Explorations beyond dilaton chiral perturbation theory in the eight-flavor SU(3) gauge theory

TL;DR

This paper investigates the spectroscopy of eight-flavor SU(3) gauge theory, extending dilaton chiral perturbation theory to include running effects of the mass anomalous dimension, and finds data favor the dChPT predictions.

Contribution

It introduces a phenomenological extension of dilaton chiral perturbation theory that accounts for running of m, successfully fitting lattice data across a wide fermion mass range.

Findings

The extended model describes the full fermion-mass range of the data.

Data favor the dilaton potential form predicted by dChPT.

The approach captures pion taste splittings from lattice simulations.

Abstract

We continue our study of spectroscopy data for the SU(3) gauge theory with eight fundamental fermions, motivated by the effective field theory framework of dilaton chiral perturbation theory (dChPT). At leading order dChPT predicts a constant mass anomalous dimension $\gamma_m$, consistent with the assumed proximity of an infrared fixed point. For the relatively large fermion masses simulated by the LatKMI collaboration, the influence of the infrared fixed point diminishes, and our fits suggest that $\gamma_m$ starts running. Since a complete higher-order analysis is not feasible with presently available data, we adopt a more phenomenological approach. We propose a partial extension to higher orders, which incorporates the running of $\gamma_m$ into the tree-level lagrangian. We find that this extension successfully describes the full fermion-mass range of the LatKMI data, including the pion taste splittings which arise from using staggered fermions in the lattice simulations. We also investigate a more general class of dilaton potentials proposed in the literature, using both the LSD and LatKMI data sets, concluding that these data favor the form predicted by dChPT.