Effective Fermion-Photon Vertex in a Rotating Relativistic Medium: Tree-Level Structure

Alejandro Ayala; Enrique Mu\~noz; J. E. Mart\'inez-Herrera; Jorge David Casta\~no-Yepes

REVIEW

Effective Fermion-Photon Vertex in a Rotating Relativistic Medium: Tree-Level Structure

Jorge David Castaño-Yepes, Alejandro Ayala, J. E. Martínez-Herrera, Enrique Muñoz

High Energy Physics - Phenomenology · Submitted 13 Oct 2026 · 46 references

Pith's verdict: Solid formal derivation of the vertex in rotating coordinates, but the on-shell amplitude vanishes and the gauge invariance argument has an unverified boundary assumption that should be cleaned up.

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arXiv ID2610.19124 (version 1)

Pith IDBVR6ET6U, Pith's permanent record of this paper and its review

CitationAlejandro Ayala, Enrique Mu\~noz, J. E. Mart\'inez-Herrera, Jorge David Casta\~no-Yepes. "Effective Fermion-Photon Vertex in a Rotating Relativistic Medium: Tree-Level Structure." arXiv:2610.19124 (2026). https://pith.science/paper/BVR6ET6U

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Claim paper

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Editor's note

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The paper computes the tree-level fermion-photon effective vertex in a rigidly rotating background. It is a straightforward but nontrivial extension of the authors' earlier mode constructions. The result is a decomposition into 24 form factors, with selection rules that show transverse momentum is not conserved (only magnitudes are constrained by triple-Bessel integrals). The derivation is clear and the mathematics is handled carefully. The authors also honestly acknowledge that when all external particles are on shell and the photon is described by a rotating mode, the tree-level amplitude vanishes identically—so the vertex does not directly open new decay or absorption channels. That is a useful thing to know, and the paper says so explicitly.

What is new: the vertex structure itself, the form-factor basis, and the kinematic constraints from the radial integrals. These are solid contributions for anyone working on QFT in vortical backgrounds.

Soft spots: the gauge invariance argument in Sec. VII is incomplete. The matrix element’s gauge variation is reduced to a boundary term, and the authors assert that the fermion transition current is tangent to the cylindrical boundary, citing the same rigid-rotation approximation from earlier papers. But the fermion modes are Bessel functions that extend to infinity; it is not obvious that the radial current component vanishes at any finite R, and the cited references do not verify this either. This is a gap. It is probably fixable—one could argue that the integral over all space with appropriate falloff gives zero—but as written it is an assumption that should be justified or replaced by a proper limiting procedure. I would not call it fatal because the rest of the paper does not rely heavily on gauge invariance for the main results (the selection rules and radial integrals come from evaluating the vertex directly, not from gauge invariance). Still, the authors should address it.

The vanishing on-shell amplitude is a limitation, but the authors are upfront about it and point to future work where the photon is treated as a non-rotating plane wave in the lab frame. That is sensible.

Overall: the paper is a careful piece of formal QFT in rotating coordinates. It belongs in a journal like Physical Review D. I would accept it with a minor revision that asks the authors to clarify the boundary condition for gauge invariance.

Who it is for: specialists in thermal/rotating QFT, heavy-ion theorists working on vortical effects. It does not have immediate phenomenological punch, but it is a necessary building block.

Recommendation: send to peer review. Minor revision.

Referee report

Significance

If correct, this work provides the first systematic construction of the fermion-photon vertex in a rotating background, explicitly incorporating the breaking of transverse translational invariance. The analytic treatment of the triple-Bessel radial integrals and the identification of the non-conservation of transverse momentum are important conceptual results. The vanishing of the on-shell tree-level amplitude for physical photon modes is a nontrivial finding that clarifies the role of the rotating background in electromagnetic processes. The framework opens a path toward studying radiative corrections and photon production in vortical matter, which is relevant for heavy-ion collisions. The derivation is detailed, the notation is consistent, and the authors are transparent about assumptions and limitations.

Major objections (1)

[Sec. VII, Eq. (113)-(114)] The verification of gauge invariance reduces the gauge variation of the matrix element to a boundary term (Eq. 113). To eliminate this term, the authors assert that for a rigidly rotating fermion configuration with fixed orbital radius R, the transition current is tangent to the cylindrical boundary, j^μ_{fi} dΣ_μ = 0. This claim is not derived or checked against the explicit Bessel-function modes given in Sec. IV and Appendix A. The fermion modes are extended eigenstates of the free rotating Dirac operator; at ρ=R, the radial component of the current is a sum of products of Bessel functions and does not vanish automatically. Because the boundary term is the only potential obstruction to gauge invariance, this gap undermines the claim that the tree-level matrix element is gauge invariant under the conditions stated. The authors should either (a) provide a direct evaluation of the boundary integral using the explicit mode functions and show that it vanishes for all quantum numbers, or (b) modify the gauge-invariance argument to rely on a different boundary condition (e.g., taking R→∞ and using the asymptotic decay of Bessel functions, with a careful treatment of the light-cylinder condition). Without this, the gauge-variance argument is incomplete.

