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

Ali, Ahmed; Ahmed, Ishtiaq; Aslam, M. Jamil; Rehman, Abdur

Preprint/Report

PUBDB-2016-02653

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

Ali, A. (Corresponding author)DESY* ; Ahmed, I. ; Aslam, M. J. ; Rehman, A.

2016

[10.3204/PUBDB-2016-02653]

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Please use a persistent id in citations: doi:10.3204/PUBDB-2016-02653

Report No.: DESY-16-102; arXiv:1607.00987

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 $c \bar{c} u u d$. Interpreted as hidden charm diquark-diquark-antiquark baryons, the assigned spin and angular momentum quantum numbers are $P_c^+(4380)= \{\bar{c} [cu]_{s=1} [ud]_{s=1}; L_{\mathcal{P}}=0, J^{\rm P}=\frac{3}{2}^- \}$ and $P_c^+(4450)= \{\bar{c} [cu]_{s=1} [ud]_{s=0}; L_{\mathcal{P}}=1, J^{\rm P}=\frac{5}{2}^+ \}$, 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 $\{\bar{c} [cu]_{s=1} [ud]_{s=0}; L_{\mathcal{P}}=0, J^{\rm P}=\frac{3}{2}^- \}$ 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.

Keyword(s): heavy quark: symmetry ; diquark: spin ; pentaquark: quantum number ; pentaquark: mass ; angular momentum ; mass difference ; LHC-B ; quark ; effective Hamiltonian ; Hamiltonian formalism ; charmed baryon ; baryon ; charm