- Open Access
Hyperbolic recoil and the Unruh effect at CERN-NA63
Phys. Rev. D 112, 085016 – Published 17 October, 2025
DOI: https://doi.org/10.1103/8ynl-xpn4
Abstract
In this manuscript we examine the high energy channeling radiation datasets from the CERN-NA63 experiment using ultrarelativistic synchrotron emission. To incorporate recoil, we examine the standard quasiclassical formalism as well as develop a formalism that includes the Unruh effect by utilizing a hyperbolic recoil acceleration, based on conservation of momentum, in the classical synchrotron trajectory. We also perform an asymptotic radiation timescale analysis that predicts a photon energy threshold, beyond which the Unruh effect dominates. We then compare the classical, quasiclassical, and Unruh synchrotron theories to the data. We find that above threshold, the Unruh effect saturates the spectrum of all datasets.
Physics Subject Headings (PhySH)
Article Text
References (57)
- Leonard Emanuel Parker, The creation of particles in AN expanding universe, Ph.D. thesis, Harvard University, Massachusetts, 1967.
- L. Parker, Particle creation in expanding universes, Phys. Rev. Lett. 21, 562 (1968).
- Leonard Parker, Quantized fields and particle creation in expanding universes. I, Phys. Rev. 183, 1057 (1969).
- Leonard Parker, Quantized fields and particle creation in expanding universes. II, Phys. Rev. D 3, 346 (1971).
- Stephen W. Hawking, Black hole explosions?, Nature (London) 248, 30 (1974).
- Stephen A. Fulling, Nonuniqueness of canonical field quantization in Riemannian space-time, Phys. Rev. D 7, 2850 (1973).
- P. C. W. Davies, Scalar particle production in Schwarzschild and Rindler metrics, J. Phys. A 8, 609 (1975).
- W. G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14, 870 (1976).
- Ivan Agullo and Leonard Parker, Non-gaussianities and the Stimulated creation of quanta in the inflationary universe, Phys. Rev. D 83, 063526 (2011).
- L. Parker, Thermal radiation produced by the expansion of the Universe, Nature (London) 261, 20 (1976).
- L. H. Ford, Gravitational particle creation and inflation, Phys. Rev. D 35, 2955 (1987).
- Jeff Steinhauer, Murad Abuzarli, Tangui Aladjidi, Tom Bienaimé, Clara Piekarski, Wei Liu, Elisabeth Giacobino, Alberto Bramati, and Quentin Glorieux, Analogue cosmological particle creation in an ultracold quantum fluid of light, Nat. Commun. 13, 2890 (2022).
- Jahed Abedi, Luís Felipe Longo Micchi, and Niayesh Afshordi, GW190521: Search for echoes due to stimulated Hawking radiation from black holes, Phys. Rev. D 108, 044047 (2023).
- Jahed Abedi, Hannah Dykaar, and Niayesh Afshordi, Echoes from the abyss: Tentative evidence for Planck-scale structure at black hole horizons, Phys. Rev. D 96, 082004 (2017).
- Jahed Abedi and Niayesh Afshordi, Echoes from the abyss: A highly spinning black hole remnant for the binary neutron star merger GW170817, J. Cosmol. Astropart. Phys. 11 (2019) 010.
- Jahed Abedi, Niayesh Afshordi, Naritaka Oshita, and Qingwen Wang, Quantum black holes in the sky, Universe 6, 43 (2020).
- Jeffrey S. Nico, Maynard S. Dewey, Thomas R. Gentile, H. Pieter Mumm, Alan K. Thompson, Brian M. Fisher, Isaac Kremsky, Fred E. Wietfeldt, Timothy E. Chupp, Robert L. Cooper et al., Observation of the radiative decay mode of the free neutron, Nature (London) 444, 1059 (2006).
- M. J. Bales, R. Alarcon, C. D. Bass, E. J. Beise, H. Breuer, J. Byrne, T. E. Chupp, K. J. Coakley, R. L. Cooper, M. S. Dewey et al., Precision measurement of the radiative decay of the free neutron, Phys. Rev. Lett. 116, 242501 (2016).
- Tobias N. Wistisen, Antonino Di Piazza, Helge V. Knudsen, and Ulrik I. Uggerhøj, Experimental evidence of quantum radiation reaction in aligned crystals, Nat. Commun. 9, 795 (2018).
- Michael R. R. Good and Paul C. W. Davies, Infrared acceleration radiation, Found. Phys. 53, 53 (2023).
- Morgan H. Lynch, Evgenii Ievlev, and Michael R. R. Good, Accelerated electron thermometer: Observation of 1D Planck radiation, Prog. Theor. Exp. Phys. 2024, 023D01 (2024).
- S. A. Fulling and P. C. W. Davies, Radiation from a moving mirror in two dimensional space-time: Conformal anomaly, Proc. R. Soc. A 348, 393 (1976).
- P. C. W. Davies and S. A. Fulling, Radiation from moving mirrors and from black holes, Proc. R. Soc. A A356, 237 (1977).
- Morgan H. Lynch, Eliahu Cohen, Yaron Hadad, and Ido Kaminer, Experimental observation of acceleration-induced thermality, Phys. Rev. D 104, 025015 (2021).
- Morgan H. Lynch, Analysis of the CERN-NA63 radiation reaction data set, assuming the Rindler bath is composed of microscopic black holes, Phys. Rev. D 109, 105009 (2024).
- Morgan H. Lynch, Experimental observation of a Rindler horizon, Gen. Relativ. Gravit. 57, 116 (2025).
