Mass radius of the proton

The mass radius is a fundamental property of the proton that so far has not been determined from experiment. Here, we show that the mass radius of the proton can be rigorously defined through the form factor of the trace of the energy-momentum tensor (EMT) of QCD in the weak gravitational field approximation, as appropriate for this problem. We then demonstrate that the scale anomaly of QCD enables the extraction of the form factor of the trace of the EMT from the data on threshold photoproduction of J/ψ and quarkonia, and use the recent GlueX Collaboration data to extract the rms mass radius of the proton Rm=0.55±0.03 fm. The extracted mass radius is significantly smaller than the rms charge radius of the proton Rc=0.8409±0.0004 fm. We attribute this difference to the interplay of asymptotic freedom and spontaneous breaking of chiral symmetry in QCD, and outline future measurements needed to determine the mass radius more precisely.