I=1 /2 S -wave and P -wave Kπ scattering and the κ and K∗ resonances from lattice QCD

Abstract

We present a lattice-QCD determination of the elastic isospin-1/2 S-wave and P-wave Kπ scattering amplitudes as a function of the center-of-mass energy using Lüscher's method. We perform global fits of K-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to 32πL; this includes irreducible representations (irreps) that mix the S- and P-waves. Several different parametrizations for the energy dependence of the K-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad κ resonance in the S-wave and the narrow K∗(892) resonance in the P-wave. Our calculations are performed with 2+1 dynamical clover fermions for two different pion masses of 317.2(2.2) and 175.9(1.8) MeV. Our preferred S-wave parametrization is based on a conformal map and includes an Adler zero; for the P-wave, we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The S-wave κ-resonance pole positions are found to be [0.86(12)-0.309(50)i] GeV at the heavier pion mass and [0.499(55)-0.379(66)i] GeV at the lighter pion mass. The P-wave K∗-resonance pole positions are found to be [0.8951(64)-0.00250(21)i] GeV at the heavier pion mass and [0.8718(82)-0.0130(11)i] GeV at the lighter pion mass, which corresponds to couplings of gK∗Kπ=5.02(26) and gK∗Kπ=4.99(22), respectively.