This is a wiki page containing experimental bounds on quantum gravity searches. After the table, there are some notes regarding articles mentioned in the table. To see the inserted image in a full-screen mode please click on the image.

**Table of content**

Reference table

Details of the articles

**Abbreviations:**

NON - no value for that attribute in the article

NA - process is not allowed

**Reference table**

Messenger | Effect | Source name | Source type | Distance | Subluminal E_{QG,1} > (x GeV) |
Subluminal E_{QG,2} > (x GeV) |
Superluminal E_{QG,1} > (x GeV) |
Superluminal E_{QG,2} > (x GeV) |
Δγ | 𝛅_{n} |
Authors | Publication year |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Cosmic rays | Neutral pion decay | NON | NON | NON | NON | NON | NON | NON | - | - | S. R. Coleman et al. | 1999 |

Cosmic rays | Pair production | NON | NON | NON | >10^{20} |
NON | NON | NON | - | - | T. Jacobson et al. | 2003 |

Cosmic rays | Neutral pion decay | NON | NON | NON | NON | NON | NON | NON | - | - | L. Maccione et al. | 2008 |

Cosmic rays | Pair production & Vacuum Cherenkov radiation | NON | NON | NON | - | 5x10^{25} |
NON | NON | - | > -2.4 x 10^{-7} |
M. Galaverni et al. | 2008 |

Cosmic rays | Proton Vacuum Cherenkov radiation | NON | NON | NON | k <= 6 x 10^{-20} |
NON | NON | NON | - | - | F.R. Klinkhamer et al. | 2008 |

Cosmic rays | Photon pair production | NON | NON | NON | NON | NON | NON | NON | - | - | G. Rubtsov et al. | 2014 |

Gamma rays | Time delay | Mrk 421 | AGN | z = 0.031 | 0.4 x 10^{17} |
NON | NON | NON | - | - | S.D. Biller et al. | 1999 |

Gamma rays | Time delay | Mrk 501 | AGN | z = 0.034 | 2.1 x 10^{17} |
2.6 x 10^{10} |
NON | NON | - | - | J. Albert et al. | 2008 |

Gamma rays | Time delay | Mrk 501 | AGN | z = 0.034 | 3.0 x 10^{17} |
5.7 x 10^{10} |
NON | NON | - | - | M. Martínez et al. | 2009 |

Gamma rays | Time delay | PKS 2155-304 | AGN | z = 0.116 | 7.2 x 10^{17} |
1.4 x 10^{9} |
NON | NON | - | - | F. Aharonian et al. | 2008 |

Gamma rays | Time delay | PKS 2155-304 | AGN | z = 0.116 | 5.2 x 10^{17} |
NON | NON | NON | - | - | F. Aharonian et al. | 2008 |

Gamma rays | Time delay | PKS 2155-304 | AGN | z = 0.116 | 2.1 x 10^{18} |
6.4 x 10^{10} |
NON | NON | - | - | A. Abramowski et al. | 2011 |

Gamma rays | Time delay | GRB 090510 | GRB | z = 0.9 | 2.2 x 10^{19} |
4.0 x 10^{10} |
3.9 x 10^{19} |
3.0 x 10^{10} |
- | - | V. Vasileiou et al. | 2013 |

Gamma rays | Time delay | GRB 080916C | GRB | z = 4.35 | 1.3 x 10^{18} |
2.8 x 10^{9} |
3.9 x 10^{18} |
5.6 x 10^{9} |
- | - | V. Vasileiou et al. | 2013 |

Gamma rays | Time delay | GRB 090902B | GRB | z = 1.822 | 1.3 x 10^{18} |
5.8 x 10^{9} |
3.9 x 10^{18} |
1.1 x 10^{10} |
- | - | V. Vasileiou et al. | 2013 |

Gamma rays | Time delay | GRB 090926A | GRB | z = 2.107 | 8.8 x 10^{18} |
7.8 x 10^{9} |
1.8 x 10^{18} |
4.1 x 10^{9} |
- | - | V. Vasileiou et al. | 2013 |

Gamma rays | Time delay | Crab | Pulsar | d = 2 kpc | 3.0 x 10^{17} |
7.0 x 10^{9} |
NON | NON | - | - | N. Otte | 2011 |

Gamma rays | Time delay | Crab | Pulsar | d = 2 kpc | 1.9 x 10^{17} |
NON | 1.7 x 10^{17} |
NON | - | - | B. Zitzer et al. | 2013 |

Gamma rays | Time delay | PG 1553+113 | AGN | z = 0.49 | 4.1 x 10^{17} |
2.1 x 10^{10} |
2.8 x 10^{17} |
1.7 x 10^{10} |
- | - | A. Abramowski et al. | 2015 |

