Interpretation of the Narrow $J/\psi p$ Peaks in ${\Lambda }_b\to J/\psi p{K}^{-}$ Decay in the Compact Diquark Model

Abstract

Recently, the LHCb Collaboration have updated their analysis of the resonant $J/\psi p$ mass spectrum in the decay ${\Lambda }_b^0\to J/\psi p{K}^{-}$. In the combined Run~1 and Run~2 LHCb data, three peaks are observed, with the former $P_c(4450{)}^{+}$ state split into two narrow states, $P_c(4440{)}^{+}$ and $P_c(4457{)}^{+}$, having the masses $M=(4440.3\pm 1.3_{-4.7}^{+4.1})$ MeV and $M=(4457.3\pm 0.6_{-1.7}^{+4.1})$ MeV, and decay widths $\Gamma =(20.6\pm 4.9_{-10.1}^{+8.7})$ MeV and $\Gamma =(6.4\pm 2.0_{-1.9}^{+5.7})$ MeV, respectively. In addition, a third narrow peak, $P_c(4312{)}^{+}$, having the mass $M=(4311.9\pm 0.7_{-0.6}^{+6.8})$ MeV and decay width $\Gamma =(9.8\pm 2.7_{-4.5}^{+3.7})$ MeV is also observed. The LHCb analysis is not sensitive to broad $J/\psi p$ contributions like the former $P_c(4380{)}^{+}$, implying that there could be more states present in the data. Also the spin-parity, $J^P$, assignments of the states are not yet determined. We interpret these resonances in the compact diquark model as hidden-charm diquark-diquark-antiquark baryons, having the following spin and angular momentum quantum numbers: $P_c(4312{)}^{+}=\{\bar{c}[cu{]}_{s=1}[ud{]}_{s=0};L_P=0,J^P=3/2^{-}\}$, the $S$-wave state, and the other two as $P$-wave states, with $P_c(4440{)}^{+}=\{\bar{c}[cu{]}_{s=1}[ud{]}_{s=0};L_P=1,J^P=3/2^{+}\}$ and $P_c(4457{)}^{+}=\{\bar{c}[cu{]}_{s=1}[ud{]}_{s=0};L_P=1,J^P=5/2^{+}\}$. The subscripts denote the spins of the diquarks and $L_P=0,1$ is the orbital angular momentum quantum number of the pentaquark. These assignments are in accord with the heavy-quark-symmetry selection rules for ${\Lambda }_b$-baryon decays, in which the spin $S=0$ of the light diquark $[ud{]}_{s=0}$ is conserved. The masses of observed states can be accommodated in this framework and the two heaviest states have the positive parities as opposed to the molecular-like interpretations.

arXiv comment14 pages, 1 figure. Matches version accepted for publication in Physics Letters B

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