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We investigate the production of the hidden-charm pentaquark $P_{cs}^0(4459)$with strangeness in the $K^- p \to J/\psi \Lambda$ reaction, employing twodifferent theoretical frameworks, i.e., the effective Lagrangian method and theRegge approach. Having determined all relevant coupling constants, we are ableto compute the total and differential cross sections for the $K^- p \to J/\psi\Lambda$ reaction. We examine the contributions of $P_{cs}$ with different setsof spin-parity quantum number assigned. The present results may give a guidefor possible future experiments.

Production of hidden-charm strange pentaquarks $P_{cs}$ from the $K^- \,p \to J/\psi \,\Lambda$ reaction