Nucleon and singly heavy baryons from the QCD instanton vacuum

초록

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, M0=359 MeV. The nucleon emerges as a state of Nc valence quarks bound by the pion mean field, which was created self-consistently by the Nc valence quarks. In the large Euclidean time, the classical nucleon mass is evaluated by minimizing the sum of the Nc discrete-level energies and the Dirac-continuum energy: Mcl=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 MΔ-N=213.67 MeV. In the same manner, singly heavy baryons can be described as a bound state of the Nc-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 MςQ-ΛQ=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. © 2025 authors.

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