Understanding <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:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4459</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> as a hadronic molecule in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi mathvariant="normal">Ξ</mml:mi><mml:mi>b</mml:mi><mml:mo>−</mml:mo></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi><mml:mi mathvariant="normal">Λ</mml:mi><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> decay
Jun-Xu Lu, Ming-Zhu Liu, Rui-Xiang Shi, Li‐Sheng Geng
Abstract
Recently, the LHCb Collaboration reported on the evidence for a hidden charm pentaquark state with strangeness, i.e., ${P}_{cs}(4459)$, in the $J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}$ invariant mass distribution of the ${\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}{K}^{\ensuremath{-}}$ decay. In this work, assuming that ${P}_{cs}(4459)$ is a ${\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}$ molecular state, we study this decay via triangle diagrams ${\mathrm{\ensuremath{\Xi}}}_{b}\ensuremath{\rightarrow}{\overline{D}}_{s}^{(*)}{\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}({\overline{D}}^{(*)}\overline{K}){\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{P}_{cs}\overline{K}\ensuremath{\rightarrow}(J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}})\overline{K}$. Our study shows that the production yield of a spin $3/2$ ${\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}$ state is approximately one order of magnitude larger than that of a spin $1/2$ state due to the interference of ${\overline{D}}_{s}{\mathrm{\ensuremath{\Xi}}}_{c}$ and ${\overline{D}}_{s}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}$ intermediate states. We obtain a model independent constraint on the product of couplings ${g}_{{P}_{cs}{\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}}$ and ${g}_{{P}_{cs}J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}}$. With the predictions of two particular molecular models as inputs, we calculate the branching ratio of ${\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}({P}_{cs}\ensuremath{\rightarrow})J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}{K}^{\ensuremath{-}}$ and compare it with the experimental measurement. We further predict the line shape of this decay that could be useful to future experimental studies.