Higgs boson decay into two photons in an electromagnetic background

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.Comment: 31 page

Removing the gauge parameter dependence of the effective potential by a field redefinition

The gauge parameter dependence of the effective potential is determined by partial differential equations involving also the Higgs boson field expectation value. Solving these equations by the method of characteristics leads to complete elimination of the gauge parameter dependence of the effective potential. The construction is carried out in the case of the standard model of electroweak unification for the renormalization group improved effective potential up to the next-leading logarithmic order.Comment: 17 page

Instanton constraints and renormalization

The renormalization is investigated of one-loop quantum fluctuations around a constrained instanton in $\phi ^4$-theory with negative coupling. It is found that the constraint should be renormalized also. This indicates that in general only renormalizable constraints are permitted.Comment: 29 page