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

Abstract Using 16 energy points of e + e − annihilation data collected in the vicinity of the J / ψ 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 / ψ decays. The relative phase between J / ψ electromagnetic decay and the continuum process ( e + e − annihilation without the J / ψ resonance) is confirmed to be zero by studying the cross section lineshape of μ + μ − production. The relative phase between J / ψ strong and electromagnetic decays is then measured to be ( 84.9 ± 3.6 ) ∘ or ( − 84.7 ± 3.1 ) ∘ for the 2 ( π + π − ) π 0 final state by investigating the interference pattern between the J / ψ decay and the continuum process. This is the first measurement of the relative phase between J / ψ 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 η π + π − with η → π + π − π 0 , which provides additional information about the phase between the J / ψ electromagnetic decay amplitude and the continuum process. Additionally, the branching fraction of J / ψ → 2 ( π + π − ) π 0 is measured to be ( 4.73 ± 0.44 ) % or ( 4.85 ± 0.45 ) % , and the branching fraction of J / ψ → η π + π − is measured to be ( 3.78 ± 0.68 ) × 10 − 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.