Graviton-photon production with a massive spin-2 particle
Joshua A. Gill, Dipan Sengupta, Anthony G. Williams
Abstract
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, $f\overline{f}\ensuremath{\rightarrow}G\ensuremath{\gamma}$, no such anomalous divergences occur at tree level. This then applies to other tree-level amplitudes related by crossing symmetry such as $\ensuremath{\gamma}f\ensuremath{\rightarrow}Gf$, $Gf\ensuremath{\rightarrow}\ensuremath{\gamma}f$, $\ensuremath{\gamma}\overline{f}\ensuremath{\rightarrow}G\overline{f}$, $f\ensuremath{\rightarrow}fG\ensuremath{\gamma}$ 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.