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

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 ${16}^3\times 32$ 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 ${\eta }^{\mathrm{\prime }}$ 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 ${\eta }^{\mathrm{\prime }}$ states and see the pattern of SU(3) flavor symmetry breaking found in Nature.