Production rates of hidden-charm pentaquark molecules in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi mathvariant="normal">Λ</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:math> decays

Abstract

The partial decay widths and production mechanism of the three pentaquark states, ${P}_{\ensuremath{\psi}}^{N}(4312)$, ${P}_{\ensuremath{\psi}}^{N}(4440)$, and ${P}_{\ensuremath{\psi}}^{N}(4457)$, discovered by the LHCb Collaboration in 2019, are still under debate. In this work, we employ the contact-range effective field theory approach to construct the ${\overline{D}}^{(*)}{\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}$, ${\overline{D}}^{*}{\mathrm{\ensuremath{\Lambda}}}_{c}$, $\overline{D}{\mathrm{\ensuremath{\Lambda}}}_{c}$, $J/\ensuremath{\psi}p$, and ${\ensuremath{\eta}}_{c}p$ coupled-channel interactions to dynamically generate the multiplet of hidden-charm pentaquark molecules by reproducing the masses and widths of ${P}_{\ensuremath{\psi}}^{N}(4312)$, ${P}_{\ensuremath{\psi}}^{N}(4440)$, and ${P}_{\ensuremath{\psi}}^{N}(4457)$. Assuming that the pentaquark molecules are produced in the ${\mathrm{\ensuremath{\Lambda}}}_{b}$ decay via the triangle diagrams, where ${\mathrm{\ensuremath{\Lambda}}}_{b}$ first decays into ${D}_{s}^{(*)}{\mathrm{\ensuremath{\Lambda}}}_{c}$, then ${D}_{s}^{(*)}$ scatters into ${\overline{D}}^{(*)}K$, and finally the molecules are dynamically generated by the ${\overline{D}}^{(*)}{\mathrm{\ensuremath{\Lambda}}}_{c}$ interactions, we calculate the branching fractions of the decays ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{P}_{\ensuremath{\psi}}^{N}K$ using the effective Lagrangian approach. With the partial decay widths of these pentaquark molecules, we further estimate the branching fractions of the decays ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}({P}_{\ensuremath{\psi}}^{N}\ensuremath{\rightarrow}J/\ensuremath{\psi}p)K$ and ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}({P}_{\ensuremath{\psi}}^{N}\ensuremath{\rightarrow}{\overline{D}}^{*}{\mathrm{\ensuremath{\Lambda}}}_{c})K$. Our results show that the pentaquark states ${P}_{\ensuremath{\psi}}^{N}(4312)$, ${P}_{\ensuremath{\psi}}^{N}(4440)$, and ${P}_{\ensuremath{\psi}}^{N}(4457)$ as hadronic molecules can be produced in the ${\mathrm{\ensuremath{\Lambda}}}_{b}$ decay, and on the other hand their heavy quark spin symmetry partners are invisible in the $J/\ensuremath{\psi}p$ invariant mass distribution because of the small production rates. Our studies show that it is possible to observe some of the pentaquark states in the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\overline{D}}^{*}{\mathrm{\ensuremath{\Lambda}}}_{c}K$ decays.

Topics & Concepts