Unveiling Mechanical Structure of a Hadron from QCD Vacuum

We present a unified framework for calculating the gluonic structure of light hadrons within the QCD instanton vacuum. At intermediate energy scales, set by the inverse instanton size, the gluon field configurations are predominantly localized and presented by liquid that consists of single instantons and instanton–anti-instanton pairs, providing a nonperturbative source of gluon content inside hadrons. Within this framework, we compute the gluonic scalar, energy-momentum tensor (EMT), and trace form factors for the pion and nucleon. Our analysis manifests a decomposition of hadron mass into contributions from the EMT, quark masses, and the QCD trace anomaly and provides insight into internal mechanical properties such as pressure and shear distributions. The results are consistent with recent lattice QCD calculations and demonstrate that topologically active gluon configurations play a central role in shaping the gluonic structure, Ji's mass sum rule, and mechanical features of hadrons at low resolution.