Search for $X(1870)$ via the decay J/ψ→ ω K⁺ K⁻η

Using a sample of (10087± 44)×10⁶ J/ψ events collected by the BESIII detector at the BEPCII collider, we search for the decay X(1870)→ K⁺ K⁻η via the J/ψ→ ω K⁺ K⁻ η process for the first time. No significant $X(1870)$ signal is observed. The upper limit on the branching fraction of the decay J/ψ→ ω X(1870) →ω K⁺ K⁻ η is determined to be 9.55× 10⁻⁷ at the $90%$ confidence level. In addition, the branching faction B(J/ψ→ω K⁺ K⁻ η) is measured to be (3.33±0.02(stat.)± 0.12(syst.))× 10⁻⁴.