Abstract
In a previous work we have studied the isospin 1/2 lowest positive and negative parity states of the pentaquark $uudc\overline{c}$, in a constituent quark model with a linear confinement and an SU(4) flavor-spin hyperfine interaction and we compared the results with the $P^+_c(4312)$, $P^+_c(4440)$ and $P^+_c(4457)$ pentaquarks observed at LHCb in 2019. Here we extend the previous work by calculating ratios of decay rates of the $P_c$ pentaquarks to $J/\Psi$ and $\eta_c$ and similarly the ratio of decay rates to $\Lambda_c {\bar D}^*$ and $\Lambda_c \bar D$. Our predictions are based on the SU(4)$\times$SU(2) structure of compact pentaquarks.
Highlights
The present work aims at understanding the role of the flavor-spin structure of the wave functions of the uudccpentaquarks studied in Ref. [20] on some of their strong decay properties
From the resulting expression of the overlap we find that the ratio of the decay rates for B 1⁄4 p is
The present study relies on a compact pentaquark picture of the uudccpentaquark based on the flavor-spin model extended to SU(4)
Summary
The observation of the narrow structures Pþc ð4312Þ, Pþc ð4440Þ and Pþc ð4457Þ in the Λ0b → J=ψK−p decay made by LHCb in 2019 and its interpretation as a pentaquark with flavor content uudcc [1] has stimulated considerable interest in further understanding the structure of these pentaquarks. A considerable amount of studies are based on the color-spin (CS) chromomagnetic interaction of the one gluon exchange model with quark/ antiquark correlations [17] or without correlations, see, for example, Refs. The present work aims at understanding the role of the flavor-spin structure of the wave functions of the uudccpentaquarks studied in Ref. A list of meson-baryon systems into which the Pc pentaquarks of positive or negative parity can decay was presented in Ref. The decay widths of the LHCb pentaquark Pcð4312Þ has been analyzed, for example, in a chiral constituent quark model containing both chromomagnetic and meson exchange interactions [28]. We study the role of the flavor-spin structure of the pentaquark wave functions on the ratios of decays of the uudccto J=ψ and to ηc and of the decays to ΛcDand to ΛcD Ã. In Appendix C we derive the spin part of the pentaquark wave function and in Appendix D we present some useful details of the flavor-spin wave function of negative parity states
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