Communications in Theoretical Physics ›› 2021, Vol. 73 ›› Issue (12): 125201. doi: 10.1088/1572-9494/ac27a2
• Particle Physics and Quantum Field Theory • Previous Articles Next Articles
Xiang-Kun Dong1,2,(
),Feng-Kun Guo1,2,(),Bing-Song Zou1,2,3,()
Received: 2021-08-06
Revised: 2021-09-16
Accepted: 2021-09-17
Published: 2021-12-01
Contact:
Xiang-Kun Dong
E-mail:dongxiangkun@itp.ac.cn;fkguo@itp.ac.cn;zoubs@itp.ac.cn
Xiang-Kun Dong, Feng-Kun Guo, Bing-Song Zou, Commun. Theor. Phys. 73 (2021) 125201.
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Table 1.
The experimental candidates of heavy baryons predicted by quark model. The notations of experimental states are taken from RPP [6]. The ${{\rm{\Sigma }}}_{b}^{(* )0}$, ${{\rm{\Xi }}}_{b}^{{\prime} 0}$ and ${{\rm{\Omega }}}_{b}^{* 0}$ do not have experimental candidates yet."
| Model | Experimental | Model | Experimental |
|---|---|---|---|
| ${{\rm{\Lambda }}}_{c}^{+}$ | ${{\rm{\Lambda }}}_{c}^{+}$ | ${{\rm{\Lambda }}}_{b}^{0}$ | ${{\rm{\Lambda }}}_{b}^{0}$ |
| ${{\rm{\Xi }}}_{c}^{+}$ | ${{\rm{\Xi }}}_{c}^{+}$ | ${{\rm{\Xi }}}_{b}^{0}$ | ${{\rm{\Xi }}}_{b}^{0}$ |
| ${{\rm{\Xi }}}_{c}^{0}$ | ${{\rm{\Xi }}}_{c}^{0}$ | ${{\rm{\Xi }}}_{b}^{-}$ | ${{\rm{\Xi }}}_{b}^{-}$ |
| Σc | Σc(2455) | Σb | Σb |
| ${{\rm{\Xi }}}_{c}^{{\prime} +}$ | ${{\rm{\Xi }}}_{c}^{{\prime} +}$ | ${{\rm{\Xi }}}_{b}^{{\prime} 0}$ | − |
| ${{\rm{\Xi }}}_{c}^{{\prime} 0}$ | ${{\rm{\Xi }}}_{c}^{{\prime} 0}$ | ${{\rm{\Xi }}}_{b}^{{\prime} -}$ | ${{\rm{\Xi }}}_{b}^{{\prime} }{\left(5935\right)}^{-}$ |
| ${{\rm{\Omega }}}_{c}^{0}$ | ${{\rm{\Omega }}}_{c}^{0}$ | ${{\rm{\Omega }}}_{b}^{-}$ | ${{\rm{\Omega }}}_{b}^{-}$ |
| ${{\rm{\Sigma }}}_{c}^{* }$ | Σc(2520) | ${{\rm{\Sigma }}}_{b}^{* }$ | ${{\rm{\Sigma }}}_{b}^{* }$ |
| ${{\rm{\Xi }}}_{c}^{* +}$ | ξc(2645)+ | ${{\rm{\Xi }}}_{b}^{* 0}$ | ξb(5945)0 |
| ${{\rm{\Xi }}}_{c}^{* 0}$ | ξc(2645)0 | ${{\rm{\Xi }}}_{b}^{* -}$ | ξb(5955)− |
| ${{\rm{\Omega }}}_{c}^{* 0}$ | ωc(2770)0 | ${{\rm{\Omega }}}_{b}^{* 0}$ | − |
Table 2.
Values of the coupling parameters used in the calculations."
| gV | β | β2 | ζ1 | βB | βS |
|---|---|---|---|---|---|
| 5.8 | 0.9 | −0.9 | 0.16 | 0.87 | −1.74 |
| [ | [ | [ | [ | [ | [ |
Figure 1.
The spectrum of hadronic molecules consisting of a pair of charmed mesons or baryons with I = 0 and P = +. The colored rectangle, green for a bound state and orange for a virtual state, covers the range of the pole position for a given system with the cutoff Λ varying in the range of [0.5, 1.0] GeV. Thresholds are marked by dotted horizontal lines. The rectangle closest to, but below, the threshold corresponds to the hadronic molecule in that system. In some cases, e.g. DD*, there are two rectangles for one system, with the upper edges exactly at the threshold. This corresponds to the situation that the pole moves from the second RS (left orange) to the first RS (right green) when Λ increases in the considered range. In some other cases where the pole positions of two systems overlap, small rectangles are used with the left (right) one for the system with the higher (lower) threshold."
Figure 2.
The spectrum of hadronic molecules consisting of a pair of charmed mesons with I = 0 and P = −. See the caption for figure 1."
Figure 3.
The spectrum of hadronic molecules consisting of a pair of charmed meson and charmed baryon with I = 1/2 and P = −. See the caption for figure 1. The right part of the dashed line for D*Λc marks the real threshold while the left part is deformed to avoid being covered by the rectangle of DΣc system."
Figure 4.
The spectrum of hadronic molecules consisting of a pair of charmed meson and charmed baryon with I = 0 and P = −. See the caption for figure 1."
Figure 5.
The spectrum of hadronic molecules consisting of a pair of charmed meson and charmed baryon with I = 1/2 and P = +. See the caption for figure 1."
Figure 6.
The spectrum of hadronic molecules consisting of a pair of charmed meson and charmed baryon with I = 0 and P = +. See the caption for figure 1."
Table 3.
