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
The Constrained Parameter 𝛅⁽ⁿ⁾ changes accordingly to each LIV parameter (see the corresponding reference)

 

Reference table

 

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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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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R. Aloisio et al. (2000)

• Title: Probing The Structure of Space-Time with Cosmic Rays
• Authors: R. Aloisio, P. Blasi, P.L. Ghia, A.F. Grillo

https://arxiv.org/abs/astro-ph/0001258
https://doi.org/10.1103/PhysRevD.62.053010

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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= k² +𝛅⁽ⁿ⁾k²(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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L. Maccione et al. (2) (2008)

https://arxiv.org/abs/0809.0220
https://doi.org/10.1103/PhysRevD.78.103003
https://ui.adsabs.harvard.edu/abs/arXiv:0809.0220

• Title: Gamma-ray polarization constraints on Planck scale violations of special relativity
• Authors: Luca Maccione, Stefano Liberati, Annalisa Celotti, John G. Kirk, Pietro Ubertini
• Method: comparison between the neutron star rotation axis - measured by the HST and Chandra satellites - and the gamma-ray polarization direction - observed by INTEGRAL.

 

• Limit |ξ| < 9 x 10⁻¹⁰ at 3σ C.L.

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

• Modified Dispersion Relation: E_γ ²= k² +Σ_m≥3 a_(m)k²(k/M_Pl)^m-2
• Constraints on photon terms

SubLuminal n=2 (n=m-2): a₍₄₎= 𝛅⁽²⁾ > - 10^-7
SubLuminal/SuperLuminal n=m-2: a₍₃₎=> |𝛅⁽²⁾| < 10^-15

• Modified Dispersion Relation: E ²=m²+p² +Σ_m≥3 b^(m)p²(p/M_Pl)^m-2
• Constraints on electrons/positrons terms

SubLuminal/SuperLuminal n=m-2: b⁽³⁾=> |𝛅⁽²⁾| < 10^-7

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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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S. Alighieri et al. (2010)

https://arxiv.org/abs/1003.4823
https://ui.adsabs.harvard.edu/abs/2010ApJ…715…33D
https://inspirehep.net/literature/849968

• Title: Limits on Cosmological Birefringence from the Ultraviolet Polarization of Distant Radio Galaxies
• Authors: S.di Serego Alighieri, F. Finelli, M. Galaverni
• Test on the rotation of the plane of linear polarization for light traveling over cosmological distances, using a comparison between the measured direction of the UV polarization in 8 radio galaxies at z>2 and the direction predicted by the model of scattering of anisotropic nuclear radiation, which explains the polarization.

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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/V07/1302
https://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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K. Toma (2012)

https://arxiv.org/abs/1208.5288
https://doi.org/10.1103/PhysRevLett.109.241104
https://inspirehep.net/literature/1182030
https://ui.adsabs.harvard.edu/abs/2012PhRvL.109x1104T

• Title: Strict Limit on CPT Violation from Polarization of Gamma-Ray Bursts
• Authors: K. Toma, S. Mukohyama, D. Yonetoku, T. Murakami, S. Gunji, T. Mihara, Y. Morihara, T. Sakashita, T. Takahashi, Y. Wakashima, H. Yonemochi, N. Toukairin

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B. Zitzer et al. (2013)

https://arxiv.org/abs/1307.8382
https://ui.adsabs.harvard.edu/abs/2013ICRC…33.2768Z/abstract
https://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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 !!!!D. Gotz et al. (2013)
https://arxiv.org/abs/1303.4186
https://ui.adsabs.harvard.edu/abs/2013MNRAS.431.3550G
https://hal.archives-ouvertes.fr/hal-02530742
https://inspirehep.net/literature/1224135

• Title: The polarized Gamma-Ray Burst GRB 061122
• Authors: D. Gotz, S. Covino, A. Fernandez-Soto, P. Laurent, Z . Bosnjak
• Method: comparison of the polarization angle of different energy bands of

the same GRB, so this measurement assumes a given energy dependence of the effect and for this reason is capable to determine the quantum-gravitational origin of the effect.
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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 Fermi-LAT*Three different analysis methods were used on each source: pair view, sharpness maximisation method and maximum likelihood..

