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

TL;DR

This paper examines how unphysical meson decays affect parameter determination in the three-flavour NJL model, comparing different regularisation methods and considering the impact of the imaginary parts of meson propagators.

Contribution

It introduces a detailed analysis of unphysical meson decay effects on parameter fixing in the NJL model across various regularisation schemes, highlighting the importance of the imaginary parts.

Findings

Parameter sets vary significantly with regularisation method.

Including the imaginary part alters the parameter fixing results.

Comparison shows the impact of unphysical decay channels on model calibration.

Abstract

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.