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The LHCb collaboration have recently updated their analysis of the resonant$J/\psi\, p$ mass spectrum in the decay $\Lambda_b^0 \to J/\psi\, p\, K^-$,making use of their combined Run~1 and Run~2 data. In the updated analysis,three narrow states, $P_c (4312)^+$, $P_c (4440)^+$, and $P_c (4457)^+$, areobserved. The spin-parity assignments of these states are not yet known. Weinterpret these narrow resonances as compact hidden-charmdiquark-diquark-antiquark pentaquarks. Using an effective Hamiltonian, based onconstituent quarks and diquarks, we calculate the pentaquark mass spectrum forthe complete $SU (3)_F$ lowest $S$- and $P$-wave multiplets, taking intoaccount dominant spin-spin, spin-orbit, orbital and tensor interactions. Theresulting spectrum is very rich and we work out the quark flavor compositions,masses, and $J^P$ quantum numbers of the pentaquarks. However, heavy quarksymmetry restricts the observable states in $\Lambda_b$-baryon, as well as inthe decays of the other weakly-decaying $b$-baryons, $\Xi_b$ and $\Omega_b$. Inaddition, some of the pentaquark states are estimated to lie below the$J/\psi\, p$ threshold in $\Lambda_b$-decays (and corresponding thresholds in$\Xi_b$- and $\Omega_b$-decays). They decay via $c \bar c$ annihilation intolight hadrons or a dilepton pair, and are expected to be narrower than the$P_c$-states observed. We anticipate their discovery, as well as of the otherpentaquark states present in the spectrum at the LHC, and in the long-termfuture at a Tera-$Z$ factory.

Interpretation of LHCb Hidden-Charm Pentaquarks within the Compact Diquark Model