UV completions of scalar-tensor EFTs

TL;DR

This paper investigates how scalar-tensor effective field theories emerge from UV models with massive particles, using on-shell amplitude methods to connect UV parameters to low-energy operators, and explores symmetry properties of generated interactions.

Contribution

It provides a detailed analysis of UV completions of scalar-tensor EFTs, including the generation of specific operators and symmetry considerations, using on-shell amplitude techniques.

Findings

Scalar Gauss-Bonnet interactions always break shift symmetry.

Dynamical Chern-Simons interactions can preserve shift symmetry with specific UV matter content.

Explicit relations between UV masses, couplings, and EFT Wilson coefficients are established.

Abstract

We study models that give rise to scalar-tensor effective field theories (EFTs) at low energies. Our framework involves massive particles of spin $S=0, 1/2, 1$ coupled to gravity and to a real massless scalar in the UV. Integrating out the massive states leads to a scalar-tensor EFT describing the massless graviton and scalar degrees of freedom. Using the on-shell amplitude methods and the spinor-helicity formalism, we match the two frameworks at one loop, so as to express the EFT Wilson coefficients in terms of the UV masses and coupling. We explore the space of the operators generated in the EFT, including the ones related to the scalar Gauss-Bonnet (SGB) and dynamical Chern-Simons (DCS) gravity theories. We demonstrate that, within our setup, the SGB interactions are always generated with shift-symmetry breaking operators. This is in contrast to the DCS case, where there is a unique choice that preserves the shift symmetry in the IR, corresponding to a theory of spin 1/2 fermions and a complex scalar with a Peccei-Quinn global symmetry.