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The thermodynamics of quantum chromodynamics at low temperatures and insufficiently strong magnetic fields is governed by neutral pions. We analyzethe interacting system of neutral pions and photons at zero baryon chemicalpotential using effective field theory. As a consequence of the axial anomalyand the external magnetic field, the pions and photons mix with one another.The resulting spectrum contains one usual, relativistic photon state, and twononrelativistic modes, one of which is gapless and the other gapped.Furthermore, we calculate the leading, one-loop contribution to the pressure ofthe system. In the chiral limit, a closed analytic expression for the pressureexists, which features an unusual scaling with temperature and magnetic field,$T^3B/f_\pi$, at low temperatures, $T\ll B/f_\pi$. Finally, we determine thepion decay rate as a function of the magnetic field at the tree level. Theresult is affected by a competition of the anisotropic kinematics and theenlarged phase space due to the anomalous mass of the neutral pion. In thechiral limit, the decay rate scales as $B^3/f_\pi^5$.

Anomalous low-temperature thermodynamics of QCD in strong magnetic fields