Pole positions of double-charm-hadron systems with I = 0 and P = +. Eth in the second column is the threshold in MeV. The results as given in the last columns corresponds to using the cutoff Λ = 0.5 (1.0) GeV for equation (17) used to determine the subtraction constant a(μ) in equation (15), respectively. In the last two columns, the first number in the parenthesis refers to the Riemann sheet (RS) where the pole is located while the second number means the distance between the pole position and the corresponding threshold, namely, EB ≡ Eth − Epole, in units of MeV."
| System | Eth [MeV] | JP | (RS, EB [MeV]) | |
|---|---|---|---|---|
| 0.5 GeV | 1.0 GeV | |||
| DD* | 3876 | 1+ | (2, 3.58) | (1, 5.96) |
| D*D* | 4017 | 1+ | (2, 2.68) | (1, 7.07) |
| D1D1 | 4844 | 1+ | (2, 0.321) | (1, 12.2) |
| D1D2 | 4885 | (1, 2, 3)+ | (2, 0.277) | (1, 12.4) |
| D2D2 | 4926 | (1, 3)+ | (2, 0.237) | (1, 12.6) |
| ΣcΣc | 4907 | 0+ | (1, 2.72) | (1, 35.2) |
| ξcξc | 4939 | 1+ | (2, 43.4) | (2,10.1) |
| ${{\rm{\Sigma }}}_{c}{{\rm{\Sigma }}}_{c}^{* }$ | 4972 | (1, 2)+ | (1, 2.79) | (1, 35.1) |
| ${{\rm{\Sigma }}}_{c}^{* }{{\rm{\Sigma }}}_{c}^{* }$ | 5036 | (0, 2)+ | (1, 2.86) | (1, 35.1) |
| ${{\rm{\Xi }}}_{c}{{\rm{\Xi }}}_{c}^{{\prime} }$ | 5048 | (0, 1)+ | (2, 40.1) | (2, 8.55) |
| ${{\rm{\Xi }}}_{c}{{\rm{\Xi }}}_{c}^{* }$ | 5115 | (1, 2)+ | (2, 38.3) | (2, 7.73) |
| ${{\rm{\Xi }}}_{c}^{{\prime} }{{\rm{\Xi }}}_{c}^{{\prime} }$ | 5158 | 1+ | (2, 36.9) | (2, 7.14) |
| ${{\rm{\Xi }}}_{c}^{* }{{\rm{\Xi }}}_{c}^{{\prime} }$ | 5225 | (1, 2)+ | (2, 35.2) | (2, 6.4) |
| ${{\rm{\Xi }}}_{c}^{* }{{\rm{\Xi }}}_{c}^{* }$ | 5292 | (1, 3)+ | (2, 33.4) | (2, 5.7) |
| D1ξc | 4891 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{+}$ | (1, 2.78) | (1, 35.5) |
| D2ξc | 4932 | ${\left(\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (1, 2.83) | (1, 35.5) |
| ${D}_{1}{{\rm{\Xi }}}_{c}^{{\prime} }$ | 5001 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{+}$ | (1, 2.89) | (1, 35.4) |
| ${D}_{2}{{\rm{\Xi }}}_{c}^{{\prime} }$ | 5042 | ${\left(\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (1, 2.94) | (1, 35.4) |
| ${D}_{1}{{\rm{\Xi }}}_{c}^{* }$ | 5068 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (1, 2.96) | (1, 35.3) |
| ${D}_{2}{{\rm{\Xi }}}_{c}^{* }$ | 5109 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2},\tfrac{7}{2}\right)}^{+}$ | (1, 3.0) | (1, 35.3) |
| Ds1ωc | 5230 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{+}$ | (1, 0.0298) | (1, 17.4) |
| Ds2ωc | 5264 | ${\left(\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (1,0.039) | (1, 17.5) |
| ${D}_{s1}{{\rm{\Omega }}}_{c}^{* }$ | 5301 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (1, 0.0474) | (1, 17.6) |
| ${D}_{s2}{{\rm{\Omega }}}_{c}^{* }$ | 5335 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2},\tfrac{7}{2}\right)}^{+}$ | (1, 0.0588) | (1, 17.7) |
Table 4.
Pole positions of double-charm-hadron systems with I = 0 and P = −. See the caption for table 3."
| System | Eth [MeV] | JP | (RS, EB [MeV]) | |
|---|---|---|---|---|
| 0.5 GeV | 1.0 GeV | |||
| D D1 | 4289 | 1− | (2, 2.48) | (1, 6.94) |
| D D2 | 4330 | 2− | (2, 1.65) | (1, 8.69) |
| D*D1 | 4431 | (0, 1, 2)− | (2, 1.35) | (1, 9.12) |
| D*D2 | 4472 | (1, 2, 3)− | (2, 1.0) | (1, 10.1) |
| D ξc | 4337 | ${\tfrac{1}{2}}^{-}$ | (1, 1.92) | (1, 35.3) |
| $D\ {{\rm{\Xi }}}_{c}^{{\prime} }$ | 4446 | ${\tfrac{1}{2}}^{-}$ | (1, 2.04) | (1, 35.4) |
| D*ξc | 4478 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{-}$ | (1, 2.19) | (1, 35.5) |
| $D\ {{\rm{\Xi }}}_{c}^{* }$ | 4513 | ${\tfrac{3}{2}}^{-}$ | (1,2.11) | (1, 35.4) |
| ${D}^{* }{{\rm{\Xi }}}_{c}^{{\prime} }$ | 4587 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{-}$ | (1, 2.31) | (1, 35.5) |
| ${D}^{* }{{\rm{\Xi }}}_{c}^{* }$ | 4655 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2}\right)}^{-}$ | (1, 2.38) | (1, 35.5) |
| Dsωc | 4664 | ${\tfrac{1}{2}}^{-}$ | (2, 0.168) | (1, 14.3) |
| ${D}_{s}{{\rm{\Omega }}}_{c}^{* }$ | 4734 | ${\tfrac{3}{2}}^{-}$ | (2, 0.129) | (1, 14.6) |
| ${D}_{s}^{* }{{\rm{\Omega }}}_{c}^{{\prime} }$ | 4807 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{-}$ | (2, 0.0507) | (1, 15.3) |
| ${D}_{s}^{* }{{\rm{\Omega }}}_{c}^{* }$ | 4878 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2}\right)}^{-}$ | (2, 0.0308) | (1, 15.6) |
Table 5.
