Abstract
Particle production in strong electromagnetic fields is a recurring theme in solid state physics, heavy ion collisions, early universe cosmology and formal quantum field theory. In this paper we discuss the Dirac equation in a background of parallel electric and magnetic fields. We review the Schwinger particle production rate, clarify the emergence of the chiral anomaly equation and compute the induced current of charged fermions. We distinguish the contributions from non-perturbative particle production, from the running of the gauge coupling constant and from non-linearities in the effective QED Lagrangian, and clarify how these contributions arise within a single framework. We apply these results to axion inflation. A Chern-Simons coupling between the pseudoscalar particle driving cosmic inflaton and an abelian gauge group induces a dual production of gauge fields and charged fermions. We show that the resulting scalar and gravitational wave power spectra strongly depend on the fermion mass.
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W. Heisenberg and H. Euler, Consequences of Dirac’s theory of positrons, Z. Phys. 98 (1936) 714 [physics/0605038] [INSPIRE].
J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].
A.I. Nikishov, Pair production by a constant external field, Zh. Eksp. Teor. Fiz. 57 (1969) 1210 [INSPIRE].
F.V. Bunkin and I.I. Tugov, The possibility of electron-positron pair production in vacuum when laser radiation is focussed, Dokl. Akad. Nauk Ser. Fiz. 187 (1969) 541 [INSPIRE].
K. von Klitzing, G. Dorda and M. Pepper, New method for high accuracy determination of the fine structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45 (1980) 494 [INSPIRE].
S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].
J.S. Bell and R. Jackiw, A PCAC puzzle: π0 → γγ in the σ model, Nuovo Cim. A 60 (1969) 47 [INSPIRE].
H.J. Warringa, Dynamics of the chiral magnetic effect in a weak magnetic field, Phys. Rev. D 86 (2012) 085029 [arXiv:1205.5679] [INSPIRE].
V. Domcke and K. Mukaida, Gauge field and fermion production during axion inflation, JCAP 11 (2018) 020 [arXiv:1806.08769] [INSPIRE].
P. Copinger, K. Fukushima and S. Pu, Axial Ward identity and the Schwinger mechanism — applications to the real-time chiral magnetic effect and condensates, Phys. Rev. Lett. 121 (2018) 261602 [arXiv:1807.04416] [INSPIRE].
H.B. Nielsen and M. Ninomiya, Adler-Bell-Jackiw anomaly and Weyl fermions in crystal, Phys. Lett. B 130 (1983) 389 [INSPIRE].
V. Domcke, Y. Ema, K. Mukaida and R. Sato, Chiral anomaly and Schwinger effect in non-Abelian gauge theories, JHEP 03 (2019) 111 [arXiv:1812.08021] [INSPIRE].
D. Kharzeev, R.D. Pisarski and M.H.G. Tytgat, Possibility of spontaneous parity violation in hot QCD, Phys. Rev. Lett. 81 (1998) 512 [hep-ph/9804221] [INSPIRE].
A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].
A. Yu. Alekseev, V.V. Cheianov and J. Fröhlich, Universality of transport properties in equilibrium, Goldstone theorem and chiral anomaly, Phys. Rev. Lett. 81 (1998) 3503 [cond-mat/9803346] [INSPIRE].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].
D.T. Son and N. Yamamoto, Berry curvature, triangle anomalies and the chiral magnetic effect in Fermi liquids, Phys. Rev. Lett. 109 (2012) 181602 [arXiv:1203.2697] [INSPIRE].
D.T. Son and B.Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B 88 (2013) 104412 [arXiv:1206.1627] [INSPIRE].
A.A. Zyuzin and A.A. Burkov, Topological response in Weyl semimetals and the chiral anomaly, Phys. Rev. B 86 (2012) 115133 [arXiv:1206.1868] [INSPIRE].
D. Kharzeev and A. Zhitnitsky, Charge separation induced by P-odd bubbles in QCD matter, Nucl. Phys. A 797 (2007) 67 [arXiv:0706.1026] [INSPIRE].
D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The effects of topological charge change in heavy ion collisions: ‘event by event P and CP-violation’, Nucl. Phys. A 803 (2008) 227 [arXiv:0711.0950] [INSPIRE].
D.E. Kharzeev, The chiral magnetic effect and anomaly-induced transport, Prog. Part. Nucl. Phys. 75 (2014) 133 [arXiv:1312.3348] [INSPIRE].
M.S. Turner and L.M. Widrow, Gravitational production of scalar particles in inflationary universe models, Phys. Rev. D 37 (1988) 3428 [INSPIRE].
W.D. Garretson, G.B. Field and S.M. Carroll, Primordial magnetic fields from pseudo-Goldstone bosons, Phys. Rev. D 46 (1992) 5346 [hep-ph/9209238] [INSPIRE].
