Magnetic Induced Axion Mass

We study the effect of a uniform magnetic field on the dynamics of axions. In particular, we show that the Peccei-Quinn symmetry is explicitly broken by the presence of an external magnetic field. This breaking is induced by the non-conservation of the magnetic helicity and generates an electromagnetic contribution to the axion mass. We compute the magnetic axion mass in one loop approximation, with no restriction on the intensity of the magnetic field, and including thermal effects.