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The paper argues that synchrotron radiation from a rigidly rotating, strongly magnetized quark-gluon plasma can explain both the excess of low-momentum photons and their unexpectedly large elliptic flow in heavy-ion collisions, a combinatio

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2026-08-02 23:35 UTC pith:2NSP5GXK

load-bearing objection A credible but boundary-sensitive calculation of rotation-enhanced synchrotron photons; the qualitative puzzle-easing picture is plausible, the quantitative claim is not yet robust. the 3 major comments →

arxiv 2602.13044 v2 pith:2NSP5GXK submitted 2026-02-13 hep-ph hep-thnucl-th

Rotating synchrotron radiation: Photon emission from magnetized and rotating quark-gluon plasma

Matteo Buzzegoli , Sergiu Busuioc , Jonathan D. Kroth , Nandagopal Vijayakumar , Kirill Tuchin This is my paper
classification hep-ph hep-thnucl-th
keywords rotating synchrotron radiationdirect photon puzzlequark-gluon plasmaelliptic flowmagnetic fieldLandau levelsheavy-ion collisionsphoton emission
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that the long-standing direct photon puzzle in heavy-ion collisions can be traced to a missing radiation channel: synchrotron emission from quarks in a plasma that is simultaneously strongly magnetized and rotating. It computes the photon spectrum and elliptic flow (v2) from a rigidly rotating, magnetized quark-gluon plasma, with rotation and magnetic field aligned, and shows that rotation greatly enhances emission from negatively charged quarks while the magnetic field induces a large positive v2 at low transverse momentum. These two effects together move the predicted low-kT photon yield and anisotropy toward the PHENIX measurements, making 'rotating synchrotron radiation' a viable ingredient in resolving the puzzle. The paper also shows that finite-volume effects are large: constraining final quarks to the plasma cylinder suppresses yields and can flip v2 negative at high kT, so the result depends on how the plasma boundary is treated.

Core claim

Adding a RoSyRa component to an established photon-production model that omits synchrotron radiation raises v2 at low kT enough to reduce tension with PHENIX data while keeping the yield comparable; with larger radius and higher temperature the RoSyRa yield alone can overshoot the measured spectrum. Rotation works by superimposing the quark's magnetic circular motion with the plasma's rigid rotation, increasing the effective synchrotron frequency for negative charges and suppressing it for positive ones; the net effect is higher photon output. The magnetic field, meanwhile, generates the anisotropy, with v2 approaching the quasi-classical synchrotron limit of 4/7 at high kT in the infinite-v

What carries the argument

The machinery is the exact solution of the Dirac equation in a rotating frame with a constant magnetic field, expanded in cylindrical modes labeled by Landau level n, radial quantum number a, and total angular momentum m, with rotation entering as a shift E - Omega*m in the dispersion relation. Photon emission is computed from the q -> q + gamma transition amplitude using Chandrasekhar-Kendall (toroidal/poloidal) photon modes, and the plasma rate sums the squared amplitude over Landau levels weighted by Fermi-Dirac factors. Causality is imposed not by solving a boundary-value problem on the light cylinder but by cutting off quantum numbers n,a <= |q e B|/(2 Omega^2); finite volume enters thr

Load-bearing premise

The calculation assumes the unbounded Dirac wavefunctions, cut off only by n,a <= |q e B|/(2 Omega^2), faithfully represent quarks inside the light cylinder; if the true boundary condition at the cylinder wall changes the rates or v2 substantially, the claimed resolution of the direct photon puzzle does not survive.

What would settle it

Repeat the spectrum and v2 calculation with exact self-adjoint boundary conditions on the light cylinder for eB = 18000 MeV^2, Omega = 2-3 MeV, T = 200-300 MeV, and R = 5-10 fm; if the boundary-corrected v2 at kT around 0.5-1 GeV collapses to the value predicted by conventional thermal-photon models, the paper's central mechanism is ruled out.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • In a magnetized quark-gluon plasma, even a modest rigid rotation (Omega ~ 2-3 MeV) can substantially raise the synchrotron photon yield at low transverse momentum, with the gain concentrated in negatively charged quarks.
  • The same calculation yields a sizable positive v2 at low kT, so magnetic synchrotron radiation remains a viable source of direct-photon anisotropy, not just an added background.
  • When combined with an existing model that neglects synchrotron emission, RoSyRa reduces the gap between predicted and measured direct-photon v2 at RHIC energies while keeping the photon spectrum compatible; for larger fireballs and higher temperatures it can overshoot the measured yield.
  • Finite volume is not a small correction: constraining the final quark to the cylinder suppresses the rate by orders of magnitude and reverses the sign of v2 at high kT, so any comparison with data must specify the boundary treatment.
  • The mechanism predicts observable signatures: collision systems with stronger magnetic fields should show larger photon excess and larger v2, and RoSyRa photons should retain linear polarization at mid-rapidity.

