SU(3) gauge theory with four degenerate fundamental fermions on the lattice

TL;DR

This study investigates the properties of SU(3) gauge theory with four fundamental fermions using lattice simulations, aiming to compare it with theories having different fermion flavors and to understand its relevance to real-world QCD.

Contribution

The paper presents lattice simulation results for four-flavor QCD using a consistent improved lattice action, providing data on meson and baryon masses and the scalar bound state.

Findings

Fermion mass dependence of various hadron masses and decay constants

Chiral extrapolations of measured quantities

Preliminary results on the flavor-singlet scalar mass

Abstract

As a part of the project studying large $N_f$ QCD, the LatKMI Collaboration has been investigating the SU(3) gauge theory with four fundamental fermions (four-flavor QCD). The main purpose of studying four-flavor QCD is to provide a qualitative comparison to $N_f= 8$, $12$, $16$ QCD; however, a quantitative comparison to real-world QCD is also interesting. To make such comparisons more meaningful, it is desirable to use the same kind of lattice action consistently, so that qualitative difference of different theories are less affected by artifacts of lattice discretization. Here, we adopt the highly-improved staggered quark action with the tree-level Symanzik gauge action (HISQ/tree), which is exactly the same as the setup for our simulations for $SU(3)$ gauge theories with $N_f=8$, $12$ and $16$ fundamental fermions~\cite{Aoki:2013xza, Aoki:2012eq, Aoki:2014oma}. In the next section, we show the fermion mass dependence of $F_\pi$, $\langle\bar{\psi}\psi\rangle$, $M_\pi$, $M_\rho$, $M_N$ and their chiral extrapolations. In section 3, preliminary results of the measurement of the mass of the flavor-singlet scalar bound state will be reported.