Speaker
Description
Parameterizing low-lying scalar resonances remains a challenge. Such is the case for $K^{\star}_{0}(700)$ for which the near threshold experimental results for the corresponding $K\pi$ scattering amplitude are limited. However, production channel data, e.g. $D\to K\pi\pi$, from experiments BES and E791 show clearer evidence of the existence of this resonance. I will present our results for the S and P-wave elastic scattering amplitudes obtained from multi-hadron spectroscopy on the lattice using Lüscher's method. I will comment on the dependence of the S-wave amplitude and the $K^{\star}_{0}(700)$ pole position, if identifiable, on the different parameterizations. These calculations were done for two different ensembles with pion masses of $317(2)$ and $178(2)$ MeV. The need for these scattering amplitudes for the infinite volume determination of $B\to K\pi \ell^{+}\ell^{-}$ matrix elements is also discussed briefly.