Study of the $KN\text{−}{K}^{*}N$ coupled system in $s$-wave

We study the strangeness $+1$ meson-baryon systems to obtain improved $KN$ and $K^{*}N$ amplitudes and to look for a possible resonance formation by the $KN\text{−}{K}^{*}N$ coupled interaction. We obtain amplitudes for light vector meson–baryon systems by implementing the $s$-, $t$- and $u$-channel diagrams and a contact interaction. The pseudoscalar meson-baryon interactions are obtained by relying on the Weinberg-Tomozawa theorem. The transition amplitudes between the systems consisting of pseudoscalars and vector mesons are calculated by extending the Kroll-Ruderman term for pion photoproduction by replacing the photon by a vector meson. We fix the subtraction constants required to calculate the loops by fitting our $KN$ amplitudes to the data available for the isospin 0 and 1 $s$-wave phase shifts. We provide the scattering lengths and the total cross sections for the $KN$ and $K^{*}N$ systems obtained in our model, which can be useful in future in-medium calculations. Our amplitudes do not correspond to the formation of a resonance in any of the isospin and spin configurations.

Figure 1

Diagrams involving a $u$-channel exchange of $\mathrm{\Lambda }$ resonances.

Figure 2

Scattering phase shifts for the $KN$ system in $S_{01}$ and $S_{11}$ partial waves. The solid lines show the results obtained within our $KN\text{−}{K}^{*}N$ coupled-channel formalism [i.e., using the value of $g_{\mathrm{KR}}$ given by Eq. (24)] by using the same subtraction constants as those used to reproduce the experimental data for the strangeness $-1$ coupled-channel scattering [37]. The dashed lines are obtained using the same subtraction constants but setting the coupling between $KN\text{−}{K}^{*}N$ to zero. The data from the partial wave analysis, represented by filled circles, boxes and empty triangles are taken from Refs. [20, 21, 22], respectively.

Figure 3

Scattering phase shifts for the $KN$ system obtained by using the parameter set II (subtraction constants: $b_{KN}^{I=0}=-6.82$, $b_{K^{*}N}^{I=0}=1.84$, $b_{KN}^{I=1}=-1.59$ and $b_{K^{*}N}^{I=1}=-1$, with $\mu =630\mathrm{MeV}$), and for $\mathrm{\Lambda }$ in Eq. (26) varying between 650 and 1000 MeV. The lines and symbols here have the same meaning as in Fig. 2.

Figure 4

A comparison of the kernel $V$ for $KN$ system obtained in Sec. 2a and defined by Eq. (34). Here $V_{\text{our model}}$ is the sum of the amplitudes obtained from Eqs. (3) and (18).

Figure 5

Same as Fig. 4 but for $K^{*}N$ system with $V_{\text{our model}}$ being the sum of the amplitudes obtained from Eqs. (14) and (19).

Figure 6

Contribution of the resonance exchange in the $u$-channel diagram to the $KN$ amplitude in the $S_{01}$ partial wave obtained with parameter set II. Notice that the dashed and solid curves are almost indistinguishable.

Figure 7

Our results for the total cross sections for the $KN$ (left panel) and $K^{*}N$ (right panel) $s$-wave interaction which leads to a total spin $1/2$ (solid line) in the former case and total spin $1/2$ (solid line) and $3/2$ (dashed line) in the latter one. The data represented by filled circles, boxes and empty triangles are taken from Refs. [20, 21, 22], respectively.