Pole positions of double-charm-hadron systems with I = 1/2 and P = −. See the caption for table 3."
| System | Eth [MeV] | JP | (RS, EB [MeV]) | |
|---|---|---|---|---|
| 0.5 GeV | 1.0 GeV | |||
| D Λc | 4154 | ${\tfrac{1}{2}}^{-}$ | (2, 3.44) | (1, 5.62) |
| D*Λc | 4295 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{-}$ | (2, 2.53) | (1, 6.73) |
| D Σc | 4321 | ${\tfrac{1}{2}}^{-}$ | (1, 5.81) | (1, 50.5) |
| $D\ {{\rm{\Sigma }}}_{c}^{* }$ | 4385 | ${\tfrac{3}{2}}^{-}$ | (1, 5.85) | (1, 50.2) |
| D*Σc | 4462 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{-}$ | (1, 5.97) | (1, 49.7) |
| ${D}^{* }{{\rm{\Sigma }}}_{c}^{* }$ | 4527 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2}\right)}^{-}$ | (1,6.01) | (1, 49.5) |
| Dsξc | 4438 | ${\tfrac{1}{2}}^{-}$ | (2, 25.7) | (2, 1.76) |
| ${D}_{s}{{\rm{\Xi }}}_{c}^{{\prime} }$ | 4547 | ${\tfrac{1}{2}}^{-}$ | (2, 23.7) | (2, 1.29) |
| ${D}_{s}^{* }{{\rm{\Xi }}}_{c}$ | 4582 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{-}$ | (2, 21.8) | (2, 0.882) |
| ${D}_{s}{{\rm{\Xi }}}_{c}^{* }$ | 4614 | ${\tfrac{3}{2}}^{-}$ | (2, 22.6) | (2, 1.05) |
| ${D}_{s}^{* }{{\rm{\Xi }}}_{c}^{{\prime} }$ | 4691 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{-}$ | (2, 20.0) | (2, 0.564) |
| ${D}_{s}^{* }{{\rm{\Xi }}}_{c}^{* }$ | 4758 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2}\right)}^{-}$ | (2, 19.0) | (2, 0.416) |
Table 6.
Pole positions of double-charm-hadron systems with I = 1/2 and P = +. See the caption for table 3."
| System | Eth [MeV] | JP | (RS, EB [MeV]) | |
|---|---|---|---|---|
| 0.5 GeV | 1.0 GeV | |||
| D1Λc | 4708 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{+}$ | (2, 1.04) | (1, 9.31) |
| D2Λc | 4750 | ${\left(\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (2, 0.95) | (1, 9.51) |
| D1Σc | 4876 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{+}$ | (1, 6.25) | (1, 47.5) |
| D2Σc | 4917 | ${\left(\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (1, 6.27) | (1, 47.3) |
| ${D}_{1}{{\rm{\Sigma }}}_{c}^{* }$ | 4940 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (1,6.28) | (1, 47.2) |
| ${D}_{2}{{\rm{\Sigma }}}_{c}^{* }$ | 4981 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2},\tfrac{7}{2}\right)}^{+}$ | (1, 6.29) | (1, 47.0) |
| Ds1ξc | 5005 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{+}$ | (2, 14.2) | (2, 0.00911) |
| Ds2ξc | 5039 | ${\left(\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (2, 13.8) | (2, 0.00176) |
| ${D}_{s1}{{\rm{\Xi }}}_{c}^{{\prime} }$ | 5114 | ${\left(\tfrac{1}{2},\tfrac{3}{2}\right)}^{+}$ | (2, 12.8) | (1, 0.00636) |
| ${D}_{s2}{{\rm{\Xi }}}_{c}^{{\prime} }$ | 5148 | ${\left(\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (2, 12.4) | (1, 0.0175) |
| ${D}_{s1}{{\rm{\Xi }}}_{c}^{* }$ | 5181 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2}\right)}^{+}$ | (2, 12.0) | (1, 0.0319) |
| ${D}_{s2}{{\rm{\Xi }}}_{c}^{* }$ | 5215 | ${\left(\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2},\tfrac{7}{2}\right)}^{+}$ | (2, 11.6) | (1, 0.0532) |
Table 7.
The group theory factor F, defined in equation (13), for the interaction of charm–anticharm/charm–charm hadron pairs with only the light vector-meson exchanges. Here both charm hadrons are the S-wave ground states. I is the isospin and S is the strangeness. Note that we have collect the pairs with the heavy hadrons in the same spin multiples (such as DD, DD*, etc) in one row, and the several numbers in the column of 'Thresholds' represent the thresholds of these different pairs in an increasing order. Positive F means that the interaction attractive. The values in the column of 'F' correspond to those for the exchanged particles in the column of 'Exchanged particles' in order."
| System | I | S | Thresholds [MeV] | Exchanged particles | F |
|---|---|---|---|---|---|
| ${D}^{(* )}{\bar{D}}^{(* )}/{D}^{(* )}{D}^{(* )}$ | 1 | 0/0 | (3734, 3876, 4017) | ρ, ω | $-\tfrac{1}{2},\tfrac{1}{2}/-\tfrac{1}{2},-\tfrac{1}{2}$ |
