Journal of Holography Applications in Physics

Imprints of Quantum Gravity on the Cooper-Frye Freeze-Out

Document Type : Letter

Author

Canadian Quantum Research Center, 460 Doyle Ave 106, Kelowna, BC V1Y 0C2, Canada; Department of Computer Sciences, Asian School of Business, Noida, Uttar Pradesh, 201303, India

Abstract

This work shows that quantum-gravity-motivated generalized uncertainty principles (GUP) produce calculable and phenomenologically relevant modifications to the Cooper-Frye freeze-out prescription that maps hydrodynamic fields to hadronic momentum spectra in relativistic heavy-ion collisions. Using the linear Ali Das Vagenas GUP, which alters both the phase-space measure and the single-particle dispersion relation, the corresponding deformed particle current is constructed and its flux across a freeze-out hypersurface is evaluated. The resulting invariant spectrum acquires a momentum-dependent correction governed by a single dimensionless function that enhances high-momentum modes. For a static, homogeneous hypersurface the full expression can be written in closed analytic form, and the structure of the correction allows straightforward implementation in blast-wave-type models. The result is also directly relevant to holography-informed heavy-ion modeling, where gauge/gravity duality constrains the strongly coupled plasma dynamics but the conversion to hadron spectra is still performed through a Cooper-Frye freeze-out map.  Our findings demonstrate that Planck-scale deformations of quantum mechanics can leave characteristic imprints on freeze-out observables, opening a novel avenue for constraining GUP scenarios with heavy-ion data.