M.M. Anber and L. Sorbo, N-flationary magnetic fields, JCAP 10 (2006) 018 [astro-ph/0606534] [INSPIRE].
R. Durrer and A. Neronov, Cosmological magnetic fields: their generation, evolution and observation, Astron. Astrophys. Rev. 21 (2013) 62 [arXiv:1303.7121] [INSPIRE].
M. Joyce and M.E. Shaposhnikov, Primordial magnetic fields, right-handed electrons and the Abelian anomaly, Phys. Rev. Lett. 79 (1997) 1193 [astro-ph/9703005] [INSPIRE].
K. Bamba, Baryon asymmetry from hypermagnetic helicity in dilaton hypercharge electromagnetism, Phys. Rev. D 74 (2006) 123504 [hep-ph/0611152] [INSPIRE].
K. Kamada and A.J. Long, Baryogenesis from decaying magnetic helicity, Phys. Rev. D 94 (2016) 063501 [arXiv:1606.08891] [INSPIRE].
K. Kamada and A.J. Long, Evolution of the baryon asymmetry through the electroweak crossover in the presence of a helical magnetic field, Phys. Rev. D 94 (2016) 123509 [arXiv:1610.03074] [INSPIRE].
M.M. Anber and E. Sabancilar, Hypermagnetic fields and baryon asymmetry from pseudoscalar inflation, Phys. Rev. D 92 (2015) 101501 [arXiv:1507.00744] [INSPIRE].
D. Jiḿenez, K. Kamada, K. Schmitz and X.-J. Xu, Baryon asymmetry and gravitational waves from pseudoscalar inflation, JCAP 12 (2017) 011 [arXiv:1707.07943] [INSPIRE].
V. Domcke, B. von Harling, E. Morgante and K. Mukaida, Baryogenesis from axion inflation, JCAP 10 (2019) 032 [arXiv:1905.13318] [INSPIRE].
A. Hook and G. Marques-Tavares, Relaxation from particle production, JHEP 12 (2016) 101 [arXiv:1607.01786] [INSPIRE].
K. Choi, H. Kim and T. Sekiguchi, Dynamics of the cosmological relaxation after reheating, Phys. Rev. D 95 (2017) 075008 [arXiv:1611.08569] [INSPIRE].
W. Tangarife, K. Tobioka, L. Ubaldi and T. Volansky, Relaxed inflation, arXiv:1706.00438 [INSPIRE].
W. Tangarife, K. Tobioka, L. Ubaldi and T. Volansky, Dynamics of relaxed inflation, JHEP 02 (2018) 084 [arXiv:1706.03072] [INSPIRE].
N. Fonseca, E. Morgante and G. Servant, Higgs relaxation after inflation, JHEP 10 (2018) 020 [arXiv:1805.04543] [INSPIRE].
R.A. Abramchuk and M.A. Zubkov, Schwinger pair creation in Dirac semimetals in the presence of external magnetic and electric fields, Phys. Rev. D 94 (2016) 116012 [arXiv:1605.02379] [INSPIRE].
E. Bavarsad, S.P. Kim, C. Stahl and S.-S. Xue, Effect of a magnetic field on Schwinger mechanism in de Sitter spacetime, Phys. Rev. D 97 (2018) 025017 [arXiv:1707.03975] [INSPIRE].
G.V. Dunne, Heisenberg-Euler effective Lagrangians: basics and extensions, in From fields to strings: circumnavigating theoretical physics. Ian Kogan memorial collection (3 volume set), M. Shifman, A. Vainshtein and J. Wheater eds., World Scientific, Singapore (2004), pg. 445 [hep-th/0406216] [INSPIRE].
N. Tanji, Dynamical view of pair creation in uniform electric and magnetic fields, Annals Phys. 324 (2009) 1691 [arXiv:0810.4429] [INSPIRE].
M. Banyeres, G. Domènech and J. Garriga, Vacuum birefringence and the Schwinger effect in (3 + 1) de Sitter, JCAP 10 (2018) 023 [arXiv:1809.08977] [INSPIRE].
T.D. Cohen and D.A. McGady, The Schwinger mechanism revisited, Phys. Rev. D 78 (2008) 036008 [arXiv:0807.1117] [INSPIRE].
K. Fujikawa, Path integral measure for gauge invariant fermion theories, Phys. Rev. Lett. 42 (1979) 1195 [INSPIRE].
K. Fujikawa, Path integral for gauge theories with fermions, Phys. Rev. D 21 (1980) 2848 [Erratum ibid. D 22 (1980) 1499] [INSPIRE].
M.F. Atiyah and I.M. Singer, The index of elliptic operators on compact manifolds, Bull. Am. Math. Soc. 69 (1963) 422 [INSPIRE].
