Trace Anomalies and the Graviton-Dilaton Amplitude

We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to $\mathrm{\Delta }c-\mathrm{\Delta }a$ along any RG flow, where $\mathrm{\Delta }c$ and $\mathrm{\Delta }a$ are the differences of the UV and IR $c$- and $a$-trace anomalies respectively. This allows us to relate $\mathrm{\Delta }c-\mathrm{\Delta }a$ to spinning massive states in the spectrum of the QFT. We test our predictions in two simple examples: in the theory of a massive free scalar and in the theory of a massive Dirac fermion (a more complicated example is provided in a companion paper [1]). We discuss possible applications.