# KM3NeT Constraint on Lorentz-Violating Superluminal Neutrino Velocity

O Adriani, S Aiello, A Albert, A.R Alhebsi, M Alshamsi, S. Alves Garre, A Ambrosone, F Ameli, M Andre, L Aphecetche, et al.

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O Adriani, S Aiello, A Albert, A.R Alhebsi, M Alshamsi, et al. KM3NeT Constraint on Lorentz-Violating Superluminal Neutrino Velocity. Communications Physics, 2025, 8 (1), pp.457. 10.1038/s42005-025-02347-z. hal-04975438

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# KM3NeT constraint on Lorentz-violating superluminal neutrino velocity

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The KM3NeT Collaboration<fnref n="1" />*

Lorentz invariance is a fundamental symmetry of spacetime and foundational to modern physics. One of its most important consequences is the constancy of the speed of light. This invariance, together with the geometry of spacetime, implies that no particle can move faster than the speed of light. In this article, we present the most stringent neutrino-based test of this prediction, using the highest-energy neutrino ever detected to date, KM3-230213A. If we assume an extragalactic source as the origin, the arrival of this event, with an energy of $220_{-110}^{+570}$ PeV, sets a constraint on $\delta \equiv c_{\nu}^2 - 1 < 4.2_{-3.7}^{+9.2} \times 10^{-22}$.

Lorentz invariance, which states that physical phenomena look the same for all inertial observers, is a key component underlying the Standard Model of particle physics. Lorentz invariance violation (LIV), while so far unobserved, is predicted by models of quantum gravity<fnref n="1" />⁻³ which are parametrized by effective field theories such as the Standard Model Extension (SME)⁴⁻⁷.

Since an observation of LIV would provide compelling evidence of such new physics, it has experimentally been tested in various ways: for example, using electronic transitions⁸, gamma-ray bursts⁹, high-energy neutrino oscillations¹⁰, and top quark production at colliders¹¹.

Lorentz invariance also predicts the constancy of the speed of light and, therefore, that the speed of light in vacuum is the upper bound on the speed of any massive particle; if one is found to be superluminal, that would unambiguously indicate LIV. As such, superluminality has been probed with particles such as electrons and cosmic rays¹²⁻¹⁵. Neutrinos, as the lightest known massive particles, can provide another probe of LIV as they propagate. Several experimental searches for superluminal neutrino propagation have been performed, for instance, at OPERA¹⁶ and MINOS¹⁷,¹⁸; while conclusive evidences of superluminal propagation, and therefore LIV, has not been observed, limits have been set.

We characterize superluminal propagation¹⁹,²⁰ by a parameter

$$\delta \equiv c_{\nu}^2 - 1,$$

where $c_{\nu}$ is the neutrino speed in units of the speed of light. Note that in our definition, $\delta$ is consistent with the definition in refs. 15,19 but twice that of the definition used in ref. 21. A superluminal neutrino rapidly loses energy primarily via the process of pair emission of electrons $v \to v + e^+ + e^{-19,20,22}$. In this work, we assume that the electron is not also superluminal, which has been independently constrained in, for instance, ref. 14. The calculation of the decay width $\Gamma = \Gamma(E, \delta)$, where E is the neutrino energy, is presented in refs. 19,20 and used, for instance, in ref. 21 to set a limit on $\delta$. It is generally possible to set a limit on $\delta$ using any neutrino if we know its energy and

propagated distance. Astrophysical neutrinos, which are neutrinos originating from outside the Solar System, are uniquely useful for this purpose because they arrive at high energies and from long distances, both of which serve to competitively constrain the size of the LIV effect, via the $\delta$ parameter. Indeed, there have been many previous efforts using astrophysical neutrinos to constrain LIV; see, for example, refs. 22–32.

KM3NeT³³ is a research infrastructure comprising two detector arrays in the Mediterranean Sea which, among other scientific aims, is being built to detect such astrophysical neutrinos. The larger detector array is known as Astroparticle Research with Cosmics in the Abyss (ARCA). Using photodetectors, ARCA is able to detect the Cherenkov light induced by the passage of relativistic charged particles produced in neutrino interactions; based on the timing, sensor position, and amount of light collected, ARCA can reconstruct its energy and direction. Moreover, ARCA can reconstruct different event morphologies, discriminating primarily between muons and particle showers. It offers the ability to measure the particle types and flavours of neutrino interactions. Recently, ARCA observed a muon indicative of an ultra-high-energy (UHE) neutrino event, termed KM3-230213A³⁴, with an estimated neutrino energy

