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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2501.12114 |
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| _version_ | 1866917898543431680 |
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| author | Choi, Yongwoo Kim, Hyun-CHul |
| author_facet | Choi, Yongwoo Kim, Hyun-CHul |
| contents | 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 $Δ-N$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nucleon and singly heavy baryons from the QCD instanton vacuum Choi, Yongwoo Kim, Hyun-CHul High Energy Physics - Phenomenology High Energy Physics - Lattice 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 $Δ-N$ 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. |
| title | Nucleon and singly heavy baryons from the QCD instanton vacuum |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2501.12114 |