Tadpole contribution to magnetic photon-graviton conversion

Photon-graviton conversion in a magnetic field is a process that is usually studied at tree-level, but the one-loop corrections due to scalars and spinors have also been calculated. Differently from the tree-level process, at one-loop one finds the amplitude to depend on the photon polarization, leading to dichroism. However, previous calculations overlooked tadpole contribution of the type that was considered to be vanishing in QED for decades but erroneously so, as shown by H. Gies and one of the authors in 2016. Here we compute this missing diagram in closed form and show that it does not contribute to dichroism.