The sigma meson from lattice QCD with two-pion interpolating operators

TL;DR

This study uses lattice QCD with two-pion operators to investigate the sigma meson, identifying a resonance consistent with the f_0(500) and introducing a novel computational technique for all-to-all diagrams.

Contribution

The paper presents the first lattice QCD calculation of the sigma meson using two-pion correlation functions with a new method for computing all-to-all diagrams.

Findings

Identified a sigma meson resonance at approximately 609 MeV.

Developed a novel technique for efficient computation of all-to-all diagrams.

Results are consistent with the properties of the physical sigma meson.

Abstract

In this article we describe our studies of the sigma meson, f_0(500), using two-pion correlation functions. We use lattice quantum chromodynamics in the quenched approximation with so-called clover fermions. By working at unphysical pion masses we are able to identify a would-be resonance with mass less than $2 m_\pi$, and then extrapolate to the physical point. We include the most important annihilation diagram, which is "partially disconnnected" or "single annihilation." Because this diagram is quite expensive to compute, we introduce a somewhat novel technique for the computation of all-to-all diagrams, based on momentum sources and a truncation in momentum space. In practice, we use only ${\bf p}=0$ modes, so the method reduces to wall sources. At the point where the mass of the pion takes its physical value, we find a resonance in the $0^{++}$ two-pion channel with a mass of approximately $609 \pm 80$ MeV, consistent with the expected properties of the sigma meson, given the approximations we are making.