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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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G. Rubtsov et al. (2014)

https://arxiv.org/abs/1312.4368
https://cds.cern.ch/record/1637253/files/PhysRevD.89.123011.pdf

• Title: Prospective constraints on Lorentz violation from ultrahigh-energy photon detection
• Authors: G. Rubtsov, P. Satunin and S. Sibiryakov
• Modified Dispersion Relation: E_γ ²= k² +Σ_n≥3 a⁽ⁿ⁾k²(k/M_Pl)^n-2
• Constraints on photon terms

SubLuminal n=2: a⁽⁴⁾= 𝛅⁽²⁾ > - 10^-7

• Modified Dispersion Relation: E ²=m²+p² +Σ_n≥3 b⁽ⁿ⁾p²(p/M_Pl)^n-2
• Constraints on electrons/positrons terms

SubLuminal n=2: b⁽⁴⁾=𝛅⁽²⁾ > - 10^-7

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D. Boncioli et al. (2015)

 

• Title:Future prospects of testing Lorentz invariance with UHECRs
• Authors:

D. Boncioli, A. di Matteo, F. Salamida, R. Aloisio, P. Blasi, P. L. Ghia, A. F. Grillo, S. Petrera, T. Pierog

https://pos.sissa.it/236/521/pdf

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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. S. Diaz et al. (2016)

• Title: Changes in extensive air showers from isotropic Lorentz violation in the photon sector
• Authors: J.S. Diaz, F.R. Klinkhamer, M. Risse

https://arxiv.org/abs/1607.02099
https://doi.org/10.1103/PhysRevD.94.085025

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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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D. Boncioli et al. (2017)

 

• Title:Probing Lorentz symmetry with the Pierre Auger Observatory
• Authors:D. Boncioli for the Pierre Auger Collaborationb

https://pos.sissa.it/301/561/pdf

• Update
• Modified Dispersion Relation: E_γ ²= k² +Σ_m≥3 a_mk²(k/M_Pl)^m-2
• Constraints on photon terms

SubLuminal n=2 (n=m-2): a₄= 𝛅₂ > - 10^-7
SubLuminal/SuperLuminal n=m-2: a₃=> |𝛅₂| < 10^-15

• Modified Dispersion Relation: E ²=m²+p² +Σ_m≥3 b_mp²(p/M_Pl)^m-2
• Constraints on electrons/positrons terms

SubLuminal/SuperLuminal n=m-2: b₃=> |𝛅₂| < 10^-7

• Update

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F. R. Klinkhamer et al. (2017)

• Title: Improved bound on isotropic Lorentz violation in the photon sector from extensive air showers
• Authors: F.R. Klinkhamer, M. Niechciol, M. Risse

https://arxiv.org/abs/1710.02507
https://doi.org/10.1103/PhysRevD.96.116011

• Process: Fast Photon decay
• LIV parameter k: k =𝛅₁ = 1 - v _photon/v _{fermion, max}

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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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L. Whittaker et al. 2017_

https://arxiv.org/abs/1702.01700
https://ui.adsabs.harvard.edu/abs/2018MNRAS.474..460W/abstract
https://inspirehep.net/literature/1512278

• Title: Measuring cosmic shear and birefringence using resolved radio sources
• Authors: L. Whittaker, R.A.Battye, M. L. Brown
• Method: Simultaneous measurements of weak lensing shear and a local rotation of the plane of polarization using observations of resolved radio sources.

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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 10¹⁷  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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R. G. Lang et al. (2018)

 

• Title:Testing Lorentz Invariance Violation at the Pierre Auger Observatory
• Authors:R. G. Lang

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R. G. Lang et al. (2019)

 

• Title:Testing Lorentz Invariance Violation at the Pierre Auger Observatory
• Authors:R. G. Lang for the Pierre Auger Collaboration

https://pos.sissa.it/358/327/pdf

• Modified Dispersion Relation: E_γ ²= k² +Σ_n=0 a⁽ⁿ⁾Eⁿ⁺²
• Constraints on photon terms

SubLuminal n=1: a⁽¹⁾ > - 10^-40
SubLuminal n=2: a⁽²⁾ > - 10^-60
a⁽ⁿ⁾ = 𝛅⁽ⁿ⁾ / M_Planckⁿ

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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) = φE_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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