$$E_{\text{UHE}} = 220_{-110}^{+570} \text{ PeV},$$

which is the highest-energy neutrino ever observed to date. In particular, for KM3-230213A, a median muon energy of 120 PeV is reconstructed by observing the number of triggered photodetectors, and comparing the observation to Monte Carlo simulations of similar high-energy muons. To translate this muon energy to a neutrino energy, Monte Carlo simulations of neutrinos with an $E^{-2}$ energy spectrum producing a muon of 120 PeV, are generated; $E_{\text{UHE}}$ is the median energy of these simulated neutrinos. For details, see ref. 34. The minimum neutrino energy is the reconstructed muon energy of 120 PeV; this conservative bound still leads to limits with the same order of magnitude as those assuming the median neutrino energy $E_{\text{UHE}}$. While the source of KM3-230213A is not yet known, its high energy and

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<footnote n="1">¹INFN, Sezione di Firenze, Sesto Fiorentino, Italy. *A list of authors and their affiliations appears at the end of the paper.</footnote>

<footnote>e-mail: carguelles@fas.harvard.edu; aagarciasoto@km3net.de; alexwen@fas.harvard.edu</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 1 | Upper limits.** We plot the value of δ scanning over a wide range of L assuming we hold the energy constant at $E_{UHE}$. The bands correspond to the 68% and 90% confidence intervals in the energy estimation of KM3-230213A³⁴. We also indicate in the vertical dashed lines some length scales of interest: the size of the Milky Way, intergalactic distances (1 Mpc), and the size of the observable Universe.</figcaption></figure>

likely extragalactic³⁴,³⁵ ($L \ge 1$Mpc) nature, assuming an astrophysical source as the origin, already allows us to set a strong constraint on δ. In this work, we find that in a likely scenario, $\delta < 4.2^{+9.2}_{-3.7} \times 10^{-22}$, further reducing the parameter space in which LIV can exist.

## Results and discussion

We evaluate the limit on δ using the procedure described in ref. 20. First, we calculate the decay width Γ as given in ref. 19 and determine a decay length $c_s/\Gamma$. The width has a strong energy dependence, $\Gamma(E, \delta) \propto E^2 \delta^3$, which can be estimated from dimensional analysis as done in ref. 19 or obtained via a full matrix element calculation as done in ref. 20. Secondly, we consider the propagated distance L as ten times the decay length, $L = 10c_s/\Gamma$. The choice of ten decay lengths is purely conventional, as done in ref. 20, but also conservative - assuming fewer decay lengths travelled for the same L will yield more stringent limits on δ. Finally, we compute the δ which is required to produce this L value at a fixed energy $E_{UHE}$. The result of this calculation, scanning over a wide range of L, is shown in Fig. 1.

Conservatively taking the minimum distance travelled to be of Galactic scale, which means $L \approx 4 \times 10^{20}$ m, around the radius of the Milky Way, we can set the limit

$$ \delta < 1.8^{+3.9}_{-1.7} \times 10^{-21}, $$

where the range stems from the 68% confidence interval in the energy measurement³⁴.

Given the event direction³⁵, a more likely scenario would be an intergalactic lengthscale, $L \approx 1$Mpc, which results in the limit

$$ \delta < 4.2^{+9.2}_{-3.7} \times 10^{-22}. $$

To place this into context, we can cast a limit on δ in terms of a minimal $d=4$ SME parameter $c^{(4)}$ if we assume the isotropic limit and the rest frame of the cosmic microwave background (CMB), as discussed in ref. 36. The relation is straightforward, $\delta/2 = -c^{(4)}$, yielding the limit

$$ c^{(4)} > -2.1^{+1.9}_{-4.6} \times 10^{-22}. $$

which can be compared to other limits, for instance, in table D34 of ref. 7. We emphasize that the assumption of an isotropic frame here is a simplifying assumption; in general, LIV will be anisotropic in most inertial reference frames. For details, see ref. 36.

