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Cited by 240Noncommutative and Quantum Gravity TheoriesAstrophysics and Cosmic PhenomenaCosmology and Gravitation Theories

Threshold effects and Planck scale Lorentz violation: Combined constraints from high energy astrophysics

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Jacobson, T., Liberati, S., Mattingly, D.·2003·Physical Review D
DOI 10.1103/physrevd.67.124011
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Abstract

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, the photon decay constraint translates to kF/2 + c ≤ 4 × 10−16.

    “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]

  • A vacuum Čerenkov effect must be forbidden up to the highest observed UHECR energy.

    “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]

  • For n = 2 vacuum Čerenkov, the constraint in mSME parameters is c − |d| − kF/2 ≤ 10−16.

    “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]

  • If d ≠ 0, both helicities of electrons/positrons must satisfy kF/2 + (c ± d) ≤ 4 · 10−16.

    “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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2 of the 114 references couldn’t be matched to a known paper.

Research works printed but not linked: 1

  1. [80]T. Miller et al. , ' 'From AMANDA to IceCube: Current and future high energy neutrino telescopes at the South Pole'. Published in the Proceedings of 'Baltimore 1999, Neutrinos in the new millennium', pg. 47-61. Edited by G. Domokos, S. Kovesi-Domokos. Singapore, World Scientific, 2000. C. Spiering [AMANDA Collaboration], Annalen Phys. 10 , 131 (2001).

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Authors
Jacobson, T., Liberati, S., & Mattingly, D.
Affiliations
University of Maryland, College Park (US)
ORCID
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
2003-06-11
Volume
67
Issue
12
ISSN
  • 0556-2821 (ISSN-L)
  • 1089-4918
DOI
10.1103/physrevd.67.124011
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
Licence
link.aps.org/licenses/aps-default-license (vor)
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 › Statistical and Nonlinear 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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