Study of $\chi_{cJ}\to \eta \eta \eta^\prime$ via intermediate charmed meson loop mechanisms and its implications for non-observation of $\eta_1(1855)$ in $\chi_{cJ}$ decays

Abstract

Recently, the BESIII Collaboration reported the first observation of the decays $\chi_{cJ} \to \eta \eta \eta^\prime$ in order to search for the $1^{-+}$ exotic state $\eta_1(1855)$. A partial wave analysis of the $\eta \eta^\prime$ invariant mass spectrum shows no significant signal for the $\eta_1(1855)$. In this work, we, using an effective Lagrangian approach, investigate the processes $\chi_{cJ} \to \eta \eta \eta^\prime$ via the box and triangle loops involving charmed mesons and the scalar meson $f_0(1500)$. Our calculations reproduce well the experimental branching fractions of $\chi_{cJ} \to \eta \eta \eta^\prime$. Furthermore, we present the predictions of the relevant invariant mass spectra of $\eta \eta^\prime$ and $\eta \eta$ produced in the $\chi_{c1}$ decay, which seem overall consistent with the BESIII measurements. In the present model, the decay $\chi_{c1} \to \eta \eta \eta^\prime$ is dominated by the triangle and box loop contributions. The consistency between our theoretical results and the BESIII measurements sheds light on the underlying decay mechanism of the $\chi_{cJ}$ decaying into light mesons and might be helpful to understand the absence of the $\eta_1(1855)$ signal in the decay channels $\chi_{cJ} \to \eta \eta \eta^\prime$.