Minor objections (7)

[Title] The title contains a typographical error: 'V ertex' should be 'Vertex' (extra space). Please correct.
[Abstract] In the abstract, 'T ree-Level' appears to have a formatting artifact; ensure the capitalization and spacing are consistent.
[Sec. IV, Eq. (34)] The normalization factor N is defined twice: once in the main text (Eq. 35) and again in Appendix A (Eq. A102). The definitions are consistent, but the repetition may confuse readers. Consider citing the appendix explicitly.
[Sec. V, Eq. (50)] The notation 'eC^{+}_{1}' etc. is somewhat dense. Adding a brief verbal description of the coefficients' momentum dependences immediately after Eq. (51) would improve readability.
[Sec. VIII A, Eq. (135)-(141)] The mapping of the master integrals to the Gervois-Navelet form uses J_{-n}(x)=(-1)^n J_n(x) for integer n. While standard, a short reminder of this property would help readers not intimately familiar with Bessel functions.
[Sec. VIII B, Fig. 1] The caption for Fig. 1 is long and refers to 'the upper row' and 'lower row' without clearly labeling panels. Adding panel labels (a1, a2, etc.) would aid interpretation.
[Sec. VIII D, para beginning 'From a more general perspective'] The discussion leading to Eq. (192) is clear but uses the notation 'j-(l'-l)' repeatedly. Since j is the total angular momentum of the photon mode and l,l' are orbital quantum numbers of the fermions, it would be helpful to remind the reader of this relation at the start of the paragraph.

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The paper

The paper claims

In a rotating relativistic medium, the tree-level fermion-photon vertex does not conserve transverse momentum, and the on-shell amplitude vanishes for physical photons.

The reading

This paper studies the tree-level interaction between a fermion and a photon in a rigidly rotating relativistic medium at zero temperature. The authors show that the rotating background breaks translational symmetry in the transverse plane, so transverse momentum is not conserved, while energy and longitudinal momentum remain conserved. The vertex is expressed in terms of radial integrals involving three Bessel functions, leading to a set of angular-momentum selection rules. When contracted with physical photon polarization vectors, the on-shell tree-level amplitude vanishes identically for absorption, pair annihilation, and bremsstrahlung. The authors emphasize that this suppression applies when the photon is described by a rotating mode, and that a different treatment is needed for phenomenological applications where the photon propagates in the laboratory frame.

What carries the argument

The rotating fermion and photon modes constructed as eigenstates of the free rotating Hamiltonian, and the triple-Bessel radial integrals \(I_{l'l}\), \(J_{l'l}\), \(K_{l'l}\) that encode the transverse kinematic support. The vertex is expressed in a circular basis for transverse components and a Cartesian basis along the rotation axis, with form factors proportional to these integrals.

Extended reading notes

Core claim

The paper establishes that the tree-level fermion-photon vertex in a rigidly rotating background has a fundamentally different kinematic structure from its vacuum counterpart. The energy and the longitudinal component of the momentum are conserved, but no independent transverse momentum-conservation condition arises. Instead, the transverse dependence is governed by radial triple-Bessel integrals whose support constrains the magnitudes of the transverse momentum projections, not their vector directions. The vertex can be decomposed into six Dirac structures yielding 24 form-factor components. After projecting onto physical photon states, the on-shell tree-level amplitude vanishes for all three basic processes: photon absorption, pair annihilation, and bremsstrahlung. This cancellation follows from the angular-momentum selection rules and the kinematic restrictions imposed by the Bessel integrals, together with the structure of the physical polarization vectors.

Load-bearing premise

The photon must be described by a mode constructed in the rotating frame (Eq. 50); the authors note in Sec. VIII D that for phenomenological applications the photon should be treated as a non-rotating Minkowski state.

Editorial extensions

If this is right

The tree-level on-shell fermion-photon amplitude vanishes in a rigidly rotating background when the photon is described by a rotating mode, implying that leading-order photon production via QED processes is suppressed in such a setup.
The rotational modification of energy and angular-momentum selection rules opens kinematic channels that are forbidden in vacuum, but the dynamical cancellation prevents any on-shell tree-level transition.
The 24 form-factor decomposition provides a complete basis for computing one-loop radiative corrections to the vertex in vortical backgrounds.
The absence of transverse momentum conservation implies that off-shell processes or finite-temperature/density effects could yield nonzero amplitudes, motivating further study of the vertex beyond tree level.
The results establish a baseline for distinguishing pure kinematic rotation effects from dynamical medium-induced modifications in electromagnetic processes in rotating matter.

Reading between the lines

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

If the photon is treated as a non-rotating Minkowski plane wave while the fermions experience the rotating background, the tree-level amplitude may no longer vanish. This would align with heavy-ion phenomenology where photons escape the vortical medium without participating in the rotation. The authors acknowledge this and state that such work is in progress.
The suppression of on-shell tree-level processes suggests that loop corrections, thermal effects, or the inclusion of strong interactions (e.g., QCD backgrounds) are necessary to generate observable photon emission from rotating quark-gluon plasma. The present tree-level result may not preclude photon production via more complex mechanisms.
The auxiliary-triangle condition on transverse momentum magnitudes (Eq. 153a) provides a testable kinematic signature: in processes where the vertex contributes, the transverse momenta should satisfy this triangle inequality rather than vector conservation. This could be searched for in simulations of rotating matter.
The paper's formalism could be extended to other vector interactions (e.g., gluon-quark vertices in rotating QCD) where similar kinematic modifications and cancellations may occur, with implications for jet quenching and spin alignment in heavy-ion collisions.

