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, $f\overline{f}\to G\gamma$, no such anomalous divergences occur at tree level. This then applies to other tree-level amplitudes related by crossing symmetry such as $\gamma f\to Gf$, $Gf\to \gamma f$, $\gamma \overline{f}\to G\overline{f}$, $f\to fG\gamma$ 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.

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• Braneworlds
• Effective field theory
• Hierarchy problem
• Higher-dimensional field theories
• Naturalness
• Sum rules