Abstract
In this contribution, we re-assess some aspects of axionic electrodynamics by coupling non-linear electromagnetic effects to axion physics. We present a number of motivations to justify the coupling of the axion to the photon in terms of a general non-linear extension of the electromagnetic sector. Our emphasis in the paper relies on the investigation of the constitutive permittivity and permeability tensors, for which the axion contributes by introducing dependence on the frequency and wave vector of the propagating radiation. Also, we point out how the axion mass and the axion-photon-photon coupling constant contribute to a dispersive behavior of the electromagnetic waves, in contrast to what happens in the case of non-linear extensions, when effective refractive indices appear which depend only on the direction of the propagation with respect to the external fields. The axion changes this picture by yielding refractive indices with dependence on the wavelength. We apply our results to the special case of the (non-birefringent) Born-Infeld Electrodynamics and we show that it becomes birefringent whenever the axion is coupled. The paper is supplemented by an appendix, where we follow our own path to approach the recent discussion on a controversy in the definition of the Poynting vector of axionic electrodynamics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
R.D. Peccei and H.R. Quinn, Constraints Imposed by CP Conservation in the Presence of Instantons, Phys. Rev. D 16 (1977) 1791 [INSPIRE].
J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the Invisible Axion, Phys. Lett. B 120 (1983) 127 [INSPIRE].
L.F. Abbott and P. Sikivie, A Cosmological Bound on the Invisible Axion, Phys. Lett. B 120 (1983) 133 [INSPIRE].
M. Dine and W. Fischler, The Not So Harmless Axion, Phys. Lett. B 120 (1983) 137 [INSPIRE].
A. Ayala, I. Domínguez, M. Giannotti, A. Mirizzi and O. Straniero, Revisiting the bound on axion-photon coupling from Globular Clusters, Phys. Rev. Lett. 113 (2014) 191302 [ar**v:1406.6053] [INSPIRE].
C.S. Reynolds et al., Astrophysical limits on very light axion-like particles from Chandra grating spectroscopy of NGC 1275, Astrophys. J. 890 (2020) 59 [ar**v:1907.05475] [INSPIRE].
K. Bondarenko, A. Boyarsky, J. Pradler and A. Sokolenko, Neutron stars as photon double-lenses: constraining resonant conversion into ALPs, ar**v:2203.08663 [INSPIRE].
CAST collaboration, New CAST Limit on the Axion-Photon Interaction, Nature Phys. 13 (2017) 584 [ar**v:1705.02290] [INSPIRE].
L. Schoeffel, C. Baldenegro, H. Hamdaoui, S. Hassani, C. Royon and M. Saimpert, Photon–photon physics at the LHC and laser beam experiments, present and future, Prog. Part. Nucl. Phys. 120 (2021) 103889 [ar**v:2010.07855] [INSPIRE].
C. Baldenegro, S. Fichet, G. von Gersdorff and C. Royon, Searching for axion-like particles with proton tagging at the LHC, JHEP 06 (2018) 131 [ar**v:1803.10835] [INSPIRE].
C. Baldenegro, S. Hassani, C. Royon and L. Schoeffel, Extending the constraint for axion-like particles as resonances at the LHC and laser beam experiments, Phys. Lett. B 795 (2019) 339 [ar**v:1903.04151] [INSPIRE].
D. d’Enterria, Collider constraints on axion-like particles, in Workshop on Feebly Interacting Particles, 2, 2021 [ar**v:2102.08971] [INSPIRE].
J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].
R.C. Duncan and C. Thompson, Formation of very strongly magnetized neutron stars - implications for gamma-ray bursts, Astrophys. J. Lett. 392 (1992) L9 [INSPIRE].
S. Jacobsen, T. Linden and K. Freese, Constraining Axion-Like Particles with HAWC Observations of TeV Blazars, ar**v:2203.04332 [INSPIRE].
