Measurement of the phase between strong and electromagnetic amplitudes in the decay $J\mathrm{/}\psi \to \phi \eta$

The first direct measurement of the relative phase between the strong and electromagnetic amplitudes for a $J\mathrm{/}\psi$ decaying into a vector-pseudoscalar final state is performed using 26 energy points of $e^{+}{e}^{-}$ annihilation data between $3.00\text{ GeV}$ and \mbox{3.12 GeV}. The data sets were collected by the BESIII detector with a total integrated luminosity of 452 pb${}^{-1}$. By investigating the interference pattern in the cross section lineshape of $e^{+}{e}^{-}\to \phi \eta$, the relative phase between the strong and electromagnetic amplitudes of $J\mathrm{/}\psi$ decay is determined to be within $[{133}^{\circ },{228}^{\circ }]$ at 68% confidence level.