Original abstract

We study the tree-level fermion-photon effective vertex for on-shell particles in a relativistic environment undergoing rigid rotation at zero temperature. The rotational background breaks translational invariance in the transverse plane and introduces a preferred direction, leading to a distinct decomposition of the vertex into longitudinal and transverse structures with respect to the rotation axis. Using fermion and photon modes constructed in the rotating frame, we derive the corresponding selection rules and show that the energy and the longitudinal component of the momentum are conserved, whereas no independent transverse momentum-conservation condition arises. Instead, the transverse dependence is governed by radial integrals involving three Bessel functions, whose support constrains the magnitudes of the transverse momentum projections. The vertex can be organized in a circular basis for the transverse components and a Cartesian basis along the rotation axis, and expressed in terms of six Dirac structures. Their coefficients define 24 form-factor components associated with the photon-mode components, physical photon states, and spin-dependent structures induced by the rotating background. We also verify current conservation and gauge invariance of the resulting tree-level matrix element under the boundary conditions considered. These results provide the tree-level structure of the fermion-photon interaction in rotating relativistic matter and establish the basis for the study of radiative corrections in vortical backgrounds.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-15: 1 request, 6,349 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.35 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We study the tree-level fermion-photon effective vertex for on-shell particles in a relativistic environment undergoing rigid rotation at zero temperature. The rotational background breaks translational invariance in the transverse plane and introduces a preferred direction, leading to a distinct decomposition of the vertex into longitudinal and transverse structures with respect to the rotation axis. Using fermion and photon modes constructed in the rotating frame, we derive the corresponding selection rules and show that the energy and the longitudinal component of the momentum are conserved, whereas no independent transverse momentum-conservation condition arises. Instead, the transverse dependence is governed by radial integrals involving three Bessel functions, whose support constrains the magnitudes of the transverse momentum projections. The vertex can be organized in a circular basis for the transverse components and a Cartesian basis along the rotation axis, and expressed in terms of six Dirac structures. Their coefficients define 24 form-factor components associated with the photon-mode components, physical photon states, and spin-dependent structures induced by the rotating background. We also verify current conservation and gauge invariance of the resulting tree-level matrix element under the boundary conditions considered. These results provide the tree-level structure of the fermion-photon interaction in rotating relativistic matter and establish the basis for the study of radiative corrections in vortical backgrounds.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the tree-level fermion-photon effective vertex for on-shell particles in a relativistic environment undergoing rigid rotation at zero temperature.	contribution 0.97	0.94	0.06	asserted 0.89
s1	The rotational background breaks translational invariance in the transverse plane and introduces a preferred direction, leading to a distinct decomposition of the vertex into longitudinal and transverse structures with respect to the rotation axis.	result 0.61	0.50	0.12	asserted 1.00
s2	Using fermion and photon modes constructed in the rotating frame, we derive the corresponding selection rules and show that the energy and the longitudinal component of the momentum are conserved, whereas no independent transverse momentum-conservation condition arises.	result 0.89	0.96	0.21	asserted 1.00
s3	Instead, the transverse dependence is governed by radial integrals involving three Bessel functions, whose support constrains the magnitudes of the transverse momentum projections.	result 0.94	0.90	0.09	asserted 1.00
s4	The vertex can be organized in a circular basis for the transverse components and a Cartesian basis along the rotation axis, and expressed in terms of six Dirac structures.	result 0.46	0.89	0.07	asserted 1.00
s5	Their coefficients define 24 form-factor components associated with the photon-mode components, physical photon states, and spin-dependent structures induced by the rotating background.	result 0.90	0.91	0.08	asserted 1.00
s6	We also verify current conservation and gauge invariance of the resulting tree-level matrix element under the boundary conditions considered.	result 0.90	0.96	0.07	asserted 1.00
s7	These results provide the tree-level structure of the fermion-photon interaction in rotating relativistic matter and establish the basis for the study of radiative corrections in vortical backgrounds.	interpretation 0.49	0.83	0.84	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: Allowed range of the polar angle

**Figure 2.** FIG. 2: Kinematic support for

Figures reproduced from arXiv:2610.19124 by the authors.

References

Works cited (46)

[1]

Normalization of the rotating fermion modes The normalization of the rotating fermion modes is fixed by the momentum-space measure in Eq. (A80) and the canonical anticommutation relations in Eqs. (A82)–(A84). For the positive-energy modes, we require the orthonormality condition Z d3x U†α′(x)Uα(x) =δ ll′δhh′δ(pz −p ′z) δ(|p ⊥| − |p′⊥|)|p⊥| .(A85) Using Eq...