Gamma rays | Time delay | Vela | Pulsar | d = 0.3 kpc | 4.0 x 10^{15} |
NON | 3.7 x 10^{15} |
NON | - | - | M. Chrétien et al. | 2015 |

Gamma rays | Pair production on EBL | Multiple | AGN | z = 0.019 − 0.287 | 8.6 x 10^{18} |
NON | NON | NON | - | - | J. Biteau et al. | 2015 |

Gamma rays | Bethe–Heitler | Crab | Nebula | d = 2 kpc | NON | 2.1 x 10^{11} |
NON | NON | - | - | G. Rubtsov et al. | 2017 |

Gamma rays | Time delay | Crab | Pulsar | d = 2 kpc | 1.1 x 10^{17} |
1.4 x 10^{10} |
1.1 x 10^{17} |
1.5 x 10^{10} |
- | - | M. L. Ahnen et al. | 2017 |

Gamma rays | Time delay | Crab | Pulsar | d = 2 kpc | 5.5 x 10^{17} |
5.9 x 10^{10} |
4.5 x 10^{17} |
5.3 x 10^{10} |
- | - | M. L. Ahnen et al. | 2017 |

Gamma rays | Pair production on EBL | Mrk 501 | AGN | z = 0.034 | 2.6 x 10^{19} |
7.8 x 10^{11} |
NON | NON | - | - | H. Abdalla et al. | 2019 |

Gamma rays | Time delay | Mrk 501 | AGN | z = 0.034 | 3.6 x 10^{17} |
8.5 x 10^{10} |
2.6 x 10^{17} |
7.3 x 10^{10} |
- | - | H. Abdalla et al. | 2019 |

Gamma rays | Pair production on EBL | Multiple | AGN | z = 0.031 − 0.188 | 6.9 x 10^{19} |
1.6 x 10^{12} |
NON | NON | - | - | R. G. Lang et al. | 2019 |

Gamma rays | Photon decay | Multiple | Galactic | d = 1.55 − 2.37 kpc | NA | NA | 2.2 x 10^{22} |
8.0 x 10^{13} |
- | - | A. Albert et al. | 2020 |

Gamma rays | Photon decay | J1825-134 | Galactic | d = 1.55 kpc | NA | NA | 1.4 x 10^{22} |
5.8 x 10^{13} |
- | - | A. Albert et al. | 2020 |

Gamma rays | Photon decay | J1907+063 | Galactic | d = 2.37 kpc | NA | NA | 9.9 x 10^{21} |
4.7 x 10^{13} |
- | - | A. Albert et al. | 2020 |

Gamma rays | Photon splitting | J1825-134 | Galactic | d = 1.55 kpc | NA | NA | NON | 1.2 x 10^{15} |
- | - | A. Albert et al. | 2020 |

Gamma rays | Photon splitting | J1907+063 | Galactic | d = 2.37 kpc | NA | NA | NON | 1.0 x 10^{15} |
- | - | A. Albert et al. | 2020 |

Gamma rays | Time delay | GRB190114C | GRB | z = 0.4245 | 5.8 x 10^{18} |
6.3 x 10^{10} |
5.5 x 10^{18} |
5.6 x 10^{10} |
- | - | V. A. Acciari et al. | 2020 |

Gamma rays | Photon decay | J2032+4102 | Stellar cluster | d = 1.4 kpc | NA | NA | 1.7 x 10^{24} |
1.4 x 10^{15} |
- | - | Z. Cao et al. | 2021 |

Gamma rays | Photon splitting | J2032+4102 | Stellar cluster | d = 1.4 kpc | NA | NA | NON | 2.5 x 10^{16} |
- | - | Z. Cao et al. | 2021 |

Neutrinos | Time delay | TXS 0506+056 | AGN | z = 0.3365 | 3.2 x 10^{15} |
4.0 x 10^{10} |
NON | NON | 8.5 x 10^{-6} |
- | J-J. Wei et. al | 2018 |

Neutrinos | Time delay | TXS 0506+056 | AGN | z = 0.3365 | 3 x 10^{16} |
1.0 x 10^{11} |
NON | NON | NON | - | J. Ellis et. al | 2018 |

Neutrinos | Time delay | PKS B1424-418 | AGN | z = 1.522 | 1.1 x 10^{17} |
7.2 x 10^{11} |
NON | NON | 7.0 x 10^{-6} |
- | Z-Y. Wang et. al | 2016 |