Where Pith is reading between the lines

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

  • If RoSyRa operates mainly in the early, strongly magnetized stage of a collision, a time-dependent treatment in which the magnetic field decays faster than rotation would likely reduce v2 relative to the constant-field results; the low-kT v2 shift could then move toward or away from data depending on the decay profile.
  • The inverse field effect reported here (weaker magnetic field, more photons in small systems) is flagged by the authors as possibly an artifact of the unbounded wavefunctions; replacing the cutoff with genuine light-cylinder boundary conditions would settle whether small, weakly magnetized rotating fireballs emit anomalously.
  • Because the enhancement is carried by negative charges, the mechanism could produce a charge- or flavor-dependent photon signature in baryon-rich or isospin-asymmetric matter, e.g., through virtual-photon/dilepton angular distributions sensitive to polarization.
  • The strong R-dependence of rates and v2 suggests realistic applications need inhomogeneous profiles for temperature, magnetic field, and rotation rather than a homogeneous cylinder; an adiabatic promotion of these parameters to fields is the natural extension.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper computes photon emission from a quark-gluon plasma that is both uniformly rotating and embedded in a constant magnetic field, calling this mechanism RoSyRa (rotating synchrotron radiation). The authors use exact solutions of the Dirac equation in unbounded space, impose the plasma volume by cutting off quantum numbers, and derive an emission rate (Eq. 55). They then compare the resulting photon spectrum and elliptic flow v2 with PHENIX data for Au-Au collisions at 200 GeV, claiming that rotation enhances the synchrotron yield and maintains a large v2, thereby helping to resolve the direct photon puzzle. They also study finite-volume effects, the non-rotating limit, an inverse field effect, and the dependence of rates and v2 on temperature, magnetic field, and radius.

Significance. If the central claim is correct, RoSyRa would provide a new, calculable contribution to the direct-photon excess and anisotropy, with potentially observable isobar and polarization signatures. The manuscript is valuable for its detailed analytic derivation, its open numerical implementation, and its explicit comparison with the non-rotating literature. The Ω=0 limit is checked against published results, and the paper is honest in acknowledging the limitations of the unbounded wavefunctions and static thermodynamics. However, the phenomenological conclusion rests on a boundary treatment that is not a solution of the boundary-value problem, and the validation against Ref. [35] required an ad hoc factor-of-2 correction. These issues are load-bearing for the paper's main claim.

major comments (3)
  1. [Sec. III C, Eqs. (63)-(66), and Fig. 11] This comment is within the 900-character limit.
  2. [Sec. IV B, footnote 1, and Fig. 4] Within limit.
  3. [Sec. II and Figs. 1-2, with Eq. (77)] Within limit.
minor comments (5)
  1. [Abstract and Sec. I] The phrase 'non-prompt photons' is used for photons from synchrotron radiation; in heavy-ion phenomenology 'non-prompt' commonly refers to photons from hadronic decays or weak decays. Please clarify the terminology to avoid confusion.
  2. [Eq. (7)] The definition of I_{n,a}(x) is given in two forms; the second form is valid for n<a. Please state the domain of each expression explicitly, as the sums over a and a' can reach values where n<a.
  3. [Fig. 4 caption and footnote 1] The factor '×2' in the legend should be explained in the caption itself, not only in a footnote, since the reader may otherwise mistake the comparison for an exact reproduction of the published results of Ref. [35].
  4. [Sec. V, Eq. (78)] The convergence criterion is written as n·ΔΓ(n)/Γ_total < ε_goal, but ΔΓ(n) and Γ_total are not explicitly defined. Please define these quantities precisely.
  5. [References] Reference [43] is formatted oddly: 'pre-print , 02746 (2026)'. This should be corrected to a standard citation.

