Towards a first principles light-front Hamiltonian for the nucleon

Abstract: We solve the nucleon's wave functions from the eigenstates of the light-front quantum chromodynamics Hamiltonian for the first time, using a fully relativistic and nonperturbative approach based on light-front quantization, 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 this, we calculate the nucleon's quark and gluon matter densities, helicity, and transversity distributions, which show qualitative consistency with experimental extractions. We also compute the contributions of quark and gluon helicity to the proton spin and the tensor charges. The obtained light-front wave functions represent a significant advancement towards a unified description of various hadron distribution functions in both longitudinal and transverse momentum space.