<table><caption>**Table 1 | A comparison of various limits on δ set with the same method of using 10 decay lengths**</caption><thead><tr><td>Method</td><td>Energy scale</td><td>Limit on δ</td></tr></thead><tbody><tr><td>IceCube TXS 0506+056</td><td>~290 TeV</td><td>2.4 × 10<sup>-18</sup></td></tr><tr><td>Stecker et al. (ref. 21)</td><td>60TeV-2 PeV</td><td>2 × 5.2 × 10<sup>-21</sup></td></tr><tr><td>KM3-230213A (conservative)</td><td>~220 PeV</td><td>1.8 × 10<sup>-21</sup></td></tr><tr><td>KM3-230213A (extragalactic)</td><td>~220 PeV</td><td>4.2 × 10<sup>-22</sup></td></tr></tbody></table>

The exception is the limit set by ref. 21, which is detailed in that respective work; the factor of 2 accounts for the difference in the definitions of δ. Limits here are obtained assuming that the electron is not superluminal. For context, we have also included the energy scale used to set these limits.

In Table 1 we show the upper limits on δ, calculated using the same method described above, for other high-energy events and baselines of note. In particular, we consider the best values obtained using IceCube observations of TXS 0506+056³⁷,³⁸.

Competitive limits of around $10^{-18}-10^{-20}$ have also been obtained with more sophisticated methods such as in refs. 14,21,29. For comparison in Table 1, we also show the most competitive limit, from ref. 21, for which a Monte Carlo approach is used to model spectral distortions in neutrino observations. This approach is more dependent on the astrophysical flux modelling compared to our method.

As done in ref. 19, there is also the possibility of setting a limit using a defined terminal energy, which is the energy scale after which significant losses do not occur. We have confirmed that this method yields a similar limit to within one order of magnitude: $\delta < 2.6 \times 10^{-22}$ at $E_{UHE}$ for the likely extragalactic scenario.

The effect of cosmological redshift can also be considered, which manifests as an effective energy loss that contributes in addition to the pair emission. If we assume that the neutrino source distribution follows the star formation rate, which peaks at redshift of a few $z^{39}$, this represents a $O(1)$ factor of energy loss and will not have a significant effect that competes with the electron pair emission on intergalactic distances. If we assume larger redshifts from even more distant sources, ignoring this additional energy loss effect in the calculation of our δ limit renders it more conservative.

Finally, the criteria for the primary energy loss mechanism, electron pair emission, is energy-dependent. A superluminal neutrino behaves as a particle with an effective mass $E\sqrt{\delta}$; therefore, the energy E of the neutrino must satisfy $E > 2m_e/\sqrt{\delta}$ for pair emission to be possible, where $m_e$ is the electron mass. Therefore, as δ is constrained to be successively smaller, we approach the regime where pair emission may require arbitrarily high neutrino energies, and this mechanism cannot be used to further constrain δ. For instance, already at $\delta = 10^{-22}$ we require $E > 100$ PeV, where E is the energy at which the neutrino decays, necessarily higher than the energy $E_{UHE}$ at detection (which is assumed in Fig. 1). Despite this limitation, observable effects, such as distortions in cosmogenic neutrino energy spectra, may still be expected and used to set even tighter limits at ultra-high energies⁴⁰.

## Conclusion

We report on a limit on the LIV parameter δ (and SME parameter $c^{(4)}$) using KM3-230213A, the most energetic neutrino ever detected to date. Our result, to our knowledge, improves upon the current best limits by one order of magnitude, while making minimal and conservative assumptions about the origin of the neutrino.

Repeated searches for LIV, and corresponding limits set, serve as a critical, ongoing, test of one of the cornerstones of modern physics. At the fundamental level, an observation of LIV would change our understanding of causality and spacetime structure, and permit models of quantum gravity that predict LIV¹,⁴⁻⁷. At the more phenomenological level, LIV could affect well-known phenomena like the GZK cutoff⁴¹, and the neutrino dispersion relation. These possibilities clearly warrant a comprehensive search for LIV;
to this end, our limit shows that Lorentz invariance is, so far, on solid ground – and that avenues for LIV to occur are shrinking.

Given electron pair emission in vacuum as the primary energy loss mechanism, our constraints cannot be significantly improved upon using this method without detecting a neutrino of significantly higher energy, or relieving some of our conservative assumptions. The competitiveness of our limit highlights the growing role that UHE neutrinos, and neutrino telescopes, can play in testing fundamental symmetries.

## Data availability

The data required to reproduce the results in this work consists of the energy of KM3-230213A, which is detailed in ref. 34.