View on Pith
[2]

L. Adamczyk et al. (STAR), GlobalΛhyperon polarization in nuclear collisions, Nature548, 62 (2017), arXiv:1701.06657 [nucl-ex]

View on Pith Pith review arXiv 2017
[3]

J. Adam et al. (STAR), Global polarization ofΛhyperons in Au+Au collisions at √sN N = 200 GeV, Phys. Rev. C98, 014910 (2018), arXiv:1805.04400 [nucl-ex]

View on Pith Pith review arXiv 2018
[4]

M. S. Abdallah et al. (STAR), GlobalΛ-hyperon polarization in Au+Au collisions at √sN N = 3GeV, Phys. Rev. C104, L061901 (2021), arXiv:2108.00044 [nucl-ex]

View on Pith arXiv 2021
[5]

M. I. Abdulhamid et al. (STAR), Global polarization ofΛand ¯Λhyperons in Au+Au collisions at √sN N= 19.6and 27 GeV, Phys. Rev. C108, 014910 (2023), arXiv:2305.08705 [nucl-ex]

View on Pith Pith review arXiv 2023
[6]

S. Acharya et al. (ALICE), Global polarization ofΛand ¯Λhy- perons in Pb-Pb collisions at √sN N = 2.76and 5.02 TeV, Phys. Rev. C101, 044611 (2020), [Erratum: Phys.Rev.C 105, 029902 (2022)], arXiv:1909.01281 [nucl-ex]

View on Pith Pith review arXiv 2020
[7]

R. Abou Yassine et al. (HADES), Measurement of global polar- ization ofΛhyperons in few-GeV heavy-ion collisions, Phys. Lett. B835, 137506 (2022), arXiv:2207.05160 [nucl-ex]

View on Pith Pith review arXiv 2022
[8]

J. Adam et al. (STAR), Global Polarization ofΞandΩHy- perons in Au+Au Collisions at √sN N = 200GeV, Phys. Rev. Lett.126, 162301 (2021), [Erratum: Phys.Rev.Lett. 131, 089901 (2023)], arXiv:2012.13601 [nucl-ex]

View on Pith arXiv 2021
[9]

J. Adam et al. (STAR), Polarization ofΛ( ¯Λ) hyperons along the beam direction in Au+Au collisions at √sN N= 200GeV, Phys. Rev. Lett.123, 132301 (2019), arXiv:1905.11917 [nucl- ex]

View on Pith arXiv 2019
[10]

M. Abdulhamid et al. (STAR), Hyperon Polarization along the Beam Direction Relative to the Second and Third Harmonic Event Planes in Isobar Collisions at √sN N= 200GeV, Phys. Rev. Lett.131, 202301 (2023), arXiv:2303.09074 [nucl-ex]

View on Pith arXiv 2023
[11]

D. Sarkar (ALICE), Global and local polarization ofΛ( ¯Λ) hy- perons in Pb-Pb collisions in ALICE at the LHC, EPJ Web Conf.259, 06001 (2022), arXiv:2209.04798 [hep-ex]

View on Pith Pith review arXiv 2022
[12]

D. Ali Hassan Abdallah et al. (ALICE), Hyperon (Λ) polariza- tion along the beam axis in Pb-Pb collisions at √sNN = 5.36 TeV (2026), arXiv:2606.18070 [nucl-ex]

View on Pith Pith review arXiv 2026
[13]

M. S. Abdallah et al. (STAR), Pattern of global spin alignment ofϕandK ∗0 mesons in heavy-ion collisions, Nature614, 244 (2023), arXiv:2204.02302 [hep-ph]

View on Pith arXiv 2023
[14]

Z.-T. Liang and X.-N. Wang, Globally polarized quark-gluon plasma in non-central A+A collisions, Phys. Rev. Lett.94, 102301 (2005), [Erratum: Phys.Rev.Lett. 96, 039901 (2006)], arXiv:nucl-th/0410079

View on Pith Pith review arXiv 2005
[15]

B. Betz, M. Gyulassy, and G. Torrieri, Polarization probes of vorticity in heavy ion collisions, Phys. Rev. C76, 044901 (2007), arXiv:0708.0035 [nucl-th]

View on Pith Pith review arXiv 2007
[16]

J.-H. Gao, S.-W. Chen, W.-t. Deng, Z.-T. Liang, Q. Wang, and X.-N. Wang, Global quark polarization in non-central A+A collisions, Phys. Rev. C77, 044902 (2008), arXiv:0710.2943 [nucl-th]

View on Pith Pith review arXiv 2008
[17]

F. Becattini, F. Piccinini, and J. Rizzo, Angular momentum con- servation in heavy ion collisions at very high energy, Phys. Rev. C77, 024906 (2008), arXiv:0711.1253 [nucl-th]

View on Pith Pith review arXiv 2008
[18]

F. Becattini, V . Chandra, L. Del Zanna, and E. Grossi, Rel- ativistic distribution function for particles with spin at local thermodynamical equilibrium, Annals Phys.338, 32 (2013), arXiv:1303.3431 [nucl-th]

View on Pith Pith review arXiv 2013
[19]

F. Becattini, G. Inghirami, V . Rolando, A. Beraudo, L. Del Zanna, A. De Pace, M. Nardi, G. Pagliara, and V . Chan- dra, A study of vorticity formation in high energy nuclear col- lisions, Eur. Phys. J. C75, 406 (2015), [Erratum: Eur.Phys.J.C 26 78, 354 (2018)], arXiv:1501.04468 [nucl-th]

View on Pith Pith review arXiv 2015
[20]

F. Becattini, I. Karpenko, M. Lisa, I. Upsal, and S. V oloshin, Global hyperon polarization at local thermodynamic equilib- rium with vorticity, magnetic field and feed-down, Phys. Rev. C95, 054902 (2017), arXiv:1610.02506 [nucl-th]

