A study of the $KN$-$K^{\ast }N$ coupled systems

We study the strangeness $+1$ meson-baryon systems to obtain improved $KN$ and $K^{\ast }N$ amplitudes and to look for a possible resonance formation by the $KN$-$K^{\ast }N$ coupled interaction. We obtain amplitudes for light vector meson-baryon systems by implementing the $s$-, $t$-, $u$- 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 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 $K^{\ast }N$ systems obtained in our model, which can be useful in future in-medium calculations. Our amplitudes do not correspond to formation of any resonance in none of the isospin and spin configurations.