Application of dilaton chiral perturbation theory to Nf=8 , SU(3) spectral data

Maarten Golterman,Yigal Shamir,Ethan T Neil

doi:10.1103/physrevd.102.034515

Abstract

We extend dilaton chiral perturbation theory (dChPT) to include the taste splittings in the Nambu--Goldstone sector observed in lattice simulations of near-conformal theories with staggered fermions. We then apply dChPT to a recent simulation by the LSD collaboration of the SU(3) gauge theory with 8 fermions in the fundamental representation, which is believed to exhibit near-conformal behavior in the infrared, and in which a light singlet scalar state, nearly degenerate with the pions, has been found. We find that the mesonic sector of this theory can be successfully described by dChPT, including, in particular, the mesonic taste splittings found in the simulation. We confirm that current simulations of this theory are in the "large-mass" regime.

Highlights

There has been a growing interest in the nonperturbative dynamics of gauge theories with more light fermionic degrees of freedom than QCD, obtained by increasing the number of fundamental fermions or by taking fermions to be in larger representations, or both
We extend dilaton chiral perturbation theory to include the taste splittings in the NambuGoldstone sector observed in lattice simulations of near-conformal theories with staggered fermions
The simulations reported in Ref. [6] were carried out with n-HYP smeared staggered fermions, and exhibit taste splitting of the pion multiplet

Summary

INTRODUCTION

There has been a growing interest in the nonperturbative dynamics of gauge theories with more light fermionic degrees of freedom than QCD, obtained by increasing the number of fundamental fermions or by taking fermions to be in larger representations, or both. In the case of theories with a light scalar, which in current simulations is roughly degenerate with the pions, the light scalar will have to be included in an effective field theory (EFT) approach to interpreting the data Any such EFT should be constructed using the (approximate) symmetries of the underlying theory, and be based on a hypothesis for the parametrical smallness of the mass of the light scalar, much like the usual assumption of chiral symmetry breaking explains the smallness of the pion mass. The behavior of the taste-split pion spectrum as a function of the fermion mass is rather different from that in QCD, and provides a interesting way to test dChPT, extended to include the effects of taste breaking. Preliminary results have been presented in Ref. [34]

TREE-LEVEL DCHPT

EXTENSION TO TASTE SPLITTINGS

FITS TO SPECTROSCOPIC DATA

Fit including taste splittings

Fits with 4 ensembles

CONCLUSION