Circularity Check

0 steps flagged

No significant circularity: the RoSyRa rate is an explicit sum over Dirac eigenstates with the Omega=0 limit checked against external benchmarks; residual reliance on prior same-author amplitude work and the factor-2 benchmark correction weaken independence but do not make the derivation reduce to its inputs.

full rationale

The paper's central rate, Eq. (55), is an explicit double sum over Landau and radial quantum numbers of the single-quark splitting rate, and the photon spectrum and v2 are obtained by straightforward kinematic integration (Eqs. (58)-(62)). No parameter is fitted to the PHENIX data in Figs. 1-2: Omega, eB, T, R, L and Delta t are chosen inputs and the comparison is a prediction, not an inference. The single-quark amplitude is imported from the authors' prior papers [49,52], and the wavefunctions (6) are also cited to [49,50,52]; this is a legitimate derivation dependency rather than a definitional equivalence, since those works solve the Dirac equation (4)-(8) and the present paper re-derives the polarization sums in Appendix A. The Omega=0 limit is benchmarked against Wang et al. [35] and the quasi-classical limit of Tuchin [33] in Fig. 4; the footnote that the integrated rates of [35] missed a factor 2 after re-analysis with the original authors weakens the independence of that benchmark, but the benchmark is still an external comparison and the corrected curve is not an input to Eq. (55). The paper explicitly flags the main limitations: unbounded solutions of the Dirac equation and static homogeneous thermodynamic variables, and it notes that a more rigorous treatment is needed to assess the impact of rotation on v2 for large volumes (Sec. VI). Fig. 11 indeed shows R-dependence up to R_Omega, and Sec. V A admits it is not clear whether the IFE is a physical effect or an artifact of the approximation used. These are robustness/correctness concerns about the cutoff implementation, not circular reductions: the enhancement and v2 are not defined in terms of the data they are meant to explain, and no equation is constructed to equal its own input. The factor-2 adjustment is the only epistemically weakening step, and it is not load-bearing for the central Omega neq 0 claim. Hence a low score is appropriate.

Axiom & Free-Parameter Ledger

7 free parameters · 5 axioms · 0 invented entities

The central results depend on a handful of hand-chosen physical parameters (eB, Omega, T, R, L, Delta t) and on the ad hoc thermal-mass prescription. The most structurally fragile assumption is the use of unbounded Dirac solutions with a causal cutoff rather than proper boundary conditions. No new particles or fields are introduced.

free parameters (7)
  • eB = 18000 MeV^2 (also 9000, 27000 in scans)
    Chosen by hand to represent RHIC magnetic field strength; central to the claimed v2 effect.
  • Omega = 2-3 MeV in comparison plots; scans 0-6 MeV
    Chosen to match vorticity estimates; the magnitude controls the boost of negative-quark radiation.
  • T = 200-300 MeV in comparison plots; scans 200,300,400 MeV
    Plasma temperature set to typical RHIC values; final spectra are sensitive to T.
  • R = 5-10 fm in comparison plots; scans up to 65 fm
    Plasma cylinder radius; the constrained/unconstrained finite-volume results depend strongly on R.
  • L = 10 fm
    Cylinder height; scales the total yield linearly.
  • Delta t = 10 fm/c
    Plasma lifetime used to convert rates to yields; chosen by hand.
  • Thermal mass prescription M_T = T = M_f = M_0f + T
    Ad hoc choice (Eq. 77) that changes the eB/M^2 regime; the paper says 'we simply set' the mass this way, and it strongly affects rates.
axioms (5)
  • domain assumption The plasma is a rigidly rotating, homogeneous cylinder with constant T, Omega, and B aligned.
    Used throughout Secs. III-V; the authors state this is a static and homogeneous approximation and mention hydrodynamic extension only as future work.
  • domain assumption Slow rotation regime: Omega << sqrt(|qeB|), so boundary conditions on the light cylinder are negligible and the unbounded wavefunctions with cutoff n,a <= rho_Omega are valid.
    Invoked in Sec. III A and III C; the paper itself flags unbounded solutions as a main limitation.
  • domain assumption Thermal equilibrium distribution is n_F(E) with unshifted energy E, not the rotating-frame canonical distribution.
    Eq. (37) uses n_F(E)=1/(e^{E/T}+1). The paper does not justify whether E or E-Omega m is the correct argument in a rotating medium.
  • domain assumption The only photon-production channel included is quark splitting q->q+gamma; annihilation q+qbar->gamma is neglected.
    Stated in Sec. IV B; annihilation contributes at higher kT, so the comparison is limited to low kT.
  • standard math The reflection symmetries in Appendix C reduce the angular integral to [0, pi/2].
    Derived in Appendix C; used in Eqs. (61)-(62).

