A Relativistic QCD-Based Study of Proton Properties Using Advanced Dirac Wavefunctions and Lattice Constraints

We present a relativistic three-quark Dirac model to predict the proton’s mass and charge radius, employing advanced variational wave-functions constrained by lattice QCD. The model uses a Jastrow-type correlated Dirac spinor with a hybrid Gaussian-exponential basis, exact small-component spinors, and explicit quark-quark correlations. Kinetic and potential energies—including screened Coulomb, linear confinement, hyperfine, and pion exchange terms—are evaluated via Monte Carlo integration, validated analytically. Fixed gluon (300 MeV) and sea-quark (50 MeV) contributions from lattice QCD are applied post-variationally. The model yields a proton mass of 925 MeV (1.4% discrepancy) and a charge radius of 0.83 fm (1.2% discrepancy) compared to experimental values (938.272 MeV, 0.84 fm). Discrepancies are attributed to the simplified variational basis and neglected higher-order interactions. The framework is transparent, reproducible, and partitions the proton’s mass into valence quark, gluon, and sea-quark contributions (The framework is a robust, physically consistent framework for simplified QCD modeling).