Probing Quantum Phenomena through Photoproduction in Relativistic Heavy-Ion Collisions

James Daniel Brandenburg; Jian Zhou; Shuai Yang; Spencer R. Klein; Wangmei Zha; Zhangbu Xu

REVIEW 3 major objections 6 minor 1 cited by

Probing Quantum Phenomena through Photoproduction in Relativistic Heavy-Ion Collisions

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Photoproduction in heavy-ion collisions makes Fermi-scale double-slit interference visible.

desk verdict Useful review of a real experimental program, but the entanglement billing outruns what the paper itself supports; the E2I2-to-data link is explicitly deferred. read the letter →

arxiv 2504.18342 v1 pith:IM2BJBIC submitted 2025-04-25 nucl-ex nucl-thquant-ph

James Daniel Brandenburg , Spencer R. Klein , Zhangbu Xu , Shuai Yang , Wangmei Zha , Jian Zhou This is my paper · ORCID

classification nucl-exnucl-thquant-ph

keywords RelativisticHeavy-ionCollisionsDiffractivePhotoproductionCoherentLinearPolarizationSpinInterferenceQuantumEntanglementUltra-peripheralVectorMesonDominance

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 review argues that coherent photoproduction of vector mesons in relativistic heavy-ion collisions realizes a two-source, double-slit-like interference experiment at the femtometer scale, with the two colliding nuclei acting as the slits. The central discovery surveyed is the observed spin-interference pattern in $\rho^0 \to \pi^+\pi^-$ photoproduction, which the authors call the first instances of Fermi-scale single-particle double-slit interference. The review invokes the Entanglement Enabled Intensity Interferometry (E2I2) framework to argue that the decay pion pair is entangled, so the interference observed in the $\pi^+\pi^-$ pair probes quantum entanglement even though the $\rho^0$ decays before the two nuclear sources are far separated. If this reading holds, the measurement offers a new quantitative probe of quantum mechanics in high-energy nuclear collisions and of the gluon distribution inside nuclei.

What carries the argument

The carrying object is Entanglement Enabled Intensity Interferometry (E2I2), a formalism adapted from the study of two-photon intensity interferometry, in which interference can persist in the correlation of two distinguishable particles emitted from two sources because the particles are entangled. In this paper the two sources are the photoproduction amplitudes $\gamma_A + P_B \to \rho^0$ and $\gamma_B + P_A \to \rho^0$, and the detected pair is the $\pi^+\pi^-$ from the $\rho^0$ decay; retaining the phase terms of the two amplitudes yields extra cross terms, including a term analogous to the E2I2 correlation, that are absent for uncorrelated pion emission. The Vector Meson Dominance and color dipole models supply the production amplitudes that feed this interference, and their comparison with the STAR data determines how the modulation depends on the nuclear density profile.

What would settle it

Measure the $\cos(2\phi)$ modulation of $\rho^0 \to \pi^+\pi^-$ as a function of neutron-tagged impact parameter in a single collision system, and compare with a calculation that treats the two pions as independently emitted from the two sources: if the E2I2 entanglement claim is wrong, the extra phase terms carrying the $P_\perp \cdot B$ dependence should be absent and the modulation should not follow the predicted impact-parameter scaling.

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Extended reading notes

Core claim

The paper's central claim is that diffractive photoproduction, especially $\rho^0$ photoproduction in ultra-peripheral heavy-ion collisions, shows genuine two-source quantum interference at a femtometer scale, with the two nuclei serving as the slits. In the $\rho^0 \to \pi^+\pi^-$ channel, the two amplitudes in which nucleus A emits the photon and nucleus B is the target, and vice versa, have opposite signs because the vector meson has negative parity, producing destructive interference at low transverse momentum and an azimuthal $\cos(2\phi)$ modulation in the decay distribution. The review presents the STAR and ALICE measurements of this spin-interference pattern, and argues through the E2I2 formalism that the interference survives in the simultaneous detection of two distinguishable decay daughters only if the $\pi^+$ and $\pi^-$ are treated as entangled, which in turn implies that particle decay does not collapse the wavefunction. The authors state that the quantitative relation between the E2I2 formalism and the measured $\cos(2\phi)$ modulation still requires further numerical investigation.

