionally inconsistent for a three-subevent resolution and does not match Eq. (28), R^y_1{a(b,c)} = sqrt( <Y_a Y_b><Y_a Y_c>/<Y_b Y_c> ). Moreover, if the latter is used together with v1 = 2<y1 Y_a*>/R^y_1, the standard scalar-product derivation for y-components gives R_y = sqrt(2<Y_aY_b><Y_aY_c>/<Y_bY_c>), i.e. a factor sqrt(2) larger than Eq. (28). As written, the formula would overestimate v1 by sqrt(2), which directly scales every v1 point and the extracted slope. The implemented formula needs to be stated unambiguously and validated, for example by reproducing the known JAM input v1 in the closed-symbol curves of Figure 37.
[Section 3.3, QA run removal] The 3-sigma bad-run rejection (Section 3.2) removes about 18M events based on the deviation of run-averaged observables from the global mean. If bad runs cluster in specific time periods, this can bias the multiplicity distribution used for centrality, especially because the note later states that the average FSD+GEM multiplicity changed during run8. The magnitude of this effect should be quantified as part of the centrality systematics, or at least discussed in Section 3.4.

minor comments (7)

[Abstract] The abstract says 'The systematic uncertainty study will also be presented and discussed', but the study is in fact included in Section 4.4; the future tense should be replaced with a present-tense statement.
[Section 3.4] In the paragraph describing the application to experimental data, the sentence 'Figure shows the results' is missing the figure number; it should refer to Figure 28.
[Throughout] There are numerous typos and grammatical errors that should be cleaned up: 'standart', 'creats', 'resgion', 'colid', 'bellow', 'calculatad', 'persented', 'previus', and 'pior' among others. These do not affect the physics but make the note harder to read.
[Section 4.1, Eqs. (17)-(19)] The notation for the three- and four-subevent resolutions would benefit from a short derivation or a reference to the standard scalar-product formalism, because the current text moves quickly from Q-vector correlations to the component form and the definitions of a, b, c, d are implicit.
[Section 4.4, first bullet] The statement that the momentum-reconstruction systematic uncertainty is 'bellow 2-5%' is overly broad; it would be clearer to report the uncertainty separately for the pT and rapidity ranges where it was evaluated, and to state whether the quoted range is a maximum or a typical value.
[Section 5, Figure 47] The right panel shows v1 as a function of pT, but the text does not describe the pT dependence in words or compare it with the known behavior from HADES/STAR; a brief qualitative statement would help the reader interpret the figure.
[References] The note relies heavily on two self-citations from the same group (Refs. [17] and [21]) for the JAM model setup and for the performance studies. This is acceptable, but the paper should state explicitly which JAM parameters and EOS variants were used in the comparison shown in Figure 47, so that the model curve is reproducible without consulting the unpublished analysis-note chain.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the v1 measurement is self-contained, and the JAM comparison and slope extraction are external benchmarks rather than fitted inputs.

full rationale

The central observable, directed flow v1 of protons, is measured directly from BM@N run8 data using standard event-plane and scalar-product techniques (Eqs. 27-29) with QnTools acceptance corrections and resolution correction factors from three- and four-sub-event methods. No parameter of the flow analysis is fitted to the v1 result, and no equation reduces v1 to an input assumption. The comparison with the JAM transport model is a benchmark, not a fit: the model is generated independently at fixed EOS options, and the note states only that JAM 'roughly captures the overall magnitude and trend' of the measured signal. The same-group papers cited for the JAM mean-field setup ([17, 21]) supply model parameters and prior validation against HADES/STAR data; they do not impose the BM@N v1 values by construction. The centrality determination is indeed labelled 'very preliminary' and depends on fits to the FSD+GEM multiplicity distribution, but this affects the interpretation of the 10-30% bin, not the derivation of v1 itself; an incorrect centrality mapping would be a systematic uncertainty, not a circular step. The midrapidity slope is extracted by a polynomial fit to measured v1 and then compared with published slopes, which is a data summary rather than a self-referential prediction. No self-definitional, fitted-input-as-prediction, or self-citation-chain circularity is present.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

