Measurement of the phase between strong and electromagnetic amplitudes of J/ψ decays

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 100pb^-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^-)π⁰ 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 ηπ⁺π^- with η →π⁺π^-π⁰, 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^-)π⁰ is measured to be (4.73 ± 0.44)% or (4.85 ± 0.45)%, and the branching fraction of J / ψ → ηπ⁺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.