Particle seismology: mechanical and gravitational properties from parton-hadron duality

The internal structure of hadrons is characterized by form factors which correspond to matrix elements of currents. Among those, the stress-energy-momentum tensor is a universally conserved quantity providing the gravitational form factors, from which mechanical properties may be derived via the response to the space-time fluctuations. They have received much attention due to their role as moments of the Generalized Parton Distributions, where the stress-energy-momentum tensor couples to two photons, and more recently, due to the explicit lattice QCD determination for the pion and nucleon. In these lectures, we attempt a pedagogical review of the topic from a purely hadronic point of view, based on the notion of dispersion relations, meson dominance, and parton–hadron duality. We show that despite the overwhelming simplicity of the approach, a rather successful description of the lattice QCD data is achieved. Published by the Jagiellonian University 2026 authors