A.C. Keser, Y. Lyanda-Geller and O.P. Sushkov, Nonlinear Quantum Electrodynamics in Dirac Materials, Phys. Rev. Lett. 128 (2022) 066402 [ar**v:2101.09714] [INSPIRE].
J. Plebanski, Lectures on nonlinear electrodynamics, Cycle of lectures delivered at The Niels Bohr Institute and NORDITA, Copenhagen (October 1968).
G. Boillat, Nonlinear electrodynamics - Lagrangians and equations of motion, J. Math. Phys. 11 (1970) 941 [INSPIRE].
Z. Bialynicka-Birula and I. Bialynicki-Birula, Nonlinear effects in Quantum Electrodynamics. Photon propagation and photon splitting in an external field, Phys. Rev. D 2 (1970) 2341 [INSPIRE].
I. Bialynicki-Birula, Nonlinear Electrodynamics: Variations on a theme by Born and Infeld, in B. Jancewicz and J. Lukierski eds., Quantum Theory of Particles and Fields: birthday volume dedicated to Jan Lopuszański, World Scientific (1983) p. 31.
D.P. Sorokin, Introductory Notes on Non-linear Electrodynamics and its Applications, Fortsch. Phys. 70 (2022) 2200092 [ar**v:2112.12118] [INSPIRE].
H. Babaei-Aghbolagh, K.B. Velni, D.M. Yekta and H. Mohammadzadeh, Emergence of non-linear electrodynamic theories from TT−-like deformations, Phys. Lett. B 829 (2022) 137079 [ar**v:2202.11156] [INSPIRE].
H. Babaei-Aghbolagh, K.B. Velni, D.M. Yekta and H. Mohammadzadeh, \( T\overline{T} \)-like flows in non-linear electrodynamic theories and S-duality, JHEP 04 (2021) 187 [ar**v:2012.13636] [INSPIRE].
M. Born and L. Infeld, Foundations of the new field theory, Proc. Roy. Soc. Lond. A 144 (1934) 425 [INSPIRE].
E.M. Murchikova, On nonlinear classical electrodynamics with an axionic term, J. Phys. A 44 (2011) 045401 [ar**v:1005.5027] [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Nonlinear Electrodynamics from Quantized Strings, Phys. Lett. B 163 (1985) 123 [INSPIRE].
E. Bergshoeff, E. Sezgin, C.N. Pope and P.K. Townsend, The Born-Infeld Action From Conformal Invariance of the Open Superstring, Phys. Lett. B 188 (1987) 70 [INSPIRE].
R. Banerjee and D. Roychowdhury, Critical behavior of Born Infeld AdS black holes in higher dimensions, Phys. Rev. D 85 (2012) 104043 [ar**v:1203.0118] [INSPIRE].
S. Gunasekaran, R.B. Mann and D. Kubiznak, Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization, JHEP 11 (2012) 110 [ar**v:1208.6251] [INSPIRE].
E. Ayon-Beato and A. Garcia, The Bardeen model as a nonlinear magnetic monopole, Phys. Lett. B 493 (2000) 149 [gr-qc/0009077] [INSPIRE].
P. Niau Akmansoy and L.G. Medeiros, Constraining Born–Infeld-like nonlinear electrodynamics using hydrogen’s ionization energy, Eur. Phys. J. C 78 (2018) 143 [ar**v:1712.05486] [INSPIRE].
P. Niau Akmansoy and L.G. Medeiros, Constraining nonlinear corrections to Maxwell electrodynamics using γγ scattering, Phys. Rev. D 99 (2019) 115005 [ar**v:1809.01296] [INSPIRE].
J. Ellis, N.E. Mavromatos and T. You, Light-by-Light Scattering Constraint on Born-Infeld Theory, Phys. Rev. Lett. 118 (2017) 261802 [ar**v:1703.08450] [INSPIRE].
M.J. Neves, L.P.R. Ospedal, J.A. Helayël-Neto and P. Gaete, Considerations on anomalous photon and Z-boson self-couplings from the Born–Infeld weak hypercharge action, Eur. Phys. J. C 82 (2022) 327 [ar**v:2109.11004] [INSPIRE].
