The discovery of the baryonic states $P_c^{+}(4380)$ and $P_c^{+}(4450)$ by the LHCb collaboration in the process $pp\to b\overline{b}\to {\mathrm{\Lambda }}_b^{0}X$, followed by the decay ${\mathrm{\Lambda }}_b^0\to J/\psi p{K}^{-}$ has evoked a lot of theoretical interest. These states have the minimal quark content $c\overline{c}uud$, as suggested by their discovery mode $J/\psi p$, and the preferred $J^P$ assignments are ${\frac{5}{2}}^{+}$ for the $P_c^{+}(4450)$ and ${\frac{3}{2}}^{-}$ 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 $P_c^{+}(4380)=\{\overline{c}[cu{]}_{s=1}[ud{]}_{s=1};L_{\mathcal{P}}=0,J^{\mathrm{P}}={\frac{3}{2}}^{-}\}$ and $P_c^{+}(4450)=\{\overline{c}[cu{]}_{s=1}[ud{]}_{s=0};L_{\mathcal{P}}=1,J^{\mathrm{P}}={\frac{5}{2}}^{+}\}$. The subscripts denote the spin of the diquarks and $L_{\mathcal{P}}=0$, 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 ${\mathrm{\Lambda }}_b^0\to J/\psi p{K}^{-}$. 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 ${\mathrm{\Lambda }}_b^0$ 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 $J^P={\frac{3}{2}}^{-}$ state, which has the correct light diquark spin $\{\overline{c}[cu{]}_{s=1}[ud{]}_{s=0};L_{\mathcal{P}}=0,J^{\mathrm{P}}={\frac{3}{2}}^{-}\}$ to be produced in ${\mathrm{\Lambda }}_b^0$ 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, $m[{\mathrm{\Lambda }}_c^{+}(2625);J^P={\frac{3}{2}}^{-}]-m[{\mathrm{\Lambda }}_c^{+}(2286);J^P={\frac{1}{2}}^{+}]\simeq 341\mathrm{MeV}$, we estimate the mass of the lower pentaquark $J^P=3/2^{-}$ 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 $c\overline{c}$ pair and three light quarks ($u$, $d$, $s$) in their Fock space, we present the spectroscopy of the $S$- and $P$-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.

• Received 5 July 2016

DOI:https://doi.org/10.1103/PhysRevD.94.054001