Neutrinos | Time delay | GRB 101213A | GRB | z = 0.414 | 1.1 x 10^{19} |
4.7 x 10^{11} |
NON | NON | 1.0 x 10^{-10} |
- | J-J. Wei et. al | 2016 |

Neutrinos | Time delay | GRB 110101B | GRB | z = 0.17 | 1.2 x 10^{19} |
8.1 x 10^{11} |
NON | NON | 1.6 x 10^{-10} |
- | J-J. Wei et. al | 2016 |

Neutrinos | Time delay | GRB 110521B | GRB | z = 0.237 | 6.3 x 10^{19} |
6.0 x 10^{11} |
NON | NON | 3.0 x 10^{-12} |
- | J-J. Wei et. al | 2016 |

Neutrinos | Time delay | GRB 111212A | GRB | z = 0.269 | 5.8 x 10^{19} |
1.7 x 10^{12} |
NON | NON | 3.5 x 10^{-11} |
- | J-J. Wei et. al | 2016 |

Neutrinos | Time delay | GRB 120114A | GRB | z = 0.197 | 6.3 x 10^{19} |
2.0 x 10^{11} |
NON | NON | 1.9 x 10^{-11} |
- | J-J. Wei et. al | 2016 |

Neutrinos | Time delay | Multiple | GRB | NON | 6.5 x 10^{17} |
NON | NON | NON | NON | - | Y. Huang et. al | 2018 |

Neutrinos | Time delay | SN1987a | Supernova | d = 51.4 kpc | NON | NON | NON | NON | 8.0 x 10^{-03 } |
- | L. Krauss et. al | 1988 |

Neutrinos | Time delay | SN1987a | Supernova | d = 51.4 kpc | NON | NON | NON | NON | 3.4 x 10^{-03 } |
- | M. J. Longo | 1988 |

Neutrinos | Time delay | SN1987a | Supernova | d = 51.4 kpc | 2.7 x 10^{10 } |
4.6 x 10 ^{4 } |
2.5 x 10^{10 } |
4.1 x 10 ^{4 } |
NON | - | J. Ellis et al. | 2008 |

Neutrinos | Vacuum Pair Prodiction | NON | NON | NON | NA | NA | 7.6 x 10^{24 } |
3.9 x 10 ^{15 } |
NON | - | J. M. Carmona et al. | 2019 |

Neutrinos | Vacuum Pair Prodiction | NON | NON | NON | NA | NA | NON | 1.4 x 10 ^{17 } |
NON | - | F. W. Stecker et al. | 2014 |

Gravitational waves | Time delay | GW17081 | Neutron star merger | z = 0.008 | NON | NON | NON | NON | 1x 10 ^{-6} |
- | B. P. Abbott et al. | 2017 |

**Details of the articles**

**L. Krauss et al. (1988)**

https://doi.org/10.1103/PhysRevLett.60.176

https://ui.adsabs.harvard.edu/abs/1988PhRvL..60..176K

https://www.osti.gov/scitech/biblio/5717284

https://lib-extopc.kek.jp/preprints/PDF/1988/8803/8803123.pdf

**Title:**Test of the Weak Equivalence Principle for Neutrinos and Photons**Authors:**Lawrence M. Krauss, Scott Tremaine- Limits on neutrino velocity δ = v
_{ν }−1 from the time delay of neutrinos with respect to an optical burst of the supernova 1987a.

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**M. J. Longo (1988)**

https://doi.org/10.1103/PhysRevLett.60.173

https://ui.adsabs.harvard.edu/abs/1988PhRvL..60..173L

https://www.osti.gov/scitech/biblio/5598017

**Title:**New precision tests of the Einstein Equivalence Principle from SN1987a**Author:**Michael J. Longo- From the time delay between the neutrino and optical signal of SN1987A, the author derives bounds on the parameter γ
_{ν}. This parameter is characteristic of post-newtonian formalism and it is predicted to be equal to unity in General Relativity. - Studying the time delay between neutrinos of different energies, it sets a bound on the energy dependence of this γ
_{ν}parameter:

γ_{ν}(40 MeV) - γ_{ν}(7.5 MeV) < 1.6 x 10^{-6}.