R. Battesti and C. Rizzo, Magnetic and electric properties of quantum vacuum, Rept. Prog. Phys. 76 (2013) 016401 [ar**v:1211.1933] [INSPIRE].
W. Heisenberg and H. Euler, Consequences of Dirac’s theory of positrons, Z. Phys. 98 (1936) 714 [physics/0605038] [INSPIRE].
V. S. Weisskopf, Über die elektrodynamik des vakuums auf grund des quanten-theorie des elektrons, Dan. Mat. Fys. Medd. 14 (1936) 1.
A. Ejlli et al., The PVLAS experiment: A 25 year effort to measure vacuum magnetic birefringence, Phys. Rept. 871 (2020) 1 [ar**v:2005.12913] [INSPIRE].
G. Zavattini, U. Gastaldi, R. Pengo, G. Ruoso, F. Della Valle and E. Milotti, Measuring the magnetic birefringence of vacuum: the PVLAS experiment, Int. J. Mod. Phys. A 27 (2012) 1260017 [ar**v:1201.2309] [INSPIRE].
F. Della Valle et al., The PVLAS experiment: measuring vacuum magnetic birefringence and dichroism with a birefringent Fabry–Perot cavity, Eur. Phys. J. C 76 (2016) 24 [ar**v:1510.08052] [INSPIRE].
G. Zavattini and F. Della Valle, Optical Polarimetry for Fundamental Physics, Universe 7 (2021) 252 [INSPIRE].
R.P. Mignani, V. Testa, D. Gonzalez Caniulef, R. Taverna, R. Turolla, S. Zane and K. Wu, Evidence for vacuum birefringence from the first optical polarimetry measurement of the isolated neutron star RX J1856. 5-3754, Monthly Not. Roy. Astron. Soc. (2016) stw2798.
T. Yamazaki et al., Repeating Pulsed Magnet System for Axion-like Particle Searches and Vacuum Birefringence Experiments, Nucl. Instrum. Meth. A 833 (2016) 122 [ar**v:1604.06556] [INSPIRE].
L. Maiani, R. Petronzio and E. Zavattini, Effects of Nearly Massless, Spin Zero Particles on Light Propagation in a Magnetic Field, Phys. Lett. B 175 (1986) 359 [INSPIRE].
S. Villalba-Chavez and A. Piazza, Axion-induced birefringence effects in laser driven nonlinear vacuum interaction, JHEP 11 (2013) 136 [ar**v:1307.7935] [INSPIRE].
S. Robertson, Optical Kerr effect in vacuum, Phys. Rev. A 100 (2019) 063831 [ar**v:1908.00896] [INSPIRE].
G.L.J.A. Rikken and C. Rizzo, Magnetoelectric birefringences of the quantum vacuum, Phys. Rev. A 63 (2001) 012107 [INSPIRE].
G. Raffelt and L. Stodolsky, Mixing of the Photon with Low Mass Particles, Phys. Rev. D 37 (1988) 1237 [INSPIRE].
P. Gaete, Some Considerations About Podolsky-Axionic Electrodynamics, Int. J. Mod. Phys. A 27 (2012) 1250061 [ar**v:1110.4816] [INSPIRE].
P. Gaete and I. Schmidt, Properties of noncommutative axionic electrodynamics, Phys. Rev. D 76 (2007) 027702 [ar**v:0706.3176] [INSPIRE].
P. Gaete and E. Spallucci, Finite axionic electrodynamics from a new noncommutative approach, J. Phys. A 45 (2012) 065401 [ar**v:1102.3777] [INSPIRE].
C.-D. Li and Y.-F. Cheng, Proca effects of axion-like particle-photon interactions on light polarization in external magnetic fields, Int. J. Theor. Phys. 47 (2008) 1911 [INSPIRE].
