ar X iv : 1 11 0 . 39 18 v 2 [ he p - la t ] 1 7 Ju n 20 12 Lattice QCD calculation of ππ scattering length

We study s-wave pion-pion (ππ) scattering length in lattice QCD for pion masses ranging from 330 MeV to 466 MeV. In the “Asqtad” improved staggered fermion formulation, we calculate the ππ four-point functions for isospin I = 0 and 2 channels, and use chiral perturbation theory at next-to-leading order to extrapolate our simulation results. Extrapolating to the physical pion mass gives the scattering lengths as mπa I=2 0 = −0.0416(2) and mπa I=0 0 = 0.186(2) for isospin I = 2 and 0 channels, respectively. Our lattice simulation for ππ scattering length in the I = 0 channel is an exploratory study, where we include the disconnected contribution, and our preliminary result is near to its experimental value. These simulations are performed with MILC 2 + 1 flavor gauge configurations at lattice spacing a ≈ 0.15 fm.