Dilaton chiral perturbation theory at next-to-leading order

TL;DR

This paper extends dilaton chiral perturbation theory to next-to-leading order to analyze lattice data for eight-flavor SU(3) gauge theory, but results are inconclusive due to complex constants and data limitations.

Contribution

It provides the next-to-leading order calculations in dilaton chiral perturbation theory and assesses their applicability to lattice data.

Findings

Next-to-leading order corrections are complex and introduce many new constants.

Fits to data are inconclusive, suggesting possible limitations of dChPT.

Data quality for dilaton mass is insufficient for firm conclusions.

Abstract

We apply dilaton chiral perturbation theory (dChPT) at next-to-leading order to lattice data from the LatKMI collaboration for the eight-flavor SU(3) gauge theory. In previous work, we found that leading-order dChPT does not account for these data, but that a model extension of leading-order dChPT with a varying mass anomalous dimension describes these data well. Here we calculate the next-to-leading order corrections for the pion mass and decay constant. We focus on these quantities, as data for the dilaton mass are of poorer quality. The application of next-to-leading order dChPT is difficult because of the large number of new low-energy constants, and the results of our fits turn out to be inconclusive. They suggest -- yet cannot firmly establish -- that the LatKMI mass range might be outside the scope of dChPT.