View on Pith Pith review arXiv 2017
[21]

W. Florkowski, A. Kumar, and R. Ryblewski, Thermody- namic versus kinetic approach to polarization-vorticity cou- pling, Phys. Rev. C98, 044906 (2018), arXiv:1806.02616 [hep- ph]

View on Pith Pith review arXiv 2018
[22]

L.-G. Pang, H. Petersen, Q. Wang, and X.-N. Wang, V ortical Fluid andΛSpin Correlations in High-Energy Heavy-Ion Col- lisions, Phys. Rev. Lett.117, 192301 (2016), arXiv:1605.04024 [hep-ph]

View on Pith Pith review arXiv 2016
[23]

I. Karpenko and F. Becattini, Study ofΛpolarization in rela- tivistic nuclear collisions at √sNN = 7.7–200 GeV, Eur. Phys. J. C77, 213 (2017), arXiv:1610.04717 [nucl-th]

View on Pith Pith review arXiv 2017
[24]

Y . Sun and C. M. Ko,Λhyperon polarization in relativistic heavy ion collisions from a chiral kinetic approach, Phys. Rev. C96, 024906 (2017), arXiv:1706.09467 [nucl-th]

View on Pith Pith review arXiv 2017
[25]

H. Li, L.-G. Pang, Q. Wang, and X.-L. Xia, GlobalΛpolariza- tion in heavy-ion collisions from a transport model, Phys. Rev. C96, 054908 (2017), arXiv:1704.01507 [nucl-th]

View on Pith Pith review arXiv 2017
[26]

X.-L. Xia, H. Li, Z.-B. Tang, and Q. Wang, Probing vorticity structure in heavy-ion collisions by localΛpolarization, Phys. Rev. C98, 024905 (2018), arXiv:1803.00867 [nucl-th]

View on Pith Pith review arXiv 2018
[27]

D.-X. Wei, W.-T. Deng, and X.-G. Huang, Thermal vorticity and spin polarization in heavy-ion collisions, Phys. Rev. C99, 014905 (2019), arXiv:1810.00151 [nucl-th]

View on Pith Pith review arXiv 2019
[28]

B. Fu, K. Xu, X.-G. Huang, and H. Song, Hydrodynamic study of hyperon spin polarization in relativistic heavy ion collisions, Phys. Rev. C103, 024903 (2021), arXiv:2011.03740 [nucl-th]

View on Pith Pith review arXiv 2021
[29]

S. Y . F. Liu and Y . Yin, Spin polarization induced by the hy- drodynamic gradients, JHEP2021(07), 188, arXiv:2103.09200 [hep-ph]

View on Pith Pith review arXiv
[30]

A. Ayala, I. Dom ´ınguez, I. Maldonado, and M. E. Tejeda- Yeomans, Rise and fall ofΛand ¯Λglobal polarization in semi- central heavy-ion collisions at HADES, NICA and RHIC en- ergies from the core-corona model, Phys. Rev. C105, 034907 (2022), arXiv:2106.14379 [hep-ph]

View on Pith Pith review arXiv 2022
[31]

A. Ayala et al., Core meets corona: A two-component source to explainΛand ¯Λglobal polarization in semi-central heavy-ion collisions, Phys. Lett. B810, 135818 (2020), arXiv:2003.13757 [hep-ph]

View on Pith Pith review arXiv 2020
[32]

A. Ayala, I. Dominguez, I. Maldonado, and M. E. Tejeda- Yeomans, An Improved Core-Corona Model forΛand ¯ΛPo- larization in Relativistic Heavy-Ion Collisions, Particles6, 405 (2023)

View on Pith 2023
[34]

F. Becattini and M. A. Lisa, Polarization and V orticity in the Quark–Gluon Plasma, Ann. Rev. Nucl. Part. Sci.70, 395 (2020), arXiv:2003.03640 [nucl-ex]

View on Pith Pith review arXiv 2020
[35]

A. Ayala, L. A. Hern ´andez, K. Raya, and R. Zamora, Fermion propagator in a rotating environment, Phys. Rev. D103, 076021 (2021), [Erratum: Phys. Rev. D 104, 039901 (2021)], arXiv:2102.03476 [hep-ph]

View on Pith Pith review arXiv 2021
[36]

I. I. Gaspar, L. A. Hern ´andez, and R. Zamora, Chiral symme- try restoration in a rotating medium, Phys. Rev. D108, 094020 (2023), arXiv:2305.00101 [hep-ph]

View on Pith Pith review arXiv 2023
[37]

A. Ayala, J. J. Medina-Serna, I. Dom ´ınguez, and M. E. Tejeda- Yeomans, Excitation function for globalΛpolarization in rela- tivistic heavy-ion collisions with the core-corona model, Phys. Rev. D114, 016034 (2026)

View on Pith 2026
[38]

J. D. Casta ˜no Yepes and E. Mu˜noz, Dilepton production in a ro- tating thermal medium: The rigid rotation approximation, Phys. Rev. D113, 116001 (2026)

View on Pith 2026
[39]

V . E. Ambrus ¸ and E. Winstanley, Rotating fermions inside a cylindrical boundary, Phys. Rev. D93, 104014 (2016)

