Heavy quark symmetry in multihadron systems

We discuss the properties of hadronic systems containing one heavy quark in the heavy quark limit. The heavy quark symmetry guarantees the mass degeneracy of the states with total spin and parity $(j-1/2{)}^P$ and $(j+1/2{)}^P$ with $j\ge 1/2$, because the heavy quark spin is decoupled from the total spin $j$ of the light components called brown muck. We apply this idea to heavy multihadron systems and formulate the general framework to analyze their properties. We demonstrate explicitly the spin degeneracy and the decomposition of the wave functions in exotic heavy hadron systems generated by the one-boson-exchange potential. The masses of the brown muck can be extracted from theoretical and experimental hadron spectra, leading to the color nonsinglet spectroscopy.

Figure 1

Energy levels of the bound ${\overline{P}}_{\mathrm{Q}}^{(*)}N$ states with $I=0$ and $J^P=1/2^{\pm }$ and $3/2^{\pm }$ in the heavy quark limit when the $\pi \rho \omega$ potential is used.

Figure 2

Energies of the $J^P=1/2^{\pm }$ and $3/2^{\pm }$ states with $I=0$ measured from the $\overline{P}N$ threshold as functions of heavy vector meson mass $m_{P^{*}}$, when the $\pi \rho \omega$ potential is used. The thick solid (thick dashed) line shows the $1/2^{-}$ ($3/2^{-}$) state, and the thin solid (thin dashed) line shows the $1/2^{+}$ ($3/2^{+}$) state. The horizontal axis sets the logarithmic scale.

Figure 3

The mass spectrum of the brown muck extrapolated from the experimental data of the charm and bottom baryons. The masses are measured from the ground state with $S,I(j^{\mathcal{P}})=0,0(0^{+})$. See also Table 5.

Figure 4

Comparison of the mass spectrum of the charm baryons in the constituent quark model (CQM) [52] (left) and the experimental data [10] (right). The masses are given in units of MeV. $J^P$ with half-integer $J$ is the total spin and parity of the baryon in Ref. [52], and $j^{\mathcal{P}}$ ($\mathcal{P}=P$) with integer $j$ is the total spin and parity of the brown muck identified in Ref. [52]. We use the square and round brackets as $[j^{\mathcal{P}}]$ and $(j^{\mathcal{P}})$ to indicate the flavor antitriplet and sextet states, respectively.

Figure 5

Comparison of the mass spectrum of the bottom baryons in the constituent quark model (CQM) [52] (left) and the experimental data [10] (right). The conventions are the same as Fig. 4.

Figure 6

The mass spectrum of the brown muck extrapolated from the prediction of the constituent quark model [52] and the boson exchange potential model [28, 29, 30]. The numbers on the left of the bars are the excitation energy measured from the ground state of each flavor. The numbers in the dashed arrows are the mass difference of the ground states in each quantum number from the lowest $[ud]$ brown muck in $0^{+}$.