| 0 | $\tfrac{3}{2},\tfrac{1}{2}$/$\tfrac{3}{2},-\tfrac{1}{2}$ | ||||
| ${D}_{s}^{(* )}{\bar{D}}^{(* )}$/${D}_{s}^{(* )}{D}^{(* )}$ | $\tfrac{1}{2}$ | 1/1 | (3836, 3977, 3979, 4121) | K* | 0/−1 |
| ${D}_{s}^{(* )}{\bar{D}}_{s}^{(* )}$/${D}_{s}^{(* )}{D}_{s}^{(* )}$ | 0 | 0/2 | (3937, 4081, 4224) | φ | 1/−1 |
| ${\bar{D}}^{(* )}{{\rm{\Lambda }}}_{c}$/D(*)Λc | $\tfrac{1}{2}$ | 0/0 | (4154, 4295) | ω | −1/1 |
| ${\bar{D}}_{s}^{(* )}{{\rm{\Lambda }}}_{c}$/${D}_{s}^{(* )}{{\rm{\Lambda }}}_{c}$ | 0 | − 1/1 | (4255, 4399) | − | 0/0 |
| ${\bar{D}}^{(* )}{{\rm{\Xi }}}_{c}$/D(*)ξc | 1 | − 1/ − 1 | (4337, 4478) | ρ, ω | $-\tfrac{1}{2},-\tfrac{1}{2}$/$-\tfrac{1}{2},\tfrac{1}{2}$ |
| 0 | $\tfrac{3}{2},-\tfrac{1}{2}/\tfrac{3}{2},\tfrac{1}{2}$ | ||||
| ${\bar{D}}_{s}^{(* )}{{\rm{\Xi }}}_{c}$/${D}_{s}^{(* )}{{\rm{\Xi }}}_{c}$ | $\tfrac{1}{2}$ | − 2/0 | (4438, 4582) | φ | −1/1 |
| ${\bar{D}}^{(* )}{{\rm{\Sigma }}}_{c}^{(* )}$/${D}^{(* )}{{\rm{\Sigma }}}_{c}^{(* )}$ | $\tfrac{3}{2}$ | 0/0 | (4321, 4385, 4462, 4527) | ρ, ω | − 1, − 1/ − 1, 1 |
| $\tfrac{1}{2}$ | 2, − 1/2,1 | ||||
| ${\bar{D}}_{s}^{(* )}{{\rm{\Sigma }}}_{c}^{(* )}$/${D}_{s}^{(* )}{{\rm{\Sigma }}}_{c}^{(* )}$ | 1 | − 1/1 | (4422, 4486, 4566, 4630) | − | 0/0 |
| ${\bar{D}}^{(* )}{{\rm{\Xi }}}_{c}^{{\prime} (* )}$/${D}^{(* )}{{\rm{\Xi }}}_{c}^{{\prime} (* )}$ | 1 | − 1/ − 1 | (4446, 4513, 4587, 4655) | ρ, ω | $-\tfrac{1}{2},-\tfrac{1}{2}$/$-\tfrac{1}{2},\tfrac{1}{2}$ |
| 0 | $\tfrac{3}{2},-\tfrac{1}{2}$/$\tfrac{3}{2},\tfrac{1}{2}$ | ||||
| ${\bar{D}}_{s}^{(* )}{{\rm{\Xi }}}_{c}^{{\prime} (* )}$/${D}_{s}^{(* )}{{\rm{\Xi }}}_{c}^{{\prime} (* )}$ | $\tfrac{1}{2}$ | − 2/0 | (4547, 4614, 4691, 4758) | φ | − 1/1 |
| ${\bar{D}}^{(* )}{{\rm{\Omega }}}_{c}^{(* )}$/${D}^{(* )}{{\rm{\Omega }}}_{c}^{(* )}$ | $\tfrac{1}{2}$ | − 2/0 | (4562, 4633, 4704, 4774) | − | 0/0 |
| ${\bar{D}}_{s}^{(* )}{{\rm{\Omega }}}_{c}^{(* )}$/${D}_{s}^{(* )}{{\rm{\Omega }}}_{c}^{(* )}$ | 0 | − 3/ − 1 | (4664, 4734, 4807, 4878) | φ | − 2/2 |
| ${{\rm{\Lambda }}}_{c}{\bar{{\rm{\Lambda }}}}_{c}$/ΛcΛc | 0 | 0/0 | (4573) | ω | 2/−2 |
| ${{\rm{\Lambda }}}_{c}{\bar{{\rm{\Xi }}}}_{c}$/Λcξc | $\tfrac{1}{2}$ | 1/ − 1 | (4756) | ω/K* | 1, 0/ − 1, − 1 |
| ${{\rm{\Xi }}}_{c}{\bar{{\rm{\Xi }}}}_{c}$/ξcξc | 1 | 0/ − 2 | (4939) | ρ, ω, φ | $-\tfrac{1}{2},\tfrac{1}{2},1$/$-\tfrac{1}{2},-\tfrac{1}{2},-1$ |
| 0 | $\tfrac{3}{2},\tfrac{1}{2},1$/$\tfrac{3}{2},-\tfrac{1}{2},-1$ | ||||
| ${{\rm{\Lambda }}}_{c}{\bar{{\rm{\Sigma }}}}_{c}^{(* )}$/${{\rm{\Lambda }}}_{c}{{\rm{\Sigma }}}_{c}^{(* )}$ | 1 | 0/0 | (4740, 4805) | ω/K* | 1, 0/ − 1, − 1 |
| ${{\rm{\Lambda }}}_{c}{\bar{{\rm{\Xi }}}}_{c}^{{\prime} (* )}$/${{\rm{\Lambda }}}_{c}{{\rm{\Xi }}}_{c}^{{\prime} (* )}$ | $\tfrac{1}{2}$ | 1/ − 1 | (4865, 4932) | ω | 1/−1 |
| ${{\rm{\Lambda }}}_{c}{\bar{{\rm{\Omega }}}}_{c}^{(* )}$/${{\rm{\Lambda }}}_{c}{{\rm{\Omega }}}_{c}^{(* )}$ | 0 | 2/ − 2 | (4982, 5052) | − | 0/0 |
| ${{\rm{\Sigma }}}_{c}^{(* )}{\bar{{\rm{\Xi }}}}_{c}$/${{\rm{\Sigma }}}_{c}^{(* )}{{\rm{\Xi }}}_{c}$ | $\tfrac{3}{2}$ | 1/ − 1 | (4923, 4988) | ρ, ω, K* | − 1, 1, 0/ − 1, − 1, − 2 |
| $\tfrac{1}{2}$ | 2, 1, 0/2, − 1, − 2 | ||||
| ${{\rm{\Xi }}}_{c}{\bar{{\rm{\Xi }}}}_{c}^{{\prime} (* )}$/${{\rm{\Xi }}}_{c}{{\rm{\Xi }}}_{c}^{{\prime} (* )}$ | 1 | 0/ − 2 | (5048, 5115) | ρ, ω, φ | $-\tfrac{1}{2},\tfrac{1}{2},1$/$-\tfrac{1}{2},-\tfrac{1}{2},-1$ |
| 0 | $\tfrac{3}{2},\tfrac{1}{2},1$/$\tfrac{3}{2},-\tfrac{1}{2},-1$ | ||||
| ${{\rm{\Xi }}}_{c}{\bar{{\rm{\Omega }}}}_{c}^{(* )}$/${{\rm{\Xi }}}_{c}{{\rm{\Omega }}}_{c}^{(* )}$ | $\tfrac{1}{2}$ | 1/ − 3 | (5165, 5235) | φ, K* | 2, 0/ − 2, − 2 |
| ${{\rm{\Sigma }}}_{c}^{(* )}{\bar{{\rm{\Sigma }}}}_{c}^{(* )}$/${{\rm{\Sigma }}}_{c}^{(* )}{{\rm{\Sigma }}}_{c}^{(* )}$ | 2 | 0/0 | (4907, 4972, 5036) | ρ, ω | − 2, 2/ − 2, − 2 |
| 1 | 2, 2/2, − 2 | ||||
| 0 | 4, 2/4, − 2 | ||||
| ${{\rm{\Sigma }}}_{c}^{(* )}{\bar{{\rm{\Xi }}}}_{c}^{{\prime} (* )}$/${{\rm{\Sigma }}}_{c}^{(* )}{{\rm{\Xi }}}_{c}^{{\prime} (* )}$ | $\tfrac{3}{2}$ | 1/ − 1 | (5032, 5097, 5100, 5164) | ρ, ω, K* | − 1, 1, 0/ − 1, − 1 − 2 |