Received: 27 March 2025; Accepted: 1 October 2025;
Published online: 11 November 2025

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## Acknowledgements

The authors acknowledge the financial support of: KM3NeT-INFRADEV2 project, funded by the European Union Horizon Europe Research and Innovation Programme under grant agreement No 101079679; Funds for Scientific Research (FRS-FNRS), Francqui foundation, BAEF foundation. Czech Science Foundation (GAČR 24-12702S); Agence Nationale de la Recherche (contract ANR-15-CE31-0020), Centre National de la Recherche Scientifique (CNRS), Commission Européenne (FEDER fund and Marie Curie Programme), LabEx
UnivEarthS (ANR-10-LABX-0023 and ANR-18-IDEX-0001), Paris I^le-de-France Region, Normandy Region (Alpha, Blue-waves and Neptune), France, The Provence-Alpes-Côte d'Azur Delegation for Research and Innovation (DRARI), the Provence-Alpes-Côte d'Azur region, the Bouches-du-Rhône Departmental Council, the Metropolis of Aix-Marseille Provence and the City of Marseille through the CPER 2021-2027 NEUMED project, The CNRS Institut National de Physique Nucléaire et de Physique des Particules (IN2P3); Shota Rustaveli National Science Foundation of Georgia (SRNSFG, FR-22-13708), Georgia; This work is part of the MuSES project which has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme (grant agreement No 101142396); The General Secretariat of Research and Innovation (GSRI), Greece; Istituto Nazionale di Fisica Nucleare (INFN) and Ministero dell'Università e della Ricerca (MUR), through PRIN 2022 programme (Grant PANTHEON 2022E2J4RK, Next Generation EU) and PON R&I programme (Avviso n. 424 del 28 febbraio 2018, Progetto PACK-PIR01 00021), Italy; IDMAR project Po-Fesr Sicilian Region az. 1.5.1; A. De Benedittis, W. Idrissi Ibsalih, M. Bendahman, A. Nayerhoda, G. Papalashvili, I. C. Rea, A. Simonelli have been supported by the Italian Ministero dell'Università e della Ricerca (MUR), Progetto CIR01 00021 (Avviso n. 2595 del 24 dicembre 2019); KM3NeT4RR MUR Project National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 3.1, Funded by the European Union - NextGenerationEU, CUP I57G21000040001, Concession Decree MUR No. n. Prot. 123 del 21/06/2022; Ministry of Higher Education, Scientific Research and Innovation, Morocco, and the Arab Fund for Economic and Social Development, Kuwait; Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands; The grant "AstroCeNT: Particle Astrophysics Science and Technology Centre", carried out within the International Research Agendas programme of the Foundation for Polish Science financed by the European Union under the European Regional Development Fund; The programme: "Excellence initiative-research university" for the AGH University in Krakow; The ARTIQ project: UMO-2021/01/2/ST6/00004 and ARTIQ/0004/2021; Ministry of Research, Innovation and Digitalisation, Romania; Slovak Research and Development Agency under Contract No. APV-22-0413; Ministry of Education, Research, Development and Youth of the Slovak Republic; MCIN for PID2021-124591NB-C41, -C42, -C43 and PDC2023-145913-I00 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe", for ASFAE/2022/014 and ASFAE/2022/023 with funding from the EU Next-GenerationEU (PRTR-C17.I01) and Generalitat Valenciana, for Grant AST22_6.2 with funding from Consejería de Universidad, Investigación e Innovación y Gobierno de España and European Union - NextGenerationEU, for CSIC-INFRA23013 and for CNS2023-144099, Generalitat Valenciana for CIDEGENT/2018/034, /2019/043, /2020/049, /2021/23, for CIDEIG/2023/20, for CIPROM/2023/51 and for GRISOLIAP/2021/192 and EU for MSC/101025085, Spain; Khalifa University internal grants (ESIG-2023-008, RIG-2023-070 and RIG-2024-047), United Arab Emirates; The European

Union's Horizon 2020 Research and Innovation Programme (ChETEC-INFRA - Project no. 101008324); C. A. Argüelles and N. W. Kamp were supported by the David & Lucille Packard Foundation; A. Y. Wen was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number PGSD-577971-2023.

## Author contributions

This work is the result of all the institutes and authors of the KM3NeT Collaboration. Their contributions include designing, constructing, and operating the detector, collecting the data, performing simulations, conducting data analysis, and discussing the results. All authors reviewed and approved the final manuscript.

## Competing interests

The authors declare no competing interests.

## Additional information

Correspondence and requests for materials should be addressed to C. Argüelles, A. Garcia Soto or A. Y. Wen.

