Study of the Magnetic Dipole Transition of J / ψ → γ η c via η c → p p ¯

Using (10.087±0.044)×10^{9} J/ψ events collected with the BESIII detector at the e^{+}e^{-} BEPCII collider, we present the first amplitude analysis of J/ψ→γpp[over ¯] with the pp[over ¯] invariant mass in the η_{c} mass region [2.70,3.05] GeV/c^{2}. The product branching fraction B(J/ψ→γη_{c})×B(η_{c}→pp[over ¯]) is determined to be (2.11±0.02_{stat}±0.07_{syst})×10^{-5} with precision improved by 1 order of magnitude. Combining with the product branching fractions B(η_{c}→pp[over ¯])×B(η_{c}→γγ) and B(J/ψ→γη_{c})×B(η_{c}→γγ), the branching fractions of B(J/ψ→γη_{c}) and B(η_{c}→γγ) are calculated to be (2.29±0.01_{stat}±0.04_{syst}±0.18_{opbf})% and (2.28±0.01_{stat}±0.04_{syst}±0.18_{opbf})×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.