Speaker
Description
We present a lattice-QCD validation of multiple sum rules associated with quark–gluon decomposition of hadron mass by computing all relevant tensor components of the quark and gluon energy--momentum tensor matrix elements from first principles. We achieve this through nonperturbative renormalization of the QCD energy–momentum tensor, including its trace, in a gradient-flow scheme, followed by continuum extrapolations, two-loop matching to the $\overline{\rm MS}$ scheme, and zero-flow-time extrapolations. These ingredients enable a direct and simultaneous verification, in a common renormalization scheme and scale, of multiple energy-density-based and trace-based mass decomposition sum rules proposed in the literature. We demonstrate the framework for the $\eta_c$ and $J/\psi$ charmonia using three fine lattice spacings with a physical strange-quark and near-physical up- and down-quark masses. The method is general and can be straightforwardly adopted for lattice-QCD calculations of mass and spin decompositions as well as gravitational form factors of other hadrons and nuclei.
