Impact of unphysical meson decays on the parameter fixing in the three-flavour Nambu-Jona-Lasinio model for different regularisation methods

We investigate the influence of the allowed unphysical meson decay into a quark-antiquark pair of the three flavour Nambu--Jona-Lasinio (NJL) model on its parameter fixing. This decay manifests in a non-vanishing imaginary part of the corresponding meson propagator and its polarisation loop, respectively. In order to handle the emerging divergent integrals, we focus on the Pauli-Villars, three- and four momentum cutoff regularisation method. Here, we fix the parameters to certain observables, which are effected by the non-vanishing imaginary part. The resulting parameter-sets for each regularisation scheme are compared to each other with and without taking the imaginary part of the polarisation loop into account.