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Mass spectrum of the hidden-charm pentaquarks in the compact diquark model

The LHCb collaboration have recently updated their analysis of the resonant $J/ψp$ mass spectrum in the decay $Λ_b^0 \to J/ψp K^-$, 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 $Λ_b$-baryon, as well as in the decays of the other weakly-decaying $b$-baryons, $Ξ_b$ and $Ω_b$. In addition, some of the pentaquark states are estimated to lie below the $J/ψp$ threshold in $Λ_b$-decays (and corresponding thresholds in $Ξ_b$- and $Ω_b$-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.