Graviton-photon production with a massive spin-2 particle

A recent paper [1] within a phenomenological dark matter framework with a massive graviton in the external state argued that a divergence with increasing center-of-momentum energy arising from the longitudinal polarizations of the graviton. In this paper we point out that in processes such as graviton-photon production from matter annihilation, ff̄→Gγ, no such anomalous divergences occur at tree level. This then applies to other tree-level amplitudes related by crossing symmetry such as γf→Gf, Gf→γf, γf̄→Gf̄, f→fGγ and so on. We show this by explicitly computing the relevant tree-level diagrams, where we find that delicate cancellations ensure that all anomalously growing terms are well-regulated. Effectively at tree level this is consistent with the operation of a Ward identity associated with the external photon for such amplitudes. The same tree-level results apply if the photon is replaced by a gluon. These results have important consequences for model construction in areas including dark matter, gravity and high-energy physics.