View on Pith 2016
[40]

A. Ayala, E. Mu ˜noz, M. Loewe, J. C. Rojas, and N. Scoccola, QED vertex and anomalous magnetic moment in the presence of a magnetic field (2026), arXiv:2607.10015 [hep-ph]

View on Pith Pith review arXiv 2026
[41]

A. Ayala, S. Bernal-Langarica, J. D. Casta ˜no-Yepes, and J. J. Medina-Serna, Photon quantization and propagator in rotating coordinates, arXiv (2026), arXiv:2610.02656 [hep-ph]

View on Pith Pith review arXiv 2026
[42]

J. D. Casta ˜no-Yepes and L. A. Cer ´on-Su´arez, Finite-size ef- fects on symmetry restoration in a rotating scalar system with spatially dependent thermal self-energy, arXiv (2026), arXiv:2609.34038 [hep-ph]

View on Pith Pith review arXiv 2026
[43]

A. Gervois and H. Navelet, Some integrals involving three bessel functions when their arguments satisfy the triangle in- equalities, Journal of Mathematical Physics25, 3350 (1984)

View on Pith 1984
[44]

C. Shen, Studying qgp with flow: A theory overview, Nucl. Phys. A1005, 121788 (2021)

View on Pith 2021
[45]

U. Heinz and R. Snellings, Collective flow and viscosity in rela- tivistic heavy-ion collisions, Annu. Rev. Nucl. Part. Sci.63, 123 (2013)

View on Pith 2013
[46]

G. David, Direct real photons in relativistic heavy ion col- lisions, Reports on Progress in Physics83, 046301 (2020), arXiv:1907.08893 [nucl-ex]

View on Pith Pith review arXiv 2020
[47]

F. Geurts and R.-A. Tripolt, Electromagnetic probes: Theory and experiment, Progress in Particle and Nuclear Physics128, 104004 (2023), arXiv:2210.01622 [hep-ph]

View on Pith Pith review arXiv 2023

Discussion

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[1] [1]

Normalization of the rotating fermion modes The normalization of the rotating fermion modes is fixed by the momentum-space measure in Eq. (A80) and the canonical anticommutation relations in Eqs. (A82)–(A84). For the positive-energy modes, we require the orthonormality condition Z d3x U†α′(x)Uα(x) =δ ll′δhh′δ(pz −p ′z) δ(|p ⊥| − |p′⊥|)|p⊥| .(A85) Using Eq...

View on Pith

[2] [2]

L. Adamczyk et al. (STAR), GlobalΛhyperon polarization in nuclear collisions, Nature548, 62 (2017), arXiv:1701.06657 [nucl-ex]

View on Pith Pith review arXiv 2017

[3] [3]

J. Adam et al. (STAR), Global polarization ofΛhyperons in Au+Au collisions at √sN N = 200 GeV, Phys. Rev. C98, 014910 (2018), arXiv:1805.04400 [nucl-ex]

View on Pith Pith review arXiv 2018

[4] [4]

M. S. Abdallah et al. (STAR), GlobalΛ-hyperon polarization in Au+Au collisions at √sN N = 3GeV, Phys. Rev. C104, L061901 (2021), arXiv:2108.00044 [nucl-ex]

View on Pith arXiv 2021

[5] [5]

M. I. Abdulhamid et al. (STAR), Global polarization ofΛand ¯Λhyperons in Au+Au collisions at √sN N= 19.6and 27 GeV, Phys. Rev. C108, 014910 (2023), arXiv:2305.08705 [nucl-ex]

View on Pith Pith review arXiv 2023

[6] [6]

S. Acharya et al. (ALICE), Global polarization ofΛand ¯Λhy- perons in Pb-Pb collisions at √sN N = 2.76and 5.02 TeV, Phys. Rev. C101, 044611 (2020), [Erratum: Phys.Rev.C 105, 029902 (2022)], arXiv:1909.01281 [nucl-ex]

View on Pith Pith review arXiv 2020

[7] [7]

R. Abou Yassine et al. (HADES), Measurement of global polar- ization ofΛhyperons in few-GeV heavy-ion collisions, Phys. Lett. B835, 137506 (2022), arXiv:2207.05160 [nucl-ex]

View on Pith Pith review arXiv 2022

[8] [8]

J. Adam et al. (STAR), Global Polarization ofΞandΩHy- perons in Au+Au Collisions at √sN N = 200GeV, Phys. Rev. Lett.126, 162301 (2021), [Erratum: Phys.Rev.Lett. 131, 089901 (2023)], arXiv:2012.13601 [nucl-ex]

View on Pith arXiv 2021

[9] [9]

J. Adam et al. (STAR), Polarization ofΛ( ¯Λ) hyperons along the beam direction in Au+Au collisions at √sN N= 200GeV, Phys. Rev. Lett.123, 132301 (2019), arXiv:1905.11917 [nucl- ex]

View on Pith arXiv 2019

[10] [10]

M. Abdulhamid et al. (STAR), Hyperon Polarization along the Beam Direction Relative to the Second and Third Harmonic Event Planes in Isobar Collisions at √sN N= 200GeV, Phys. Rev. Lett.131, 202301 (2023), arXiv:2303.09074 [nucl-ex]