No new particles or forces are introduced. The central measurement depends on calibration fits for centrality, on assumed multiplicity-fluctuation models, and on the JAM event generator, but these are standard external tools. The only free parameters that directly enter the reported v1 are the centrality-fit parameters and the polynomial coefficients used to extract the slope.

free parameters (3)

MC-Glauber NBD parameters f, mu, k = not quoted
Fitted to the FSD+GEM multiplicity distribution (Eq. 5) to define centrality classes; the 10-30% bin used for v1 depends on this fit.
Gamma-fit parameters theta, k0, a1, a2, a3 = not quoted
Fitted to the same multiplicity distribution via Eqs. 7-9; used as a cross-check of the centrality calibration.
v1(y_cm) polynomial coefficients a, b, c = not quoted
Fitted to the measured v1(y_cm) to extract the midrapidity slope b = dv1/dy|0 used for the energy-dependence comparison in Fig. 48.

assumptions (6)

standard math The azimuthal distribution of particles can be expanded as 1 + 2 sum_n v_n cos(n(phi - Psi_R)) with a well-defined reaction plane Psi_R.
Eq. 1, Section 2; foundation of the flow formalism.
domain assumption Spectator fragments carry a positive directed flow v1 > 0 in the forward rapidity region and deposit energy in FHCal modules that tracks the first-order event plane.
Section 4.2, used to define Q1 vectors from FHCal sub-events F1, F2, F3.
domain assumption Non-flow correlations are suppressed by requiring pseudorapidity separation between the sub-events used in the three- and four-sub-event resolution formulas.
Section 4.1, Eqs. 18-19; standard but not proven in this paper.
domain assumption The nuclear density profiles for Xe and Cs and the inelastic NN cross section sigma_inel = 27.7 mb from the PHOBOS MC-Glauber model describe the collision geometry.
Section 3.4, Eq. 4; centrality calibration depends on these inputs.
domain assumption The multiplicity fluctuations at fixed impact parameter follow the NBD parameterization (MC-Glauber) or a gamma distribution (Gamma-fit method).
Section 3.4, Eqs. 5 and 7; centrality classification relies on these assumed fluctuation kernels.
domain assumption The JAM transport model with momentum-dependent RQMD.RMF mean field gives a realistic description of the collision dynamics.
Sections 2 and 4.2; used for efficiency corrections and for the physics comparison.

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Cite this review

Pith. "Pith review of Analysis Note: Directed flow $v_1$ of protons in the Xe+Cs(I) collisions at 3.8 AGeV." pith.science (2026). https://pith.science/paper/P3TEEHQ4

@misc{pith2026241208570,
  author       = {Pith},
  title        = {Pith review of: Analysis Note: Directed flow $v_1$ of protons in the Xe+Cs(I) collisions at 3.8 AGeV},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P3TEEHQ4}},
  note         = {Machine review of arXiv:2412.08570}
}

abstract

In this note, we present the directed flow $v_1$ measurements of protons from Xe+Cs(I) collisions at 3.8 AGeV (BM@N run8). We show the datasets, event and track selection cuts, centrality definition, event plane reconstruction and resolution. The $v_1$ results are presented as function of transverse momentum ($p_T$) and rapidity ($y_{cm}$) for 10-30\% central Xe+Cs(I) collisions. The systematic uncertainty study will also be presented and discussed. The $v_1$ measurements are compared with results of JAM transport model calculations and published data from other experiments.

Figures

Figures reproduced from arXiv: 2412.08570 by the authors.

**Figure 1.** Left panel: Pressure as function of baryon density for symmetric nuclear [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** Elliptic flow 𝑣2 (upper panel) and slope of the directed flow at mid-rapidity 𝑑𝑣1/𝑑𝑦|𝑦=0 (low panel) for different paricle species from 10-40% central Au+Au collisions at √ 𝑠𝑁𝑁 =3.0, 3.2, 3.5 and 3.9 GeV from the STAR Beam Energy Scan II program [19; 20] existing measurements of 𝑣1 and 𝑣2 of protons were performed with respect to the first-order event plane, which is determined by the directed flow 𝑣1 of the specta… view at source ↗

Figures from the paper (49 more)