Peer review information *Communications Physics* thanks the anonymous reviewer(s) for their contribution to the peer review of this work.

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© The Author(s) 2025

## The KM3NeT Collaboration

O. Adriani<sup>1,2</sup>, S. Aiello<sup>3</sup>, A. Albert<sup>4,5</sup>, A. R. Alhebsi<sup>6</sup>, M. Alshamsi<sup>7</sup>, S. Alves Garre<sup>8</sup>, A. Ambrosone<sup>9,10</sup>, F. Ameli<sup>11</sup>, M. Andre<sup>12</sup>, L. Aphecetche<sup>13</sup>, M. Ardid<sup>14</sup>, S. Ardid<sup>14</sup>, C. Argüelles<sup>15</sup>✉, J. Aublin<sup>16</sup>, F. Badaracco<sup>17,18</sup>, L. Bailly-Salins<sup>19</sup>, Z. Bardačová<sup>20,21</sup>, A. Bariego-Quintana<sup>8</sup>, Y. Becherini<sup>16</sup>, M. Bendahman<sup>10</sup>, F. Benfenati Gualandi<sup>22,23</sup>, M. Benhassi<sup>10,24</sup>, M. Bennani<sup>19</sup>, D. M. Benoit<sup>25</sup>, E. Berbee<sup>26</sup>, E. Berti<sup>1</sup>, V. Bertin<sup>7</sup>, P. Betti<sup>1</sup>, S. Biagi<sup>27</sup>, M. Boettcher<sup>28</sup>, D. Bonanno<sup>27</sup>, S. Bottai<sup>1</sup>, A. B. Bouasla<sup>29</sup>, J. Boumaaza<sup>30</sup>, M. Bouta<sup>7</sup>, M. Bouwhuis<sup>26</sup>, C. Bozza<sup>10,31</sup>, R. M. Bozza<sup>9,10</sup>, H. Brânzas<sup>32</sup>, F. Bretaudau<sup>13</sup>, M. Breuhaus<sup>7</sup>, R. Bruijn<sup>26,33</sup>, J. Brunner<sup>7</sup>, R. Bruno<sup>3</sup>, E. Buis<sup>26,34</sup>, R. Buompane<sup>10,24</sup>, J. Busto<sup>7</sup>, B. Caiffi<sup>17</sup>, D. Calvo<sup>8</sup>, A. Capone<sup>11,35</sup>, F. Carenini<sup>22,23</sup>, V. Carretero<sup>26,33</sup>, T. Cartraud<sup>16</sup>, P. Castaldi<sup>23,36</sup>, V. Cecchini<sup>8</sup>, S. Celli<sup>11,35</sup>, L. Cerisy<sup>7</sup>, M. Chabab<sup>37</sup>, A. Chen<sup>38</sup>, S. Cherubini<sup>27,39</sup>, T. Chiarusi<sup>23</sup>, M. Circella<sup>40</sup>, R. Clark<sup>41</sup>, R. Cocimano<sup>27</sup>, J. A. B. Coelho<sup>16</sup>, A. Coleiro<sup>16</sup>, A. Condorelli<sup>16</sup>, R. Coniglione<sup>27</sup>, P. Coyle<sup>7</sup>, A. Creusot<sup>16</sup>, G. Cuttone<sup>27</sup>, R. Dallier<sup>13</sup>, A. De