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 UA(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 mN=939.53 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 gA=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.
Related
- Gluonic nucleon energy correlators and fracture functions for Color Glass Condensate
- Third moments of nucleon unpolarized, polarized, and transversity parton distribution functions from physical-point lattice QCD
- On the topology of the space of vacuum initial data sets
- Nucleon parton distribution functions from boosted correlations in the Coulomb gauge
- Breaking de Sitter Symmetry with Cosmic Topology: Cosmological Role of Infrared Vacuum Freedom
BibTeX
@misc{liu2026nucleon,
title = {{Nucleon Wave Functions from QCD Vacuum Topology}},
author = {Wei-Yang Liu and Ismail Zahed},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39215},
eprint = {2610.39215},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39215},
}
RIS
TY - UNPB
TI - Nucleon Wave Functions from QCD Vacuum Topology
AU - Wei-Yang Liu
AU - Ismail Zahed
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39215
UR - https://arxiv.org/abs/2610.39215
AB - 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 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.
ER -