Load-bearing premise

The entanglement interpretation assumes that the two pions from the $\rho^0$ decay remain entangled and that particle decay does not collapse the wavefunction, so interference can appear in the pion pair even though the $\rho^0$ decays about 1.2 fm before the two nuclear sources are separated by 20 to 300 fm.

Editorial extensions

If this is right

The observed $\cos(2\phi)$ modulation in $\rho^0$ photoproduction provides a quantitative handle on the gluon distribution and on the transverse size of the nucleus, as demonstrated by the extracted radii for gold and uranium.
The E2I2 interpretation implies that the same entanglement-enabled interference should appear in other vector meson decay channels, including $\phi$ and $J/\psi$, allowing model-independent extraction of the effective Pomeron flux.
The interference strength is expected to depend on the impact parameter, which can be selected experimentally through forward-neutron tagging; ALICE's neutron-class data show the modulation increasing by an order of magnitude from 0n0n to XnXn classes.
If particle decay does not cause wavefunction collapse, the same formalism should apply to pseudoscalar production through Odderon exchange, where the azimuthal asymmetry order would differ according to the spin quantum numbers.
Coherent photoproduction in hadronic heavy-ion collisions, where the overlap region partially 'observes' which slit was used, offers a test of decoherence and of which-way information in a femtometer-scale interferometer.

Reading between the lines

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

A decisive extension would be to compare the $\cos(2\phi)$ modulation in Au+Au, U+U, and Pb+Pb collisions at matched impact parameter: if the E2I2 entanglement reading is correct, the modulation amplitude should track the slit separation, and models that treat the two pions as independently emitted should fail to reproduce the phase terms.
The interpretation implies a sharp, testable contrast with classical coherence: the two-source interference should survive even when the $\rho^0$ decay length is far smaller than the nuclear separation, which is exactly the regime where a naive 'two decaying mesons' picture would predict no interference.
A natural follow-up measurement would be the $\cos(4\phi)$ azimuthal asymmetry in $\rho^0$ photoproduction, which the paper connects to the elliptic gluon Wigner distribution; observing it with the predicted sign and magnitude would independently confirm that linearly polarized photons, not final-state interactions, drive the pattern.

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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

Colleague—

Read this as a review, not a new result. What it does well: it pulls together the STAR and ALICE measurements on coherent rho0 photoproduction, the two-source interference and spin-interference patterns, and the VMD and dipole frameworks in one place. The nuclear tomography section is the most solid part: extracting apparent radii, correcting for photon pT and polarization resolution, and comparing Au and U radii and neutron skins is concrete, and the numbers are interesting even if model-dependent. The review is also honest about open problems: the coherence paradox for coherent photoproduction with nuclear breakup or in hadronic collisions is flagged as unresolved, and the text explicitly says the quantitative E2I2-to-data connection needs further work in [341]. That candor is welcome.

The soft spot is the central interpretive claim. Section 1.4 calls the spin-interference patterns "the first instances of Fermi-scale single-particle double-slit interference experiments," and Section 4.2 argues the decay pion pair is entangled via E2I2, so the measurement probes entanglement. But the measured cos(2phi) modulation is already described, at least qualitatively, by standard two-source interference of linearly polarized photons in Model I and Model II, with no E2I2 input. The E2I2 derivation in Sec. 4.2 is an illustration with distinguishable daughters; the text concedes the connection to the measured modulation requires numerical investigation in the companion paper [341]. So the entanglement interpretation is not load-bearing yet. It may turn out right, but this preprint does not establish it, and a reader should not cite Sec. 1.4 as evidence for entanglement.

The citation pattern is heavy on the authors' own work, but that is normal for a review built around recent measurements they made or modeled. The main missing piece is that [341] is not available for checking; a referee should ask for it or for a quantitative derivation.