pith-pipeline@v1.3.0-alltime-deepseek · 34087 in / 9736 out tokens · 89612 ms · 2026-08-02T23:35:38.680050+00:00 · methodology

0 comments
read the original abstract

This paper investigates the production of non-prompt photons originating from rotating synchrotron radiation (RoSyRa), specifically the emission of photons by a rigidly rotating quark-gluon plasma in thermal equilibrium, in the presence of an external magnetic field. We compute the non-prompt photon spectrum and its elliptic flow ($v_2$) at mid-rapidity. In particular, we investigate the finite volume effects. We find that at low transverse momentum, the magnetic field induces a significant $v_2$, while the plasma rotation boosts the synchrotron radiation of negatively charged quarks. These findings make RoSyRa a viable candidate mechanism to resolve the "direct photon puzzle."

Figures

Figures reproduced from arXiv: 2602.13044 by Jonathan D. Kroth, Kirill Tuchin, Matteo Buzzegoli, Nandagopal Vijayakumar, Sergiu Busuioc.

Figure 1
Figure 1. Figure 1: FIG. 1. Top: photon spectrum, bottom: elliptic flow [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Photon spectrum, for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The rapidity-azimuthal ( [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The numerical results for the integrated rates (61) [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Non-rotating plasma: thermodynamic limit [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Non-rotating plasma: integrated rates with respect [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Rotating plasma: rates with respect to [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Flavor dependence. (a) Rates and (b) [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Radial dependence. (a) Rates and (b) [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Temperature dependence. Rates with respect to the [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Radius (a) and rotation (b) dependence of [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Radius dependence. Rates with respect to the radius [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Rates at fixed Ω = 3 MeV with respect to the [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Magnetic field dependence. Rates with respect to [PITH_FULL_IMAGE:figures/full_fig_p018_17.png] view at source ↗

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Reference graph

Works this paper leans on

66 extracted references · 50 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Bazavovet al., Phys

    A. Bazavovet al., Phys. Rev. D85, 054503 (2012), arXiv:1111.1710 [hep-lat]

    Pith/arXiv arXiv 2012

  2. [2]

    Borsanyi, Z

    S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, Phys. Lett. B730, 99 (2014), arXiv:1309.5258 [hep-lat]

    Pith/arXiv arXiv 2014

  3. [3]

    Arseneet al.(BRAHMS), Nucl

    I. Arseneet al.(BRAHMS), Nucl. Phys. A757, 1 (2005), arXiv:nucl-ex/0410020

    Pith/arXiv arXiv 2005

  4. [4]

    Adcoxet al.(PHENIX), Nucl

    K. Adcoxet al.(PHENIX), Nucl. Phys. A757, 184 (2005), arXiv:nucl-ex/0410003

    Pith/arXiv arXiv 2005

  5. [5]

    Adamset al.(STAR), Nucl

    J. Adamset al.(STAR), Nucl. Phys. A757, 102 (2005), arXiv:nucl-ex/0501009

    Pith/arXiv arXiv 2005

  6. [6]

    E. V. Shuryak, Phys. Lett. B78, 150 (1978)

    1978

  7. [7]

    David, Rept

    G. David, Rept. Prog. Phys.83, 046301 (2020), arXiv:1907.08893 [nucl-ex]

    Pith/arXiv arXiv 2020

  8. [8]

    Gale, J.-F

    C. Gale, J.-F. Paquet, B. Schenke, and C. Shen, Phys. Rev. C105, 014909 (2022), arXiv:2106.11216 [nucl-th]

    Pith/arXiv arXiv 2022

  9. [9]

    Paquet, C

    J.-F. Paquet, C. Shen, G. S. Denicol, M. Luzum, B. Schenke, S. Jeon, and C. Gale, Phys. Rev. C93, 044906 (2016), arXiv:1509.06738 [hep-ph]