| $\tfrac{1}{2}$ | 2, 1, 0/2, − 1, − 2 | ||||
| ${{\rm{\Sigma }}}_{c}^{(* )}{\bar{{\rm{\Omega }}}}_{c}^{(* )}$/${{\rm{\Sigma }}}_{c}^{(* )}{{\rm{\Omega }}}_{c}^{(* )}$ | 0 | 2/ − 2 | (5149, 5213, 5219, 5284) | − | 0/0 |
| ${{\rm{\Xi }}}_{c}^{{\prime} (* )}{\bar{{\rm{\Xi }}}}_{c}^{{\prime} (* )}$/${{\rm{\Xi }}}_{c}^{{\prime} (* )}{{\rm{\Xi }}}_{c}^{{\prime} (* )}$ | 1 | 0/ − 2 | (5158, 5225, 5292) | ρ, ω, φ | $-\tfrac{1}{2},\tfrac{1}{2},1$/$-\tfrac{1}{2},-\tfrac{1}{2},-1$ |
| 0 | $\tfrac{3}{2},\tfrac{1}{2},1$/$\tfrac{3}{2},-\tfrac{1}{2},-1$ | ||||
| ${{\rm{\Xi }}}_{c}^{{\prime} (* )}{\bar{{\rm{\Omega }}}}_{c}^{(* )}$/${{\rm{\Xi }}}_{c}^{{\prime} (* )}{{\rm{\Omega }}}_{c}^{(* )}$ | $\tfrac{1}{2}$ | 1/ − 3 | (5272, 5341, 5345, 5412) | φ, K* | 2, 0/ − 2, − 2 |
| ${{\rm{\Omega }}}_{c}^{(* )}{\bar{{\rm{\Omega }}}}_{c}^{(* )}$/${{\rm{\Omega }}}_{c}^{(* )}{{\rm{\Omega }}}_{c}^{(* )}$ | 0 | 0/ − 4 | (5390, 5461, 5532) | φ | 4/−4 |
Table 8.
The group theory factor F, defined in equation (13), for the interaction of charm–anticharm/charm–charm hadron pairs with only the light vector-meson exchanges. Here one of the charm hadrons is an sℓ = 3/2 charm meson. See the caption of table 7."
| System | I | S | Thresholds [MeV] | Exchanged particles | F |
|---|---|---|---|---|---|
| ${D}^{(* )}{\bar{D}}_{\mathrm{1,2}}$/D(*)D1,2 | 0 | 0/0 | (4289, 4330, 4431, 4472) | ρ, ω | $\tfrac{3}{2},\tfrac{1}{2}$/$\tfrac{3}{2},-\tfrac{1}{2}$ |
| 1 | 0/0 | $-\tfrac{1}{2},\tfrac{1}{2}$/ $-\tfrac{1}{2},-\tfrac{1}{2}$ | |||
| ${D}^{(* )}{\bar{D}}_{s1,s2}$/D(*)Ds1,s2 | $\tfrac{1}{2}$ | 1/ − 1 | (4390, 4431, 4534, 4575) | − | 0/0 |
| ${D}_{s}^{(* )}{\bar{D}}_{\mathrm{1,2}}$/${D}_{s}^{(* )}{D}_{\mathrm{1,2}}$ | $\tfrac{1}{2}$ | − 1/1 | (4402, 4436, 4544, 4578) | − | 0/0 |
| ${D}_{s}^{(* )}{\bar{D}}_{s1,s2}$/${D}_{s}^{(* )}{D}_{s1,s2}$ | 0 | 0/−2 | (4503, 4537, 4647, 4681) | φ | 1/−1 |
| ${D}_{\mathrm{1,2}}{\bar{D}}_{\mathrm{1,2}}$/D1,2D1,2 | 0 | 0/0 | (4844, 4885, 4926) | ρ, ω | $\tfrac{3}{2},\tfrac{1}{2}$/$\tfrac{3}{2},-\tfrac{1}{2}$ |
| 1 | $-\tfrac{1}{2},\tfrac{1}{2}$/$-\tfrac{1}{2},-\tfrac{1}{2}$ | ||||
| ${D}_{s1,s2}{\bar{D}}_{\mathrm{1,2}}$/Ds1,s2D1,2 | $\tfrac{1}{2}$ | 1/1 | (4957, 4991, 4998, 5032) | 0/0 | |
| ${D}_{s1,s2}{\bar{D}}_{s1,s2}$/Ds1,s2Ds1,s2 | 0 | 0/ − 2 | (5070, 5104, 5138) | φ | 1/1 |
| ${{\rm{\Lambda }}}_{c}{\bar{D}}_{\mathrm{1,2}}$/ΛcD1,2 | $\tfrac{1}{2}$ | 0/0 | (4708, 4750) | ω | −1/1 |
| ${{\rm{\Lambda }}}_{c}{\bar{D}}_{s1,s2}$/ΛcDs1,s2 | 0 | − 1/1 | (4822, 4856) | − | 0/0 |
| ${{\rm{\Xi }}}_{c}{\bar{D}}_{\mathrm{1,2}}$/ξcD1,2 | 1 | − 1/ − 1 | (4891, 4932) | ρ, ω | $-\tfrac{1}{2},-\tfrac{1}{2}$/$-\tfrac{1}{2},\tfrac{1}{2}$ |
| 0 | $\tfrac{3}{2},-\tfrac{1}{2}$/$\tfrac{3}{2},\tfrac{1}{2}$ | ||||
| ${{\rm{\Xi }}}_{c}{\bar{D}}_{s1,s2}$/ξcDs1,s2 | $\tfrac{1}{2}$ | − 2/0 | (5005, 5039) | φ | −1/1 |
| ${{\rm{\Sigma }}}_{c}^{(* )}{\bar{D}}_{\mathrm{1,2}}$/${{\rm{\Sigma }}}_{c}^{(* )}{D}_{\mathrm{1,2}}$ | $\tfrac{3}{2}$ | 0/0 | (4876, 4917, 4940, 4981) | ρ, ω | − 1, − 1/ − 1, 1 |
| $\tfrac{1}{2}$ | 2, − 1/2,1 | ||||
| ${{\rm{\Sigma }}}_{c}^{(* )}{\bar{D}}_{s1,s2}$/${{\rm{\Sigma }}}_{c}^{(* )}{D}_{s1,s2}$ | 1 | 1/ − 1 | (4989, 5023, 5053, 5087) | − | 0/0 |
| ${{\rm{\Xi }}}_{c}^{{\prime} (* )}{\bar{D}}_{\mathrm{1,2}}$/${{\rm{\Xi }}}_{c}^{{\prime} (* )}{D}_{\mathrm{1,2}}$ | 1 | − 1/ − 1 | (5001, 5042, 5068, 5109) | ρ, ω | $-\tfrac{1}{2},-\tfrac{1}{2}$/$-\tfrac{1}{2},\tfrac{1}{2}$ |
| 0 | $\tfrac{3}{2},-\tfrac{1}{2}$/$\tfrac{3}{2},\tfrac{1}{2}$ | ||||
| ${{\rm{\Xi }}}_{c}^{{\prime} (* )}{\bar{D}}_{s1,s2}$/${{\rm{\Xi }}}_{c}^{{\prime} (* )}{D}_{s1,s2}$ | $\tfrac{1}{2}$ | − 2/0 | (5114, 5148, 5181, 5215) | φ | −1/1 |
| ${{\rm{\Omega }}}_{c}^{(* )}{\bar{D}}_{\mathrm{1,2}}$/${{\rm{\Omega }}}_{c}^{(* )}{D}_{\mathrm{1,2}}$ | $\tfrac{1}{2}$ | − 2/ − 2 | (5117, 5158, 5188, 5229) | − | 0/0 |
| ${{\rm{\Omega }}}_{c}^{(* )}{\bar{D}}_{s1,s2}$/${{\rm{\Omega }}}_{c}^{(* )}{D}_{s1,s2}$ | 0 | − 3/ − 1 | (5230, 5264, 5301, 5335) | φ | −2/2 |
Table 9.