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**S. R. Coleman et al. (1999)**

**Title:**High-Energy Tests of Lorentz Invariance**Authors:**S. R. Coleman, S. L. Glashow

https://arxiv.org/abs/hep-ph/9812418

https://doi.org/10.1103/PhysRevD.59.116008

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**S. D. Biller et al. (1999)**

https://arxiv.org/abs/gr-qc/9810044

https://ui.adsabs.harvard.edu/abs/1999PhRvL..83.2108B/abstract

https://inspirehep.net/literature/477814

**Title:**Limits to Quantum Gravity Effects from Observations of TeV Flares in Active Galaxies**Authors:**S.D. Biller, A.C. Breslin, J. Buckley, M. Catanese, M. Carson, D.A. Carter-Lewis, M.F. Cawley, D.J. Fegan, J. Finley, J.A. Gaidos, A.M. Hillas, F. Krennrich, R.C. Lamb, R. Lessard, C. Masterson, J.E. McEnery, B. McKernan, P. Moriarty, J. Quinn, H.J. Rose, F. Samuelson, G. Sembroski, P. Skelton, T.C. Weekes**Data:**Markarian 421 from May 15, 1996; observed by the**Whipple**telescope- First test of LIV performed using data from IACTs
- Flux doubling time of less than 15 minutes and photons of energies up to
**several TeV** - The authors used the likelihood-ratio test to compare the contents of time bins in the two energy ranges (E 2 TeV)

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**T. Jacobson et al. (2003)**

**Title:**Threshold effects and Planck scale Lorentz violation: combined constraints from high energy astrophysics**Authors:**T. Jacobson, S. Liberati, D. Mattingly

https://arxiv.org/abs/hep-ph/0209264

https://doi.org/10.1103/PhysRevD.67.124011

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**M. Galaverni et al. (2008)**

https://arxiv.org/abs/0708.1737

https://doi.org/10.1103/PhysRevLett.100.021102

**Title:**Lorentz Violation for Photons and Ultra-High Energy Cosmic Rays**Authors:**M. Galaverni, G. Sigl**Modified Dispersion Relation:**ω^{ 2}= k^{2}+𝛅_{n}k^{2}(k/M_{Pl})^{n}**Constraints on photon terms**

SubLuminal n=1: 𝛅_{1} > -2.4 10^{-15}

SubLuminal n=2: 𝛅_{2} > -2.4 10^{-7}

**Resulting LIV effect:**Photon component in cosmic rays above 10^{(19)}eV

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**F. R. Klinkhamer et al. (2008)**

**Title:**Addendum: Ultrahigh-energy cosmic-ray bounds on nonbirefringent modified Maxwell theory**Authors:**F. R. Klinkhamer, M. Risse

https://doi.org/10.1103/PhysRevD.77.117901

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**J. Albert et al. (2008)**

https://arxiv.org/abs/0708.2889

https://ui.adsabs.harvard.edu/abs/2008PhLB..668..253M/abstract

https://inspirehep.net/literature/758764

**Title:**Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope**Authors:**J. Albert et al. (for the**MAGIC**Collaboration), John Ellis, N.E. Mavromatos, D.V. Nanopoulos, A.S. Sakharov, E.K.G. Sarkisyan**Data:**…

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**J. Ellis et al. (2008)**

https://arxiv.org/abs/0805.0253

https://doi.org/10.1103/PhysRevD.78.033013

https://ui.adsabs.harvard.edu/abs/arXiv:0805.0253

http://cds.cern.ch/record/1102652

https://hal.archives-ouvertes.fr/in2p3-00329984

**Title:**Probes of Lorentz Violation in Neutrino Propagation**Authors:**John Ellis, Nicholas Harries, Anselmo Meregaglia, André Rubbia, Alexander S. Sakharov**Neutrino data**: from SN1987a at the Kamioka II, IMB and Baksan experiments.- Limit based on the study of time delays between neutrinos, not between neutrinos and photons.*Analysis based on a
**Minimal Dispersion Method**. - Bounds are derived for a linear and quadratic model in the subluminal and superluminal regime.

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**F. Aharonian et al. (2008)**

https://arxiv.org/abs/0810.3475

https://ui.adsabs.harvard.edu/abs/2008PhRvL.101q0402A/abstracthttps://inspirehep.net/literature/799977

**Title:**Limits on an Energy Dependence of the Speed of Light from a Flare of the Active Galaxy PKS 2155-304**Authors:**U. Barres de Almeida, R. Bühler and A. Jacholkowska for the**H.E.S.S.**collaboration**Data:**PKS 2155-304 from July 28, 2006

- Time delays between light curves of different energies were sought in order to quantify a possible energy dispersion. For this, two different methods were applied: modified cross correlation function and continuous wavelet transform

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**L. Maccione et al. (2008)**

**Title:**GZK photon constraints on Planck scale Lorentz violation in QED**Authors:**L. Maccione, S. Liberati

https://arxiv.org/abs/0805.2548https://doi.org/10.1088/1475-7516/2008/08/027

**M. Martínez et al. (2009)**

https://arxiv.org/abs/0803.2120

https://ui.adsabs.harvard.edu/abs/2009APh….31..226M/abstracthttps://inspirehep.net/literature/781375

**Title:**A new method to study energy-dependent arrival delays on photons from astrophysical sources**Authors:**M. Martínez and M. Errando**Data:**Markarian 501 from July 9, 2006 (observed by the**MAGIC**collaboration)- First application of the maximum likelihood method
- The light curve was modeled with a Gaussian superimposed on top of a constant baseline emission from the source.

