Scattering from finite size methods in lattice QCD

Abstract

Using two flavors of maximally twisted mass fermions, we calc ulate the S-wave pion-pion scattering length in the isospin I = 2 channel and the P-wave pion-pion scattering phase in the isospin I = 1 channel. In the former channel, the lattice calculations a re performed at pion masses ranging from 270 MeV to 485 MeV. We use chiral perturbation theory at next-to-leading order to extrapolate our results. At the physical pion mass, we find mπa I=2 ππ = −0:04385(28)(38) for the scattering length. In the latter channel, the calculation i s currently performed at a single pion mass of 391 MeV. Making use of finite size methods, we evaluate the scattering phase in both the center of mass frame and the moving frame. The effective range formula is employed to fit our results, from which the rho resonance mass and decay width are evaluated.