The branching fraction measurements of $J/\psi$ decay into $\rho \eta$ and $\phi \eta$ final states
We present measurements of the branching fractions for the $J/\psi$ meson decays into the $\rho\eta$ and $\phi\eta$ final states, based on data collected with the KEDR detector at the VEPP-4M collider. The data set consisted of 4.93 million $J/\psi$ events. The resulting branching fractions are: - $\mathcal{B}(J/\psi \to \rho\eta) = (2.04 \pm 0.58 \pm 0.39)\times 10^{-4}$, - $\mathcal{B}(J/\psi \to \phi\eta) = (7.82 \pm 1.17 \pm 0.58) \times 10^{-4}$, where the first uncertainty is statistical and the second one is systematic. In the study of the $\rho\eta$ decay, the dynamics of $J/\psi\to\pi^+\pi^-\eta$ is analyzed. The hints from contributions of $\rho(1450)\eta$ and $a^{\pm}_2\pi^{\mp}$ intermediate states are observed. Additional measured branching fractions in the model that includes $\rho(1450)\eta$ and $a^{\pm}_2\pi^{\mp}$ are: - $\mathcal{B}(J/\psi \to \pi^+\pi^-\eta) = (4.73 \pm 0.49 \pm 1.17)\times10^{-4}$, - $\mathcal{B}(J/\psi \to (a_2^+\pi^- + a_2^- \pi^+)) = (1.05\pm 0.37 \pm 0.34)\times 10^{-3}$, - $\mathcal{B}(J/\psi \to \rho(1450)\eta \to \pi^+\pi^-\eta) < 1.51 \times 10^{-4}$, at a confidence level of 90\%. All results are consistent with previous studies.