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**A. Abramowski et al. (2011)**

https://arxiv.org/abs/1101.3650

https://ui.adsabs.harvard.edu/abs/2011APh….34..738H/abstracthttps://inspirehep.net/literature/884748

**Title:**Search for Lorentz Invariance breaking with a likelihood fit of the PKS 2155-304 flare data taken on MJD 53944**Authors:**J. Bolmont and A. Jacholkowska for the**H.E.S.S.**collaboration**Data:**PKS 2155-304 from July 28, 2006*Following a previous publication of the (H.E.S.S.) collaboration (F. Aharonian et al.), a more sensitive event-by-event method consisting of a likelihood fit is applied to PKS 2155-304 flare data of MJD 53944 (July 28, 2006) as used in the previous publication.*Analysis was focused on the initial 4000 s of the observation(flux and its variability were highest)*Only**3526 events**remained (out of more than 11 000 in the original data set) in the**0.25–4.0 TeV**energy range.

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**N. Otte (2011)**

doi:10.7529/ICRC2011/V07/1302https://ui.adsabs.harvard.edu/abs/2011ICRC….7..256O/abstracthttps://inspirehep.net/literature/1127202

**Title:**Prospects of performing Lorentz invariance tests with VHE emission from Pulsars**Authors:**N. Otte***Data:**Crab Pulsar**VERITAS**collaboration…

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**B. Zitzer et al. (2013)**

https://arxiv.org/abs/1307.8382

https://ui.adsabs.harvard.edu/abs/2013ICRC…33.2768Z/abstracthttps://inspirehep.net/literature/1245458

**Title:**Lorentz Invariance Violation Limits from the Crab Pulsar using VERITAS**Authors:**B. Zitzer for the**VERITAS**collaboration***Data:**Crab Pulsar…

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**V. Vasileiou et al. (2013)**

https://arxiv.org/abs/1305.3463

https://ui.adsabs.harvard.edu/abs/2013PhRvD..87l2001V/abstracthttps://inspirehep.net/literature/1233487

**Title:**Constraints on Lorentz Invariance Violation from Fermi-Large Area Telescope Observations of Gamma-Ray Bursts**Authors:**V. Vasileiou, A. Jacholkowska, F. Piron, J. Bolmont, C. Couturier, J. Granot, F. W. Stecker, J. Cohen-Tanugi, F. Longo**Data:**GRB 080916C, GRB 090510, GRB 090902B, and GRB 090926A obtained with*Three different analysis methods were used on each source: pair view, sharpness maximisation method and maximum likelihood..*Fermi-*LAT

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**F. W. Stecker et al. (2014)**

https://arxiv.org/abs/1411.5889

https://doi.org/10.1103/PhysRevD.91.045009

https://ui.adsabs.harvard.edu/abs/arXiv:1411.5889

**Title:**Searching for Traces of Planck-Scale Physics with High Energy Neutrinos**Authors:**Floyd W. Stecker, Sean T. Scully, Stefano Liberati, David Mattingly.- This analysis includes
**vacuum pair production**and**neutrino splitting**in numerical simulations.*It is assumed that the drop off in the neutrino flux above ∼ 2 PeV is caused by Planck scale physics.*The results are prior to the IceCube event compatible with the Glashow resonance.*The authors use an**Effective Field Theory**description for**Lorentz Invariance Violation**.

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**A. Abramowski et al. (2015)**

https://arxiv.org/abs/1501.05087

https://ui.adsabs.harvard.edu/abs/2015ApJ…802…65A/abstracthttps://inspirehep.net/literature/1340438

**Title:**The 2012 flare of PG 1553+113 seen with H.E.S.S. and*Fermi*-LAT**Authors:**D.A. Sanchez, F. Brun, C. Couturier, J. Lefaucheur and J.-P. Lenain for the**H.E.E.S.**collaboration**Data:**PG 1553+113 from April 26 and 27, 2012*The redshift of the source had been only loosely constrained prior to this study*Signal to background ratio = 2 -> PDF for the background had to be introduced into the likelihood function for the first time*Energy range**300–789 GeV***Maximum likelihood method was used to constrain LIV energy scale

