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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 $m_πa_0^{I=2} = -0.0416(2)$ and $m_πa_0^{I=0} = 0.186(2)$ 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 $a \approx 0.15$ fm.