Role of the $N^*(2080)$ in $pp \to pK^+ \Lambda(1520)$ and $\pi^- p \to K^0 \Lambda(1520)$ reactions

We investigate the $\Lambda(1520)$ hadronic production in the $p p \to p K^+ \Lambda(1520)$ and $\pi^- p \to K^0 \Lambda(1520)$ reactions within the effective Lagrangian method. For $\pi^- p \to K^0 \Lambda(1520)$ reaction, in addition to the "background" contributions from $t-$channel $K^*$ exchange, $u-$channel $\Sigma^+$ exchange, and $s-$channel nucleon pole terms, we also consider the contribution from the nucleon resonance $N^*(2080)$ (spin-parity $J^P = 3/2^-$), which has significant coupling to $K\Lambda(1520)$ channel. We show that the inclusion of the nucleon resonance $N^*(2080)$ leads to a fairly good description of the low energy experimental total cross section data of $\pi^- p \to K^0 \Lambda(1520)$ reaction. From fitting to the experimental data, we get the $N^*(2080)N\pi$ coupling constant $g_{N^*(2080)N \pi} = 0.14 \pm 0.04$. By using this value and with the assumption that the excitation of $N^*(2080)$ is due to the $\pi^0$-meson exchanges, we calculate the total and differential cross sections of $p p \to p K^+ \Lambda(1520)$ reaction. We also demonstrate that the invariant mass distribution and the Dalitz Plot provide direct information of the $\Lambda(1520)$ production, which can be tested by future experiments.