Study of the Magnetic Dipole Transition of J=ψ → γηc via ηc → pp

Using (10.087±0.044)×109  𝐽/𝜓 events collected with the BESIII detector at the 𝑒+⁢𝑒− BEPCII collider, we present the first amplitude analysis of 𝐽/𝜓 →𝛾⁢𝑝⁢¯𝑝 with the 𝑝⁢¯𝑝 invariant mass in the 𝜂𝑐 mass region [2.70,3.05]  GeV/𝑐2. The product branching fraction ℬ⁡(𝐽/𝜓→𝛾⁢𝜂𝑐)×ℬ⁡(𝜂𝑐→𝑝⁢¯𝑝) is determined to be (2.11±0.0⁢2stat±0.0⁢7syst)×10−5 with precision improved by 1 order of magnitude. Combining with the product branching fractions ℬ⁡(𝜂𝑐→𝑝⁢¯𝑝)×ℬ⁡(𝜂𝑐→𝛾⁢𝛾) and ℬ⁡(𝐽/𝜓→𝛾⁢𝜂𝑐)×ℬ⁡(𝜂𝑐→𝛾⁢𝛾), the branching fractions of ℬ⁡(𝐽/𝜓 →𝛾⁢𝜂𝑐) and ℬ⁡(𝜂𝑐 →𝛾⁢𝛾) are calculated to be (2.29±0.0⁢1stat±0.0⁢4syst±0.1⁢8opbf)% and (2.28±0.0⁢1stat±0.0⁢4syst±0.1⁢8opbf)×10−4, respectively, which are consistent with the latest lattice quantum chromodynamics calculations. Here, opbf is the uncertainty from the other product branching fractions used in the calculation.