Lattice study of Kπ scattering in I=3/2 and 1/2 channels

We report the first lattice QCD results of the scattering amplitudes of the K pi system for I = 1/2 channel together with the I = 3/2 case. We investigate all quark diagrams contributing to these isospin states, and find that the scattering amplitudes are expressed as combinations of only three diagrams after setting the masses of u-quark and d-quark to be the same. The lattice simulations are performed in the quenched approximation at beta = 2.23 on a 12(3) x 24 lattice with an improved Iwasaki gauge action. We employ a new dilution-type noise method to get an accuracy of data with reasonable CPU time. A simple method is proposed and applied to eliminate lattice artefact due to the finite extent of the lattice along the time direction. A clear difference in the quark mass dependence between the I = 3/2 and I = 1/2 channels is observed. Although the chiral extrapolation is subtle, we assume E-K pi(2) proportional to m(u,d)(2), and obtain the S-wave scattering lengths as a(0)(I = 3/2)m(pi) = -0.084(-0.064)(+0.051) and a(0)(I = 1/2)m(pi) = -0.625 +/- 0.012. We show all necessary formulas which make the calculation possible. We argue that Lambda N is the most appropriate target of Luscher's formula for the baryonic system because it has no pi exchange diagrams and has a scattering length suitable for a lattice QCD simulation.