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**M. Chrétien et al. (2015)**

https://arxiv.org/abs/1509.03545

https://ui.adsabs.harvard.edu/abs/2015ICRC…34..764C/abstracthttps://inspirehep.net/literature/1393044

**Title:**Constraining photon dispersion relations from observations of the Vela pulsar with H.E.S.S**Authors:**M. Chrétien, J. Bolmont and A. Jacholkowska for the**H.E.S.S.**collaboration**Data:**Vela pulsar; 24h of good quality data from March 2013 to April 2014*Energy range was**20-100 GeV**20 to 100 GeV, ∼9300 excess events were associated to the pulsar and signal to noise ratio was ∼0.025*Maximum likelihood method was used to constrain LIV energy scale. The signal template was obtained from the fitting of the low energy (20–45 GeV) events from the ON phase region by an asymetrical Lorentzian function (for the signal) plus a constant (for the background).

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**J. Biteau et al. (2015)**

https://arxiv.org/abs/1502.04166

https://ui.adsabs.harvard.edu/abs/2015ApJ…812…60B/abstracthttps://inspirehep.net/literature/1344977

**Title:**The Extragalactic Background Light, the Hubble Constant, and Anomalies: Conclusions from 20 Years of TeV Gamma-ray Observations**Authors:**J. Biteau1 and D. A. Williams**Data:**86 published gamma-ray spectra of 30 blazars*The first experimental test of LIV on the EBL absorption of gamma rays using data from IACTs*A total of ∼270,000 gamma rays constituted this gamma-ray sample*The effect of LIV was quantified using a test statistic (TS)

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**Z-Y. Wang et al. (2016)**

https://arxiv.org/abs/1602.06805

https://doi.org/10.1103/PhysRevLett.116.151101

https://ui.adsabs.harvard.edu/abs/2016PhRvL.116o1101W

**Title:**Testing the Equivalence Principle and Lorentz Invariance with PeV Neutrinos from Blazar Flares**Authors:**Zi-Yi Wang, Ruo-Yu Liu, Xiang-Yu Wang*Based on the association of the giant flare of the blazar PKS B1424-418 with a PeV neutrino event from**IceCube**.**Neutrino event:**IC 35 as from Supplementary Table 1 in https://arxiv.org/abs/1405.5303***Neutrino energy:**(2004^{+236}_{-262}

) TeV

**Position:**median positional uncertainty of R50 = 15.9◦ centered at the coordinate RA=208.4◦, Dec=−55.8◦ (J2000).- A time delay of
**Δt = 160 days**is estimated.

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**J-J. Wei et al. (2016)**

https://arxiv.org/abs/1603.07568

https://doi.org/10.1088/1475-7516/2016/08/031

https://ui.adsabs.harvard.edu/abs/2016JCAP…08..031W

**Title:**Limits on the Neutrino Velocity, Lorentz Invariance, and the Weak Equivalence Principle with TeV Neutrinos from Gamma-Ray Bursts**Authors:**Jun-Jie Wei, Xue-Feng Wu, He Gao, Peter Mészáros- Based on the study of the time delays between the TeV neutrinos and gamma-ray photons from GRBs.
- It considers 5 neutrino events measured at IceCube, as in Ref.
- The limits reported in the Reference table are derived taking into account the duration of the GRB. Hence, they are considered to be conservative. They correspond to Table 2 from the original article.

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**G. Rubtsov et al. (2017)**

https://arxiv.org/abs/1611.10125

https://ui.adsabs.harvard.edu/abs/2017JCAP…05..049R/abstract

https://inspirehep.net/literature/1500959

**Title:**Constraints on violation of Lorentz invariance from atmospheric showers initiated by multi-TeV photons**Authors:**G. Rubtsov, P. Satunin and S. Sibiryakov**Data:**Two independent measurements of the Crab nebula spectrum obtained by**HEGRA**collaboration (385 h between 1997 and 2002)and**H.E.S.S.**collaboration (4.4 h during the flaring episode in March 2013)- The
**highest energy bin**in the**HEGRA**collaboration spectrum was centered at**75 GeV**. In the**H.E.S.S.**collaboration spectrum, the spectrum was determined up to**∼40 TeV**. - Maximum likelihood method was used to constrain LIV energy scale.

