Hints of the \(J^{PC}=0^{--}\) and \(1^{--}\) \(K^*\bar K_1(1270)\) Molecules in the \(J/\psi\to\phi\eta\eta'\) Decay

Abstract

The primary objective of this study is to investigate hadronic molecules of \(K^*\bar K_1(1270)\) 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 \(K_1(1270)\to K^*\pi\). Then the BESIII data of the \(J/\psi\to\phi\eta\eta'\) process is fitted using the \(K^*\bar K_1(1270)\) scattering amplitude with \(J^{PC}=0^{--}\) or \(1^{--}\). The analysis reveals that both the \(J^{PC}=0^{--}\) and \(1^{--}\) assumptions for \(K^*\bar K_1(1270)\) scattering provide good descriptions of the data, with similar fit qualities. Notably, the parameters obtained from the best fits indicate the existence of \(K^*\bar K_1(1270)\) bound states, denoted by \(\phi(2100)\) and \(\phi_0(2100)\) for the \(1^{--}\) and \(0^{--}\) states, respectively. The current experimental data, including the \(\eta\) polar angular distribution, cannot distinguish which \(K^*\bar K_1(1270)\) bound state contributes to the \(J/\psi\to\phi\eta\eta'\) 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 \(J/\psi\) events to disentangle the different possibilities.