Scalar meson in dynamical and partially quenched two-flavor QCD: lattice results and chiral loops

TL;DR

This study investigates the light scalar meson in two-flavor QCD using lattice simulations with domain wall fermions, analyzing both dynamical and partially quenched correlators to determine the meson mass and understand unphysical effects.

Contribution

It provides the first lattice determination of the scalar meson mass in two-flavor QCD and introduces a chiral perturbation theory analysis to interpret partially quenched correlator behavior.

Findings

Scalar meson mass estimated at ~1.5 GeV

Partially quenched correlators show unphysical negative values for lighter valence quarks

Chiral perturbation theory explains unphysical effects and improves mass extraction

Abstract

This is an exploratory study of the lightest non-singlet scalar $q\bar q$ state on the lattice with two dynamical quarks. Domain Wall fermions are used for both sea and valence quarks on a 16^3*32 lattice with an inverse lattice spacing of 1.7 GeV. We extract the scalar meson mass 1.58(34) GeV from the exponential time-dependence of the dynamical correlators with $m_{val}=m_{sea}$ and N_f=2. Since this statistical error-bar from dynamical correlators is rather large, we analyze also the partially quenched lattice correlators with $m_{val}$ not equal $m_{sea}$. They are positive for $m_{val}>=m_{sea}$ and negative for $m_{val}<m_{sea}$. In order to understand this striking effect of partial quenching, we derive the scalar correlator within the Partially Quenched ChPT and find it describes lattice correlators well. The leading unphysical contribution in Partially Quenched ChPT comes from the exchange of the two pseudoscalar fields and is also positive for $m_{val}>=m_{sea}$ and negative for $m_{val}<m_{sea}$ at large t. After the subtraction of this unphysical contribution from the partially quenched lattice correlators, the correlators are positive and exponentially falling. The resulting scalar meson mass 1.51(19) GeV from the partially quenched correlators is consistent with the dynamical result and has appreciably smaller error-bar.