𝑋(1870) and 𝜂₂(1870): Which Can Be Assigned as a Hybrid State?

Table 7

The second and third columns for the flavor weight factors corresponding to two topological diagrams shown in Figure 6. The last column for the flavor multiplicity factor ℱ. Here, |𝜂⟩=(|𝑛𝑛⟩−|𝑠𝑠⟩)/√2 and |𝜂^′⟩=(|𝑛𝑛⟩+|𝑠𝑠⟩)/√2 have been taken for simplicity.

Decay channels	ℐflavor(𝑑1)	ℐflavor(𝑑1)	ℱ
𝜌→𝜋𝜋	+1/√2	−1/√2	1
𝑓2→𝜋𝜋	−1/√2	−1/√2	3/2
𝑓2→𝐾𝐾	0	−1/√2	2
𝑓^′1→𝐾^∗𝐾	+1	0	4
𝑓^′2→𝐾𝐾	+1	0	2
𝑎2→𝐾𝐾	0	−1	1
𝑎2→𝜂𝜋	+1/2	+1/2	1
𝜂2→𝜔𝜔	−1/√2	−1/√2	1/2
𝜂2→𝑎𝑖𝜋	−1/√2	−1/√2	3
𝜂2→𝑓𝑖𝜂	+1/2	+1/2	1