Measurement of the absolute branching fractions of $J/\psi \to \gamma \eta $ and $\eta $ decay modes

Based on a data sample of $\left(1.0087±0.0044\right)×{10}^{10}\text{}\text{}J/\psi $ events collected by the BESIII detector at the BEPCII accelerator, the absolute branching fraction (BF) of the decay $J/\psi \to \gamma \eta $ is measured with high precision using events in which the radiative photon converts to ${e}^{+}{e}^{-}$. Using the measured absolute BF of $J/\psi \to \gamma \eta $, the absolute BFs of four dominant $\eta $ decay modes are measured for the first time. The results are $B\left(J/\psi \to \gamma \eta \right)=\left(1.067±0.005±0.023\right)×{10}^{-3}$, $B\left(\eta \to \gamma \gamma \right)=\left(39.86±0.04±0.99\right)%$, $B\left(\eta \to {\pi }^{0}{\pi }^{0}{\pi }^{0}\right)=\phantom{\rule{0ex}{0ex}}\left(31.96±0.07±0.84\right)%$, $B\left(\eta \to {\pi }^{+}{\pi }^{-}{\pi }^{0}\right)=\left(23.04±0.03±0.54\right)%$, and $B\left(\eta \to {\pi }^{+}{\pi }^{-}\gamma \right)=\left(4.38±\phantom{\rule{0ex}{0ex}}0.02±0.10\right)%$, where the first and second uncertainties are statistical and systematic, respectively. The results are consistent with the world average values within two standard deviations.