**Figure 3.** Figure 3: Rapidity (𝑦𝑐𝑚) dependence of 𝑣1 (left) and 𝑣2 (right) of protons with 1.0 < 𝑝𝑇 < 1.5 Gev/c in the 20-30% central Au+Au collisions at √ 𝑠𝑁𝑁 = 2.4 GeV. The closed star symbols represent the published HADES data [10]. The blue (MD2), purple (MD4), red (NS1) and yellow (NS…

**Figure 4.** Figure 4: The slope 𝑑𝑣1/𝑑𝑦′ |𝑦 ′=0 (left panel) and elliptic 𝑣2 (right panel) flow of protons in the interval 0.6 < 𝑝𝑇 < 0.9 GeV/c at mid-rapidity in Au+Au collisions at √ 𝑠𝑁𝑁 = 2.4 GeV for four centrality classes. The HADES data are compared to several model predictions. The fi…

**Figure 5.** Figure 5: The centrality dependence of the slope 𝑑𝑣1/|𝑦=0 (upper panel) and elliptic 𝑣2 (lower panel) flow of protons, pions and kaons at mid-rapidity in Au+Au collisions at √ 𝑠𝑁𝑁 = 3.0 GeV. The STAR data are compared to UrQMD model prediction. The figure is taken from [12; 19] …

**Figure 6.** Figure 6: The layout of the BM@N experiment for the Xe+Cs(I) run8 2022-2023. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: Distribution of the number of digits in the FSD (a) and GEM (c) de [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

**Figure 8.** Figure 8: Distribution of the number of digits in the TOF400 (a) and TOF700 (c) [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

**Figure 9.** Figure 9: Left panel: distribution of the number of tracks in the vertex reconstruc [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]

**Figure 10.** Figure 10: Upper panels: distribution of the x, y and z positions of vertex. The red [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]

**Figure 11.** Figure 11: Upper panels: Distribution of the number of charged particles [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]

**Figure 12.** Figure 12: Left panel: distribution of the total energy [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]

**Figure 13.** Figure 13: Left panel: distribution of the charge ( [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]

**Figure 14.** Figure 14: Upper panels: Distribution of the x, y and z components of momentum of [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]

**Figure 15.** Figure 15: Upper panels: Distributions of the 𝑝𝑇 (left), azimuthal angle 𝜑 (center) and 𝜂 (right) of charged particles. The red marker corresponds to the distribution from the "outlier" RunId. Bottom panels: Mean 𝑝𝑇 , 𝜑 and 𝜂 as a function of RunID. Black dotted horizontal line …

**Figure 16.** Figure 16: Correlation between the 𝜂 and the 𝜑 (left), 𝜂 and 𝑝𝑇 (center), 𝜑 and 𝑝𝑇 (right) for charged particles 18 [PITH_FULL_IMAGE:figures/full_fig_p018_16.png]

**Figure 17.** Figure 17: Upper panels: Distribution of the number of nHits to accurate the track [PITH_FULL_IMAGE:figures/full_fig_p019_17.png]

**Figure 18.** Figure 18: Population of charged particles in the mass squared ( [PITH_FULL_IMAGE:figures/full_fig_p019_18.png]

**Figure 19.** Figure 19: Distribution of the mass squared (𝑚2 ) and Gaussian fit of the proton peak in the TOF-400 (left upper panel) and TOF-700 (left bottom panel) detectors. Center and right panels: mean of the mass squared of proton and 𝜎𝑚2 as a function of RunID. Black dotted horizontal …

**Figure 20.** Figure 20: Left and center panels: Dependence of the number of FSD digits and the [PITH_FULL_IMAGE:figures/full_fig_p021_20.png]

**Figure 21.** Figure 21: Population of charged particles in the 𝑚2 vs. rigidity (p/q) plane for the TOF-400 (left panel) and TOF-700 (right panel) detectors [PITH_FULL_IMAGE:figures/full_fig_p022_21.png]

