Abstract
We study the spectrum of the isoscalar pentaquark $udsc\overline{c}$, of either positive or negative parity, in a constituent quark model with linear confinement and a flavor-spin hyperfine interaction previously extended to SU(4) and used to describe the spectrum of the $uudc\overline{c}$ pentaquarks observed at LHCb in 2019. For positive parity we make a distinction between the case where one unit of angular momentum is located in the subsystem of four quarks and the case where the angular momentum is located in the relative motion between a ground state four-quark subsystem and the antiquark. The novelty is that we introduce the coupling between different flavor states, due to the breaking of exact SU(4)-flavor symmetry of the Hamiltonian model, both for positive and negative parity states. An important consequence is that the lowest state, located at 4404 MeV, has quantum numbers $J^P$ = $1/2^-$ while without coupling the lowest state has $J^P$ = $1/2^+$ or $3/2^+$.
Highlights
The 2019 LHCb observation of the narrow structures Pþc ð4312Þ, Pþc ð4440Þ and Pþc ð4457Þ in the Λ0b → J=ψK−p decay [1] has given a new impetus to the study of hidden charm pentaquarks
Observed in the J=ψp channel, the proximity of the mass of the Pþc ð4312Þ to the Σþc D 0 threshold (4318 MeV) and of the masses of Pþc ð4440Þ and Pþc ð4457Þ to the Σþc D Ã0 threshold (4460 MeV), favored a molecular S-wave interpretation of the Σþc þD 0 and Σþc þ D Ã0 systems respectively [2,3,4,5,6,7,8,9,10,11,12,13,14,15]
The binding arises via meson exchanges between point particles and in the elastic channel all resonances acquire a negative parity
Summary
The 2019 LHCb observation of the narrow structures Pþc ð4312Þ, Pþc ð4440Þ and Pþc ð4457Þ in the Λ0b → J=ψK−p decay [1] has given a new impetus to the study of hidden charm pentaquarks. The 2019 LHCb pentaquarks have been analyzed in compact pentaquark models based on the chromomagnetic interaction of the one-gluon-exchange model, with quark/ antiquark correlations [18] or without correlations [19,20] In both cases the lowest state has negative parity. The merit of the flavor-spin (FS) model is that it reproduces the correct ordering of positive- and negative-parity states of both nonstrange and strange baryons [30,31,32] in contrast to the one-gluon-exchange model It cannot explain the hyperfine splitting in mesons, because it does not explicitly contain a quark-antiquark interaction. [33], in the context of a schematic flavor-spin interaction, i.e., exact SU(4) symmetry, it was shown that the lowest pentaquark state has a positive parity with the orbital excitation in the internal motion of the four-quark subsystem. In Appendix C we present explicit forms of the flavor states of content udsc in the Young-Yamanouchi-Rutherford basis, for specific irreducible representations 1⁄2fF
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