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

TL;DR

This study uses an effective Lagrangian approach to analyze $oldsymbol{ ext{chi}_{cJ} o ext{eta} ext{eta} ext{eta}'}$ decays via charmed meson loops, explaining experimental results and the non-observation of $ ext{eta}_1(1855)$.

Contribution

It provides a theoretical model that reproduces experimental branching fractions and predicts invariant mass spectra, clarifying decay mechanisms and the absence of $ ext{eta}_1(1855)$ signals.

Findings

The model reproduces BESIII branching fractions.

Predicted invariant mass spectra align with measurements.

Decay dominated by triangle and box loop contributions.

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 $\chi_{cJ} \to \eta \eta \eta^\prime$.