Observation of X(2370) and search for X(2120) in $$J/\psi \rightarrow \gamma K{\bar{K}} \eta '$$

Using a sample of $$1.31\times 10^{9} ~J/\psi $$1.31×109J/ψ events collected with the BESIII detector, we perform a study of $$J/\psi \rightarrow \gamma K{\bar{K}}\eta '$$J/ψ→γKK¯η′. X(2370) is observed in the $$K{\bar{K}}\eta '$$KK¯η′ invariant-mass distribution with a statistical significance of $$8.3\sigma $$8.3σ. Its resonance parameters are measured to be $$M=2341.6\pm 6.5 \, \text {(stat.)} \pm 5.7 \, \text {(syst.)}~ \hbox {MeV}/c^{2}$$M=2341.6±6.5(stat.)±5.7(syst.)MeV/c2 and $$\Gamma = 117\pm 10 \, \text {(stat.)}\pm 8 \, \text {(syst.)}~\hbox {MeV}$$Γ=117±10(stat.)±8(syst.)MeV. The product branching fractions for $$J/\psi \rightarrow \gamma X(2370),X(2370)\rightarrow K^{+}K^{-}\eta '$$J/ψ→γX(2370),X(2370)→K+K-η′ and $$J/\psi \rightarrow \gamma X(2370),X(2370)\rightarrow K_{S}^{0}K_{S}^{0}\eta '$$J/ψ→γX(2370),X(2370)→KS0KS0η′ are determined to be $$(1.79\pm 0.23\, \text {(stat.)}\pm 0.65\,\text {(syst.)})\times 10^{-5}$$(1.79±0.23(stat.)±0.65(syst.))×10-5 and $$(1.18\pm 0.32\, \text {(stat.)}\pm 0.39\, \text {(syst.)})\times 10^{-5}$$(1.18±0.32(stat.)±0.39(syst.))×10-5, respectively. No evident signal for X(2120) is observed in the $$K{\bar{K}}\eta '$$KK¯η′ invariant-mass distribution. The upper limits for the product branching fractions of $${\mathcal {B}}(J/\psi \rightarrow \gamma X(2120)\rightarrow \gamma K^{+} K^{-} \eta ')$$B(J/ψ→γX(2120)→γK+K-η′) and $${\mathcal {B}}(J/\psi \rightarrow \gamma X(2120)\rightarrow \gamma K_{S}^{0} K_{S}^{0} \eta ')$$B(J/ψ→γX(2120)→γKS0KS0η′) are determined to be $$1.49\times 10^{-5}$$1.49×10-5 and $$6.38\times 10^{-6}$$6.38×10-6 at the 90% confidence level, respectively.