The group theory factor F, defined in equation (13), for the interaction of bottom–antibottom/bottom–bottom hadron pairs with only the light vector-meson exchanges. Here both bottom hadrons are the S-wave ground states. I is the isospin and S is the strangeness. Positive F means that the interaction is attractive."
| System | I | S | Thresholds [MeV] | Exchanged particles | F |
|---|---|---|---|---|---|
| ${B}^{(* )}{\bar{B}}^{(* )}/{B}^{(* )}{B}^{(* )}$ | 1 | 0/0 | (10559, 10604, 10649) | ρ, ω | $-\tfrac{1}{2},\tfrac{1}{2}/-\tfrac{1}{2},-\tfrac{1}{2}$ |
| 0 | $\tfrac{3}{2},\tfrac{1}{2}$/$\tfrac{3}{2},-\tfrac{1}{2}$ | ||||
| ${B}_{s}^{(* )}{\bar{B}}^{(* )}$/${B}_{s}^{(* )}{B}^{(* )}$ | $\tfrac{1}{2}$ | 1/1 | (10646, 10695, 10692, 10740) | K* | 0/ − 1 |
| ${B}_{s}^{(* )}{\bar{B}}_{s}^{(* )}$/${B}_{s}^{(* )}{B}_{s}^{(* )}$ | 0 | 0/2 | (10734, 10782, 10831) | φ | 1/−1 |
| ${\bar{B}}^{(* )}{{\rm{\Lambda }}}_{b}$/B(*)Λb | $\tfrac{1}{2}$ | 0/0 | (10899, 10944) | ω | −1/1 |
| ${\bar{B}}_{s}^{(* )}{{\rm{\Lambda }}}_{b}$/${B}_{s}^{(* )}{{\rm{\Lambda }}}_{b}$ | 0 | − 1/1 | (10986, 11035) | − | 0/0 |
| ${\bar{B}}^{(* )}{{\rm{\Xi }}}_{b}$/B(*)ξb | 1 | − 1/ − 1 | (11074, 11119) | ρ, ω | $-\tfrac{1}{2},-\tfrac{1}{2}$/$-\tfrac{1}{2},\tfrac{1}{2}$ |
| 0 | $\tfrac{3}{2},-\tfrac{1}{2}/\tfrac{3}{2},\tfrac{1}{2}$ | ||||
| ${\bar{B}}_{s}^{(* )}{{\rm{\Xi }}}_{b}$/${B}_{s}^{(* )}{{\rm{\Xi }}}_{b}$ | $\tfrac{1}{2}$ | − 2/0 | (11161, 11210) | φ | −1/1 |
| ${\bar{B}}^{(* )}{{\rm{\Sigma }}}_{b}^{(* )}$/${B}^{(* )}{{\rm{\Sigma }}}_{b}^{(* )}$ | $\tfrac{3}{2}$ | 0/0 | (11093, 11138, 11112, 11157) | ρ, ω | − 1, − 1/ − 1, 1 |
| $\tfrac{1}{2}$ | 2, − 1/2,1 | ||||
| ${\bar{B}}_{s}^{(* )}{{\rm{\Sigma }}}_{b}^{(* )}$/${B}_{s}^{(* )}{{\rm{\Sigma }}}_{b}^{(* )}$ | 1 | − 1/1 | (11180, 11228, 11199, 11248) | − | 0/0 |
| ${\bar{B}}^{(* )}{{\rm{\Xi }}}_{b}^{{\prime} (* )}$/${B}^{(* )}{{\rm{\Xi }}}_{b}^{{\prime} (* )}$ | 1 | − 1/ − 1 | (11215, 11260, 11233, 11279) | ρ, ω | $-\tfrac{1}{2},-\tfrac{1}{2}$/$-\tfrac{1}{2},\tfrac{1}{2}$ |
| 0 | $\tfrac{3}{2},-\tfrac{1}{2}$/$\tfrac{3}{2},\tfrac{1}{2}$ | ||||
| ${\bar{B}}_{s}^{(* )}{{\rm{\Xi }}}_{b}^{{\prime} (* )}$/${B}_{s}^{(* )}{{\rm{\Xi }}}_{b}^{{\prime} (* )}$ | $\tfrac{1}{2}$ | − 2/0 | (11302, 11350, 11321, 11369) | φ | − 1/1 |
| ${\bar{B}}^{(* )}{{\rm{\Omega }}}_{b}^{(* )}$/${B}^{(* )}{{\rm{\Omega }}}_{b}^{(* )}$ | $\tfrac{1}{2}$ | − 2/0 | (11326, 11371, 11349, 11395) | − | 0/0 |
| ${\bar{B}}_{s}^{(* )}{{\rm{\Omega }}}_{b}^{(* )}$/${B}_{s}^{(* )}{{\rm{\Omega }}}_{b}^{(* )}$ | 0 | − 3/ − 1 | (11413, 11462, 11437, 11485) | φ | − 2/2 |
| ${{\rm{\Lambda }}}_{b}{\bar{{\rm{\Lambda }}}}_{b}$/ΛbΛb | 0 | 0/0 | (11239) | ω | 2/−2 |
| ${{\rm{\Lambda }}}_{b}{\bar{{\rm{\Xi }}}}_{b}$/Λbξb | $\tfrac{1}{2}$ | 1/ − 1 | (11414) | ω,K* | 1, 0/ − 1, − 1 |
