Regarding the possibility to observe the LHCb hidden-charm strange pentaquark $P_{cs}$(4459)0 in antikaon-induced $J/\psi$ meson production on protons and nuclei near the $J/\psi \Lambda$ production threshold

We study the near-threshold <math altimg="si1.svg"><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi></math> meson production on protons and nuclei by considering incoherent direct non-resonant <math altimg="si151.svg"><msup><mrow><mi>K</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> and two-step resonant <math altimg="si3.svg"><msup><mrow><mi>K</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> charmonium production processes. We calculate the absolute excitation functions, energy and momentum distributions for the non-resonant, resonant and for the combined (non-resonant plus resonant) production of <math altimg="si1.svg"><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi></math> mesons off protons as well as off carbon and tungsten target nuclei at near-threshold incident antikaon energies by considering these elementary production channels as well as by assuming the spin-parity assignment of the hidden-charm resonance <math altimg="si4.svg"><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></math> with strangeness as <math altimg="si5.svg"><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo linebreak="goodbreak" linebreakstyle="after">=</mo><msup><mrow><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">/</mo><mn>2</mn><mo stretchy="false">)</mo></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup></math> within six different scenarios for the branching ratio <math altimg="si6.svg"><mi>B</mi><mi>r</mi><mo stretchy="false">[</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mo stretchy="false">]</mo></math> of the decay <math altimg="si7.svg"><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math>. We show that the combined observables considered reveal definite sensitivity to these scenarios, which means that they may be an important tool to provide further evidence for the existence of the pentaquark <math altimg="si4.svg"><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></math> resonance and to get valuable information on its decay rate to the <math altimg="si8.svg"><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> final state. Their measurements could be performed in the future at the J-PARC Hadron Experimental Facility.