Heavy quark symmetry and weak decays of the $b$-baryons in pentaquarks with a $c\bar{c}$ component

Abstract

The discovery of the baryonic states $P_c^{+}(4380)$ and $P_c^{+}(4450)$ by the LHCb collaboration has evoked a lot of theoretical interest. These states have the minimal quark content $c\bar{c}uud$. Interpreted as hidden charm diquark-diquark-antiquark baryons, the assigned spin and angular momentum quantum numbers are $P_c^{+}(4380)=\{\bar{c}[cu{]}_{s=1}[ud{]}_{s=1};L_{\mathcal{P}}=0,J^{\mathrm{P}}={\frac{3}{2}}^{-}\}$ and $P_c^{+}(4450)=\{\bar{c}[cu{]}_{s=1}[ud{]}_{s=0};L_{\mathcal{P}}=1,J^{\mathrm{P}}={\frac{5}{2}}^{+}\}$, where $s=0,1$ are the spins of the diquarks and $L_{\mathcal{P}}=0,1$ are the orbital angular momentum quantum numbers of the pentaquarks. We point out that heavy quark symmetry allows only the higher mass pentaquark state $P_c^{+}(4450)$ having $[ud{]}_{s=0}$ to be produced in ${\Lambda }_b^0$ decays, whereas the lower mass state $P_c^{+}(4380)$ having $[ud{]}_{s=1}$ is disfavored. Pentaquark spectrum is rich enough to accommodate a $J^P={\frac{3}{2}}^{-}$ state, which has the correct light diquark spin $\{\bar{c}[cu{]}_{s=1}[ud{]}_{s=0};L_{\mathcal{P}}=0,J^{\mathrm{P}}={\frac{3}{2}}^{-}\}$ to be produced in ${\Lambda }_b^0$ decays. Assuming that the orbital mass difference between the charmed pentaquarks is similar to the corresponding mass difference in the charmed baryons, 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. We present the spectroscopy of the $S$- and $P$-wave pentaquark states having a $c\bar{c}$ pair and three light quarks using 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.

18 pages,7 figures, 12 tables

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