| ${{\rm{\Xi }}}_{b}{\bar{{\rm{\Xi }}}}_{b}$/ξbξb | 1 | 0/ − 2 | (11589) | ρ, ω, φ | $-\tfrac{1}{2},\tfrac{1}{2},1$/$-\tfrac{1}{2},-\tfrac{1}{2},-1$ |
| 0 | $\tfrac{3}{2},\tfrac{1}{2},1$/$\tfrac{3}{2},-\tfrac{1}{2},-1$ | ||||
| ${{\rm{\Lambda }}}_{b}{\bar{{\rm{\Sigma }}}}_{b}^{(* )}$/${{\rm{\Lambda }}}_{b}{{\rm{\Sigma }}}_{b}^{(* )}$ | 1 | 0/0 | (11433, 11452) | ω | 2/−2 |
| ${{\rm{\Lambda }}}_{b}{\bar{{\rm{\Xi }}}}_{b}^{{\prime} (* )}$/${{\rm{\Lambda }}}_{b}{{\rm{\Xi }}}_{b}^{{\prime} (* )}$ | $\tfrac{1}{2}$ | 1/ − 1 | (11555, 11573) | ω, K* | 1, 0/ − 1, − 1 |
| ${{\rm{\Lambda }}}_{b}{\bar{{\rm{\Omega }}}}_{b}^{(* )}$/${{\rm{\Lambda }}}_{b}{{\rm{\Omega }}}_{b}^{(* )}$ | 0 | 2/ − 2 | (11666, 11690) | − | 0/0 |
| ${{\rm{\Xi }}}_{b}{\bar{{\rm{\Sigma }}}}_{b}^{(* )}$/${{\rm{\Xi }}}_{b}{{\rm{\Sigma }}}_{b}^{(* )}$ | $\tfrac{3}{2}$ | − 1/ − 1 | (11608, 11627) | ρ, ω, K* | − 1, 1, 0/ − 1, − 1, − 2 |
| $\tfrac{1}{2}$ | 2, 1, 0/2, − 1, − 2 | ||||
| ${{\rm{\Xi }}}_{b}{\bar{{\rm{\Xi }}}}_{b}^{{\prime} (* )}$/${{\rm{\Xi }}}_{b}{{\rm{\Xi }}}_{b}^{{\prime} (* )}$ | 1 | 0/ − 2 | (11729, 11748) | ρ, ω, φ | $-\tfrac{1}{2},\tfrac{1}{2},1$/$-\tfrac{1}{2},-\tfrac{1}{2},-1$ |
| 0 | $\tfrac{3}{2},\tfrac{1}{2},1$/$\tfrac{3}{2},-\tfrac{1}{2},-1$ | ||||
| ${{\rm{\Xi }}}_{b}{\bar{{\rm{\Omega }}}}_{b}^{(* )}$/${{\rm{\Xi }}}_{b}{{\rm{\Omega }}}_{b}^{(* )}$ | $\tfrac{1}{2}$ | 1/ − 3 | (11841, 11864) | φ, K* | 2, 0/ − 2, − 2 |
| ${{\rm{\Sigma }}}_{b}^{(* )}{\bar{{\rm{\Sigma }}}}_{b}^{(* )}$/${{\rm{\Sigma }}}_{b}^{(* )}{{\rm{\Sigma }}}_{b}^{(* )}$ | 2 | 0/0 | (11626, 11646, 11665) | ρ, ω | − 2, 2/ − 2, − 2 |
| 1 | 2, 2/2, − 2 | ||||
| 0 | 4, 2/4, − 2 | ||||
| ${{\rm{\Sigma }}}_{b}^{(* )}{\bar{{\rm{\Xi }}}}_{b}^{{\prime} (* )}$/${{\rm{\Sigma }}}_{b}^{(* )}{{\rm{\Xi }}}_{b}^{{\prime} (* )}$ | $\tfrac{3}{2}$ | 1/ − 1 | (11748, 11768, 11767, 11786) | ρ, ω, K* | − 1, 1, 0/ − 1, − 1, − 2 |
| $\tfrac{1}{2}$ | 2, 1, 0/2, − 1, − 2 | ||||
| ${{\rm{\Sigma }}}_{b}^{(* )}{\bar{{\rm{\Omega }}}}_{b}^{(* )}$/${{\rm{\Sigma }}}_{b}^{(* )}{{\rm{\Omega }}}_{b}^{(* )}$ | 0 | 2/ − 2 | (11859, 11879, 11883, 11903) | K* | 0/−4 |
| ${{\rm{\Xi }}}_{b}^{{\prime} (* )}{\bar{{\rm{\Xi }}}}_{b}^{{\prime} (* )}$/${{\rm{\Xi }}}_{b}^{{\prime} (* )}{{\rm{\Xi }}}_{b}^{{\prime} (* )}$ | 1 | 0/ − 2 | (11870, 11889, 11908) | ρ, ω, φ | $-\tfrac{1}{2},\tfrac{1}{2},1$/$-\tfrac{1}{2},-\tfrac{1}{2},-1$ |
| 0 | $\tfrac{3}{2},\tfrac{1}{2},1$/$\tfrac{3}{2},-\tfrac{1}{2},-1$ | ||||
| ${{\rm{\Xi }}}_{b}^{{\prime} (* )}{\bar{{\rm{\Omega }}}}_{b}^{(* )}$/${{\rm{\Xi }}}_{b}^{{\prime} (* )}{{\rm{\Omega }}}_{b}^{(* )}$ | $\tfrac{1}{2}$ | 1/ − 3 | (11981, 12000, 12005, 12024) | φ, K* | 2, 0/ − 2, − 2 |
| ${{\rm{\Omega }}}_{b}^{(* )}{\bar{{\rm{\Omega }}}}_{b}^{(* )}$/${{\rm{\Omega }}}_{b}^{(* )}{{\rm{\Omega }}}_{b}^{(* )}$ | 0 | 0/ − 4 | (12092, 12116, 12140) | φ | 4/−4 |
Table 10.
