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

TL;DR

This work reexamines one-loop photon–graviton conversion in a constant external field within Einstein–Maxwell theory, identifying a nonvanishing tadpole diagram that had been assumed to vanish. Using the worldline formalism, the authors provide a unified calculation for irreducible, tadpole, and ext reducible contributions for both scalar and spinor loops and for general field configurations, deriving explicit representations of the vacuum polarization tensor and the full one-loop amplitude. They show the tadpole contributes to the amplitude but does not alter magnetic dichroism, and they verify gauge and gravitational Ward identities as consistency checks. The analysis also offers a weak-field expansion and discusses renormalization, with implications for strong-field physics and potential extensions to new charged sectors or higher-loop corrections. Overall, the work completes the one-loop treatment of photon–graviton conversion in external fields and clarifies the role of reducible diagrams in background-field QED.

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.

Figures (8)

• Figure 1: Tree-level vertex photon-photon-graviton vertex.
• Figure 2: The three one-loop contributions to electromagnetic photon–graviton conversion. Here “irr” and “ext” denote the irreducible and "extra" contributions, respectively.
• Figure 3: Full scalar or spinor propagator in a constant field.
• Figure 4: One-photon amplitude in a constant electromagnetic field.
• Figure 5: "Handcuff" diagram in a constant field.