# The Dilaton Potential and Lattice Data

## TL;DR

This paper develops an effective field theory to analyze lattice data showing a light scalar particle, exploring how conformal symmetry breaking influences the scalar potential and extracting model parameters from lattice measurements.

## Contribution

It introduces a simple scalar potential form within an EFT framework that fits lattice data, highlighting non-marginal conformal deformations and their impact on scalar and pNGB properties.

## Key findings

- Scalar mass and decay constants are consistent with non-marginal conformal deformation.
- The EFT describes departures from conformality using a single operator.
- Model parameters extracted align with lattice measurements.

## Abstract

We study an effective field theory (EFT) describing the interaction of an approximate dilaton with a set of pseudo-Nambu-Goldstone bosons (pNGBs). The EFT is inspired by, and employed to analyse, recent results from lattice calculations that reveal the presence of a remarkably light singlet scalar particle. We adopt a simple form for the scalar potential for the EFT, which interpolates among earlier proposals. It describes departures from conformal symmetry, by the insertion of a single operator at leading order in the EFT. To fit the lattice results, the global internal symmetry is explicitly broken, producing a common mass for the pNGBs, as well as a further, additive deformation of the scalar potential. We discuss sub-leading corrections arising in the EFT from quantum loops. From lattice measurements of the scalar and pNGB masses and of the pNGB decay constant, we extract model parameter values, including those that characterise the scalar potential. The result includes the possibility that the conformal deformation is clearly non-marginal. The extrapolated values for the decay constants and the scalar mass would then be not far below the current lattice-determined values.