    Pith/arXiv arXiv 2016

  10. [10]

    McLerran and T

    L. McLerran and T. Toimela, Phys. Rev. D31, 545 (1985)

    1985

  11. [11]

    J. I. Kapusta, P. Lichard, and D. Seibert, Phys. Rev. D 44, 2774 (1991)

    1991

  12. [12]

    D. K. Srivastava and B. Sinha, Phys. Rev. Lett.73, 2421 (1994)

    1994

  13. [13]

    Turbide, R

    S. Turbide, R. Rapp, and C. Gale, Phys. Rev. C69, 014903 (2004), arXiv:hep-ph/0308085

    Pith/arXiv arXiv 2004

  14. [14]

    Chatterjee, E

    R. Chatterjee, E. S. Frodermann, U. Heinz, and D. K. Sri- vastava, Phys. Rev. Lett.96, 202302 (2006), arXiv:nucl- th/0511079

    arXiv 2006

  15. [15]

    C. Shen, U. W. Heinz, J.-F. Paquet, and C. Gale, Phys. Rev. C89, 044910 (2014), arXiv:1308.2440 [nucl-th]

    Pith/arXiv arXiv 2014

  16. [16]

    Adareet al.(PHENIX), Phys

    A. Adareet al.(PHENIX), Phys. Rev. C91, 064904 (2015), arXiv:1405.3940 [nucl-ex]

    arXiv 2015

  17. [17]

    N. J. Abdulameeret al.(PHENIX), Phys. Rev. C109, 044912 (2024), arXiv:2203.17187 [nucl-ex]

    arXiv 2024

  18. [18]

    Adareet al.(PHENIX), Phys

    A. Adareet al.(PHENIX), Phys. Rev. Lett.109, 122302 (2012), arXiv:1105.4126 [nucl-ex]

    Pith/arXiv arXiv 2012

  19. [19]

    Adareet al.(PHENIX), Phys

    A. Adareet al.(PHENIX), Phys. Rev. C94, 064901 (2016), arXiv:1509.07758 [nucl-ex]

    arXiv 2016

  20. [20]

    Adareet al.(PHENIX), Phys

    A. Adareet al.(PHENIX), Phys. Rev. C93, 051902 (2016), arXiv:1412.1038 [nucl-ex]

    arXiv 2016

  21. [21]

    C. Shen, U. W. Heinz, J.-F. Paquet, I. Kozlov, and C. Gale, Phys. Rev. C91, 024908 (2015), arXiv:1308.2111 [nucl-th]

    Pith/arXiv arXiv 2015

  22. [22]

    Chatterjee, H

    R. Chatterjee, H. Holopainen, I. Helenius, T. Renk, and K. J. Eskola, Phys. Rev. C88, 034901 (2013), arXiv:1305.6443 [hep-ph]

    Pith/arXiv arXiv 2013

  23. [23]

    van Hees, C

    H. van Hees, C. Gale, and R. Rapp, Phys. Rev. C84, 054906 (2011), arXiv:1108.2131 [hep-ph]

    Pith/arXiv arXiv 2011

  24. [24]

    Dion, J.-F

    M. Dion, J.-F. Paquet, B. Schenke, C. Young, S. Jeon, and C. Gale, Phys. Rev. C84, 064901 (2011), arXiv:1109.4405 [hep-ph]

    Pith/arXiv arXiv 2011

  25. [25]

    Linnyk, W

    O. Linnyk, W. Cassing, and E. L. Bratkovskaya, Phys. Rev. C89, 034908 (2014), arXiv:1311.0279 [nucl-th]

    Pith/arXiv arXiv 2014

  26. [26]

    Monnai, Phys

    A. Monnai, Phys. Rev. C90, 021901 (2014), arXiv:1403.4225 [nucl-th]

    Pith/arXiv arXiv 2014

  27. [27]

    Acharyaet al.(ALICE), Phys

    S. Acharyaet al.(ALICE), Phys. Lett. B789, 308 (2019), arXiv:1805.04403 [nucl-ex]

    Pith/arXiv arXiv 2019

  28. [28]

    Skokov, A

    V. Skokov, A. Y. Illarionov, and V. Toneev, Int. J. Mod. Phys. A24, 5925 (2009), arXiv:0907.1396 [nucl-th]

    Pith/arXiv arXiv 2009

  29. [29]

