Diquark-diquark-antiquark model for pentaquarks with hidden charm: current status and problems

The $J/\psi p$ signals at 4380 MeV and 4450 MeV which were seen by the LHCb collaboration in the decay $\Lambda^0_b\to K^-J/\psi p$ are discussed following the hypothesis of the existence of diquark-diquark-antiquark composite states. The discussed problems concern: (i) estimation of masses and mass splittings for low-lying states, (ii) determination of decay modes in the quark recombination scheme, (iii) unitarity and analyticity constrains for pentaquark propagators, (iv) hadronic deuteron-like components in the diquark-diquark-antiquark multiplet.