Who gets value: graduate students and experimentalists wanting a map of UPC photoproduction and its quantum-mechanics framing, and theorists working on nuclear gluon imaging. It deserves a serious referee; the review is competent and useful, and the entanglement claim needs a clear referee demand for the quantitative link before publication.

Referee Report

3 major / 6 minor

Summary. The manuscript is a review of coherent photoproduction in relativistic heavy-ion collisions, organized around quantum-interference phenomena: two-source Young's double-slit interference in the transverse-momentum spectra, spin interference (the cos(2φ) modulation in ρ0→π+π− decays), and a proposed interpretation of the latter as evidence for quantum entanglement of the decay pions via the 'entanglement-enabled intensity interferometry' (E2I2) framework. It surveys RHIC and LHC measurements (STAR, ALICE, CMS, LHCb), theoretical models (VMD, color dipole/CGC), coherence requirements and the Good-Walker paradigm, applications to nuclear tomography and reaction-plane determination, and future facilities and opportunities.

Significance. If the E2I2 interpretation were quantitatively established, the review would identify a genuinely new quantum probe: Fermi-scale two-source interference with an entangled final state, offering access to non-perturbative dynamics and nuclear gluon structure. The review is useful as a compilation of experimental results and model comparisons, and it reports published data with uncertainties and gives the standard theoretical frameworks for the measurements. It also states several falsifiable expectations (e.g., universality across vector mesons, Odderon-exchange signatures) that could be tested at RHIC, the LHC, and the EIC. Its main deficit is that the central interpretive step is not derived quantitatively: the authors explicitly defer the E2I2-to-data connection to future work, and the same measurements are already described by standard two-source interference models without invoking entanglement.

major comments (3)

[Sec. 1.4 and Sec. 3.3] There is an internal contradiction in the central claim. Section 1.4 calls the observed spin-interference patterns 'the first instances of Fermi-scale single-particle double-slit interference experiments,' but Section 3.3 states that, unlike the standard double-slit experiment, the measurement involves the simultaneous observation of two particles (the π+ and π− daughters) and is closer to intensity interferometry. Since the review itself concedes that the measurement is of a pair of particles, the 'single-particle' label is inaccurate and should be corrected consistently throughout the text.
[Sec. 4.2] The load-bearing step for the entanglement interpretation is missing. The text states that the quantitative relation between the E2I2 illustration and the measured cos(2φ) modulation with a realistic ρ0→π+π− decay 'requires further numerical investigations [341].' Because the same data are already described by Model I (VMD) and Model II (dipole) in Sec. 3.5.2 as standard two-source interference of linearly polarized photons, the E2I2/entanglement conclusion is not yet an established result. The abstract's claim that these studies 'enrich our understanding of non-local realism' and the phrasing in Sec. 4.2 that 'particle decay does not cause wavefunction collapse' go beyond what is demonstrated. The review should either supply the quantitative E2I2 prediction or explicitly label the entanglement conclusion as a proposed interpretation awaiting validation.
[Sec. 4.2, Eqs. (4.14)-(4.19)] The E2I2 derivation as presented does not by itself establish entanglement. The two-particle state written in Eq. (4.14) is a product of single-particle states, and the subsequent step imposes phase relations between the π+ and π− amplitudes rather than constructing a non-separable two-particle state. The text says 'we can consider the case where the π+ and π− daughters of a ρ0 decay are entangled,' but a product state with correlated phases is not an entangled state in the standard sense and does not, by itself, lead to a Bell-like or entanglement-certifying observable. Please clarify which notion of 'entangled' is intended and how the proposed interference measurement would certify it, or soften the terminology accordingly.

minor comments (6)