The group theory factor F, defined in equation (13), for the interaction of bottom–antibottom/bottom–bottom hadron pairs with only the light vector-meson exchanges. Here one of the bottom hadrons is an sℓ = 3/2 bottom meson. See the caption of table 9."
| System | I | S | Thresholds [MeV] | Exchanged particles | F |
|---|---|---|---|---|---|
| ${B}^{(* )}{\bar{B}}_{\mathrm{1,2}}$/B(*)B1,2 | 0 | 0/0 | (11005, 11051, 11018, 11063) | ρ, ω | $\tfrac{3}{2},\tfrac{1}{2}$/$\tfrac{3}{2},-\tfrac{1}{2}$ |
| 1 | 0/0 | $-\tfrac{1}{2},\tfrac{1}{2}$/ $-\tfrac{1}{2},-\tfrac{1}{2}$ | |||
| ${B}^{(* )}{\bar{B}}_{s1,s2}$/B(*)Bs1,s2 | $\tfrac{1}{2}$ | 1/ − 1 | (11093, 11141, 11105, 11154) | − | 0/0 |
| ${B}_{s}^{(* )}{\bar{B}}_{\mathrm{1,2}}$/${B}_{s}^{(* )}{B}_{\mathrm{1,2}}$ | $\tfrac{1}{2}$ | − 1/1 | (11108, 11153, 11119, 11165) | − | 0/0 |
| ${B}_{s}^{(* )}{\bar{B}}_{s1,s2}$/${B}_{s}^{(* )}{B}_{s1,s2}$ | 0 | 0/−2 | (11196, 11207, 11244, 11255) | φ | 1/−1 |
| ${B}_{\mathrm{1,2}}{\bar{B}}_{\mathrm{1,2}}$/B1,2B1,2 | 0 | 0/0 | (11452, 11464, 11477) | ρ, ω | $\tfrac{3}{2},\tfrac{1}{2}$/$\tfrac{3}{2},-\tfrac{1}{2}$ |
| 1 | $-\tfrac{1}{2},\tfrac{1}{2}$/$-\tfrac{1}{2},-\tfrac{1}{2}$ | ||||
| ${B}_{s1,s2}{\bar{B}}_{\mathrm{1,2}}$/Bs1,s2B1,2 | $\tfrac{1}{2}$ | 1/1 | (11555, 11566, 11567, 11578) | 0/0 | |
| ${B}_{s1,s2}{\bar{B}}_{s1,s2}$/Bs1,s2Bs1,s2 | 0 | 0/ − 2 | (11657, 11669, 11680) | φ | 1/1 |
| ${{\rm{\Lambda }}}_{b}{\bar{B}}_{\mathrm{1,2}}$/ΛbB1,2 | $\tfrac{1}{2}$ | 0/0 | (11346, 11358) | ω | −1/1 |
| ${{\rm{\Lambda }}}_{b}{\bar{B}}_{s1,s2}$/ΛbBs1,s2 | 0 | − 1/1 | (11448, 11459) | − | 0/0 |
| ${{\rm{\Xi }}}_{b}{\bar{B}}_{\mathrm{1,2}}$/ξbB1,2 | 1 | − 1/ − 1 | (11520, 11533) | ρ, ω | $-\tfrac{1}{2},-\tfrac{1}{2}$/$-\tfrac{1}{2},\tfrac{1}{2}$ |
| 0 | $\tfrac{3}{2},-\tfrac{1}{2}$/$\tfrac{3}{2},\tfrac{1}{2}$ | ||||
| ${{\rm{\Xi }}}_{b}{\bar{B}}_{s1,s2}$/ξbBs1,s2 | $\tfrac{1}{2}$ | − 2/0 | (11623, 11634) | φ | −1/1 |
| ${{\rm{\Sigma }}}_{b}^{(* )}{\bar{B}}_{\mathrm{1,2}}$/${{\rm{\Sigma }}}_{b}^{(* )}{B}_{\mathrm{1,2}}$ | $\tfrac{3}{2}$ | 0/0 | (11539, 11551, 11559, 11571) | ρ, ω | − 1, − 1/ − 1, 1 |
| $\tfrac{1}{2}$ | 2, − 1/2,1 | ||||
| ${{\rm{\Sigma }}}_{b}^{(* )}{\bar{B}}_{s1,s2}$/${{\rm{\Sigma }}}_{b}^{(* )}{B}_{s1,s2}$ | 1 | 1/ − 1 | (11642, 11653, 11661, 11672) | − | 0/0 |
| ${{\rm{\Xi }}}_{b}^{{\prime} (* )}{\bar{B}}_{\mathrm{1,2}}$/${{\rm{\Xi }}}_{b}^{{\prime} (* )}{B}_{\mathrm{1,2}}$ | 1 | − 1/ − 1 | (11661, 11673, 11680, 11692) | ρ, ω | $-\tfrac{1}{2},-\tfrac{1}{2}$/$-\tfrac{1}{2},\tfrac{1}{2}$ |
| 0 | $\tfrac{3}{2},-\tfrac{1}{2}$/$\tfrac{3}{2},\tfrac{1}{2}$ | ||||
| ${{\rm{\Xi }}}_{b}^{{\prime} (* )}{\bar{B}}_{s1,s2}$/${{\rm{\Xi }}}_{b}^{{\prime} (* )}{B}_{s1,s2}$ | $\tfrac{1}{2}$ | − 2/0 | (11764, 11775, 11783, 11794) | φ | −1/1 |
| ${{\rm{\Omega }}}_{b}^{(* )}{\bar{B}}_{\mathrm{1,2}}$/${{\rm{\Omega }}}_{b}^{(* )}{B}_{\mathrm{1,2}}$ | $\tfrac{1}{2}$ | − 2/ − 2 | (11772, 11784, 11796, 11808) | − | 0/0 |
| ${{\rm{\Omega }}}_{b}^{(* )}{\bar{B}}_{s1,s2}$/${{\rm{\Omega }}}_{b}^{(* )}{B}_{s1,s2}$ | 0 | − 3/ − 1 | (11875, 11886, 11899, 11910) | φ | −2/2 |
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