Hints of the JPC = 0−− and 1−− K⁎K¯1(1270) molecules in the J/ψ → ϕηη′ decay

The primary objective of this study is to investigate hadronic molecules of K⁎K¯1(1270) using a one-boson-exchange model, which incorporates exchanges of vector and pseudoscalar mesons in the t-channel, as well as the pion exchange in the u-channel. Additionally, careful consideration is given to the three-body effects resulting from the on-shell pion originating from K1(1270)→K⁎π. Then the BESIII data of the J/ψ→ϕηη′ process is fitted using the K⁎K¯1(1270) scattering amplitude with JPC=0−− or 1−−. The analysis reveals that both the JPC=0−− and 1−− assumptions for K⁎K¯1(1270) scattering provide good descriptions of the data, with similar fit qualities. Notably, the parameters obtained from the best fits indicate the existence of K⁎K¯1(1270) bound states, denoted by ϕ(2100) and ϕ0(2100) for the 1−− and 0−− states, respectively. The current experimental data, including the η polar angular distribution, cannot distinguish which K⁎K¯1(1270) bound state contributes to the J/ψ→ϕηη′ process, or if both are involved. Therefore, we propose further explorations of this process, as well as other processes, in upcoming experiments with many more J/ψ events to disentangle the different possibilities.