Gravitational form factors of hadrons from lattice QCD

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, and can be constrained using the framework of lattice quantum chromodynamics (QCD). In this thesis, we explore the gravitational structure of hadrons through two main results. The first result [1] is an extraction of the gluon GFFs of the pion, nucleon, 𝜌 meson, and Δ baryon as functions of the squared momentum transfer 𝑡 in the region 0 ≤ −𝑡 < 2 GeV², as determined in a lattice QCD study at pion mass 𝑚 subscript 𝜋 = 450 MeV. By fitting the extracted GFFs, we extract various gluon contributions to the energy, pressure, and shear force distributions of the hadrons. 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 four hadrons. Our results for the gluon GFFs of the proton were found to be in agreement with the first phenomenological extraction [2]. The second result [3] is a decomposition of the GFFs of the pion between the different quark flavor and gluon contributions, in the kinematic region 0 ≤ −𝑡 < 2 GeV², on a lattice ensemble with quark masses yielding pion mass 𝑚 subscript 𝜋 = 170 MeV. From these results, we obtain the renormalization scheme- and scale-independent total GFFs of the pion, which are in agreement with the momentum fraction sum rule and the nex-to-leading order chiral perturbation theory prediction for its 𝐷-term, which is a fundamental hadron charge related to the internal forces.