Higgs boson decay into two photons in an electromagnetic background field

The amplitude for Higgs boson decay into two photons in a homogeneous and time-independent magnetic field is investigated by proper-time regularization in a gauge-invariant manner and is found to be singular at large field values. The singularity is caused by the component of the charged vector boson field that is tachyonic in a strong magnetic field. Also, tools for the computation of the amplitude in a more general electromagnetic background are developed.

Figure 1

Feynman diagram representation of the effective action in its final form.

Figure 2

Feynman diagram representation of the effective action obtained from (2).