M.F. Atiyah and I.M. Singer, The index of elliptic operators: I, Annals Math. 87 (1968) 484 [INSPIRE].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, Real-time dynamics of the chiral magnetic effect, Phys. Rev. Lett. 104 (2010) 212001 [arXiv:1002.2495] [INSPIRE].
F. Sauter, Uber das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs (in German), Z. Phys. 69 (1931) 742 [INSPIRE].
P. Adshead, J.T. Giblin, T.R. Scully and E.I. Sfakianakis, Gauge-preheating and the end of axion inflation, JCAP 12 (2015) 034 [arXiv:1502.06506] [INSPIRE].
J.R.C. Cuissa and D.G. Figueroa, Lattice formulation of axion inflation. Application to preheating, JCAP 06 (2019) 002 [arXiv:1812.03132] [INSPIRE].
P. Adshead, J.T. Giblin, M. Pieroni and Z.J. Weiner, Constraining axion inflation with gravitational waves from preheating, arXiv:1909.12842 [INSPIRE].
P. Adshead, J.T. Giblin, M. Pieroni and Z.J. Weiner, Constraining axion inflation with gravitational waves across 29 decades in frequency, arXiv:1909.12843 [INSPIRE].
C. Caprini and L. Sorbo, Adding helicity to inflationary magnetogenesis, JCAP 10 (2014) 056 [arXiv:1407.2809] [INSPIRE].
P. Adshead, J.T. Giblin, T.R. Scully and E.I. Sfakianakis, Magnetogenesis from axion inflation, JCAP 10 (2016) 039 [arXiv:1606.08474] [INSPIRE].
C. Caprini, M.C. Guzzetti and L. Sorbo, Inflationary magnetogenesis with added helicity: constraints from non-Gaussianities, Class. Quant. Grav. 35 (2018) 124003 [arXiv:1707.09750] [INSPIRE].
K. Choi, H. Kim and T. Sekiguchi, Late-time magnetogenesis driven by axionlike particle dark matter and a dark photon, Phys. Rev. Lett. 121 (2018) 031102 [arXiv:1802.07269] [INSPIRE].
O.O. Sobol, E.V. Gorbar and S.I. Vilchinskii, Backreaction of electromagnetic fields and the Schwinger effect in pseudoscalar inflation magnetogenesis, Phys. Rev. D 100 (2019) 063523 [arXiv:1907.10443] [INSPIRE].
T. Chiba, F. Takahashi and M. Yamaguchi, Baryogenesis in a flat direction with neither baryon nor lepton charge, Phys. Rev. Lett. 92 (2004) 011301 [Erratum ibid. 114 (2015) 209901] [hep-ph/0304102] [INSPIRE].
A. Kusenko, L. Pearce and L. Yang, Postinflationary Higgs relaxation and the origin of matter-antimatter asymmetry, Phys. Rev. Lett. 114 (2015) 061302 [arXiv:1410.0722] [INSPIRE].
A. Kusenko, K. Schmitz and T.T. Yanagida, Leptogenesis via axion oscillations after inflation, Phys. Rev. Lett. 115 (2015) 011302 [arXiv:1412.2043] [INSPIRE].
L. Pearce, L. Yang, A. Kusenko and M. Peloso, Leptogenesis via neutrino production during Higgs condensate relaxation, Phys. Rev. D 92 (2015) 023509 [arXiv:1505.02461] [INSPIRE].
L. Yang, L. Pearce and A. Kusenko, Leptogenesis via Higgs condensate relaxation, Phys. Rev. D 92 (2015) 043506 [arXiv:1505.07912] [INSPIRE].
M.S. Turner and L.M. Widrow, Inflation produced, large scale magnetic fields, Phys. Rev. D 37 (1988) 2743 [INSPIRE].
P. Adshead and E.I. Sfakianakis, Fermion production during and after axion inflation, JCAP 11 (2015) 021 [arXiv:1508.00891] [INSPIRE].
P. Adshead, L. Pearce, M. Peloso, M.A. Roberts and L. Sorbo, Phenomenology of fermion production during axion inflation, JCAP 06 (2018) 020 [arXiv:1803.04501] [INSPIRE].
V. Domcke, M. Pieroni and P. Binétruy, Primordial gravitational waves for universality classes of pseudoscalar inflation, JCAP 06 (2016) 031 [arXiv:1603.01287] [INSPIRE].
T. Kobayashi and N. Afshordi, Schwinger effect in 4D de Sitter space and constraints on magnetogenesis in the early universe, JHEP 10 (2014) 166 [arXiv:1408.4141] [INSPIRE].
T. Hayashinaka, T. Fujita and J. Yokoyama, Fermionic Schwinger effect and induced current in de Sitter space, JCAP 07 (2016) 010 [arXiv:1603.04165] [INSPIRE].
