Measurement of the phase between strong and electromagnetic amplitudes of $J/\psi$ decays

Using 16 energy points of $e^{+}e^{-}$ annihilation data collected in the vicinity of the $J/\psi$ resonance with the BESIII detector and with a total integrated luminosity of around 100 pb$^{-1}$, we study the relative phase between the strong and electromagnetic amplitudes of $J/\psi$ decays. The relative phase between $J\psi$ electromagnetic decay and the continuum process ($e^{+}e^{-}$ annihilation without the $J/\psi$ resonance) is confirmed to be zero by studying the cross section lineshape of $\mu^{+}\mu^{-}$ production. The relative phase between $J/\psi$ strong and electromagnetic decays is then measured to be $(84.9\pm3.6)^\circ$ or $(-84.7\pm3.1)^\circ$ for the $2(\pi^{+}\pi^{-})\pi^{0}$ final state by investigating the interference pattern between the $J/\psi$ decay and the continuum process. This is the first measurement of the relative phase between $J/\psi$ strong and electromagnetic decays into a multihadron final state using the lineshape of the production cross section. We also study the production lineshape of the multihadron final state $\eta\pi^{+}\pi^{-}$ with $\eta\to\pi^{+}\pi^{-}\pi^{0}$, which provides additional information about the phase between the $J/\psi$ electromagnetic decay amplitude and the continuum process. Additionally, the branching fraction of $J/\psi\to 2(\pi^{+}\pi^{-})\pi^{0}$ is measured to be $(4.73\pm0.44)\%$ or $(4.85\pm0.45)\%$, and the branching fraction of $J/\psi\to\eta\pi^{+}\pi^{-}$ is measured to be $(3.78\pm0.68)\times10^{-4}$. Both of them are consistent with the world average values. The quoted uncertainties include both statistical and systematic uncertainties, which are mainly caused by the low statistics.