The mass radius of the proton

TL;DR

This paper introduces a method to determine the proton's mass radius from experimental data using QCD form factors, revealing it to be smaller than the charge radius and highlighting fundamental QCD effects.

Contribution

It provides a rigorous definition of the proton's mass radius via the energy-momentum tensor form factor and demonstrates its extraction from photoproduction data, a novel experimental approach.

Findings

Mass radius of proton = 0.55 ± 0.03 fm

Mass radius is smaller than charge radius

QCD effects explain the size difference

Abstract

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 formfactor 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 formfactor of the trace of the EMT from the data on threshold photoproduction of $J/\psi$ and $\Upsilon$ quarkonia, and use the recent GlueX Collaboration data to extract the r.m.s. mass radius of the proton ${\rm R_m = 0.55 \pm 0.03 \ fm}$. The extracted mass radius is significantly smaller than the charge radius of the proton ${\rm R_C = 0.8409 \pm 0.0004 \ fm}$. 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.