Nucleon and singly heavy baryons from the QCD instanton vacuum

TL;DR

This paper develops an effective chiral theory for nucleons and singly heavy baryons based on the QCD instanton vacuum, accurately predicting mass splittings and providing a framework for studying their gluonic properties.

Contribution

It introduces a novel effective chiral model derived from the QCD instanton vacuum, incorporating momentum-dependent quark masses and describing both nucleons and heavy baryons.

Findings

Predicted the nucleon mass as 1.268 GeV.

Calculated the $ ext{Delta}-N$ mass splitting as 213.67 MeV.

Obtained the heavy baryon mass splitting as 206.20 MeV, matching experimental data.

Abstract

We construct an effective chiral theory for the nucleon, based on the low-energy effective 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: $M_{\text{cl}}=1.2680$ 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 $\Delta -N$ mass splitting $M_{\Delta-N} =213.67$ 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 $M_{\Sigma_Q-\Lambda_Q}=206.20$ 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.