Operator relations for gravitational form factors of a spin-0 hadron

The gravitational form factors for a hadron, the form factors for the hadron matrix element of the QCD energy-momentum tensor, not only describe the coupling of the hadron with a graviton, but also serve as unique quantities for describing the shape inside the hadron reflecting dynamics of quarks and gluons, such as the internal shear forces acting on the quarks/gluons and their pressure distributions. We consider the quark contribution to the gravitational form factors for a (pseudo)scalar hadron, and derive and clarify the relations satisfied by them as direct consequences of the symmetries and the equations of motion in QCD, and connections to the generalized parton distributions. Our results reveal the connections between the gravitational form factors and the higher-twist quark-gluon correlation effects inside the hadrons.