Quantum numbers of the pentaquark states ${{\rm{P}}}_{{\rm{c}}}^{+}$ via symmetry analysis

Chong-yao Chen,Muyang Chen,Yu-Xin Liu

Table 3. Spin-flavor decomposition of the ${q}^{4}\bar{q}$ states (taken from reference [47]. The subscripts stand for the dimensions of the IRREP).

[f]O SUsf(6) SUf(3) ⨂ SUs(2) [4] [51111]700 [51]35 ⨂ [5]6 [51]35 ⨂ [41]4 [42]27 ⨂ [41]4 [42]27 ⨂ [32]2 [33]10 ⨂ [32]2 [411]10 ⨂ [5]6 [411]10 ⨂ [41]4 [411]10 ⨂ [32]2 [321]8 ⨂ [41]4 [321]8 ⨂ [32]2 [4] + [31] [411111]56 [411]10 ⨂ [41]4 [321]8 ⨂ [32]2 [31] [42111]1134 [51]35 ⨂ [41]4 [51]35 ⨂ [32]2 [42]27 ⨂ [5]6 2([42]27 ⨂ [41]4) 2([42]27 ⨂ [32]2) [33]10 ⨂ [41]4 [33]10 ⨂ [32]2 [411]10 ⨂ [5]6 2([411]10 ⨂ [41]4) 2([411]10 ⨂ [32]2) [321]8 ⨂ [5]6 2([321]8 ⨂ [41]4) 2([321]8 ⨂ [32]2) [222]1 ⨂ [41]4 [222]1 ⨂ [32]2 [f]O SUsf(6) SUf(3) ⨂ SUs(2) [31] + [22] + [211] [321111]70 [411]10 ⨂ [32]2 ${[321]}_{8}$ ⨂ [41]4 [321]8 ⨂ [32]2 [222]1 ⨂ [32]2 [22] [33111]560 [51]35 ⨂ [32]2 [42]27 ⨂ [41]4 [42]27 ⨂ [32]2 [33]10 ⨂ [5]6 [33]10 ⨂ [41]4 [33]10 ⨂ [32]2 [411]10 ⨂ [41]4 [411]10 ⨂ [32]2 [321]8 ⨂ [5]6 2([321]8 ⨂ [41]4) 2([321]8 ⨂ [32]2) [222]1 ⨂ [41]4 [211] [3211]540 [42]7 ⨂ [41]4 2([42]7 ⨂ [32]2 [33]10 ⨂ [41]4 [33]10 ⨂ [32]2 [411]10 ⨂ [41]4 [411]10 ⨂ [32]2 [321]8 ⨂ [5]6 2([321]8 ⨂ [41]4) 2([321]8 ⨂ [32]2) [222]1 ⨂ [5]6 [222]1 ⨂ [41]4 [222]1 ⨂ [32]2 [211] + [1111] [222111]20 [321]8 ⨂ [32]2 [222]1 ⨂ [41]4 [1111] [22221]70 [33]10 ⨂ [32]2 [321]8 ⨂ [41]4 [321]8 ⨂ [32]2 [222]1 ⨂ [32]2