[Sec. 2.1] The sentence 'and significant background of secondary particles scattered from the magnets' is an incomplete sentence and appears to be missing a main clause.
[Sec. 4.2] The text contains several typographical errors, including 'Quicklyafterthefirstphotonuclearmeasurements' and 'the E2I2 framework provides a unified formalism1' with a stray footnote marker; a careful proofread is needed.
[Sec. 5.5.1] The phrase 'complete complete reconstruction' is duplicated and should be corrected.
[Fig. 5.2 caption] The caption refers to 'theoretical models []' without the actual citation numbers; the bracket appears to have been left empty.
[Sec. 3.3 and Sec. 3.5.2] The explanation for the relative sign in Eq. (3.11) and for the positive sign in p+p collisions is presented in a compressed way; a more precise statement in terms of C-parity and, for p+p, identical-particle exchange would help readers not already familiar with the literature.
[Sec. 5.3] The sentence 'By precisely adjusting these parameters, the complex quantum effects can be studied researchers' is ungrammatical; 'by' should be inserted before 'researchers' or the sentence should be rephrased.

Circularity Check

2 steps flagged · score 4.0 of 10

The spin-interference measurement is external and not fitted, but the entanglement interpretation is built into the E2I2 ansatz and the quantitative E2I2-to-data link is deferred to a companion paper.

self definitional [Sec. 4.2, Eqs. (4.9)-(4.12), (4.17)-(4.18)]
"Another important note is that the above notation expresses the ρ wavefunction as transitioning to a π+ and a π− such that the π+ and π− cannot be written as a simple product of individual wavefunctions,i.e they are entangled."

The E2I2-inspired derivation starts by writing the ρ0→π+π− decay amplitude as the symmetrized two-particle state |π+,1⟩|π−,2⟩ + |π+,2⟩|π−,1⟩ (Eqs. 4.9-4.12). That state is entangled by construction. The later claim that the formalism provides a formal description of non-collapse by describing the daughter particles as an entangled state therefore restates the input ansatz rather than deriving entanglement from the measured cos(2φ). The same cos(2φ) modulation is already reproduced in Sec. 3.5.2 by ordinary two-source interference of linearly polarized photons (VMD and dipole models) without this entangled-state assumption, so the entanglement conclusion is an interpretation inserted via the notation, not a forced consequence of the data.
self citation load bearing [Sec. 4.2, paragraph after Eq. (4.19)]
"However, how this illustration could be quantitatively related to the experimental measurements in Sec.5.1 and the formula discussed in Sec. 3.3 with a realistic decay ρ0→π+π− of JPC = 1−− requires further numerical investigations [341]."

The review's headline claim that the STAR/ALICE patterns are the first Fermi-scale double-slit experiments and that the π+π− pair is entangled depends on the quantitative connection between the E2I2 formalism and the measured cos(2φ) modulation. The text explicitly defers that connection to reference [341], the authors' own E2I2 companion program. Thus the central interpretive step is not derived in this paper; it is routed to a self-citation whose promised numerical link is not supplied. Because standard two-source interference models already describe the same observable, the E2I2/entanglement layer is not independently evidenced here.

full rationale

The observed cos(2φ) azimuthal modulation is external STAR/ALICE data, and the leading-order two-source interference prediction of Sec. 3.5.2 (Eqs. 3.13 and 3.15) is not fitted to that modulation; Model I and Model II are independent calculations. The core spin-interference effect is therefore not circular. The circularity that does exist is at the interpretive layer: the E2I2 formalism used to claim entanglement writes the ρ0→π+π− amplitude as a symmetrized two-particle state, which is entangled by definition, and then presents that as the formal description of why decay does not collapse the wavefunction. The paper also explicitly defers the quantitative E2I2-to-data connection for a realistic JPC=1−− decay to companion work [341], so the headline entanglement claim is not derived in this manuscript. The nuclear-tomography extraction in Sec. 5.1 uses measured |t| shapes and a correction parameter σ_b fitted from the interference pattern; this is a data-analysis model rather than a renamed prediction. Overall, the measurement and the standard interference interpretation stand independently; the entanglement-specific claims are ansatz-driven and self-citation-linked, but the paper is honest about the missing numerical link.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The review's interpretive claims rest on standard quantum mechanics and photon models, plus two assumptions specific to this paper: that coherence survives nuclear breakup in hadronic collisions, and that the E2I2 entanglement of decay daughters explains the observed spin interference. The latter is self-cited and unquantified.