Benedittis<sup>10</sup>, G. De Wasseige<sup>41</sup>, V. Decoene<sup>13</sup>, P. Deguire<sup>7</sup>, I. Del Rosso<sup>22,23</sup>, L. S. Di Mauro<sup>27</sup>, I. Di Palma<sup>11,35</sup>, A. F. Daz<sup>42</sup>, D. Diego-Tortosa<sup>27</sup>, C. Distefano<sup>27</sup>, A. Domi<sup>43</sup>, C. Donzaud<sup>16</sup>, D. Dornic<sup>7</sup>, E. Drakopoulou<sup>44</sup>, D. Drouhin<sup>4,5</sup>, J.-G. Ducoin<sup>7</sup>, P. Duverne<sup>16</sup>, R. Dvornickyý<sup>20</sup>, T. Eberl<sup>43</sup>, E. Eckerová<sup>20,21</sup>, A. Eddymaoui<sup>30</sup>, T. van Eeden<sup>26</sup>, M. Eff<sup>16</sup>, D. van Eijk<sup>26</sup>, I. El
Bojaddaini⁴⁵, S. El Hedri¹⁶, S. El Mentawi⁷, V. Ellajosyula¹⁷,¹⁸, A. Enzenhöfer⁷, G. Ferrara²⁷,³⁹, M. D. Filipovic⁴⁶, F. Filippini²³, D. Franciotti²⁷, L. A. Fusco¹⁰,³¹, S. Gagliardini¹¹,³⁵, T. Gal⁴³, J. Garca Méndez¹⁴, A. Garcia Soto⁸, C. Gatius Oliver²⁶, N. Geißelbrecht⁴³, E. Genton⁴¹, H. Ghaddari⁴⁵, L. Gialanella¹⁰,²⁴, B. K. Gibson²⁵, E. Giorgio²⁷, I. Goos¹⁶, P. Goswami¹⁶, S. R. Gozzini⁸, R. Gracia⁴³, C. Guidi¹⁷,¹⁸, B. Guillon¹⁹, M. Gutiérrez⁴⁷, C. Haack⁴³, H. van Haren⁴⁸, A. Heijboer²⁶, L. Hennig⁴³, J. J. Hernández-Rey⁸, A. Idrissi²⁷, W. Idrissi Ibsnalih¹⁰, G. Illuminati²³, O. Janik⁴³, D. Joly⁷, M. de Jong²⁶,⁴⁹, P. de Jong²⁶,³³, B. J. Jung²⁶, P. Kalaczyński⁵⁰,⁵¹, N. Kamp¹⁵, J. Keegans²⁵, V. Kikvadze⁵², G. Kistauri⁵²,⁵³, C. Kopper⁴³, A. Kouchner¹⁶,⁵⁴, Y. Y. Kovalev⁵⁵, L. Krupa²¹, V. Kueviakoe²⁶, V. Kulikovskiy¹⁷, R. Kvatadze⁵³, M. Labalme¹⁹, R. Lahmann⁴³, M. Lamoureux⁴¹, G. Larosa²⁷, C. Lastoria¹⁹, J. Lazar⁴¹, A. Lazo⁸, S. Le Stum⁷, G. Lehaut¹⁹, V. Lemaître⁴¹, E. Leonora³, N. Lessing⁸, G. Levi²²,²³, M. Lindsey