Pseudo-scalar photon mixing in a magnetized medium

Axions are pseudo-scalar particles, those which arise because of breaking of Peccei Queen (PQ) symmetry. Axions have a tree level coupling to two photons. As a consequence there exists a tree level coupling of axion to photon in a magnetic field. However, in an external magnetic field, there exists a new loop induced, axion photon vertex that gives rise to axion photon coupling. The strength of the tree level axion photon coupling in magnetic field is known to be model dependent. However, in a magnetic field, the new loop induced coupling has some interesting features. This note discusses the new axion photon vertex in a magnetized medium and the corrections arising from there. The magnitude of the correction to axion photon coupling, because of magnetized vacuum and matter, is estimated in this note. While making this estimate we note that the form of the axion photon vertex is related to the axial polarization tensor. This vertex is shown to satisfy the Ward identity. The coupling is shown to have a momentum dependent piece in it. Astrophysical importance of this extra modification is also pointed out.