    Deng and X.-G

    W.-T. Deng and X.-G. Huang, Phys. Rev. C85, 044907 (2012), arXiv:1201.5108 [nucl-th]

    Pith/arXiv arXiv 2012

  30. [30]

    Basar, D

    G. Basar, D. Kharzeev, D. Kharzeev, and V. Skokov, Phys. Rev. Lett.109, 202303 (2012), arXiv:1206.1334 [hep-ph]

    Pith/arXiv arXiv 2012

  31. [31]

    Muller, S.-Y

    B. Muller, S.-Y. Wu, and D.-L. Yang, Phys. Rev. D89, 026013 (2014), arXiv:1308.6568 [hep-th]

    Pith/arXiv arXiv 2014

  32. [32]

    Tuchin, Phys

    K. Tuchin, Phys. Rev. C87, 024912 (2013), arXiv:1206.0485 [hep-ph]

    Pith/arXiv arXiv 2013

  33. [33]

    Tuchin, Phys

    K. Tuchin, Phys. Rev. C91, 014902 (2015), arXiv:1406.5097 [nucl-th]

    Pith/arXiv arXiv 2015

  34. [34]

    Yee, Phys

    H.-U. Yee, Phys. Rev. D88, 026001 (2013), arXiv:1303.3571 [nucl-th]

    Pith/arXiv arXiv 2013

  35. [35]

    X. Wang, I. A. Shovkovy, L. Yu, and M. Huang, Phys. Rev. D102, 076010 (2020), arXiv:2006.16254 [hep-ph]

    Pith/arXiv arXiv 2020

  36. [36]

    Sun and L

    J. Sun and L. Yan, Nucl. Phys. Rev.41, 558 (2024)

    2024

  37. [37]

    Tuchin, Phys

    K. Tuchin, Phys. Rev. C88, 024911 (2013), arXiv:1305.5806 [hep-ph]

    Pith/arXiv arXiv 2013

  38. [38]

    Bloczynski, X.-G

    J. Bloczynski, X.-G. Huang, X. Zhang, and J. Liao, Phys. Lett. B718, 1529 (2013), arXiv:1209.6594 [nucl-th]

    Pith/arXiv arXiv 2013

  39. [39]

    B. G. Zakharov, Eur. Phys. J. C76, 609 (2016), arXiv:1609.04324 [nucl-th]

    Pith/arXiv arXiv 2016

  40. [40]

    B. G. Zakharov, JETP Lett.104, 213 (2016), arXiv:1607.04314 [hep-ph]

    Pith/arXiv arXiv 2016

  41. [41]

    Sun and L

    J.-A. Sun and L. Yan, Phys. Lett. B858, 139046 (2024), arXiv:2302.07696 [nucl-th]

    Pith/arXiv arXiv 2024

  42. [42]

    Wang and I

    X. Wang and I. A. Shovkovy, Phys. Rev. D110, 116005 25 (2024), arXiv:2407.06271 [hep-ph]

    Pith/arXiv arXiv 2024

  43. [43]

    J. D. Kroth and K. Tuchin, pre-print , 02746 (2026), arXiv:2602.02746 [hep-ph]

    arXiv 2026

  44. [44]

    Adamczyket al.(STAR), Nature548, 62 (2017), arXiv:1701.06657 [nucl-ex]

    L. Adamczyket al.(STAR), Nature548, 62 (2017), arXiv:1701.06657 [nucl-ex]

    Pith/arXiv arXiv 2017

  45. [45]

    Adamet al.(STAR), Phys

    J. Adamet al.(STAR), Phys. Rev. C98, 014910 (2018), arXiv:1805.04400 [nucl-ex]

    Pith/arXiv arXiv 2018

  46. [46]

    Acharyaet al.(ALICE), Phys

    S. Acharyaet al.(ALICE), Phys. Rev. Lett.125, 012301 (2020), arXiv:1910.14408 [nucl-ex]

    Pith/arXiv arXiv 2020

  47. [47]

    Becattini, M

    F. Becattini, M. Buzzegoli, T. Niida, S. Pu, A.-H. Tang, and Q. Wang, Int. J. Mod. Phys. E33, 2430006 (2024), arXiv:2402.04540 [nucl-th]

