Influence of a $Z^{+}\left(1540\right)$ resonance on $K^{+}N$ scattering

The impact of a $\left(I=0,J^P={\frac{1}{2}}^{+}\right)Z^{+}\left(1540\right)$ resonance with a width of $5\text{MeV}$ or more on the $K^{+}N\left(I=0\right)$ elastic cross section and on the $P_{01}$ phase shift is examined within the $KN$ meson-exchange model of the Jülich group. It is shown that the rather strong enhancement of the cross section caused by the presence of a $Z^{+}$ with the above properties is not compatible with the existing empirical information on $KN$ scattering. Only a much narrower $Z^{+}$ state could be reconciled with the existing data—or, alternatively, the $Z^{+}$ state must lie at an energy much closer to the $KN$ threshold.

Figure 1

Meson-exchange contributions to the $KN$ interaction. Diagrams (a) and (b) define the original Jülich model I [10, 11] that we use in the present investigations. Diagram (c) represents the considered $Z^{+}\left(1540\right)$ contribution.

Figure 2

$KN$ elastic cross section in the isospin channels $I=0,1$. The solid line is the result of the original Jülich model I from Ref. 11. The dashed (dash-dotted) line shows results where a $Z^{+}$ resonance with a dynamically generated width of 5 $\left(20\right)\text{MeV}$ is included. Experimental data are taken from Ref. 17 (filled circles), Ref. 18 (open squares), Ref. 19 (open circles), and Ref. 20 (crosses).

Figure 3

$KN$ phase shifts in the $P_{01}$ partial wave. The solid line is the result of the original Jülich model I from Ref. 11. The dashed (dash-dotted) line shows results where a $Z^{+}$ resonance with a dynamically generated width of 5 $\left(20\right)\text{MeV}$ is included. Experimental phase shifts are taken from Ref. 21 (open circles), Ref. 22 (open squares), and Ref. 23 (filled circles and pluses).