**Figure 22.** Figure 22: Population of charged particles in the n-sigma( [PITH_FULL_IMAGE:figures/full_fig_p022_22.png]

**Figure 23.** Figure 23: Population of selected protons in the 𝑚2 vs. rigidity (p/q) plane for the TOF-400 (left) and TOF-700 (right) detectors. The protons were selected by (𝑚2 - ⟨︀ 𝑚2 𝑝 ⟩︀ ) < 3𝜎𝑚2 𝑝 cut. combined system. Efficiency of the proton reconstruction was calculated using the real…

**Figure 24.** Figure 24: The phase space coverage of identified protons as a function of the centre [PITH_FULL_IMAGE:figures/full_fig_p023_24.png]

**Figure 25.** Figure 25: Efficiency of the proton reconstruction in the phase space of rapidity [PITH_FULL_IMAGE:figures/full_fig_p024_25.png]

**Figure 26.** Figure 26: The 3.2 version of the PHOBOS MC-Glauber model [29] has been used to compose two nuclei out of nucleons and simulate their collision process event-byevent. An input of the MC-Glauber model is the nucleon density 𝜌(𝑟) inside the nucleus. It is usually parametrized by …

**Figure 26.** Figure 26: Left panel: FSD+GEM multiplicity distribution [PITH_FULL_IMAGE:figures/full_fig_p026_26.png]

**Figure 27.** Figure 27: Left panel: FSD+GEM multiplicity distribution [PITH_FULL_IMAGE:figures/full_fig_p029_27.png]

**Figure 28.** Figure 28: FSD+GEM multiplicity distribution 𝑁𝑐ℎ from the BM@N run8 experimental data for Xe+Cs(I) collisions at 3.8 AGeV (open squares) compared to the fitted distribution using the MC-Glauber method (solid blue triangles) and Γ-fit method (red solid circles). The centrality c…

**Figure 29.** Figure 29: Centrality dependence of the ⟨𝑏⟩ from the MC-Glauber (blue solid triangles) and Γ-fit (red solid triangles) methods for BM@N run8 experimental data: Xe+Cs(I) collisions at 3.8 AGeV. 31 [PITH_FULL_IMAGE:figures/full_fig_p031_29.png]

**Figure 30.** Figure 30: Schematic illustration of recentering, twist and rescale correction steps [PITH_FULL_IMAGE:figures/full_fig_p036_30.png]

**Figure 31.** Figure 31: Sketch of the multi-dimensional correction procedure in the QnTools [PITH_FULL_IMAGE:figures/full_fig_p037_31.png]

**Figure 32.** Figure 32: Left: Relative momentum resolution Δ𝑝/𝑝 as a function of the momentum 𝑝 for fully reconstructed charged tracks from Xe+Cs(I) collisions generated using the JAM model at different kinetic energies: 4 AGeV (triangles), 3 AGeV (boxes) and 2 AGeV (circles). Right: Populat…

**Figure 33.** Figure 33: Left part: schematic representation of modules of the Forwar Hadron [PITH_FULL_IMAGE:figures/full_fig_p039_33.png]

**Figure 34.** Figure 34: (Left) Raw yield of protons as a function of azimuthal angle [PITH_FULL_IMAGE:figures/full_fig_p040_34.png]

**Figure 35.** Figure 35: The centrality dependence of resolution correction factor [PITH_FULL_IMAGE:figures/full_fig_p041_35.png]

**Figure 36.** Figure 36: The centrality dependence of the resolution correction factor [PITH_FULL_IMAGE:figures/full_fig_p042_36.png]

**Figure 37.** Figure 37: Left: directed flow 𝑣1 of protons as a function of center-of-mass rapidity 𝑦𝑐𝑚 for 10-30% central Xe+Cs(I) collisions at 2 AGeV (circles), 3 AGeV (boxes) and 4 AGeV (triangles); Right: elliptic flow 𝑣2 of protons as a function of transverse momentum 𝑝𝑇 . Markers repr…

**Figure 38.** Figure 38: Two additional sub-events were introduced from the tracks of the charged particles in the inner tracking system of BM@N. All negatively charged particles with 43 [PITH_FULL_IMAGE:figures/full_fig_p043_38.png]

**Figure 38.** Figure 38: Layout of the FHCal modules division into three groups (sub-events): [PITH_FULL_IMAGE:figures/full_fig_p044_38.png]