B.A.S.D. Chrispim, R.C.L. Bruni and M.S. Guimaraes, Massive photon propagator in the presence of axionic fluctuations, Phys. Rev. B 103 (2021) 165120 [ar**v:2012.00184] [INSPIRE].
F.P. Huang and H.-S. Lee, Extension of the electrodynamics in the presence of the axion and dark photon, Int. J. Mod. Phys. A 34 (2019) 1950012 [ar**v:1806.09972] [INSPIRE].
P. Arias, A. Arza, J. Jaeckel and D. Vargas-Arancibia, Hidden Photon Dark Matter Interacting via Axion-like Particles, JCAP 05 (2021) 070 [ar**v:2007.12585] [INSPIRE].
P.D.S. Silva, L. Lisboa-Santos, M.M. Ferreira, Jr. and M. Schreck, Effects of CPT-odd terms of dimensions three and five on electromagnetic propagation in continuous matter, Phys. Rev. D 104 (2021) 116023 [ar**v:2109.04659] [INSPIRE].
P.D.S. Silva, R. Casana and M.M. Ferreira, Jr., Symmetric and antisymmetric constitutive tensors for bi-isotropic and bi-anisotropic media, Phys. Rev. A 106 (2022) 042205 [ar**v:2204.10460] [INSPIRE].
L.H.C. Borges, A.G. Dias, A.F. Ferrari, J.R. Nascimento and A.Y. Petrov, Generation of axionlike couplings via quantum corrections in a Lorentz-violating background, Phys. Rev. D 89 (2014) 045005 [ar**v:1304.5484] [INSPIRE].
P. Sikivie, Invisible Axion Search Methods, Rev. Mod. Phys. 93 (2021) 015004 [ar**v:2003.02206] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, and 2021 update, PTEP 2020 (2020) 083C01 [INSPIRE].
C. Caloz and T. Itoh, Electromagnetic metamaterials: Transmission line theory and microwave applications, John Wiley & sons, INC. (2006), pg. 03.
V. Veselago, The electrodynamics of substances with simultaneously negative permissibility and permittivity, Sov. Phys. Uspekhi 10 (1968) 50.
W.J. Padilla, D.N. Basov and D.R. Smith, Negative refractive index metamaterials, Materials today 9 (2006) 28.
M.J. Neves, J.B. de Oliveira, L.P.R. Ospedal and J.A. Helayël-Neto, Dispersion relations in nonlinear electrodynamics and the kinematics of the Compton effect in a magnetic background, Phys. Rev. D 104 (2021) 015006 [ar**v:2101.03642] [INSPIRE].
M.E. Tobar, B.T. McAllister and M. Goryachev, Poynting vector controversy in axion modified electrodynamics, Phys. Rev. D 105 (2022) 045009 [ar**v:2109.04056] [INSPIRE].
K. Zhou, Comment on “Poynting vector controversy in axion modified electrodynamics”, ar**v:2203.15821 [INSPIRE].
A. Patkos, Radiation Backreaction in Axion Electrodynamics, Symmetry 14 (2022) 1113 [ar**v:2206.02052] [INSPIRE].
L. Bonetti, L.R. dos Santos Filho, J.A. Helayël-Neto and A.D.A.M. Spallicci, Photon sector analysis of Super and Lorentz symmetry breaking: effective photon mass, bi-refringence and dissipation, Eur. Phys. J. C 78 (2018) 811 [ar**v:1709.04995] [INSPIRE].
J.A. Helayël-Neto and A.D.A.M. Spallicci, Frequency variation for in vacuo photon propagation in the Standard-Model Extension, Eur. Phys. J. C 79 (2019) 590 [ar**v:1904.11035] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2205.05442
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Paixão, J.M.A., Ospedal, L.P.R., Neves, M.J. et al. The axion-photon mixing in non-linear electrodynamic scenarios. J. High Energ. Phys. 2022, 160 (2022). https://doi.org/10.1007/JHEP10(2022)160
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2022)160