View on Pith arXiv 2023

[11] [11]

D. Sarkar (ALICE), Global and local polarization ofΛ( ¯Λ) hy- perons in Pb-Pb collisions in ALICE at the LHC, EPJ Web Conf.259, 06001 (2022), arXiv:2209.04798 [hep-ex]

View on Pith Pith review arXiv 2022

[12] [12]

D. Ali Hassan Abdallah et al. (ALICE), Hyperon (Λ) polariza- tion along the beam axis in Pb-Pb collisions at √sNN = 5.36 TeV (2026), arXiv:2606.18070 [nucl-ex]

View on Pith Pith review arXiv 2026

[13] [13]

M. S. Abdallah et al. (STAR), Pattern of global spin alignment ofϕandK ∗0 mesons in heavy-ion collisions, Nature614, 244 (2023), arXiv:2204.02302 [hep-ph]

View on Pith arXiv 2023

[14] [14]

Z.-T. Liang and X.-N. Wang, Globally polarized quark-gluon plasma in non-central A+A collisions, Phys. Rev. Lett.94, 102301 (2005), [Erratum: Phys.Rev.Lett. 96, 039901 (2006)], arXiv:nucl-th/0410079

View on Pith Pith review arXiv 2005

[15] [15]

B. Betz, M. Gyulassy, and G. Torrieri, Polarization probes of vorticity in heavy ion collisions, Phys. Rev. C76, 044901 (2007), arXiv:0708.0035 [nucl-th]

View on Pith Pith review arXiv 2007

[16] [16]

J.-H. Gao, S.-W. Chen, W.-t. Deng, Z.-T. Liang, Q. Wang, and X.-N. Wang, Global quark polarization in non-central A+A collisions, Phys. Rev. C77, 044902 (2008), arXiv:0710.2943 [nucl-th]

View on Pith Pith review arXiv 2008

[17] [17]

F. Becattini, F. Piccinini, and J. Rizzo, Angular momentum con- servation in heavy ion collisions at very high energy, Phys. Rev. C77, 024906 (2008), arXiv:0711.1253 [nucl-th]

View on Pith Pith review arXiv 2008

[18] [18]

F. Becattini, V . Chandra, L. Del Zanna, and E. Grossi, Rel- ativistic distribution function for particles with spin at local thermodynamical equilibrium, Annals Phys.338, 32 (2013), arXiv:1303.3431 [nucl-th]

View on Pith Pith review arXiv 2013

[19] [19]

F. Becattini, G. Inghirami, V . Rolando, A. Beraudo, L. Del Zanna, A. De Pace, M. Nardi, G. Pagliara, and V . Chan- dra, A study of vorticity formation in high energy nuclear col- lisions, Eur. Phys. J. C75, 406 (2015), [Erratum: Eur.Phys.J.C 26 78, 354 (2018)], arXiv:1501.04468 [nucl-th]

View on Pith Pith review arXiv 2015

[20] [20]

F. Becattini, I. Karpenko, M. Lisa, I. Upsal, and S. V oloshin, Global hyperon polarization at local thermodynamic equilib- rium with vorticity, magnetic field and feed-down, Phys. Rev. C95, 054902 (2017), arXiv:1610.02506 [nucl-th]

View on Pith Pith review arXiv 2017

[21] [21]

W. Florkowski, A. Kumar, and R. Ryblewski, Thermody- namic versus kinetic approach to polarization-vorticity cou- pling, Phys. Rev. C98, 044906 (2018), arXiv:1806.02616 [hep- ph]

View on Pith Pith review arXiv 2018

[22] [22]

L.-G. Pang, H. Petersen, Q. Wang, and X.-N. Wang, V ortical Fluid andΛSpin Correlations in High-Energy Heavy-Ion Col- lisions, Phys. Rev. Lett.117, 192301 (2016), arXiv:1605.04024 [hep-ph]

View on Pith Pith review arXiv 2016

[23] [23]

I. Karpenko and F. Becattini, Study ofΛpolarization in rela- tivistic nuclear collisions at √sNN = 7.7–200 GeV, Eur. Phys. J. C77, 213 (2017), arXiv:1610.04717 [nucl-th]

View on Pith Pith review arXiv 2017

[24] [24]

Y . Sun and C. M. Ko,Λhyperon polarization in relativistic heavy ion collisions from a chiral kinetic approach, Phys. Rev. C96, 024906 (2017), arXiv:1706.09467 [nucl-th]

View on Pith Pith review arXiv 2017

[25] [25]

H. Li, L.-G. Pang, Q. Wang, and X.-L. Xia, GlobalΛpolariza- tion in heavy-ion collisions from a transport model, Phys. Rev. C96, 054908 (2017), arXiv:1704.01507 [nucl-th]

View on Pith Pith review arXiv 2017

[26] [26]

X.-L. Xia, H. Li, Z.-B. Tang, and Q. Wang, Probing vorticity structure in heavy-ion collisions by localΛpolarization, Phys. Rev. C98, 024905 (2018), arXiv:1803.00867 [nucl-th]

View on Pith Pith review arXiv 2018

[27] [27]

D.-X. Wei, W.-T. Deng, and X.-G. Huang, Thermal vorticity and spin polarization in heavy-ion collisions, Phys. Rev. C99, 014905 (2019), arXiv:1810.00151 [nucl-th]

