Dispersive Determination of Nucleon Gravitational Form Factors

Abstract

Being closely connected to the origin of the nucleon mass, the gravitational form factors of the nucleon have attracted significant attention in recent years. We present the first model-independent determinations of the gravitational form factors of the pion and nucleon at the physical pion mass, using a data-driven dispersive approach. The so-called "last global unknown property" of the nucleon, the $D$-term, is determined to be $-3.38_{-0.35}^{+0.34}$. The root mean square radius of the scalar trace density inside the nucleon is determined to be $(0.97\pm 0.03)\text{fm}$. Notably, this value is larger than the proton charge radius, suggesting a modern structural view of the nucleon where gluons, responsible for most of the nucleon mass, are distributed over a larger spatial region than quarks, which dominate the charge distribution, indicating that the radius of the trace density may be regarded as a confinement radius. We also predict the nucleon angular momentum and mechanical radii, providing further insights into the intricate internal structure of the nucleon.

Comments: v2: 10 pages, 6 figures, 1 table. Adopted a more conservative error analysis: minor shifts in results (central values unchanged). Expanded supplementary material: added derivations of GFF unitarity relations and input discussions. Clarifications of mass radius added, title changed, main conclusions unchanged