Operator Relations for Gravitational Form Factors

The form factors for the hadronmatrix element of the QCD energy-momentum tensor not only describe the coupling of the hadronwith a gravitonas the `` gravitationalform factors'', but also serve as unique quantities for describing the shape inside the hadronreflecting dynamics of quarks and gluons, such as the internal shear forcesacting on the quarks/ gluonsand their pressure distributions. We consider the gravitationalform factors for a hadron, in particular, for a (pseudo)scalar hadronand for the nucleon. We derive and clarify the relations satisfied by the gravitationalform factors as direct consequences of the symmetries and the equations of motion in QCD, and connections to the generalized parton distributions. Our results reveal that the gravitationalform factors are related to the higher-twist quark- gluoncorrelation effects inside the hadronsand also to QCD trace anomaly.