M. Gyulassy and X.-N. Wang, Multiple collisions and induced gluon Bremsstrahlung in QCD, Nucl. Phys. B 420 (1994) 583 [nucl-th/9306003] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon emission from ultrarelativistic plasmas, JHEP 11 (2001) 057 [hep-ph/0109064] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon and gluon emission in relativistic plasmas, JHEP 06 (2002) 030 [hep-ph/0204343] [INSPIRE].
A. Kurkela and G.D. Moore, Thermalization in weakly coupled non-Abelian plasmas, JHEP 12 (2011) 044 [arXiv:1107.5050] [INSPIRE].
K. Harigaya and K. Mukaida, Thermalization after/during reheating, JHEP 05 (2014) 006 [arXiv:1312.3097] [INSPIRE].
K. Mukaida and M. Yamada, Thermalization process after inflation and effective potential of scalar field, JCAP 02 (2016) 003 [arXiv:1506.07661] [INSPIRE].
N. Barnaby, E. Pajer and M. Peloso, Gauge field production in axion inflation: consequences for monodromy, non-Gaussianity in the CMB and gravitational waves at interferometers, Phys. Rev. D 85 (2012) 023525 [arXiv:1110.3327] [INSPIRE].
N. Barnaby and M. Peloso, Large non-Gaussianity in axion inflation, Phys. Rev. Lett. 106 (2011) 181301 [arXiv:1011.1500] [INSPIRE].
N. Barnaby, R. Namba and M. Peloso, Phenomenology of a pseudo-scalar inflaton: naturally large non-Gaussianity, JCAP 04 (2011) 009 [arXiv:1102.4333] [INSPIRE].
P.D. Meerburg and E. Pajer, Observational constraints on gauge field production in axion inflation, JCAP 02 (2013) 017 [arXiv:1203.6076] [INSPIRE].
A. Linde, S. Mooij and E. Pajer, Gauge field production in supergravity inflation: local non-Gaussianity and primordial black holes, Phys. Rev. D 87 (2013) 103506 [arXiv:1212.1693] [INSPIRE].
J. García-Bellido, M. Peloso and C. Unal, Gravitational waves at interferometer scales and primordial black holes in axion inflation, JCAP 12 (2016) 031 [arXiv:1610.03763] [INSPIRE].
V. Domcke, F. Muia, M. Pieroni and L.T. Witkowski, PBH dark matter from axion inflation, JCAP 07 (2017) 048 [arXiv:1704.03464] [INSPIRE].
J.L. Cook and L. Sorbo, Particle production during inflation and gravitational waves detectable by ground-based interferometers, Phys. Rev. D 85 (2012) 023534 [Erratum ibid. D 86 (2012) 069901] [arXiv:1109.0022] [INSPIRE].
M.M. Anber and L. Sorbo, Non-Gaussianities and chiral gravitational waves in natural steep inflation, Phys. Rev. D 85 (2012) 123537 [arXiv:1203.5849] [INSPIRE].
N. Bartolo et al., Science with the space-based interferometer LISA. IV: probing inflation with gravitational waves, JCAP 12 (2016) 026 [arXiv:1610.06481] [INSPIRE].
L. McAllister, E. Silverstein and A. Westphal, Gravity waves and linear inflation from axion monodromy, Phys. Rev. D 82 (2010) 046003 [arXiv:0808.0706] [INSPIRE].
R.Z. Ferreira, J. Ganc, J. Noreña and M.S. Sloth, On the validity of the perturbative description of axions during inflation, JCAP 04 (2016) 039 [Erratum ibid. 10 (2016) E01] [arXiv:1512.06116] [INSPIRE].
M. Peloso, L. Sorbo and C. Unal, Rolling axions during inflation: perturbativity and signatures, JCAP 09 (2016) 001 [arXiv:1606.00459] [INSPIRE].
P. Adshead, L. Pearce, M. Peloso, M.A. Roberts and L. Sorbo, Gravitational waves from fermion production during axion inflation, JCAP 10 (2019) 018 [arXiv:1904.10483] [INSPIRE].
E.V. Gorbar, A.I. Momot, O.O. Sobol and S.I. Vilchinskii, Kinetic approach to the Schwinger effect during inflation, Phys. Rev. D 100 (2019) 123502 [arXiv:1909.10332] [INSPIRE].
A. Hook, J. Huang and D. Racco, Minimal signatures of the Standard Model in non-Gaussianities, Phys. Rev. D 101 (2020) 023519 [arXiv:1908.00019] [INSPIRE].
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Domcke, V., Ema, Y. & Mukaida, K. Chiral anomaly, Schwinger effect, Euler-Heisenberg Lagrangian and application to axion inflation. J. High Energ. Phys. 2020, 55 (2020). https://doi.org/10.1007/JHEP02(2020)055
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DOI: https://doi.org/10.1007/JHEP02(2020)055