Lattice QCD Calculation of ππ Scattering Length

We study s-wave pion-pion scattering length in lattice QCD for pion masses ranging from 330 MeV to 466 MeV. In the Asqtad improved staggered fermion formulation, we measure full pi pi four-point correlators 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 yields scattering lengths as m(pi)a(O)(I=2) - -0.041 6(2) and m(pi)a(O)(I=0) - 0.186(2) for isospin I = 2 and 0 channels, respectively. Our lattice simulation for pi pi scattering length in 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 carried out with MILC 2 +1 flavor gauge configurations at lattice spacing a approximate to 0.15 fm.