Clark¹⁶, F. Longhitano³, F. Magnani⁷, J. Majumdar²⁶, L. Malerba¹⁷,¹⁸, F. Mamedov²¹, A. Manfreda¹⁰, A. Manousakis⁵⁶, M. Marconi¹⁷,¹⁸, A. Margiotta²²,²³, A. Marinelli⁹,¹⁰, C. Markou⁴⁴, L. Martin¹³, M. Mastrodicasa¹¹,³⁵, S. Mastroianni¹⁰, J. Mauro⁴¹, K. C. K. Mehta⁵¹, A. Meskar⁵⁷, G. Miele⁹,¹⁰, P. Migliozzi¹⁰, E. Migneco²⁷, M. L. Mitsou¹⁰,²⁴, C. M. Mollo¹⁰, L. Morales-Gallegos¹⁰,²⁴, N. Mori¹, A. Moussa⁴⁵, I. Mozun Mateo¹⁹, R. Muller²³, M. R. Musone¹⁰,²⁴, M. Musumeci²⁷, S. Navas⁴⁷, A. Nayerhoda⁴⁰, C. A. Nicolau¹¹, B. Nkosi³⁸, B. ó Fearraigh¹⁷, V. Oliviero⁹,¹⁰, A. Orlando²⁷, E. Oukacha¹⁶, L. Pacini¹, D. Paesani²⁷, J. Palacios González⁸, G. Papalashvili⁴⁰,⁵², P. Papini¹, V. Parisi¹⁷,¹⁸, A. Parmar¹⁹, E. J. Pastor Gomez⁸, C. Pastore⁴⁰, A. M. Päun³², G. E. Päválaš³², S. Peña Martnez¹⁶, M. Perrin-Terrin⁷, V. Pestel¹⁹, R. Pestes¹⁶, M. Petropavlova²¹,⁶², P. Piattelli²⁷, A. Plavin⁵⁵,⁵⁸, C. Poiré¹⁰,³¹, V. Popa³²,⁶³, T. Pradier⁴, J. Prado⁸, S. Pulvirenti²⁷, C. A. Quiroz-Rangel¹⁴, N. Randazzo³, A. Ratnani⁵⁹, S. Razzaque⁶⁰, I. C. Rea¹⁰, D. Real⁸, G. Riccobene²⁷, J. Robinson²⁸, A. Romanov¹⁷,¹十八,¹⁹, E. Ros⁵⁵, A. Šaina⁸, F. Salesa Greus⁸, D. F. E. Samtleben²⁶,⁴⁹, A. Sánchez Losa⁸, S. Sanfilippo²⁷, M. Sanguineti¹⁷,¹十八, D. Santonocito²⁷, P. Sapienza²⁷, M. Scaringella¹, M. Scarnera¹⁶,⁴¹, J. Schnabel⁴³, J. Schumann⁴³, H. M. Schutte²⁸, J. Seneca²⁶, N. Sennan⁴⁵, P. A. Sevle Myhr⁴¹, I. Sgura⁴⁰, R. Shanidze⁵², A. Sharma¹⁶, Y. Shitov²¹, F. Šimkovic²⁰, A. Simonelli¹⁰, A. Sinopoulou³, B. Spisso¹⁰, M. Spurio²²,²³, O. Starodubtsev¹, D. Stavropoulos⁴⁴, I. Štekl²¹, D. Stocco¹³, M. Taiuti¹⁷,¹十八, G. Takadze⁵², Y. Tayalati³⁰,⁵⁹, H. Thiersen²⁸, S. Thoudam⁶, I. Tosta e Melo³,³⁹, B. Trocmé¹⁶, V. Tsourapis⁴⁴, E. Tzamariudaki⁴⁴, A. Ukleja⁵¹,⁵⁷, A. Vacheret¹⁹, V. Valsecchi²⁷, V. Van Elewyck¹⁶,⁵⁴, G. Vannoye⁷,¹十七,¹十八, E. Vannuccini¹, G. Vasileiadis⁶¹, F. Vazquez de Sola²⁶, A. Veutro¹¹,³⁵, S. Viola²⁷, D. Vivolo¹⁰,²⁴, A. van Vliet⁶, A. Y. Wen¹⁵, E. de Wolf²⁶,³³, I. Lhenry-Yvon¹⁶, S. Zavatarelli¹⁷, A. Zegarelli¹¹,³⁵, D. Zito²⁷, J. D. Zornoza⁸, J. Zúñiga⁸ & N. Zywicka²⁸

