Mass Splitting in a Linear Sigma Model

TL;DR

This paper derives the spectrum of an extended linear sigma model for an SU(3) gauge theory with multiple fermion flavors and investigates how small mass differences affect the mass spectrum, aiming to guide future lattice simulations.

Contribution

It provides a theoretical derivation of the tree level spectrum for a mass-split fermion system in an extended linear sigma model, highlighting effects of mass splitting.

Findings

Small mass splitting affects the mass spectrum predictions.

Encourages further lattice simulations with split fermion masses.

Provides a framework for analyzing flavor mass effects in gauge theories.

Abstract

We derived the tree level spectrum to an extension to the linear sigma model describing an EFT for an $SU(3)_c$ gauge theory with $N_f$ flavors of fermions and $N_1$ fermions have a mass $m_l$ and $N_2$ fermions have a mass $m_h$. We examined the effects of a small mass splitting on single mass data for 8 and 12 flavors of fermions corresponding to the unperturbed case. Our intention is to encourage more simulations of split mass theories with 8, 10 and 12 flavors of fermions.