Search for the X (2370) and observation of ηc →ηηη′ in J /ψ →γηηη′

Using a sample of 1.31×109 J/ψ events collected with the BESIII detector, we perform a study of J/ψ→γηηη′ to search for the X(2370) and ηc in the ηηη′ invariant mass distribution. No significant signal for the X(2370) is observed, and we set an upper limit for the product branching fraction of B(J/ψ→γX(2370)·B(X(2370)→ηηη′)<9.2×10-6 at the 90% confidence level. A clear ηc signal is observed for the first time, yielding a product branching fraction of B(J/ψ→γηc)·B(ηc→ηηη′)=(4.86±0.62(stat)±0.45(sys))×10-5.