Sum Rules for the Gravitational Form Factors Using Light-Front Dressed Quark State

We consider a light-front dressed quark state, per se, instead of a proton state, we consider a simple composite spin-1/2 state of a quark dressed with a gluon. This perturbative model incorporates gluonic degrees of freedom, which enable us to evaluate the gravitational form factors (GFFs) of the quark as well as the gluon in this model (More et al. Phys Rev D 105(5):056017, 2022. arXiv:2112.06550, https://doi.org/10.1103/PhysRevD.105.056017; Gluon contribution to the mechanical properties of a dressed quark in light-front Hamiltonian QCD, 2023. arXiv:2302.11906). We employ the Hamiltonian framework and choose the light-front gauge \(A^+=0\). We calculate the four GFFs and corroborate the sum rules that GFFs satisfy. The GFF DD is attributed to information like pressure, shear, and energy distributions. We analyze some of these distributions for a dressed quark state at one loop in QCD.