  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.
