Colloquium: Gravitational Form Factors of the Proton

Abstract

The physics of the gravitational form factors of the proton, and their understanding within quantum chromodynamics, has advanced significantly in the past two decades through both theory and experiment. This Colloquium provides an overview of this progress, highlights the physical insights unveiled by studies of gravitational form factors, and reviews their interpretation in terms of the mechanical properties of the proton. CONTENTS I. Introduction 1 A. Anomalous magnetic moment 1 B. The proton's finite size 1 C. Discovery of partons 2 D. Colored quarks and gluons, QCD, and confinement 2 E. Proton mass, spin and D-term 3 II. The energy-momentum tensor 3 A. Definition of the EMT operator 3 B. Trace anomaly 4 C. Definition of the proton GFFs 4 D. Decomposition of proton mass 4 E. Decomposition of proton spin 6 III. Measuring gravitational form factors 6 A. Deeply virtual Compton scattering (DVCS) 6 B. DVCS with positron and electron beams 8 C. γγ * → π 0 π 0 and J/Ψ threshold production 8 D. Time-like Compton scattering, double DVCS and deeply virtual meson production 8 IV. Theoretical Results 9 A. Chiral symmetry and the D-term of the pion 9 B. GFFs in model studies 9 C. Limits in QCD and dispersion relations 10 D. Lattice QCD 11 V. Experimental results 12 A. DVCS in fixed-target and collider experiments 13 B. First extraction of the proton GFF Dq(t) 13 C. Future experimental developments to access GFFs. 16 D. Other phenomenological studies 16 VI. Interpretation 17 A. The static EMT 17 B. The stress tensor and the D-term 17 C. Normal forces and the sign of the D-term 18 D. The mechanical radius of the proton and neutron 18 E. First visualization of forces from experiment 18 F. The D-term and long-range forces 19

Gravitational form factors of the proton from near-threshold vector meson photoproduction*

“…points. Notably, the gluon D-term contributes slightly more than the quark D-term, and our gluon A and Dterms are approximately comparable with the LQCD results [10]. The total GFFs are shown in Fig.…”

“…Here, the parameter errors include all uncertainties of the GFFs. For the quark GFFs, the quark D-term exhibits a notable agreement with the DVCS experiment data and LQCD determinations, whereas our A-term is approximately half that of the LQCD results [10]. The converse gluon A-and Dterms are displayed in Fig.…”

“…The total GFFs are shown in Fig. 5 and compared with the LQCD results [10]. For , our result is found to be consistent with the LQCD result, whereas both are slightly smaller.…”

“…As shown in Fig. 4, the values of the quark and gluon A-and D-terms are compared with the DVCS experiment data and LQCD determinations [10]. Here, the parameter errors include all uncertainties of the GFFs.…”

“…The ratios of the mass and charge radii of different hadrons appear to be consistent. (green dash-dotted curve) compared with LQCD results [10]. Bottom panel:…”