Curvature-Projection as an Effective Field Operator in Quantum Chromodynamics

We show that the mass–charge binding and curvature-projection mechanism proposed for explaining hadronic and leptonic mass hierarchies can be expressed as a legitimate effective operator within Quantum Chromodynamics (QCD) and Quantum Field Theory (QFT).
By introducing a scalar curvature mediator that couples to local mass and absolute-charge densities, integrating it out yields a non-local gauge-invariant interaction.
This term represents an entropic correction to the QCD vacuum energy associated with gluonic curvature fluctuations and is numerically consistent with lattice determinations of the topological susceptibility chi. The resulting operator preserves Lorentz invariance, locality, and renormalizability up to the confinement scale, providing a rigorous QFT basis for curvature-induced mass–charge coupling and charge-orientation projection.