free parameters (5)

sigma_b (modulation strength) = 2.38 +/- 0.04 fm (Au+Au); 1.9 +/- 0.1 fm (U+U)
Fitted in Sec. 5.1 to the phi-dependent radius modulation of rho0 photoproduction; it encodes the strength of the interference effect and is used to extract nuclear radii.
R0 (minimum apparent radius) = 6.62 +/- 0.03 fm (Au+Au); 7.37 +/- 0.06 fm (U+U)
Fitted from the |t| distribution in different phi bins; used to derive the true nuclear radius.
epsilon_p (polarization resolution) = 0.5
Set by hand to 1/2 in Eq. 5.2 to account for the resolution when using the daughter momentum as a proxy for the polarization direction.
R_rho^T (transverse radius of rho wavefunction) = 1.03 fm
Taken from HERA diffractive rho data via the dipole model; used to correct the extracted nuclear radius, and the authors note it may be model-dependent.
Woods-Saxon radius and diffuseness = e.g., R=7.47 fm, a=0.54 fm (Au) as used in Fig. 5.1
Inputs from electron scattering fits (Ref [199]); used in models for the nuclear form factor and in the empirical fits of the |t| spectra.

assumptions (6)

standard math Linear superposition and Born rule of quantum mechanics hold for the full collision and decay process.
Used throughout, e.g., Eq. 3.11 and Sec. 4.2, to add amplitudes from the two photon directions.
domain assumption The Weizsacker-Williams equivalent photon approximation describes the photon flux and its 100% linear polarization at small x.
Sec. 2.2.1 and Sec. 3.5.1; this is the basis for the photon source model and the polarization direction.
domain assumption Vector meson photoproduction conserves s-channel helicity, so the rho0 inherits the photon's linear polarization.
Sec. 3.5.2; used to connect the decay angular distribution to the polarization direction, though the review notes it has been validated by earlier measurements.
domain assumption The two production amplitudes interfere with a minus sign because vector mesons have negative parity and swapping emitter and target is a parity inversion.
Sec. 3.3, Eq. 3.11; this determines the sign of the interference term.
ad hoc to paper Coherent photoproduction can occur even when the target nucleus breaks up in hadronic collisions, and the Good-Walker definition of coherence is violated.
Sec. 4.1; the review asserts this based on data but states the resolution of the paradox is not yet known.
ad hoc to paper The decay products of the rho0 remain entangled, so particle decay does not collapse the wavefunction and the pion pair can carry the two-source interference phase (E2I2 assumption).
Sec. 4.2, Eqs. 4.17-4.19; this is the premise for the entanglement interpretation, and the paper admits the quantitative link to data is not yet established.

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Cite this review

Pith. "Pith review of Probing Quantum Phenomena through Photoproduction in Relativistic Heavy-Ion Collisions." pith.science (2026). https://pith.science/paper/IM2BJBIC

@misc{pith2026250418342,
  author       = {Pith},
  title        = {Pith review of: Probing Quantum Phenomena through Photoproduction in Relativistic Heavy-Ion Collisions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IM2BJBIC}},
  note         = {Machine review of arXiv:2504.18342}
}

read the original abstract

Photoproduction in ultra-peripheral relativistic heavy-ion collisions displays many unique features, often involving quantum mechanical coherence and two-source interference between photon emission from the two ions. We review the recent experimental results from RHIC and the LHC and theoretical studies of coherent vector meson photoproduction, emphasizing the quantum mechanical aspects of the interactions and the entanglement between the final state particles. These studies enrich our understanding of non-local realism, underscore the critical role of the polarization of the photon source, quantum interference and nuclear effect on the gluon distribution. It paves a way for quantitatively probing the quantum nature of these high-energy nuclear collisions.

