Zero-contours in low-energy K-π scattering

International audienceThe paths of zeros of the low-energy $K-π$ scattering amplitudes $A^{I_s=32}$ and $A^{I_t=1}$ are examined in a simple $K*$ and $ρ$ dominance model, where it is found that the roles of PCAC zero, $K^*$ and $ρ$ Legendre zero, and double-pole-killing zero are played by the same zero-contour in the $(s, t, u)-$plane, an ellipse for the first amplitude, an ellipse plus the lines$=u$ for the second one. The behaviour of these zero-contours in the $u-$channel physical region is studied in comparison with the experimental zeros determined from the $K^+π^−→K^+π^−$ and $K^+π^0→K^0π^−$ scattering results, and it is found that up to the $K^*$ mass region the elliptic contour of $A^{I_s=32}$ is essentially unaffected by unitarity, whilst the elliptic contour of $A^{I_t=1}$ is slightly more sensitive to such constraints. A comparison with the behaviour of the zeros of the corresponding $π-π$ amplitudes $A^{I_s=2}_{ππ}$ and $A^{I_t=1}_{ππ}$ is also performed