Dramatic implications of unitarity for meson spectroscopy

The most fundamental cornerstone of the PDG tables is the uniqueness of $S$-matrix pole positions of unstable particles, as a consequence of quantum-field-theory principles. Therefore, the unitarity property of the $S$-matrix should ideally be respected in whatever description of mesonic resonances in experiment, on the lattice, and in quark models. However, simple Breit-Wigner (BW) parametrisations that not satisfy unitarity continue to be widely used in data analyses of mesonic processes. In this short paper, the resulting discrepancies will be studied for three elastic meson resonances, viz. $\rho(770)$, $f_0(500)$ (alias $\sigma$), and $K_0^\star(700)$ (alias $\kappa$).