Figures

Figures reproduced from arXiv: 2504.18342 by the authors.

**Figure 1.1.** Top left: Observing interference pattern in the classical Young’s double-slit experiment [ [PITH_FULL_IMAGE:figures/full_fig_p006_1_1.png] view at source ↗

**Figure 2.1.** The world-wide experimental data [95–110, 110–134, 134–165, 165–177] on the total and vector meson photoproduction as a function of Wγp. The experimental data on the energy dependence of vector meson photoproduction cross sections are summarized in [PITH_FULL_IMAGE:figures/full_fig_p009_2_1.png] view at source ↗

**Figure 2.2.** The world-wide experimental data [113–134, 134–165, 165–177] on the exponential slopes of the −t distribution of vector meson photoproduction as a function of Wγp. meson interacting with the hadron. There, the light vector meson (ρ, ω, and ϕ) cross sections increase slowly with energy roughly as W0.22 γp . This may be ascribed to a photon-Pomeron reaction, where the Pomeron carries the colorless strong force, and ha… view at source ↗

Figures from the paper (26 more)

**Figure 2.3.** Figure 2.3: Extracted radius from a multi-dimensional fits to the diffractive [PITH_FULL_IMAGE:figures/full_fig_p011_2_3.png]

**Figure 2.4.** Figure 2.4: Illustration of the electromagnetic field distribution in ultra-peripheral collisions ( [PITH_FULL_IMAGE:figures/full_fig_p012_2_4.png]

**Figure 2.5.** Figure 2.5: Dependence of the equivalent photon flux on distance [PITH_FULL_IMAGE:figures/full_fig_p014_2_5.png]

**Figure 2.6.** Figure 2.6: Diagram depicting the standard configuration of a high-energy collider experiment. Accelerated particle beams, labeled A1 and [PITH_FULL_IMAGE:figures/full_fig_p016_2_6.png]

**Figure 2.7.** Figure 2.7: (left) Diagram showing how the STAR topology trigger worked. Events with hits in the North and South quadrants of the central [PITH_FULL_IMAGE:figures/full_fig_p018_2_7.png]

**Figure 2.8.** Figure 2.8: The pT spectra from the 2002 STAR ρ analysis. The left panel (a) shows the results from the topology trigger, while the right (b)nis from the minimum bias trigger, which required both nuclei to break up. The blue points and error bars are the data, while the darker h…

**Figure 2.9.** Figure 2.9: The cross-section for exclusive photoproduction of J/ [PITH_FULL_IMAGE:figures/full_fig_p021_2_9.png]

**Figure 2.10.** Figure 2.10: (left) The differential coherent J/ψ photoproduction cross section as a function of rapidity. The vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. (right) The total cross section of coherent J/ψ as a function of WP…

**Figure 2.11.** Figure 2.11: The cross section of incoherent J/ψ as a function of |t| in Pb+Pb UPCs. From Ref. [249]. 3. The quantum phenomena of photoproduction in HICs In exclusive photoproduction, vector mesons are generated alongside non-resonant continuum production, wherein the photon flu…

**Figure 3.1.** Figure 3.1: (left) The π +π− invariant mass spectrum measured by STAR in coherent photoproduction. The spectrum is fit to the sum of amplitudes from ρ 0 , direct π +π− and ω → π +π−. From Ref. [228]. (right) the K+K− invariant mass spectrum measured by ALICE in coherent photopro…

**Figure 3.2.** Figure 3.2: Amplitude (left) and momentum (right) distribution profiles for coherent J/ [PITH_FULL_IMAGE:figures/full_fig_p027_3_2.png]

**Figure 3.3.** Figure 3.3: Left Panel: STAR data on ρ photoproduction in the region |y| < 0.5 (triangles and error bars) compared with calculations including (solid histogram) and excluding (dashed histogram) interference effects. From Ref. [223]. Right Panel: Differential cross section measur…

