Abstract
We discuss the dRGT massive gravity interacting with spin-0, spin-1/2, or spin-1 matter. The effective theory of a massive spin-2 particle coupled to matter particles is constructed directly at the amplitude level. In this setting we calculate the gravitational Compton scattering amplitudes and study their UV properties. While the Compton am- plitudes generically grow with energy as O(E6), we identify regions of the parameter space where they are softened to O(E4) or even O(E3), which allows for a larger validity range of the effective theory. In these regions, both positivity and beyond-positivity of the forward Compton amplitudes are fulfilled, and the equivalence principle automatically emerges.
Highlights
Concrete, non-linear, ghost-free realization of this scenario is the dRGT gravity [5,6,7,8]
While the Compton amplitudes generically grow with energy as O(E6), we identify regions of the parameter space where they are softened to O(E4) or even O(E3), which allows for a larger validity range of the effective theory
For a generic point in the parameter space they grow with energy as Mc ∼ (E/Λ3)6 for any spin of the matter particle, which is the same behavior as for graviton self-scattering amplitudes they become strongly coupled around the same scale as M(GG → GG)
Summary
In the on-shell framework, amplitudes are cast in a form that makes manifest their little group transformation properties. Where full symmetrization of the little group indices is implicit These are nothing but the usual polarization tensors [15]. Summing a product of the polarization tensors over the little group indices one obtains the numerator of the massive graviton propagator: Nμpν,αβ ≡. A softer behavior is obtained if the p/m terms in the numerator Nμν,αβ annihilate M (jk), and do not contribute to the amplitude This is equivalent to requiring that the two-momentum-insertion terms are invariant under the transformation μν j. One could continue the EFT expansion of the 3-graviton amplitudes by adding terms with four and six momentum insertions. Lead to amplitudes with transverse polarizations growing as O(E10), and corresponds to deforming the dRGT gravity Lagrangian by a cubic term constructed out of the Weyl tensor [20]. In this paper we restrict to the usual dRGT cubic graviton interactions described on-shell by eq (2.4)
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