Mechanical properties of proton using flavor-decomposed gravitational form factors

We investigate the mechanical properties of the proton by extracting its flavor-decomposed gravitational form factors (GFFs) using Light-Cone QCD sum rules (LCSR). These form factors encode critical information about the internal dynamics and spatial distribution of energy, momentum, and internal forces within the proton. The flavor decomposition of the quark sector indicates the role of each flavor in the proton's pressure and shear force distributions. Our results show that the up quark contributes more significantly compared to the down quark in the three conserved proton GFFs, as well as in the energy and shear force distributions. Additionally, we define the non-conserved form factor $\bar{c}^q (t)$, which takes part in the distributions of energy and pressure; the latter is essential for maintaining proton stability. Furthermore, we determine the proton's mass and mechanical radii, providing valuable insight into its internal structure and dynamics.