Heavy quark symmetry and weak decays of the b-baryons in pentaquarks with a cc̄ component

The discovery of the baryonic states P c (4380) and P + c (4450) by the LHCb collaboration in the process pp → bb̄ → ΛbX, followed by the decay Λ 0 b → J/ψ p K− has evoked a lot of theoretical interest. These states have the minimal quark content cc̄uud, as suggested by their discovery mode J/ψ p, and the preferred J assignments are 52 + for the P c (4450) and 3 2 − for the P c (4380). In the compact pentaquark hypothesis, in which they are interpreted as hidden charm diquark-diquark-antiquark baryons, the assigned spin and angular momentum quantum numbers are P c (4380) = {c̄[cu]s=1[ud]s=1;LP = 0, J = 32 } and P c (4450) = {c̄[cu]s=1[ud]s=0;LP = 1, J = 5 2 }. The subscripts denote the spin of the diquarks and LP = 0, 1 are the orbital angular momentum quantum numbers of the pentaquarks. We point out that in the heavy quark limit, the spin of the light diquark in heavy baryons becomes a good quantum number, which has consequences for the decay Λb → J/ψ p K−. With the quantum numbers assigned above for the two pentaquarks, this would allow only the higher mass pentaquark state P c (4450) having [ud]s=0 to be produced in Λb decays, whereas the lower mass state P + c (4380) having [ud]s=1 is disfavored, requiring a different interpretation. Pentaquark spectrum is rich enough to accommodate a J = 3 2 − state, which has the correct light diquark spin {c̄[cu]s=1[ud]s=0;LP = 0, J = 32 } to be produced in Λb decays. Assuming that the mass difference between the charmed pentaquarks which differ in the orbital angular momentum L by one unit is similar to the corresponding mass difference in the charmed baryons, m[Λc (2625); J P = 3 2 − ]−m[Λc (2286); J = 1 2 + ] ' 341 MeV, we estimate the mass of the lower pentaquark J = 3/2− state to be about 4110 MeV and suggest to reanalyze the LHCb data to search for this third state. Extending these considerations to the pentaquark states having a cc̄ pair and three light quarks (u, d, s) in their Fock space, we present the spectroscopy of the Sand P -wave states in an effective Hamiltonian approach. Some of these pentaquarks can be produced in weak decays of the b-baryons. Combining heavy quark symmetry and the SU(3)F symmetry results in strikingly simple relations among the decay amplitudes which are presented here. 1 ar X iv :1 60 7. 00 98 7v 1 [ he pph ] 4 J ul 2 01 6