Three Pion Scattering at Maximal Isospin from Lattice QCD at Physical Mass

Abstract

In this work the scattering of two pions in $I = 2$ and three pions in $I = 3$ is analyzed with lattice QCD. The process is computed on three Wilson clover twisted mass ensembles generated by the ETMC with total momentum up to $vec P^2 leq 4$ in all irreducible representations. One ensemble has been simulated at the physical pion mass. <br /> The correlation functions are treated with methods to suppress thermal states and excited states. Energy extraction is performed with multiple different fit methods and a combination afterwards such that the systematic errors from fit range selection are taken into account. <br /> The three-pion spectrum has been fitted using the RFT approach. We obtain $a_0 M_piup = 0.0481(86)$ for the two-pion scattering length at the physical pion mass. In the three-pion sector a constant and linear coefficient of the contact interaction has been extracted. The constant term agrees both with an existing analysis and leading order ChPT, the linear term has tension with the leading order ChPT prediction at high pion masses.