Lattice study on π K scattering with moving wall source

The s-wave pion-kaon (πK) scattering lengths at zero momentum are calculated in lattice QCD with sufficiently light $u/d$ quarks and strange quark at its physical value by the finite size formula. The light quark masses correspond to m_π=0.330--0.466 GeV. In the Asqtad improved staggered fermion formulation, we measure the πK four-point correlators for both the isospin $I=1/2$ and $3/2$ channels, and analyze the lattice simulation data at the next-to-leading order in the continuum three-flavor chiral perturbation theory, which enables a simultaneous extrapolation of πK scattering lengths at the physical point. We adopt a technique with the moving wall sources without gauge fixing to obtain substantiable accuracy; moreover, for the $I=1/2$ channel, we employ the variational method to isolate the contamination from the excited states. Extrapolating to the physical point yields the scattering lengths as m_πa3/2=-0.0512(18) and m_πa1/2=0.1819(35) for the $I=3/2$ and $1/2$ channels, respectively. Our simulation results for πK scattering lengths are in agreement with the experimental reports and theoretical predictions, and can be comparable with other lattice simulations. These simulations are carried out with MILC Nf=2+1 flavor gauge configurations at lattice spacing a≈0.15 fm.