# Anomalous low-temperature thermodynamics of QCD in strong magnetic fields

## TL;DR

This paper investigates the low-temperature thermodynamics of QCD in strong magnetic fields, revealing unique spectral features, pressure scaling, and pion decay behavior influenced by the axial anomaly and magnetic field effects.

## Contribution

It provides a novel analysis of neutral pion and photon interactions under strong magnetic fields using effective field theory, including analytic pressure expressions and decay rate calculations.

## Key findings

- Pressure scales as T^3 B / f_pi at low T and strong B.
- Spectral spectrum includes relativistic photon and nonrelativistic modes.
- Pion decay rate scales as B^3 / f_pi^5 in the chiral limit.

## 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, $T^3B/f_\pi$, at low temperatures, $T\ll B/f_\pi$. 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 $B^3/f_\pi^5$.