Nucleon Wave Functions from QCD Vacuum Topology

Abstract

Instantons, as topologically nontrivial gauge field configurations, provide a microscopic mechanism for chiral symmetry breaking and the $U_A(1)$ anomaly in QCD. Within the instanton liquid model (ILM), instantons generate multi-fermion interactions governed by their density and size. Using this framework, we develop a microscopic description of the nucleon based on instanton-induced quark--quark correlations. We derive the diquark interaction kernels arising from single instantons and instanton--anti-instanton molecules, revealing a strong attraction in the scalar channel and weaker correlations in the spin-one channels. Embedding these interactions in a covariant, permutation-symmetric Bethe--Salpeter--Faddeev equation yields a nucleon mass $m_N=939.53~{\rm MeV}$, with a predominantly scalar-diquark component ($98\%$) and a small axial-vector admixture ($2\%$) around the mass pole. Despite its small weight, the small admixture generates substantial spin--isospin interference, yielding an axial charge $g_A=1.265$, close to experiment. The resulting covariant amplitude is analytically continued to the light front to obtain the leading three-quark wave function. The corresponding unpolarized, helicity, and transversity parton distributions, along with their QCD-evolved moments, provide a direct connection to lattice QCD calculations and global-fit analyses. Our results show that the topology of the QCD vacuum organizes not only the nucleon mass and spin structure, but also its leading valence partonic content, providing a microscopic foundation for a more complete description including confinement and higher Fock components.