Two pion scattering, I=0 and disconnected diagrams in Lattice QCD

TL;DR

This study performs a detailed lattice QCD calculation of I=0 and I=2 pion scattering, including disconnected diagrams, and investigates the eta and eta' mesons, revealing insights into flavor symmetry breaking.

Contribution

It presents the first high-statistics lattice QCD calculation of I=0 pion scattering with disconnected diagrams and explores eta and eta' mesons on the same configurations.

Findings

Disconnected diagrams contribute a small but measurable part of the I=0 scattering amplitude.

The calculation successfully resolves eta and eta' states.

Results show SU(3) flavor symmetry breaking consistent with experimental observations.

Abstract

A full, high-statistic I=0 and I=2 $\pi-\pi$ scattering calculation including the disconnected diagram is performed on 2+1 flavor, domain wall fermion gauge configurations generated using the Iwasaki gauge action with $\beta=2.13$, a $16^3\times32$ volume with $L_s=16$ and $a^{-1}=1.73GeV$. Using the same light quark propagators and additional strange quark propagators, we study the $\eta$ and $\eta^\prime$ mesons, where disconnected diagrams also make an important contribution. Our $\pi-\pi$ calculation shows a good exponentially decaying signal from the disconnected graph, which makes a small contribution to the I=0 scattering amplitude at least for the short times where it can be accurately computed. We are able to resolve the $\eta$ and $\eta^\prime$ states and see the pattern of SU(3) flavor symmetry breaking found in Nature.