Role of the high-spin nucleon and delta resonances in the $K\Lambda$ and $K\Sigma$ photoproduction off the nucleon

We have investigated the effect of nucleon and delta resonances with spins 11/2, 13/2, and 15/2 in the kaon photoproduction process $\gamma + N \to K + Y$ by using two covariant isobar models. The formalism for high-spin propagators and interaction Lagrangians were adopted from the works of Pascalutsa and Vrancx et al. The unknown parameters in the amplitudes, i.e., the coupling constants and hadronic form factor cutoffs, were obtained by fitting the calculated observables to experimental data. In the $K\Lambda$ channels the inclusion of $N(2600)I_{1,11}$ and $N(2700)K_{1,13}$ resonances improves the agreement between model calculations and experimental data significantly and reduces the dominance of resonances in the model by increasing the hadronic form factor cutoff of the Born terms. Furthermore, the inclusion of these resonances reduces the number of resonance structures in cross sections, including the structure in the $K^0\Lambda$ differential cross section at $W\approx 1650$ MeV, which could become a hint of the narrow resonance. In the $K\Sigma$ channels the inclusion of $N(2600)I_{1,11}$, $N(2700)K_{1,13}$, $\Delta(2420)H_{3,11}$, $\Delta(2750)I_{3,13}$, and $\Delta(2950)K_{3,15}$ states also significantly improves the model and increases the hadronic form factor cutoff of the Born terms. However, different from the $K\Lambda$ channels, the inclusion of these high-spin resonances leads to more resonance structures in the $K^+\Sigma^0$ differential cross section. This investigation reveals that the second and third peaks in the $K^+\Sigma^0$ differential cross section originate from the $\Delta(2000)F_{35}$ and $N(2290)G_{19}$ resonances, respectively. We have also evaluated the resonance properties at the pole positions and using the Breit-Wigner method.