One loop photon-graviton mixing in an electromagnetic field: Part 3

TL;DR

This paper investigates one-loop photon-graviton mixing in electromagnetic fields, revealing the significance of a previously overlooked tadpole diagram and its impact on magnetic dichroism calculations using the worldline formalism.

Contribution

It introduces the third tadpole diagram into the calculation of photon-graviton amplitudes, providing a unified worldline formalism approach for scalar and spinor loops in electric and magnetic fields.

Findings

The tadpole diagram contributes to the amplitude but not to magnetic dichroism.

The worldline formalism effectively unifies the calculation of all three diagrams.

The tadpole's contribution is consistent with the gravitational Ward identity.

Abstract

Photon-graviton conversion in an electromagnetic field is a well-known prediction of Einstein-Maxwell theory. First discussed at tree-level by Gertsenshtein in 1962, more recently it has been shown to lead to magnetic dichroism starting from one-loop. While previously only two diagrams were assumed to contribute to this one-loop photon-graviton amplitude in a constant electromagnetic field, here we point out the existence of a third one involving a tadpole subdiagram. As shown by H. Gies and one of the authors in 2016 for the pure QED case, such diagrams cannot be omitted in general even though the tadpole formally vanishes. After a short review of the calculation of one-loop photon-graviton amplitudes in the worldline formalism, we use this formalism for a unified calculation of all three diagrams. Although phenomenologically this amplitude is mainly of interest for the case of the spinor loop in a magnetic field, here we will also include the scalar loop and the electric field component, since the computational effort is essentially the same. We show that the tadpole diagram, although contributing to the amplitude, does not contribute to the magnetic dichroism. The gravitational Ward identity provides a useful check.