Gluon gravitational structure of hadrons of different spin

TL;DR

This study calculates the gluon gravitational form factors of various hadrons using lattice QCD, revealing insights into their internal energy, pressure, and angular momentum distributions, and estimating their gluon radii.

Contribution

It provides the first lattice QCD determination of gluon GFFs for multiple hadrons, including the pion, nucleon, rho meson, and Delta baryon, across a range of momentum transfers.

Findings

Gluon GFFs are extracted for several hadrons in a specific momentum transfer range.

Gluon contributions to energy, pressure, and shear force distributions are characterized.

Estimates for gluon mechanical and mass radii are provided.

Abstract

The gravitational form factors (GFFs) of hadrons encode the matrix elements of the energy momentum tensor of QCD. These quantities describe how energy, spin, and various mechanical properties of hadrons are carried by their quark and gluon constituents. We present the gluon GFFs of the pion, nucleon, $\rho$ meson, and $\Delta$ baryon as functions of the squared momentum transfer $t$ in the region $0 \leq -t < 2 \; \text{GeV}^2$, as determined in a lattice QCD study with pion mass $m_{\pi} = 450(5) \; \text{MeV}$. By fitting the extracted GFFs using multipole and z-parameter expansion functional forms, we extract various gluon contributions to the energy, pressure, and shear force distributions of the hadrons in the 3D and 2D Breit frames as well as in the infinite momentum frame. We also obtain estimates for the corresponding gluon mechanical and mass radii, as well as the forward-limit gluon contributions to the momentum fraction and angular momentum of the hadrons.