https://doi.org/10.1140/epjp/s13360-024-05200-4
Regular Article
Testing the Ampère–Maxwell law on the photon mass and Lorentz symmetry violation with MMS multi-spacecraft data
1
Laboratoire de Physique et Chimie de l’Environnement et de l’Espace (LPC2E) UMR 7328, Centre National de la Recherche Scientifique (CNRS), Centre National d’Études Spatiales (CNES), Université d’Orléans (UO), 3A Avenue de la Recherche Scientifique, 45071, Orléans, France
2
Institut Denis Poisson (IDP) UMR 7013, Centre National de la Recherche Scientifique (CNRS), Université d’Orléans (UO) et Université de Tours (UT), Parc de Grandmont, 37200, Tours, France
3
UFR Sciences et Techniques, Université d’Orléans, Rue de Chartres, 45100, Orléans, France
4
Observatoire des Sciences de l’Univers en region Centre (OSUC) UMS 3116, Centre National de la Recherche Scientifique (CNRS), Université d’Orléans (UO), Observatoire de Paris (OP), Université Paris Sciences & Lettres (PSL), 1A Rue de la Férollerie, 45071, Orléans, France
5
Osservatorio Astronomico di Capodimonte (OACN), Istituto Nazionale di Astrofisica (INAF), Salita Moiariello 16, 80131, Napoli, Italy
6
Dipartimento di Fisica E. Pancini, Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Napoli and Università degli Studi di Napoli Federico II (UNINA), Complesso Universitario Monte S. Angelo, Via Cinthia 9 Edificio G, 80126, Napoli, Italy
7
Departamento de Astrofísica, Cosmologia e Interações Fundamentais (COSMO), Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Xavier Sigaud 150, 22290-180, Urca, Rio de Janeiro, RJ, Brazil
Received:
6
December
2023
Accepted:
22
April
2024
Published online:
25
June
2024
We investigate possible evidence from Extended Theories of Electro-Magnetism (ETEM) by looking for deviations from the Ampère–Maxwell law. The photon, main messenger for interpreting the universe, is the only free massless particle in the Standard Model (SM). Indeed, the deviations may be due to a photon mass for the de Broglie–Proca (dBP) theory or the Lorentz Symmetry Violation (LSV) in the SM extension (SME), but also to non-linearities from theories as of Born–Infeld and Heisenberg–Euler. With this aim, we have analysed 6 years of data of the Magnetospheric Multi-Scale (MMS) mission, which is a four-satellite constellation, crossing mostly turbulent regions of magnetic reconnection and collecting about 95% of the downloaded data, outside the solar wind. We examined 3.8 million data points from the solar wind, magnetosheath, and magnetosphere regions. In a minority of cases, for the highest time resolution burst data and optimal tetrahedron configurations drawn by the four spacecraft, deviations have been found (
in modulus and 
in Cartesian components for all regions, but raising up in the solar wind alone to 
in modulus and 
in Cartesian components and up to 45.2% in the extreme low-mass range). The deviations might be due to unaccounted experimental errors or, less likely, to non-Maxwellian contributions, for which we have inferred the related parameters for the dBP and SME cases. Possibly, we are at the boundaries of measurability for non-dedicated missions. We discuss our experimental results (upper limit of photon mass of 
kg, and of the LSV parameter 
of 
), and the deviations in the solar wind, versus more stringent but model-dependent limits.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