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**B. P. Abbott et al.(2017)**

https://arxiv.org/abs/1710.05834

https://doi.org/10.3847/2041-8213/aa920c

https://hal.archives-ouvertes.fr/hal-01645884

https://ui.adsabs.harvard.edu/abs/2017ApJ…848L..13A

**Title:**Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A**Collaborations:**LIGO Scientific, Virgo, Fermi-GBM and INTEGRAL Collaboration.**Date of the event:**2017 August 17.**Description:**Gravitational-wave event GW170817 was observed by the Advanced LIGO and Virgo detectors, and the gamma-ray burst (GRB) GRB 170817A was observed independently by the Fermi Gamma-ray Burst Monitor, and the Anti-Coincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory. The time delay was 1.74 s.- The difference between the speed of light and the speed of gravitational waves is found to be between -3 x 10
^{-15}and 7 x 10^{-16}times the speed of light. - Bounds on Lorentz Invariance Violation are derived in the framework of the SME too.

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**M. L. Ahnen et al.(2017)**

https://arxiv.org/abs/1709.00346

https://ui.adsabs.harvard.edu/abs/2017ApJS..232….9M/abstract

https://inspirehep.net/literature/1621246

**Title:**Constraining Lorentz invariance violation using the Crab Pulsar emission observed up to TeV energies by MAGIC**Authors:**M. Gaug for the**MAGIC**collaboration**Data:**∼326 h of excellent quality Crab Pulsar data- Three energy bands (mean energies ∼75 GeV, ∼465 GeV, and ∼770 GeV,) were defined for the analysis
- Dataset was analysed with two different methods:peak comparison and maximum likelihood analysis
- The likelihood included terms to describe nuisance parameters among which the parameters used to fit the pulse profile (used to evaluate systematic uncertainties in the analysis) and the background events (important in the case of pulsar located in a Nebula).

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**J._Ellis et al. (2018)**

https://arxiv.org/abs/1807.05155

https://www.sciencedirect.com/science/article/pii/S0370269318309821?via%3Dihub

https://ui.adsabs.harvard.edu/abs/2019PhLB..789..352E

http://cds.cern.ch/record/2631515

**Title:**Limits on Neutrino Lorentz Violation from Multimessenger Observations of TXS 0506+056**Authors:**John Ellis, Nikolaos E. Mavromatos, Alexander S. Sakharov, Edward K. Sarkisyan-Grinbaum- Based on the study of the time delay between a high-energy neutrino event at
**IceCube**with a flaring blazar TXS 0506+056. **Neutrino event:**IceCube-170922A**Neutrino energy:**290 TeV**Date of the neutrino event:**22 September 2017- Only the electromagnetic counterpart of the neutrino event as detected by
**MAGIC**is considered. - The time delay assumed is
**Δt = 10 days.** - The limits derived on LIV and violation of the WEP are stronger than similar analysis with a more conservative assumption for the time delay.

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**Y. Huang et al. (2018)**

https://arxiv.org/abs/1810.01652

https://doi.org/10.1038/s42005-018-0061-0

https://ui.adsabs.harvard.edu/abs/arXiv:1810.01652

**Title:**Lorentz violation from gamma-ray burst neutrinos**Authors:**Yanqi Huang, Bo-Qiang Ma- Based on the association of TeV and PeV neutrino events from IceCube with multiple GRBs.
- The authors explore the linear dependence between the time delay and the so-called LIV factor. The authors claim an energy scale of LIV at 6.5 x 10
^{17 }TeV, which we quote as a limit. - The analysis was later extended in order to set bounds on the coefficients of the Standard Model Extension (see Ref.)

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**J-J. Wei et al. (2018)**

https://arxiv.org/abs/1807.06504

https://doi.org/10.1016/j.jheap.2019.01.002

https://ui.adsabs.harvard.edu/abs/2019JHEAp..22….1W/abstract

**Title:**Multimessenger Tests of Einstein’s Weak Equivalence Principle and Lorentz Invariance with a High-energy Neutrino from a Flaring Blazar**Authors:**Jun-Jie Wei, Bin-Bin Zhang, Lang Shao, He Gao, Ye Li, Qian-Qing Ying, Xue-Feng Wu, Xiang-Yu Wang, Bing Zhang, Zi-Gao Dai.- Based on the study of the time delay between a high-energy neutrino event at
**IceCube**with a flaring blazar TXS 0506+056. **Neutrino event:**IceCube-170922A**Neutrino energy:**290 TeV**Date of the neutrino event:**22 September 2017- Electromagnetic counterpart detected by
**Fermi-LAT**,**AGILE**and**MAGIC** - A conservative assumption for the
**time delay**is made**Δt = 175 days.**

