Dispersive Determination of Nucleon Gravitational Form Factors

TL;DR

This paper presents the first model-independent, data-driven dispersive analysis of nucleon and pion gravitational form factors at the physical pion mass, revealing new insights into the nucleon's internal structure and mass distribution.

Contribution

It introduces a novel dispersive approach to determine gravitational form factors without model assumptions, providing key parameters like the D-term and scalar radius.

Findings

The D-term of the nucleon is determined to be -3.38^{+0.34}_{-0.35}.

The scalar trace density radius is about 0.97 fm, larger than the proton charge radius.

Predictions for nucleon angular momentum and mechanical radii are provided.

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 $-3.38^{+0.34}_{-0.35}$. The root mean square radius of the scalar trace density inside the nucleon is determined to be $(0.97 \pm0.03)~\text{fm}$. 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.