S-Wave πK Scattering Length in 2+1 Flavor Lattice QCD

Abstract

The S-wave πK scattering lengths are calculated for both the isospin 1/2 and 3/2 channels in the lattice QCD by using the finite size formula. We perform the calculation with Nf = 2+1 gauge configurations generated on 323 ×64 lattice using the Iwasaki gauge action and nonperturbatively O(a)-improved Wilson action at 1/a = 2.17 GeV. The quark masses correspond to mπ= 0.29 - 0.70 GeV. For I = 1/2, to separate the contamination from excited states, we construct a 2 ×2 matrix of the time correlation function and diagonalize it. Here, we adopt the two kinds of operators, su and πK. It is found that the signs of the scattering lengths are in agreement with experiment, namely attraction in I = 1/2 and repulsion in I = 3/2. We investigate the quark-mass dependence of the scattering lengths and also discuss the limitation of chiral perturbation theory.