$I=1/2$ $S$-wave and $P$-wave $K\pi$ scattering and the $\kappa$ and $K^*$ resonances from lattice QCD

Understand

We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $K\pi$ scattering amplitudes as a function of the center-of-mass energy using L\"uscher'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 $\sqrt{3}\frac{2\pi}{L}$; this includes 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 $\kappa$ resonance in the $S$-wave and the narrow $K^*(892)$ resonance in the $P$-wave.