View on Pith Pith review arXiv 2019

[28] [28]

B. Fu, K. Xu, X.-G. Huang, and H. Song, Hydrodynamic study of hyperon spin polarization in relativistic heavy ion collisions, Phys. Rev. C103, 024903 (2021), arXiv:2011.03740 [nucl-th]

View on Pith Pith review arXiv 2021

[29] [29]

S. Y . F. Liu and Y . Yin, Spin polarization induced by the hy- drodynamic gradients, JHEP2021(07), 188, arXiv:2103.09200 [hep-ph]

View on Pith Pith review arXiv

[30] [30]

A. Ayala, I. Dom ´ınguez, I. Maldonado, and M. E. Tejeda- Yeomans, Rise and fall ofΛand ¯Λglobal polarization in semi- central heavy-ion collisions at HADES, NICA and RHIC en- ergies from the core-corona model, Phys. Rev. C105, 034907 (2022), arXiv:2106.14379 [hep-ph]

View on Pith Pith review arXiv 2022

[31] [31]

A. Ayala et al., Core meets corona: A two-component source to explainΛand ¯Λglobal polarization in semi-central heavy-ion collisions, Phys. Lett. B810, 135818 (2020), arXiv:2003.13757 [hep-ph]

View on Pith Pith review arXiv 2020

[32] [32]

A. Ayala, I. Dominguez, I. Maldonado, and M. E. Tejeda- Yeomans, An Improved Core-Corona Model forΛand ¯ΛPo- larization in Relativistic Heavy-Ion Collisions, Particles6, 405 (2023)

View on Pith 2023

[33] [34]

F. Becattini and M. A. Lisa, Polarization and V orticity in the Quark–Gluon Plasma, Ann. Rev. Nucl. Part. Sci.70, 395 (2020), arXiv:2003.03640 [nucl-ex]

View on Pith Pith review arXiv 2020

[34] [35]

A. Ayala, L. A. Hern ´andez, K. Raya, and R. Zamora, Fermion propagator in a rotating environment, Phys. Rev. D103, 076021 (2021), [Erratum: Phys. Rev. D 104, 039901 (2021)], arXiv:2102.03476 [hep-ph]

View on Pith Pith review arXiv 2021

[35] [36]

I. I. Gaspar, L. A. Hern ´andez, and R. Zamora, Chiral symme- try restoration in a rotating medium, Phys. Rev. D108, 094020 (2023), arXiv:2305.00101 [hep-ph]

View on Pith Pith review arXiv 2023

[36] [37]

A. Ayala, J. J. Medina-Serna, I. Dom ´ınguez, and M. E. Tejeda- Yeomans, Excitation function for globalΛpolarization in rela- tivistic heavy-ion collisions with the core-corona model, Phys. Rev. D114, 016034 (2026)

View on Pith 2026

[37] [38]

J. D. Casta ˜no Yepes and E. Mu˜noz, Dilepton production in a ro- tating thermal medium: The rigid rotation approximation, Phys. Rev. D113, 116001 (2026)

View on Pith 2026

[38] [39]

V . E. Ambrus ¸ and E. Winstanley, Rotating fermions inside a cylindrical boundary, Phys. Rev. D93, 104014 (2016)

View on Pith 2016

[39] [40]

A. Ayala, E. Mu ˜noz, M. Loewe, J. C. Rojas, and N. Scoccola, QED vertex and anomalous magnetic moment in the presence of a magnetic field (2026), arXiv:2607.10015 [hep-ph]

View on Pith Pith review arXiv 2026

[40] [41]

A. Ayala, S. Bernal-Langarica, J. D. Casta ˜no-Yepes, and J. J. Medina-Serna, Photon quantization and propagator in rotating coordinates, arXiv (2026), arXiv:2610.02656 [hep-ph]

View on Pith Pith review arXiv 2026

[41] [42]

J. D. Casta ˜no-Yepes and L. A. Cer ´on-Su´arez, Finite-size ef- fects on symmetry restoration in a rotating scalar system with spatially dependent thermal self-energy, arXiv (2026), arXiv:2609.34038 [hep-ph]

View on Pith Pith review arXiv 2026

[42] [43]

A. Gervois and H. Navelet, Some integrals involving three bessel functions when their arguments satisfy the triangle in- equalities, Journal of Mathematical Physics25, 3350 (1984)

View on Pith 1984

[43] [44]

C. Shen, Studying qgp with flow: A theory overview, Nucl. Phys. A1005, 121788 (2021)

View on Pith 2021

[44] [45]

U. Heinz and R. Snellings, Collective flow and viscosity in rela- tivistic heavy-ion collisions, Annu. Rev. Nucl. Part. Sci.63, 123 (2013)

View on Pith 2013

[45] [46]

G. David, Direct real photons in relativistic heavy ion col- lisions, Reports on Progress in Physics83, 046301 (2020), arXiv:1907.08893 [nucl-ex]

View on Pith Pith review arXiv 2020

[46] [47]

F. Geurts and R.-A. Tripolt, Electromagnetic probes: Theory and experiment, Progress in Particle and Nuclear Physics128, 104004 (2023), arXiv:2210.01622 [hep-ph]

View on Pith Pith review arXiv 2023