Lattice study on πK scattering with moving wall source

The s-wave pion-kaon (pi K) 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(pi) = 0.330-0.466 GeV. In the Asqtad improved staggered fermion formulation, we measure the pi K 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 pi K 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(pi)a(3/2) = -0.0512(18) and m(pi)a(1/2) = 0.1819(35) for the I = 3/2 and 1/2 channels, respectively. Our simulation results for pi K 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 N-f = 2 + 1 flavor gauge configurations at lattice spacing a approximate to 0.15 fm.