Hints of the $J^{PC}=0^{--}$ and $1^{--}$ $K^{\ast }{\bar{K}}_1(1270)$ Molecules in the $J/\psi \to \varphi \eta {\eta }^{\prime }$ Decay

Abstract

The primary objective of this study is to investigate hadronic molecules of $K^{\ast }{\bar{K}}_1(1270)$ 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 $K_1(1270)\to K^{\ast }\pi$. Then the BESIII data of the $J/\psi \to \varphi \eta {\eta }^{\prime }$ process is fitted using the $K^{\ast }{\bar{K}}_1(1270)$ scattering amplitude with $J^{PC}=0^{--}$ or $1^{--}$. The analysis reveals that both the $J^{PC}=0^{--}$ and $1^{--}$ assumptions for $K^{\ast }{\bar{K}}_1(1270)$ scattering provide good descriptions of the data, with similar fit qualities. Notably, the parameters obtained from the best fits indicate the existence of $K^{\ast }{\bar{K}}_1(1270)$ bound states, denoted by $\varphi (2100)$ and ${\varphi }_0(2100)$ for the $1^{--}$ and $0^{--}$ states, respectively. The current experimental data, including the $\eta$ polar angular distribution, cannot distinguish which $K^{\ast }{\bar{K}}_1(1270)$ bound state contributes to the $J/\psi \to \varphi \eta {\eta }^{\prime }$ 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.

Comments: 11pages, 8figures and 1 table