Role of the short-range dynamics in a simultaneous interpretation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:math> pentaqua

We investigate hidden-charm molecular states in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msubsup> <a:mi mathvariant="normal">Ξ</a:mi> <a:mi>c</a:mi> <a:mrow> <a:mo>(</a:mo> <a:mo>′</a:mo> <a:mo>,</a:mo> <a:mo>*</a:mo> <a:mo>)</a:mo> </a:mrow> </a:msubsup> <a:msup> <a:mover accent="true"> <a:mi>D</a:mi> <a:mo>¯</a:mo> </a:mover> <a:mrow> <a:mo>(</a:mo> <a:mo>*</a:mo> <a:mo>)</a:mo> </a:mrow> </a:msup> </a:mrow> </a:math> systems using the one-boson exchange model. By regulating the short-range interactions with parameter <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>a</d:mi> </d:math> and cutoff <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi mathvariant="normal">Λ</e:mi> </e:math> , we found ten bound states in isoscalar systems. Our analysis reveals that if the LHCb Collaboration's <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:msub> <g:mi>P</g:mi> <g:mrow> <g:mi>c</g:mi> <g:mi>s</g:mi> </g:mrow> </g:msub> <g:mrow> <g:mo>(</g:mo> <g:mn>4459</g:mn> <g:mo>)</g:mo> </g:mrow> </g:mrow> </g:math> and Belle Collaboration's <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:msub> <h:mi>P</h:mi> <h:mrow> <h:mi>c</h:mi> <h:mi>s</h:mi> </h:mrow> </h:msub> <h:mrow> <h:mo>(</h:mo> <h:mn>4472</h:mn> <h:mo>)</h:mo> </h:mrow> </h:mrow> </h:math> pentaqurks are indeed distinct states, their mass splitting can be resolved through <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:msubsup> <i:mi mathvariant="normal">Ξ</i:mi> <i:mi>c</i:mi> <i:mo>′</i:mo> </i:msubsup> <i:mover accent="true"> <i:mi>D</i:mi> <i:mo>¯</i:mo> </i:mover> <i:mtext>−</i:mtext> <i:msub> <i:mi mathvariant="normal">Ξ</i:mi> <i:mi>c</i:mi> </i:msub> <i:msup> <i:mover accent="true"> <i:mi>D</i:mi> <i:mo>¯</i:mo> </i:mover> <i:mo>*</i:mo> </i:msup> </i:mrow> </i:math> coupled-channel dynamics using consistent model parameters. This framework assigns <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mn>3</n:mn> <n:mo>/</n:mo> <n:msup> <n:mn>2</n:mn> <n:mo>−</n:mo> </n:msup> </n:mrow> </n:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:mn>1</o:mn> <o:mo>/</o:mo> <o:msup> <o:mn>2</o:mn> <o:mo>−</o:mo> </o:msup> </o:mrow> </o:math> spin-parity quantum numbers to <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mrow> <p:msub> <p:mi>P</p:mi> <p:mrow> <p:mi>c</p:mi> <p:mi>s</p:mi> </p:mrow> </p:msub> <p:mrow> <p:mo>(</p:mo> <p:mn>4459</p:mn> <p:mo>)</p:mo> </p:mrow> </p:mrow> </p:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:msub> <q:mi>P</q:mi> <q:mrow> <q:mi>c</q:mi> <q:mi>s</q:mi> </q:mrow> </q:msub> <q:mrow> <q:mo>(</q:mo> <q:mn>4472</q:mn> <q:mo>)</q:mo> </q:mrow> </q:mrow> </q:math> , respectively. With this consistent model parameter, we predict several new molecular candidates in the 4.3–4.7 GeV mass region, demonstrating the crucial interplay between coupled-channel effects and short-range dynamics in understanding hidden-charm pentaquarks as hadronic molecules. Additionally, we investigate the effects of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:mrow> <r:mi mathvariant="normal">Λ</r:mi> <r:msub> <r:mi>η</r:mi> <r:mi>c</r:mi> </r:msub> </r:mrow> </r:math> and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:mrow> <t:mi mathvariant="normal">Λ</t:mi> <t:mi>J</t:mi> <t:mo>/</t:mo> <t:mi>ψ</t:mi> </t:mrow> </t:math> decay channels on the predicted molecular states, showing how these channels influence pole positions and provide insights into the detectability of these states through different production mechanisms.