# Reference Table

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

Abbreviations:
NON - no value for that attribute in the article
NA - process is not allowed

### Details of the articles

#### L. Krauss et al. (1988)

• Title: Test of the Weak Equivalence Principle for Neutrinos and Photons
• Authors: Lawrence M. Krauss, Scott Tremaine
• Limits on neutrino velocity δ = vν −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)

• 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 γν. 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 γν parameter:

γν(40 MeV) - γν(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

#### S. D. Biller et al. (1999)

• 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

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#### M. Galaverni et al. (2008)

• Title: Lorentz Violation for Photons and Ultra-High Energy Cosmic Rays
• Authors: M. Galaverni, G. Sigl
• Modified Dispersion Relation: ω 2= k2 +𝛅nk2(k/MPl)n
• Constraints on photon terms

SubLuminal n=1: 𝛅1 > -2.4 10-15
SubLuminal n=2: 𝛅2 > -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

#### J. Albert et al. (2008)

• 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)

• 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)

• 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

#### M. Martínez et al. (2009)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 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 ± 0.8stat ± 1.8sys) ×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 Ωm = 0.31 and ΩΛ = 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 (Φint(Eγ) = φEγ−α)
• α = 2.03 ± 0.04stat ± 0.2sys

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#### J. M. Carmona et al. (2019)

• 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)

• 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)

• 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)

• 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)

• 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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