Abstract
We assume that the two hidden charm pentaquark discovered at $LHCb$ are built by the three light quarks and the $c \bar{c}$ pair, both colour octets. in relative P-wave for the $\frac{5}{2}^+$ state and by the eigenvectors of the chromomagnetic interaction for the five constituents in S-wave for the four $\frac{3}{2}^-$ state with masses $4360$, $4410$, $4490$ and $4560$ MeV . The "open channel" $p $ $J/\psi$ has large components along the two first states and so appear as the $4380$ resonance and the $\Lambda_c$ $ \bar{D}^{0*}$ and $\Sigma_c$ $\bar{D}^*$ are "open channels" for the lower and higher resonances, respectively. The expectation for their strange isoscalar partners is to have a mass larger by an amount of the order or smaller than the $M_{\Lambda} - M_N$ mass difference. We account for the small width of the $\frac{5}{2}^+$, since its decay needs the exchangeof a gluon and stress that the decays of particles with "beauty" provide the best experimental framework for the discovery of hidden charm multiquarks. The relevance of the production mechanics shows the reason why only some of the states with non minimal number of constituents have been found.
Highlights
The discovery of two pentaquarks with hidden charm in the decay [1]: Λb → p þ J=ψ þ K−ð1Þ confirms the propensity of particles with beauty to give rise to multiquark states with hidden charm, as previously seen [2] for the ð3872; 1þÞ resonance decaying into J=ψ þ ρ0 along with a kaon in the decay of Bq’s
As we shall stress the “beautiful” particles, due to their relative long lifetime, decay at a distance from the interaction point sufficient enough to avoid the presence of the gluons emitted there
In the Appendix, we describe some needed Clebsch-Gordon coefficients of SUð6Þ and several identities that are useful in computing the chromo-magnetic contributions and the values of the quadratic Casimir operators of SUðnÞ, which appear in the evaluation of the chromomagnetic contribution to the mass pf the states
Summary
Istituto Nazionale di Fisica Nucleare, via Cinthia 80126 Sezione di Napoli, Napoli, Italy (Received 21 June 2018; published 13 December 2018). We assume that the two hidden charm pentaquark states discovered at LHCb are built from three light quarks and a ccpair. Further assumed is that the three light quarks and the ccpair are both in colour octet states. [p þ J=ψ] has large components along the two lower mass states and they appear as a resonance with a mass 4380 MeV, whereas [ΛcD Ã] and [ΣcD Ã] are “open channels” respectively for the two lowest and the two highest mass resonances, respectively. The small width of the 5=2þ state is due to the fact that its decay requires one-gluon exchange. The decays of particles with beauty furnish the best experimental technique for discovering multiquark states with hidden charm. The mechanism of production proposed here explains why only a few states with nonminimal constituents have been discovered so far
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