  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 $P_c (4457)^+$, are observed.
The spin-parity assignments of these states are not yet known. We interpret
these narrow resonances as compact hidden-charm diquark-diquark-antiquark
pentaquarks. Using an effective Hamiltonian, based on constituent quarks and
diquarks, we calculate the pentaquark mass spectrum for the complete $SU (3)_F$
lowest $S$- and $P$-wave multiplets, taking into account dominant spin-spin,
spin-orbit, orbital and tensor interactions. The resulting spectrum is very
rich and we work out the quark flavor compositions, masses, and $J^P$ quantum
numbers of the pentaquarks. However, heavy quark symmetry restricts the
observable states in $\Lambda_b$-baryon, as well as in the decays of the other
weakly-decaying $b$-baryons, $\Xi_b$ and $\Omega_b$. In addition, 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 into light 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 other pentaquark
states present in the spectrum at the LHC, and in the long-term future at a
Tera-$Z$ factory.
