Production of $\phi \Lambda$, $D_s^{*-} \Lambda_c^+$, and $J/\psi \Lambda$ in kaon-induced reactions off the nucleon

We investigate the reaction mechanism of strangeness production in $K^- p \to \phi \Lambda$ within a hybrid Regge approach, taking into account $t$-channel $K$- and $K^*$-Reggeon exchanges. We present results for the total cross section, $t$-dependent differential cross sections, and spin-density matrix elements (SDMEs), and compare them with the available experimental data. We find that $K^*$-Reggeon exchange provides the dominant contribution, while $K$-Reggeon exchange remains nonnegligible, particularly in describing the SDMEs. In contrast, the $s$-channel $\Lambda$ and $u$-channel nucleon exchanges are negligible. To obtain reliable predictions for the open-charm reaction $K^- p \to D_s^{*-} \Lambda_c^+$, we employ a Quark-Gluon String Model (QGSM)-motivated Regge framework that incorporates both pseudoscalar- and vector-Reggeon exchanges. Within this framework, the Regge trajectories $\alpha(t)$ and energy-scale parameters $s_0$ are determined consistently, thereby constaining the model and reducing theoretical ambiguities. For the hidden-charm reaction $K^- p \to J/\psi \Lambda$, we use the same quark-level diagrammatic correspondence. The total cross sections for $K^- p \to D_s^{*-} \Lambda_c^+$ and $K^- p \to J/\psi \Lambda$ are suppressed by approximately 5-6 and 8-9 orders of magnitude, respectively, compared with that for $K^- p \to \phi \Lambda$. We also examine possible $s$-channel contributions from the hidden-charm pentaquark states with strangeness, $P_{cs}(4337)^0$ and $P_{cs}(4459)^0$, to both $D_s^{*-} \Lambda_c^+$ and $J/\psi \Lambda$ production.