Speaker
Description
We present preliminary results on the isospin-0 $\pi\pi$ scattering amplitude determined from lattice QCD at a pion mass of 280 MeV and a single lattice spacing of about 0.064 fm. At around this pion mass, the $\sigma$/$f_0(500)$ meson transitions from being a virtual bound state to a resonance. In contrast to previous work, we use CLS ensembles on the $\mathop{\mathrm{tr}} M_q = \mathrm{const.}$ trajectory. This means that the kaon mass is lower than physical, resulting in a significant coupling with the $K \bar{K}$ channel.
The scattering amplitude is reconstructed from the finite-volume spectrum using a non-parametric Bayesian method that incorporates parametrisation dependence into the uncertainty. For the analytic continuation to complex-valued energies, we employ Nevanlinna interpolation. We compare this approach to spectrum fits and discuss the prospects for a robust quantification of the parametrisation uncertainty in the scattering amplitude and the $\sigma$ pole position.