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Threshold effects and Planck scale Lorentz violation: Combined constraints from high energy astrophysics
Open accessAbstract
Recent work has shown that dispersion relations with Planck scale Lorentz violation can produce observable effects at energies many orders of magnitude below the Planck energy M. This opens a window on physics that may reveal quantum gravity phenomena. It has already constrained the possibility of Planck scale Lorentz violation, which is suggested by some approaches to quantum gravity. In this work we carry out a systematic analysis of reaction thresholds, allowing unequal deformation parameters for different particle dispersion relations. The thresholds are found to have some unusual properties compared with standard ones, such as asymmetric momenta for pair creation and upper thresholds. The results are used together with high energy observational data to determine combined constraints. We focus on the case of photons and electrons, using vacuum \ifmmode \check{C}\else \v{C}\fi{}erenkov, photon decay, and photon annihilation processes to determine order unity constraints on the parameters controlling $O(E/M)$ Lorentz violation. Interesting constraints for protons (with photons or pions) are obtained even at $O({(E/M)}^{2}),$ using the absence of vacuum \ifmmode \check{C}\else \v{C}\fi{}erenkov and the observed GZK cutoff for ultrahigh energy cosmic rays. A strong \ifmmode \check{C}\else \v{C}\fi{}erenkov limit using atmospheric PeV neutrinos is possible for $O(E/M)$ deformations provided the rate is high enough. If detected, ultrahigh energy cosmological neutrinos might yield limits at or even beyond $O({(E/M)}^{2}).$
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“For n = 2 with CPT preserved we have [154]. If we set d = 0 in Equation (39) so that there is no helicity dependence, this translates to the constraint kF/2 + c ≤ 4 × 10−16.”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [154]
In the citing paper
“A complimentary constraint to the GZK analysis can be derived by recognizing that 1019 − 1020 eV protons reach us — a vacuum Čerenkov effect must be forbidden up to the highest observed UHECR energy [88, 154, 119].”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [154]
In the citing paper
“For n = 2 the constraint is [154], where is the coefficient for one of the electron helicities. In terms of the mSME parameters this condition can be written as c − |d| − kF/2 ≤ 10−16.”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [154]
In the citing paper
“If d ≠ 0 then both helicities of electrons/positrons must satisfy this bound since the photon has a decay channel into every possible combination of electron/positron helicity. The corresponding limit is kF/2 + (c ± d) ≤ 4 · 10−16.”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [154]
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BackgroundEffects of Lorentz invariance violation on the ultra-high energy cosmic rays spectrum
Lang, R. G. (2017) · doi:10.11606/d.76.2017.tde-13042017-143220 · Cited by 4
Loop Quantum Gravity Modification of the Compton EffectPreprint
Nozari, K., & Sadatian, S. D. (2006) · Cited by 4
Momentum-resolved probing of Lorentz-violating dispersion relations via Unruh-DeWitt detector
Xu, H. (2025) · Physics Letters B · doi:10.1016/j.physletb.2025.139760 · Cited by 3
“…energy-momentum relation: where { κ i } are dimensionless coefficients parametrizing Lorentz violation. effect, gravitational coupling and additional wave modes in high energy physics [5, 6] to condensed matter analyses of quantum phase transitions in dipolar Bose-Einstein condensates [7, 8].”
Vacuum Cherenkov radiation for nonminimal dimension-5 Lorentz violation
Petrov, A. Y., Schreck, M., & Vieira, A. R. (2026) · The European Physical Journal C · doi:10.1140/epjc/s10052-025-15220-8 · Cited by 3
“Numerical approaches will be indispensable to compute decay and radiated-energy rates at all orders in Lorentz violation.”
Simulating electromagnetic cascades with Lorentz invariance violation
Saveliev, A., & Batista, R. A. (2024) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ad40f1 · Cited by 3
New Constraint for Isotropic Lorentz Violation from LHC Data
Amram, D., Bouzoud, K., Chanon, N. P., Hansen, H., Ribeiro, M. R., & Schreck, M. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.211801 · Cited by 3
Saveliev, A., Batista, R. A., & Mishin, F. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.083001 · Cited by 3
“In this case, as shown in [42], the threshold value can be written as where The constraints on the threshold momentum in the χ e 2 – χ γ 2 parameter space are shown in Fig.”
Lorentz Invariance Violation on UHECR propagation
Martínez, H., & Pérez-Lorenzana, A. (2013) · Journal of Physics Conference Series · doi:10.1088/1742-6596/468/1/012005 · Cited by 3
Satunin, P., & Sharofeev, A. (2024) · The European Physical Journal C · doi:10.1140/epjc/s10052-024-13152-3 · Cited by 3
Динамическое образование лоренц-инвариантности и киральных фермионов
Харук, И. В., Kharuk, I. V., Сибиряков, С. М., & Sibiryakov, S. M. (2016) · Теоретическая и математическая физика · doi:10.4213/tmf9104 · Cited by 3
Metadata
- Authors
- Jacobson, T., Liberati, S., & Mattingly, D.
- Affiliations
- University of Maryland, College Park (US)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2003-06-11
- Volume
- 67
- Issue
- 12
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2064950588
- Cited by
- 240
- References
- 114
- Citations by year
- 2026: 5 · 2025: 6 · 2024: 5 · 2023: 10 · 2022: 9 · 2021: 11 · 2020: 6 · 2019: 4 · 2018: 5 · 2017: 9 · 2016: 7 · 2015: 6 · 2014: 10 · 2013: 9 · 2012: 9
- FWCI
- 14.76
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- SDL (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Astrophysics and Cosmic Phenomena
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- Lorentz violation, Planck scale, dispersion relation, response threshold, quantum gravity, photon decay, photon annihilation, pair production, GZK cutoff, ultra-high-energy cosmic rays, atmospheric neutrinos, PeV neutrinos, protons, pion
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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