Strong decays of the 𝜙(2170) as a fully-strange tetraquark state

We study strong decays of the 𝜙(2170), along with its possible partner 𝑋(2436), as two fully-strange tetraquark states of 𝐽𝑃𝐶 = 1−−. We consider seven decay channels: 𝜙𝜂, 𝜙𝜂', 𝜙𝑓0(980), 𝜙𝑓1(1420), ℎ1(1415)𝜂, ℎ1(1415)𝜂', and ℎ1(1415)𝑓1(1420). Some of these channels are kinematically possible, and we calculate their relative branching ratios through the Fierz rearrangement. Future experimental measurements on these ratios can be useful in determining the nature of the 𝜙(2170) and 𝑋(2436). The 𝜙(2170) has been observed in the 𝜙𝑓0(980), 𝜙𝜂, and 𝜙𝜂' channels, and we propose to further examine it in the ℎ1(1415)𝜂 channel. Evidences of the 𝑋(2436) have been observed in the 𝜙𝑓0(980) channel, and we propose to verify whether this structure exists or not in the 𝜙𝜂, 𝜙𝜂', ℎ1(1415)𝜂, and ℎ1(1415)𝜂' channels.