Keywords

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[1] S. Das and E. C. Vagenas, “Universality of quantum gravity corrections,” Phys. Rev. Lett. 101, 221301 (2008). DOI: https://doi.org/10.1103/PhysRevLett.101.221301.
[2] A. N. Tawfik and A. M. Diab, “Generalized uncertainty principle: approaches and applications,” Int. J. Mod. Phys. D 23, 1430025 (2014). DOI:https://doi.org/10.1142/S0218271814300250.
[3] I. Elmashad, A. F. Ali, L. I. Abou-Salem, Jameel-Un Nabi and A. Tawfik, “Quantum gravity effect on the quark-gluon plasma,” SOP Trans. Theor. Phys. 1, 1 (2014). DOI: https://doi.org/10.15764/TPHY.2014.01001 [arXiv:1208.4028 [hep-ph]]
[4] N. Demir and E. C. Vagenas, “Effect of the GUP on the entropy, speed of sound, and bulk to shear viscosity ratio of an ideal QGP,” Nucl. Phys. B 933, 340 (2018). DOI: https://doi.org/10.1016/j.nuclphysb.2018.06.020 [arXiv:1806.09456 [hep-th]]
[5] S. A. Mir, “Third-harmonic signature of linear-GUP kinematics in mesoscopic Aharonov-Bohm rings,” EPL 152(4), 49001 (2025). DOI: https://doi.org/10.1209/0295-5075/ae1b39.
[6] J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U. A. Wiedemann, “Gauge/String Duality, Hot QCD and Heavy Ion Collisions,” (2011). [arXiv:1101.0618 [hep-th]] (archivePrefix: arXiv)
[7] J. M. Maldacena, “The Large N Limit of Superconformal Field Theories and Supergravity,” Adv. Theor. Math. Phys. 2, 231 (1998). DOI: https://doi.org/10.4310/ATMP.1998.v2.n2.a1 [arXiv:hep-th/9711200 [hep-th]] (archivePrefix: arXiv)
[8] S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge Theory Correlators from Non-Critical String Theory,” Phys. Lett. B 428, 105 (1998). DOI: https://doi.org/10.1016/S0370-2693(98)00377-3 [arXiv:hep-th/9802109 [hep-th]] (archivePrefix: arXiv)
[9] E. Witten, “Anti-de Sitter Space and Holography,” Adv. Theor. Math. Phys. 2, 253 (1998). DOI: https://doi.org/10.4310/ATMP.1998.v2.n2.a2 [arXiv:hep-th/9802150 [hep-th]] (archivePrefix: arXiv)
[10] S. A. Mir, ”Hawking-Page Transition from Logarithmic Entropy in f(R) Gravity,” Journal of Holography Applications in Physics, 6(1), 60 (2025). DOI: 10.22128/jhap.2025.3077.1142
[11] S. S. Gubser and A. Nellore, “Mimicking the QCD Equation of State with a Dual Black Hole,” Phys. Rev. D 78, 086007 (2008). DOI: https://doi.org/10.1103/PhysRevD.78.086007 [arXiv:0804.0434 [hep-th]] (archivePrefix: arXiv)
[12] U. Gürsoy and E. Kiritsis, “Exploring Improved Holographic Theories for QCD: Part I,” JHEP 02, 032 (2008). DOI: https://doi.org/10.1088/1126-6708/2008/02/032. [arXiv:0707.1324 [hep-th]] (archivePrefix: arXiv)
[13] U. Gürsoy, E. Kiritsis and F. Nitti, “Exploring Improved Holographic Theories for QCD: Part II,” JHEP 02, 019 (2008). DOI: https://doi.org/10.1088/1126-6708/2008/02/019 [arXiv:0707.1349 [hep-th]] (archivePrefix: arXiv)
[14] U. Gürsoy, E. Kiritsis, G. Michalogiorgakis and F. Nitti, “Thermal Transport and Drag Force in Improved Holographic QCD,” JHEP 12, 056 (2009). DOI: https://doi.org/10.1088/1126-6708/2009/12/056 [arXiv:0906.1890 [hep-ph]] (archivePrefix: arXiv)
[15] P. Kovtun, D. T. Son and A. O. Starinets, “Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics,” Phys. Rev. Lett. 94, 111601 (2005). DOI: https://doi.org/10.1103/PhysRevLett.94.111601 [arXiv:hep-th/0405231 [hep-th]] (archivePrefix: arXiv)
[16] F. Cooper and G. Frye, “Single-particle distribution in the hydrodynamic and statistical thermodynamic models of multiparticle production,” Phys. Rev. D 10, 186 (1974). DOI: https://doi.org/10.1103/PhysRevD.10.186.
[17] S. Uddin et al. “A unified approach towards describing rapidity and transverse momentum distributions in a thermal freeze-out model.” Journal of Physics G: Nuclear and Particle Physics 39.1 (2011): 015012.
[18] U. W. Heinz and R. Snellings, “Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions,” Ann. Rev. Nucl. Part. Sci. 63, 123 (2013). DOI: https://doi.org/10.1146/annurev-nucl-102212-170540 [arXiv:1301.2826 [nucl-th]] (archivePrefix: arXiv)
[19] S. A. Mir, N. A. Rather, I. Mohi Ud Din and S. Uddin, “Hadron production in ultrarelativistic nuclear collisions and finite baryon-size effects,” J. Phys. G 52(3), 035003 (2025). DOI: https://doi.org/10.1088/1361-6471/adb6c2 [arXiv:2312.13079 [hep-ph]] (archivePrefix: arXiv)
[20] S. A. Mir, I. Mohi Ud Din, N. A. Rather, S. Uddin and M. Farooq Mir, “Particle production in HRG with thermodynamically consistent EoS and partially deformable hadrons,” Annals Phys. 480, 170065 (2025). DOI: https://doi.org/10.1016/j.aop.2025.170065 [arXiv:2406.11752 [hep-ph]] (archivePrefix: arXiv)
[21] S. A. Mir, S. Uddin and S. K. Tiwari, “Influence of excluded volume corrections on hadronic yield in high-energy nuclear collisions,” Eur. Phys. J. A 61(8), 198 (2025). DOI: https://doi.org/10.1140/epja/s10050-025-01667-6.
[22] U. W. Heinz, “Chemical and kinetic freeze-out in relativistic heavy-ion collisions,” Nucl. Phys. A 661, 140c (1999).
[23] E. Schnedermann, J. Sollfrank and U. Heinz, “Thermal phenomenology of hadrons from 200A GeV S+S collisions,” Phys. Rev. C 48, 2462 (1993). DOI: https://doi.org/10.1103/PhysRevC.48.2462.
[24] A. Kempf, G. Mangano and R. B. Mann, “Hilbert space representation of the minimal length uncertainty relation,” Phys. Rev. D 52, 1108 (1995). DOI: https://doi.org/10.1103/PhysRevD.52.1108.
[25] M. Faizal, L. M. Krauss, A. Shabir and F. Marino, “Consequences of Undecidability in Physics on the Theory of Everything,” Journal of Holography Applications in Physics 5(2), 10 (2025). arXiv:2507.22950 (archivePrefix: arXiv), DOI: https://doi.org/10.22128/jhap.2025.1024.1118.
[26] M. Faizal, A. Shabir and A. K. Khan, “Consequences of Gödel’s Theorems on Quantum Gravity,” International Journal of Theoretical Physics 63, 290 (2024). DOI: https://doi.org/10.1007/s10773-024-05818-1.
[27] M. Faizal, A. Shabir and A. K. Khan, “Implications of Tarski’s Undefinability Theorem on the Theory of Everything,” EPL (Europhysics Letters) 148, 39001 (2024). DOI: https://doi.org/10.1209/0295-5075/ad80c2 [arXiv:2410.10903] (archivePrefix: arXiv)
[28] M. Faizal, A. Shabir and A. K. Khan, “Application of Chaitin’s Incompleteness Theorem to Quantum Gravity,” International Journal of Theoretical Physics 64, 194 (2025). DOI: https://doi.org/10.1007/s10773-025-06065-8.
[29] M. Faizal, A. Shabir and A. K. Khan, “Consequences of Gödel Theorems on Third Quantized Theories like String Field Theory and Group Field Theory,” Nuclear Physics B 1010, 116774 (2025). DOI: https://doi.org/10.1016/j.nuclphysb.2024.116774 [arXiv:2407.12313] (archivePrefix: arXiv) 
Journal of Holography Applications in Physics
Volume 6, Issue 3
March 2026
Pages 20-30
  • Receive Date: 06 December 2025
  • Revise Date: 31 January 2026
  • Accept Date: 31 January 2026