**Figure 39.** Figure 39: Resolution correction factor 𝑅1 calculated using different combinations as a function of centrality for sub-event symmetry planes F1, F2 and F3 from left to right. the combined (F2+F3) symmetry plane, see [PITH_FULL_IMAGE:figures/full_fig_p045_39.png]

**Figure 40.** Figure 40: Directed flow 𝑣1 of protons as a function of rapidity 𝑦𝑐𝑚 measured with respect to different spectator symmetry planes: F1, F2, F3 and combined (F2+F3), see text for the details. • Contribution due to off-target collisions. We divided the events based on the azimuthal…

**Figure 41.** Figure 41: Directed flow 𝑣1 of protons in 10-30% central Xe+Cs(I) collisions at 3.8 A GeV as a function of rapidity 𝑦𝑐𝑚 (left panel) and transverse momentum 𝑝𝑇 (right panel). 5 Results of the directed flow measurements Directed flow 𝑣1 of protons was measured in 10-30% central X…

**Figure 47.** Figure 47: Rapidity-dependence of 𝑣1 of protons from the experimental data has been compared with predictions from the model JAM transport model [26; 27] with momentum dependent mean field[17; 21]. JAM model roughly captures the overall magnitude and trend of the measured 𝑣1(𝑦𝑐𝑚…

**Figure 42.** Figure 42: Directed flow 𝑣1 of protons as a function of rapidity 𝑦𝑐𝑚 measured for different values of the track 𝜒 2/𝑁𝐷𝐹 quality (left) and the number of stations used for track reconstruction 𝑁ℎ𝑖𝑡𝑠 (right). References 1. Sorensen A. [et al.]. Dense nuclear matter equation of sta…

**Figure 43.** Figure 43: Directed flow 𝑣1 of protons as a function of rapidity 𝑦𝑐𝑚 measured for different values of the 𝐷𝐶𝐴 cut and different n-𝜎 PID cuts for the proton identification: (𝑚2 - ⟨︀ 𝑚2 𝑝 ⟩︀ ) < 1, 2, 3 𝜎𝑚2 𝑝 cut (right). 6. Liu H. [et al.]. Sideward flow in Au + Au collisions be…

**Figure 44.** Figure 44: Left: the distribution of the primary vertex in X-Y plane. Right: [PITH_FULL_IMAGE:figures/full_fig_p050_44.png]

**Figure 45.** Figure 45: Directed flow 𝑣1 of protons as a function of rapidity 𝑦𝑐𝑚 measured for protons identified using different TOF-systems (left) and protons weighted and not weighted with efficiency based on MC simulations for run8 (right). 17. Mamaev M., Taranenko A. Toward the System S…

**Figure 46.** Figure 46: Directed flow 𝑣1 of protons as a function of rapidity 𝑦𝑐𝑚 measured in the different run periods (left) and for different bins in collision centrality (right). 22. Larionov A. B. [et al.]. Squeezeout of nuclear matter in peripheral heavy ion collisions and momentum dep…

**Figure 47.** Figure 47: Directed flow 𝑣1 of protons in 10-30% central Xe+Cs(I) collisions at 3.8 A GeV as a function of rapidity 𝑦𝑐𝑚 (left panel) and transverse momentum 𝑝𝑇 (right panel). at √ 𝑠NN = 2 - 20 GeV energies // Phys. Rev. C. — 2022. — Vol. 105, no. 1. — P. 014911. 28. Nara Y., Mar…

**Figure 48.** Figure 48: The slope of 𝑣1 of protons at midrapidity 𝑑𝑣1/𝑑𝑦𝑐𝑚|𝑦𝑐𝑚=0 as a function of collision energy. The obtained BM@N results were compared with existing data from other experiments [9; 12; 19]. 32. Adamczewski-Musch J. [et al.]. Centrality determination of Au + Au collisions…

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Bayesian analysis of properties of nuclear matter with the FOPI experimental data
nucl-th 2025-09 conditional novelty 6.0 of 10

Bayesian fits to FOPI Au+Au flow and stopping data yield m*/m0 around 0.78-0.88 and F around 0.75-0.88, while K0 remains unconstrained.

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