Lattice QCD calculation of $\pi \pi$ scattering length

Abstract

We study s-wave pion-pion ($\pi \pi$) 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 $\pi \pi$ 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 $m_{\pi }{a}_0^{I=2}=-0.0416(2)$ and $m_{\pi }{a}_0^{I=0}=0.186(2)$ for isospin I=2 and 0 channels, respectively. Our lattice simulation for $\pi \pi$ 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.

Comments: Remove some typos