Abstract
The thermodynamics of quantum chromodynamics at low temperatures and in sufficiently strong magnetic fields is governed by neutral pions. We analyze the interacting system of neutral pions and photons at zero baryon chemical potential using effective field theory. As a consequence of the axial anomaly and the external magnetic field, the pions and photons mix with one another. The resulting spectrum contains one usual, relativistic photon state, and two nonrelativistic modes, one of which is gapless and the other gapped. Furthermore, we calculate the leading, one-loop contribution to the pressure of the system. In the chiral limit, a closed analytic expression for the pressure exists, which features an unusual scaling with temperature and magnetic field, T3B/fπ, at low temperatures, T ≪ B/fπ. Finally, we determine the pion decay rate as a function of the magnetic field at the tree level. The result is affected by a competition of the anisotropic kinematics and the enlarged phase space due to the anomalous mass of the neutral pion. In the chiral limit, the decay rate scales as B3/f 5 π .
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References
J.O. Andersen, W.R. Naylor and A. Tranberg, Phase diagram of QCD in a magnetic field: a review, Rev. Mod. Phys. 88 (2016) 025001 [arXiv:1411.7176] [INSPIRE].
D.T. Son and M.A. Stephanov, Axial anomaly and magnetism of nuclear and quark matter, Phys. Rev. D 77 (2008) 014021 [arXiv:0710.1084] [INSPIRE].
N. Yamamoto, Axion electrodynamics and nonrelativistic photons in nuclear and quark matter, Phys. Rev. D 93 (2016) 085036 [arXiv:1512.05668] [INSPIRE].
T. Brauner and N. Yamamoto, Chiral soliton lattice and charged pion condensation in strong magnetic fields, JHEP 04 (2017) 132 [arXiv:1609.05213] [INSPIRE].
S. Ozaki and N. Yamamoto, Axion crystals, JHEP 08 (2017) 098 [arXiv:1610.07835] [INSPIRE].
Z. Qiu, G. Cao and X.-G. Huang, On electrodynamics of chiral matter, Phys. Rev. D 95 (2017) 036002 [arXiv:1612.06364] [INSPIRE].
T. Brauner and S. Kadam, Anomalous electrodynamics of neutral pion matter in strong magnetic fields, JHEP 03 (2017) 015 [arXiv:1701.06793] [INSPIRE].
M.N. Chernodub, Spontaneous electromagnetic superconductivity of vacuum in strong magnetic field: evidence from the Nambu-Jona-Lasinio model, Phys. Rev. Lett. 106 (2011) 142003 [arXiv:1101.0117] [INSPIRE].
J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Annals Phys. 158 (1984) 142 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral perturbation theory: expansions in the mass of the strange quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE].
J. Gasser and H. Leutwyler, Thermodynamics of chiral symmetry, Phys. Lett. B 188 (1987) 477 [INSPIRE].
F. Wilczek, Two applications of axion electrodynamics, Phys. Rev. Lett. 58 (1987) 1799 [INSPIRE].
P. Sikivie, Experimental tests of the invisible axion, Phys. Rev. Lett. 51 (1983) 1415 [Erratum ibid. 52 (1984) 695] [INSPIRE].
P. Sikivie, Detection rates for ‘invisible’ axion searches, Phys. Rev. D 32 (1985) 2988 [Erratum ibid. D 36 (1987) 974] [INSPIRE].
G. Raffelt and L. Stodolsky, Mixing of the photon with low mass particles, Phys. Rev. D 37 (1988) 1237 [INSPIRE].
E.K. Akhmedov and A. Yu. Smirnov, Paradoxes of neutrino oscillations, Phys. Atom. Nucl. 72 (2009) 1363 [arXiv:0905.1903] [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].
B.L. Ioffe and A.G. Oganesian, Axial anomaly and the precise value of the π 0 → 2γ decay width, Phys. Lett. B 647 (2007) 389 [hep-ph/0701077] [INSPIRE].
N.O. Agasian and I.A. Shushpanov, Gell-Mann-Oakes-Renner relation in a magnetic field at finite temperature, JHEP 10 (2001) 006 [hep-ph/0107128] [INSPIRE].
J.O. Andersen, Thermal pions in a magnetic background, Phys. Rev. D 86 (2012) 025020 [arXiv:1202.2051] [INSPIRE].
J.O. Andersen, Chiral perturbation theory in a magnetic background — finite-temperature effects, JHEP 10 (2012) 005 [arXiv:1205.6978] [INSPIRE].
Yu. A. Simonov, Pion decay constants in a strong magnetic field, Phys. Atom. Nucl. 79 (2016) 455 [Yad. Fiz. 79 (2016) 277] [arXiv:1503.06616] [INSPIRE].
O. Bär, M. Imboden and U.-J. Wiese, Pions versus magnons: from QCD to antiferromagnets and quantum Hall ferromagnets, Nucl. Phys. B 686 (2004) 347 [cond-mat/0310353] [INSPIRE].
K. Hattori, K. Itakura and S. Ozaki, Neutral-pion reactions induced by chiral anomaly in strong magnetic fields, arXiv:1305.7224 [INSPIRE].
T. Brauner, Spontaneous symmetry breaking in the linear σ-model at finite chemical potential: one-loop corrections, Phys. Rev. D 74 (2006) 085010 [hep-ph/0607102] [INSPIRE].
S.L. Adler, J.N. Bahcall, C.G. Callan and M.N. Rosenbluth, Photon splitting in a strong magnetic field, Phys. Rev. Lett. 25 (1970) 1061 [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].
S.L. Adler, Photon splitting and photon dispersion in a strong magnetic field, Annals Phys. 67 (1971) 599 [INSPIRE].
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Brauner, T., Kadam, S.V. Anomalous low-temperature thermodynamics of QCD in strong magnetic fields. J. High Energ. Phys. 2017, 103 (2017). https://doi.org/10.1007/JHEP11(2017)103
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DOI: https://doi.org/10.1007/JHEP11(2017)103