ar X iv : 1 11 0 . 14 22 v 2 [ he p - la t ] 1 8 Ja n 20 12 Lattice study on πK 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 mπ = 0.330−0.466 GeV. In the “Asqtad” improved staggered fermion formulation, we measure the πK four-point correlators for both isospin I = 1/2 and 3/2 channels, and analyze the lattice simulation data at the next-to-leading order in the continuum threeflavor chiral perturbation theory, which enables us a simultaneous extrapolation of πK scattering lengths at physical point. We adopt a technique with the moving wall sources without gauge fixing to obtain the substantiable accuracy, moreover, for 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 mπa3/2 = −0.0505(19) and mπa1/2 = 0.1827(37) for 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.