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**H. Abdalla et al. (2019)**

https://arxiv.org/abs/1901.05209

https://ui.adsabs.harvard.edu/abs/2019ApJ…870…93A/abstract

https://inspirehep.net/literature/1714057

**Title:**The 2014 TeV Gamma-ray Flare of Mrk 501 Seen with H.E.S.S.: Temporal and Spectral Constraints on Lorentz Invariance Violation**Authors:**N. Chakraborty, A. Jacholkowska, M. Lorentz, C. Perennes and C. Romoli for the**H.E.S.S**collaboration**Data:**Mrk 501 from 23-24 June, 2014 -> 1.8h; 4 consecutive observational runs(∼28 min each))

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- ZENITH ANGLE: 63°- 65°
- ENERGY THRESHOLD: ≳ 1 TeV
- AVERAGE INTEGRAL FLUX: I(> 1 TeV)= (4.4 ± 0.8
_{stat}± 1.8_{sys}) ×10^{-11}cm^{-2}s^{-1} - Data analysis reveals an exceptional gamma-ray flux at multi-TeV energies, with a rapid flux variability and an energy spectrum extending up to 20 TeV.
- In the signal region 1930 events were observed, versus 334 events in the background region
- Signal over background ratio: 46.5
- For ToF H
_{}= 67.74 km · s^{-1}Mpc^{-1}Ω_{m}= 0.31 and Ω_{Λ}= 0.69 - EBL MODEL: Franceschini et al. (2008)
- dl/dz not defined
- Fractional variability:0.188 ± 0.003 for time binning of seven minutes
- Intrinsic spectrum fitted by an intrinsic power law (Φ
_{int}(E_{γ}) = φ_{}E_{γ}^{−α}) - α = 2.03 ± 0.04
_{stat}± 0.2_{sys}

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**J. M. Carmona et al. (2019)**

https://arxiv.org/abs/1911.12710

https://doi.org/10.3390/sym11111419

https://ui.adsabs.harvard.edu/abs/arXiv:1911.12710

**Title:**Lorentz Violation Footprints in the Spectrum of High-Energy Cosmic Neutrinos - Deformation of the Spectrum of Superluminal Neutrinos from Electron-Positron Pair Production in Vacuum**Authors:**José Manuel Carmona, José Luis Cortés, José Javier Relancio, Maykoll A. Reyes.- Bounds are set on a linear and quadratic model for the energy of LIV based on the maximum neutrino energy observed by IceCube (2 PeV at that time).
- This result is previous to the observation of the event compatible with the Glashow resonance.
- The analysis considers
**Vacuum Pair Production**only (allowed only for**superluminal**neutrinos).

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**R. G. Lang et al. (2019)**

https://arxiv.org/abs/1810.13215

https://ui.adsabs.harvard.edu/abs/2019PhRvD..99d3015L/abstract

https://inspirehep.net/literature/1701232

**Title:**Improved limits on Lorentz invariance violation from astrophysical gamma-ray sources**Authors:**R. G. Lang, H. Martínez-Huerta and V. deSouza**Data:**

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**A. Albert et al. (2020)**

https://arxiv.org/abs/1911.08070

https://ui.adsabs.harvard.edu/abs/2020PhRvL.124m1101A/abstract

https://inspirehep.net/literature/1766062

**Title:**Constraints on Lorentz invariance violation from HAWC observations of gamma rays above 100 TeV**Authors:**J.P. Harding, J.T. Linnemann, J. Lundeen and H. Martínez-Huerta for the**HAWC**collaboration**Data:**

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**V. A. Acciari et al. (2020)**

https://arxiv.org/abs/2001.09728

https://ui.adsabs.harvard.edu/abs/2020PhRvL.125b1301A/abstract

https://inspirehep.net/literature/1777499

**Title:**Bounds on Lorentz Invariance Violation from MAGIC Observation of GRB 190114C**Authors:**G. D’Amico, D. Kerszberg, C. Perennes and T. Terzić for the**MAGIC**collaboration**Data:**GRB 190114C from January 14, 2019- First discovery of a GRB with IACTs ever
- Maximum likelihood method was applied

- The MAGIC observations started 62 s after the burst
- During the first 20 min of observation about
**700 gamma rays**were detected with the energies in the range of**0.3−2 TeV** - Two templates: theoretical and minimal

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**Z. Cao et al. (2021)**

https://arxiv.org/abs/2106.12350

**Title:**Exploring Lorentz Invariance Violation from Ultra-high-energy Gamma Rays Observed by LHAASO**Authors:**X.J. Bi, E.S. Chen, L.Q. Gao, Q. Yuan, Yi Zhang and S.P. Zhao for the**LHAASO**collaboration**Data:**

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