Year: 2025
Type: article
Abstract: We construct an effective chiral theory for the nucleon, based on the low-energy effect quantum chromodynamics (QCD) partition function from the QCD instanton vacuum. We fully consider the momentum-dependent dynamical quark mass whose value at the zero virtuality of the quark is determined by the gap equation from the instanton vacuum, M 0 = 359 MeV . The nucleon emerges as a state of N c valence quarks bound by the pion mean field, which was created self-consistently by the N c valence quarks. In the large Euclidean time, the classical nucleon mass is evaluated by minimizing the sum of the N c discrete-level energies and the Dirac-continuum energy: M cl = 1.2680 GeV . The pion mean-field solution turns out broader than the local chiral quark-soliton model. The zero-mode quantization furnishes the nucleon with proper quantum numbers such as the spin and isospin. We compute the moment of inertia I = 1.3853 fm by using the self-consistent mean-field solution, which yields the Δ − N mass splitting M Δ − N = 213.67 MeV . In the same manner, singly heavy baryons can be described as a bound state of the N c − 1 valence quarks with the corresponding pion mean field, with the heavy quark regarded as a static color source. The mass splitting of the singly heavy baryons is obtained to be M Σ Q − Λ Q = 206.20 MeV , which are in good agreement with the experimental data. The effective chiral theory developed in the present work will provide a solid theoretical framework to investigate gluonic observables of both the light and singly heavy baryons.
Authors: Yongwoo Choi, Hyun-Chul Kim
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4409570568