Basis light-front quantization: Advancing a first principles approach for the nucleon

Abstract: We present our recent progress in applying the basis light-front quantization approach to investigate the nucleon's structure. We solve its wave functions from the eigenstates of the light-front QCD Hamiltonian using a fully relativistic, nonperturbative approach without an explicit confining potential. These eigenstates are determined for the three-quark, three-quark-gluon, and three-quark-quark-antiquark Fock representations, making them suitable for low-resolution probes. From these wave functions, we compute the nucleon's quark and gluon matter densities, as well as its helicity and transversity distributions, showing qualitative consistency with experimental data. We also determine the quark and gluon helicity contributions to the proton spin and the tensor charges. The resulting light-front wave functions represent a significant step toward a unified description of hadron distribution functions in both longitudinal and transverse momentum space.