Study of χ cJ→ η η η ^ via intermediate charmed meson loop mechanisms and its implications for non-observation of η ₁(1855) in χ cJ decays

Recently, the BESIII Collaboration reported the first observation of the decays χ cJ → η η η ^ χ cJ → η η η ′ in order to search for the 1⁻⁺ 1 - + exotic state η ₁(1855) η 1 ( 1855 ) . A partial wave analysis of the η η ^ η η ′ invariant mass spectrum shows no significant signal for the η ₁(1855) η 1 ( 1855 ) . In this work, we, using an effective Lagrangian approach, investigate the processes χ cJ → η η η ^ χ cJ → η η η ′ via the box and triangle loops involving charmed mesons and the scalar meson f₀(1500) f 0 ( 1500 ) . Our calculations reproduce well the experimental branching fractions of χ cJ → η η η ^ χ cJ → η η η ′ . Furthermore, we present the predictions of the relevant invariant mass spectra of η η ^ η η ′ and η η η η produced in the χ c1 χ c 1 decay, which seem overall consistent with the BESIII measurements. In the present model, the decay χ c1 → η η η ^