**Figure 3.4.** Figure 3.4: (Left Panel) The nuclear modification factor ( [PITH_FULL_IMAGE:figures/full_fig_p029_3_4.png]

**Figure 3.5.** Figure 3.5: The ∆ϕ = ϕee − ϕe distribution from ultra-peripheral and 60%–80% central Au +Au collisions at √sNN = 200 GeV for Mee > 0.45 GeV, along with calculations from QED [285], STARLight [201], and the publicly available SuperChic3 code [286]. From Ref. [190]. The linear pol…

**Figure 3.6.** Figure 3.6: (Left panel) The schematic diagram for the direction of the polarization direction of the photons for vector meson photoproduction. [PITH_FULL_IMAGE:figures/full_fig_p032_3_6.png]

**Figure 3.7.** Figure 3.7: (A) The invariant mass distribution of π +π− pairs obtained from Au+Au and U+U collisions. The vertical black lines denote the selected mass range, which maintains uniform detector acceptance and efficiency in ϕ. Panels (B) to (D) illustrate the two-dimensional distr…

**Figure 3.8.** Figure 3.8: (A) The ϕ distribution for π +π− pairs collected from Au+Au and U+U collisions with a pair pT less than 60 MeV and an invariant mass between 650 and 900 MeV. Statistical uncertainties are represented by vertical bars on all points, while systematic uncertainties are …

**Figure 4.1.** Figure 4.1: 2D momentum distribution patterns of coherent [PITH_FULL_IMAGE:figures/full_fig_p044_4_1.png]

**Figure 4.2.** Figure 4.2: Theoretical calculations [270] of coherent J/ψ production yield in the VMD framework with and without “observation” effect as a function of Npart in (left panel) Au+Au collisions at √sNN = 200 GeV and (right panel) Pb+Pb collisions at √sNN = 5.02 TeV. The experimenta…

**Figure 5.1.** Figure 5.1: The distributions dN d|t| as a function of |t| (approximately P 2 T ) for Au+Au collisions (A) and U+U collisions (B). Additionally, the dN d|t| as a function of |t| for Au+Au collisions is displayed for ϕ bins at 0° (C) and 90° (D). In panels (A-D), the long-dashed …

**Figure 5.2.** Figure 5.2: (Left panel) The radial parameter as a function of the [PITH_FULL_IMAGE:figures/full_fig_p047_5_2.png]

**Figure 5.3.** Figure 5.3: Left: The cross section as a function of [PITH_FULL_IMAGE:figures/full_fig_p049_5_3.png]

**Figure 5.4.** Figure 5.4: (Left panel) Estimates of the cos 4ϕ asymmetry as the function of impact parameter (b⊥) in Au+Au collisions at √sNN = 200 GeV. The results are integrated for dilepton rapidities [−1, 1], P⊥ is defined as P⊥ = (l1⊥ − l2⊥)/2, where l1⊥ and l2⊥ are the transverse moment…

**Figure 5.5.** Figure 5.5: Impact parameter dependence of the probabilities for the three primary forward neutron topologies, as calculated by STARLight [PITH_FULL_IMAGE:figures/full_fig_p051_5_5.png]

**Figure 5.6.** Figure 5.6: The amplitudes of the cos(2ϕ) modulation of the ρ 0 yield in Pb+Pb collisions at √sNN = 5.02 TeV for all neutron emission classes. These results are compared with the model predictions by Xing et al. [303] and W. Zhao et al. [349], and, for the XnXn class, with the S…

**Figure 5.7.** Figure 5.7: (top) The four diagrams that contribute to the photoproduction of two non-identical mesons. (bottom) The four additional [PITH_FULL_IMAGE:figures/full_fig_p056_5_7.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Probing Quantum Numbers and Decay Branching Ratios of Exotic States via Entanglement-Enabled Spin Interference
hep-ph 2026-06 unverdicted novelty 6.0 of 10

Simulated spin-interference patterns in ρ(1450)→4π decays give a distinct azimuthal modulation for the π(1300)π channel, allowing its branching fraction to be extracted.

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