Strong Decays of the ϕ(2170) as a Fully Strange Tetraquark State

We study the strong decays of the ϕ(2170), along with its possible partner X(2436), as two fully strange tetraquark states of JPC=1−−. These two states are assumed to contain two strange quarks and two anti-strange quarks, with the flavor symmetry 6ss⊗6¯s¯s¯. 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 could 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.