Trace anomalies and the graviton-dilaton amplitude

A bstract 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 ∆ c − ∆ a along any RG flow, where ∆ c and ∆ a are the differences of the UV and IR c - and a -trace anomalies respectively. This allows us to relate ∆ c − ∆ 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.