- T. N. Wistisen, A. Di Piazza, C. F. Nielsen, A. H. Sørensen, and U. I. Uggerhøj (CERN NA63 Collaboration), Quantum radiation reaction in aligned crystals beyond the local constant field approximation, Phys. Rev. Res. 1, 033014 (2019).
- A. Di Piazza, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, Extremely high-intensity laser interactions with fundamental quantum systems, Rev. Mod. Phys. 84, 1177 (2012).
- Gabriel Cozzella, André G. S. Landulfo, George E. A. Matsas, and Daniel A. T. Vanzella, Proposal for observing the Unruh effect using classical electrodynamics, Phys. Rev. Lett. 118, 161102 (2017).
- V. N. Baier, V. M. Katkov, and V. M. Strakhovenko, Electromagnetic Processes at High Energies in Oriented Single Crystals (World Scientific Publishing Company, Singapore, 1998).
- Vladimir Borisovich Berestetskii, Evgenii Mikhailovich Lifshitz, and Lev Petrovich Pitaevskii, Quantum Electrodynamics: Volume 4, Vol. 4 (Butterworth-Heinemann, Washington, DC, 1982).
- I. I. Abbasov, Boris M. Bolotovskiĭ, and V. A. Davydov, From the History of physics: High-frequency asymptotic behavior of radiation spectra of moving charges in classical electrodynamics, Sov. Phys. Usp. 29, 788 (1986).
- A. C. Booth, N. Charitonidis, P. Chatzidaki, Y. Karyotakis, E. Nowak, I. Ortega-Ruiz, M. Rosenthal, and P. Sala, Particle production, transport, and identification in the regime of , Phys. Rev. Accel. Beams 22, 061003 (2019).
- Giorgio Brianti, SPS North Experimental Area, Tech. Rep. (CERN, Geneva, 1973).
- U Uggerhøj and Kim Kirsebom, Electromagnetic Processes in Strong Crystalline Fields-2005-030, Tech. Rep. (CERN, Geneva, 2005), revised version submitted on 2006-06-16.
- U Uggerhøj, Na63’s enlightening experiments, CERN Courier 51, 15 (2011).
- J. U. Andersen, E. Bonderup, and R. H. Pantell, Channeling Radiation, Annu. Rev. Nucl. Part. Sci. 33, 453 (1983).
- V. N. Baĭer and V. M. Katkov, Processes involved in the motion of high energy particles in a magnetic field, Sov. J. Exp. Theor. Phys. 26, 854 (1968).
- V. I. Ritus, Quantum effects in the interaction of elementary particles with an intense electromagnetic field, Moscow Izdatel Nauka AN SSR Fiz. Inst. Trudy 111, 5 (1979).
- Lowell S. Brown and T. W. Kibble, Interaction of intense laser beams with electrons, Phys. Rev. 133, A705 (1964).
- R. Lieu, D. A. Leahy, and A. J. Evans, Conflict of conservation laws in cyclotron radiation, J. Phys. A 16, L669 (1983).
- R. Lieu, D. A. Leahy, and A. J. Evans, Basic conservation laws in the electromagnetic theory of cyclotron radiation: Further analysis, J. Phys. A 17, L91 (1984).
- R. Lieu, Quantum correspondence of cyclotron and synchrotron radiation, J. Phys. A 17, L223 (1984).
- P. Das Gupta, COMMENT: On ‘conflict of conservation laws in cyclotron radiation’, J. Phys. A 17, 2895 (1984).
- S. M. White and A. J. Parle, On ‘conflict of conservation laws in cyclotron radiation’, J. Phys. A 18, L111 (1985).
- A. J. Parle, Exact quantum recoil in magnetic fields, J. Phys. A 20, 2105 (1987).
- R. Lieu, Synchrotron radiation reaction, J. Phys. A 20, 2405 (1987).
- R. Lieu, J. J. Quenby, and T. J. Sumner, Cyclotron radiation, conservation laws, and a correction to the synchrotron loss formula, Astron. Astrophys. 176, L21 (1987).
- J. M. Cole et al., Experimental evidence of radiation reaction in the collision of a high-intensity laser pulse with a laser-wakefield accelerated electron beam, Phys. Rev. X 8, 011020 (2018).
- K. Poder et al., Experimental signatures of the quantum nature of radiation reaction in the field of an ultraintense laser, Phys. Rev. X 8, 031004 (2018).
- Lev Davidovich Landau and E. M. Lifshitz, The Classical Theory of Fields (Butterworth-Heinemann, Oxford, 1975).
- C. F. Nielsen, J. B. Justesen, A. H. Sørensen, U. I. Uggerhøj, and R. Holtzapple (CERN NA63 Collaboration), Experimental verification of the Landau-Lifshitz equation, New J. Phys. 23, 085001 (2021).
- A. Di Piazza, Exact solution of the Landau-Lifshitz equation in a plane wave, Lett. Math. Phys. 83, 305 (2008).
- Y. Hadad, L. Labun, J. Rafelski, N. Elkina, C. Klier, and H. Ruhl, Effects of radiation reaction in relativistic laser acceleration, Phys. Rev. D 82, 096012 (2010).
- P. Venkataramaiah, K. Gopala, A. Basavaraju, S. S. Suryanarayana, and H. Sanjeeviah, A simple relation for the Fermi function, J. Phys. G 11, 359 (1985).
- Ana Alonso-Serrano and Matt Visser, On burning a lump of coal, Phys. Lett. B 757, 383 (2016).
- Michael R. R. Good, Evgenii Ievlev, and Eric V. Linder, Particle creation from entanglement entropy, arXiv:2508.17067.