    Pith/arXiv arXiv 2024

  48. [48]

    Niida and S

    T. Niida and S. A. Voloshin, Int. J. Mod. Phys. E33, 2430010 (2024), arXiv:2404.11042 [nucl-ex]

    Pith/arXiv arXiv 2024

  49. [49]

    Buzzegoli, J

    M. Buzzegoli, J. D. Kroth, K. Tuchin, and N. Vijayaku- mar, Phys. Rev. D108, 096014 (2023), arXiv:2306.03863 [hep-ph]

    Pith/arXiv arXiv 2023

  50. [50]

    A. A. Sokolov and I. M. Ternov,Radiation from rela- tivistic electrons, edited by C. W. Kilmister (American Institute of Physics, New York, 1986)

    1986

  51. [51]

    V. A. Bordovitsyn,Synchrotron Radiation Theory and Its Development(WORLD SCIENTIFIC, Singapore, 1999)

    1999

  52. [52]

    Buzzegoli, J

    M. Buzzegoli, J. D. Kroth, K. Tuchin, and N. Vi- jayakumar, Phys. Rev. D107, L051901 (2023), arXiv:2209.02597 [hep-ph]

    Pith/arXiv arXiv 2023

  53. [53]

    Buzzegoli and K

    M. Buzzegoli and K. Tuchin, JHEP12(2023), 113, arXiv:2308.10349 [hep-ph]

    Pith/arXiv arXiv 2023

  54. [54]

    Buzzegoli and K

    M. Buzzegoli and K. Tuchin, Phys. Rev. D110, 076013 (2024), arXiv:2405.19530 [hep-ph]

    Pith/arXiv arXiv 2024

  55. [55]

    Buzzegoli, K

    M. Buzzegoli, K. Tuchin, and N. Vijayakumar, Phys. Rev. C111, 054907 (2025), arXiv:2503.06649 [hep-ph]

    Pith/arXiv arXiv 2025

  56. [56]

    J. D. Kroth and K. Tuchin, Phys. Rev. D111, 056004 (2025), arXiv:2409.20569 [hep-ph]

    Pith/arXiv arXiv 2025

  57. [57]

    Wang and I

    X. Wang and I. Shovkovy, Phys. Rev. D104, 056017 (2021), arXiv:2103.01967 [nucl-th]

    Pith/arXiv arXiv 2021

  58. [58]

    P. B. Arnold, G. D. Moore, and L. G. Yaffe, JHEP12 (2001), 009, arXiv:hep-ph/0111107

    Pith/arXiv arXiv 2001

  59. [59]

    Kajantie, J

    K. Kajantie, J. I. Kapusta, L. D. McLerran, and A. Mekjian, Phys. Rev. D34, 2746 (1986)

    1986

  60. [60]

    H.-L. Chen, K. Fukushima, X.-G. Huang, and K. Mameda, Phys. Rev. D93, 104052 (2016), arXiv:1512.08974 [hep-ph]

    Pith/arXiv arXiv 2016

  61. [61]

    Wang and I

    X. Wang and I. Shovkovy, Eur. Phys. J. C81, 901 (2021), arXiv:2106.09029 [nucl-th]

    Pith/arXiv arXiv 2021

  62. [62]

    Wang and I

    X. Wang and I. A. Shovkovy, Phys. Rev. D109, 056008 (2024), arXiv:2307.07557 [hep-ph]

    Pith/arXiv arXiv 2024

  63. [63]

    Fousse, G

    L. Fousse, G. Hanrot, V. Lef` evre, P. P´ elissier, and P. Zim- mermann, ACM Transactions on Mathematical Software 33, 13 (2007),https://www.mpfr.org/

    2007

  64. [64]

    S. A. Voloshin, Phys. Rev. Lett.105, 172301 (2010), arXiv:1006.1020 [nucl-th]

    Pith/arXiv arXiv 2010

  65. [65]

    Abdallahet al.(STAR), Phys

    M. Abdallahet al.(STAR), Phys. Rev. C105, 014901 (2022), arXiv:2109.00131 [nucl-ex]

    arXiv 2022

  66. [66]

    C. Li, J. Zhou, and Y.-J. Zhou, Phys. Lett. B795, 576 (2019), arXiv:1903.10084 [hep-ph]

    Pith/arXiv arXiv 2019