Production mechanism of the hidden charm pentaquark states <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mover accent="true"><mml:mi>c</mml:mi><mml:mo stretchy="

We investigate hidden charm pentaquark states using an off-shell coupled-channel formalism involving heavy meson and singly heavy baryon scattering. Our approach utilizes an effective Lagrangian to construct the kernel amplitudes, which respect both heavy quark symmetry and hidden local symmetry. After solving the coupled integral equations, we obtain the transition amplitudes for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>J</a:mi><a:mo>/</a:mo><a:mi>ψ</a:mi><a:mi>N</a:mi></a:math> scattering and various heavy meson and singly heavy baryon scattering processes. We identify seven distinct peaks related to molecular states of heavy mesons <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mover accent="true"><c:mi>D</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math> (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mover accent="true"><g:mi>D</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mo>*</g:mo></g:msup></g:math>) and singly heavy baryons <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi mathvariant="normal">Σ</k:mi><k:mi>c</k:mi></k:msub></k:math> (<n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msubsup><n:mi mathvariant="normal">Σ</n:mi><n:mi>c</n:mi><n:mo>*</n:mo></n:msubsup></n:math>). Four of these peaks can be associated with the known <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>P</q:mi><q:mrow><q:mi>c</q:mi><q:mover accent="true"><q:mi>c</q:mi><q:mo stretchy="false">¯</q:mo></q:mover></q:mrow></q:msub></q:math> states: <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>P</u:mi><u:mrow><u:mi>c</u:mi><u:mover accent="true"><u:mi>c</u:mi><u:mo stretchy="false">¯</u:mo></u:mover></u:mrow></u:msub><u:mo stretchy="false">(</u:mo><u:mn>4312</u:mn><u:mo stretchy="false">)</u:mo></u:math>, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>P</ab:mi><ab:mrow><ab:mi>c</ab:mi><ab:mover accent="true"><ab:mi>c</ab:mi><ab:mo stretchy="false">¯</ab:mo></ab:mover></ab:mrow></ab:msub><ab:mo stretchy="false">(</ab:mo><ab:mn>4380</ab:mn><ab:mo stretchy="false">)</ab:mo></ab:math>, <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>P</gb:mi><gb:mrow><gb:mi>c</gb:mi><gb:mover accent="true"><gb:mi>c</gb:mi><gb:mo stretchy="false">¯</gb:mo></gb:mover></gb:mrow></gb:msub><gb:mo stretchy="false">(</gb:mo><gb:mn>4440</gb:mn><gb:mo stretchy="false">)</gb:mo></gb:math>, and <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msub><mb:mi>P</mb:mi><mb:mrow><mb:mi>c</mb:mi><mb:mover accent="true"><mb:mi>c</mb:mi><mb:mo stretchy="false">¯</mb:mo></mb:mover></mb:mrow></mb:msub><mb:mo stretchy="false">(</mb:mo><mb:mn>4457</mb:mn><mb:mo stretchy="false">)</mb:mo></mb:math>. We predict two additional resonances with masses around 4.5 GeV, which we interpret as <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msup><sb:mover accent="true"><sb:mi>D</sb:mi><sb:mo stretchy="false">¯</sb:mo></sb:mover><sb:mo>*</sb:mo></sb:msup><sb:msubsup><sb:mi mathvariant="normal">Σ</sb:mi><sb:mi>c</sb:mi><sb:mo>*</sb:mo></sb:msubsup></sb:math> molecular states, and identify one cusp structure. Additionally, we predict two <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:mi>P</xb:mi></xb:math>-wave pentaquark states with positive parity, which may be candidates for genuine pentaquark configurations. Notably, these pentaquark states undergo significant modifications in the <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:mi>J</zb:mi><zb:mo>/</zb:mo><zb:mi>ψ</zb:mi><zb:mi>N</zb:mi></zb:math> elastic channel, with some even disappearing due to interference from the positive parity channel. The present investigation may provide insight into the absence of pentaquark states in <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:mi>J</bc:mi><bc:mo>/</bc:mo><bc:mi>ψ</bc:mi></bc:math> photoproduction observed by the GlueX Collaboration. Published by the American Physical Society 2024