²Università di Firenze, Dipartimento di Fisica e Astronomia, Sesto Fiorentino, Italy. ³INFN, Sezione di Catania, (INFN-CT) Via Santa Sofia 64, Catania, Italy. ⁴Università de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France. ⁵Université de Haute Alsace, rue des Frères Lumière, Mulhouse Cedex, France. ⁶Khalifa University of Science and Technology, Department of Physics, Abu Dhabi, United Arab Emirates. ⁷Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France. ⁸IFIC - Instituto de Física Corpuscular (CSIC - Universitat de València), Paterna, Valencia, Spain. ⁹Università di Napoli “Federico II”, Dip. Scienze Fisiche “E. Pancini”, Complesso Universitario di Monte S. Angelo, Napoli, Italy. ¹⁰INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli, Italy. ¹¹INFN, Sezione di Roma, Piazzale Aldo Moro 2, Roma, Italy. ¹²Universitat Politècnica de Catalunya, Laboratori d'Aplicacions Bioacústiques, Centre Tecnològic de Vilanova i la Geltrú, Avda. Rambla Exposició, s/n, Vilanova i la Geltrú, Spain. ¹³Subatech, IMT Atlantique, IN2P3-CNRS, Nantes Université, 4 rue Alfred Kastler - La Chantrerie, Nantes, France. ¹⁴Universitat Politècnica de València, Instituto de Investigación para la Gestión Integrada de las Zonas Costeras, Gandia, Spain. ¹⁵Harvard University, Department of Physics and Laboratory for Particle Physics and Cosmology, Lyman Laboratory, Cambridge, MA, USA. ¹⁶Université Paris Cité, CNRS, Astroparticule et Cosmologie, Paris, France. ¹⁷INFN, Sezione di Genova, Genova, Italy. ¹⁸Università di Genova, Genova, Italy. ¹⁹LPC CAEN, Normandie Univ, ENSICAEN, UNICAEN, CNRS/IN2P3, Caen, France. ²⁰Comenius University in Bratislava, Department of Nuclear Physics and Biophysics, Mlynska dolina F1, Bratislava, Slovak Republic. ²¹Czech Technical University in Prague, Institute of Experimental and Applied Physics, Prague, Czech Republic. ²²Università di Bologna, Dipartimento di Fisica e Astronomia, Bologna, Italy. ²³INFN, Sezione di Bologna, Bologna, Italy. ²⁴Università degli Studi della Campania “Luigi Vanvitelli”, Dipartimento di Matematica e Fisica, Caserta, Italy. ²⁵E. A. Milne Centre for Astrophysics, University of Hull, Hull, UK. ²⁶Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands. ²⁷INFN, Laboratori Nazionali del Sud, (LNS) Via S. Sofia 62, Catania, Italy. ²⁸North-West University, Centre for Space Research, Potchefstroom, South Africa. ²⁹Université Badji Mokhtar, Département de Physique, Faculté des Sciences, Laboratoire de Physique des Rayonnements, Annaba, Algeria. ³⁰University Mohammed V in Rabat, Faculty of Sciences, 4 av. Ibn Battouta, Rabat, Morocco. ³¹Università di Salerno e INFN Gruppo Collegato di Salerno, Dipartimento di Fisica, Fisciano, Italy. ³²Institute of Space Science - INFLPR Subsidiary, Magurele, Ilfov, Romania. ³³University of Amsterdam, Institute of Physics/IHEF, Amsterdam, North Holland, Netherlands. ³⁴TNO, Technical Sciences, Delft, South Holand, Netherlands. ³⁵Università La Sapienza, Dipartimento di Fisica, Roma, Italy. ³⁶Università di Bologna, Dipartimento di Ingegneria dell'Energia Elettrica e del l'Informazione "Guglielmo Marconi", Cesena, Italia. ³⁷Cadi Ayyad University, Physics Department, Faculty of Science Semlalia, Marrakech, Morocco. ³⁸University of the Witwatersrand, School of Physics, Johannesburg, Wits, South Africa. ³⁹Università di Catania, Dipartimento di Fisica e Astronomia "Ettore Majorana", (INFN-CT) Via Santa Sofia 64, Catania, Italy. ⁴⁰INFN, Sezione di Bari, Bari, Italy. ⁴¹UCLouvain, Centre for Cosmology, Particle Physics and Phenomenology, Chemin du Cyclotron, 2, Louvain-la-Neuve, Belgium. ⁴²University of Granada, Department of Computer Engineering, Automation and Robotics / CITIC, Granada, Spain. ⁴³Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen Centre for Astroparticle Physics, Erlangen, Germany. ⁴⁴NCSR Demokritos, Institute of Nuclear and Particle Physics, Athens, Greece. ⁴⁵University Mohammed I, Faculty of Sciences, BV Mohammed VI, Oujda, Morocco. ⁴⁶Western Sydney University, School of Computing, Engineering and Mathematics, Penrith, NSW, Australia. ⁴⁷University of Granada, Dpto. de Física Teórica y del Cosmos C.A.F.P.E., Granada, Spain. ⁴⁸NIOZ (Royal Netherlands Institute for Sea Research), Den Burg, Texel, the Netherlands. ⁴⁹Leiden University, Leiden Institute of Physics, Leiden, Netherlands. ⁵⁰AstroCeNT, Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw, Poland. ⁵¹AGH University of Krakow, Krakow, Poland. ⁵²Tbilisi State University, Department of Physics, Tbilisi, Georgia. ⁵³The University of Georgia, Institute of Physics, Tbilisi, Georgia. ⁵⁴Institut Universitaire de France, Paris, France. ⁵⁵Max-Planck-Institut für Radioastronomie, Bonn, Germany. ⁵⁶University of Sharjah, Sharjah Academy for Astronomy, Space Sciences, and Technology, University Campus, Sharjah, United Arab Emirates. ⁵⁷National Centre for Nuclear Research, Warsaw, Poland. ⁵⁸Harvard University, Black Hole Initiative, Cambridge, MA, USA. ⁵⁹School of Applied and Engineering Physics, Mohammed VI Polytechnic University, Ben Guerir, Morocco. ⁶⁰University of Johannesburg, Department Physics, Auckland Park, South Africa. ⁶¹Laboratoire Univers et Particules de Montpellier, Place Eugène Bataillon - CC 72, Montpellier Cédex 05, France. ⁶²Faculty of Mathematics and Physics, Charles University in Prague, Prague, Czech Republic. ⁶³Deceased: V. Popa.