{"title":"来自 QCD 瞬子真空的核子和单重重子","authors":"Yongwoo Choi, Hyun-Chul Kim","doi":"10.1103/physrevd.111.074023","DOIUrl":null,"url":null,"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</a:mi>0</a:mn></a:msub>=</a:mo>359</a:mn></a:mtext></a:mtext>MeV</a:mi></a:math>. The nucleon emerges as a state of <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:msub><c:mi>N</c:mi><c:mi>c</c:mi></c:msub></c:math> valence quarks bound by the pion mean field, which was created self-consistently by the <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:msub><e:mi>N</e:mi><e:mi>c</e:mi></e:msub></e:math> valence quarks. In the large Euclidean time, the classical nucleon mass is evaluated by minimizing the sum of the <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><g:msub><g:mi>N</g:mi><g:mi>c</g:mi></g:msub></g:math> discrete-level energies and the Dirac-continuum energy: <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><i:msub><i:mi>M</i:mi><i:mi>cl</i:mi></i:msub><i:mo>=</i:mo><i:mn>1.2680</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi>GeV</i:mi></i:math>. 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 <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><k:mi>I</k:mi><k:mo>=</k:mo><k:mn>1.3853</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>fm</k:mi></k:math> by using the self-consistent mean-field solution, which yields the <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><m:mi mathvariant=\"normal\">Δ</m:mi><m:mo>−</m:mo><m:mi>N</m:mi></m:math> mass splitting <p:math xmlns:p=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><p:msub><p:mi>M</p:mi><p:mrow><p:mi mathvariant=\"normal\">Δ</p:mi><p:mo>−</p:mo><p:mi>N</p:mi></p:mrow></p:msub><p:mo>=</p:mo><p:mn>213.67</p:mn><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>MeV</p:mi></p:math>. In the same manner, singly heavy baryons can be described as a bound state of the <s:math xmlns:s=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><s:msub><s:mi>N</s:mi><s:mi>c</s:mi></s:msub><s:mo>−</s:mo><s:mn>1</s:mn></s:math> 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 <u:math xmlns:u=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><u:msub><u:mi>M</u:mi><u:mrow><u:msub><u:mi mathvariant=\"normal\">Σ</u:mi><u:mi>Q</u:mi></u:msub><u:mo>−</u:mo><u:msub><u:mi mathvariant=\"normal\">Λ</u:mi><u:mi>Q</u:mi></u:msub></u:mrow></u:msub><u:mo>=</u:mo><u:mn>206.20</u:mn><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mi>MeV</u:mi></u:math>, 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. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"23 1","pages":""},"PeriodicalIF":5.3000,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nucleon and singly heavy baryons from the QCD instanton vacuum\",\"authors\":\"Yongwoo Choi, Hyun-Chul Kim\",\"doi\":\"10.1103/physrevd.111.074023\",\"DOIUrl\":null,\"url\":null,\"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</a:mi>0</a:mn></a:msub>=</a:mo>359</a:mn></a:mtext></a:mtext>MeV</a:mi></a:math>. The nucleon emerges as a state of <c:math xmlns:c=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><c:msub><c:mi>N</c:mi><c:mi>c</c:mi></c:msub></c:math> valence quarks bound by the pion mean field, which was created self-consistently by the <e:math xmlns:e=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><e:msub><e:mi>N</e:mi><e:mi>c</e:mi></e:msub></e:math> valence quarks. In the large Euclidean time, the classical nucleon mass is evaluated by minimizing the sum of the <g:math xmlns:g=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><g:msub><g:mi>N</g:mi><g:mi>c</g:mi></g:msub></g:math> discrete-level energies and the Dirac-continuum energy: <i:math xmlns:i=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><i:msub><i:mi>M</i:mi><i:mi>cl</i:mi></i:msub><i:mo>=</i:mo><i:mn>1.2680</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi>GeV</i:mi></i:math>. 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 <k:math xmlns:k=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><k:mi>I</k:mi><k:mo>=</k:mo><k:mn>1.3853</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>fm</k:mi></k:math> by using the self-consistent mean-field solution, which yields the <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><m:mi mathvariant=\\\"normal\\\">Δ</m:mi><m:mo>−</m:mo><m:mi>N</m:mi></m:math> mass splitting <p:math xmlns:p=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><p:msub><p:mi>M</p:mi><p:mrow><p:mi mathvariant=\\\"normal\\\">Δ</p:mi><p:mo>−</p:mo><p:mi>N</p:mi></p:mrow></p:msub><p:mo>=</p:mo><p:mn>213.67</p:mn><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>MeV</p:mi></p:math>. In the same manner, singly heavy baryons can be described as a bound state of the <s:math xmlns:s=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><s:msub><s:mi>N</s:mi><s:mi>c</s:mi></s:msub><s:mo>−</s:mo><s:mn>1</s:mn></s:math> 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 <u:math xmlns:u=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><u:msub><u:mi>M</u:mi><u:mrow><u:msub><u:mi mathvariant=\\\"normal\\\">Σ</u:mi><u:mi>Q</u:mi></u:msub><u:mo>−</u:mo><u:msub><u:mi mathvariant=\\\"normal\\\">Λ</u:mi><u:mi>Q</u:mi></u:msub></u:mrow></u:msub><u:mo>=</u:mo><u:mn>206.20</u:mn><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mi>MeV</u:mi></u:math>, 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. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>\",\"PeriodicalId\":20167,\"journal\":{\"name\":\"Physical Review D\",\"volume\":\"23 1\",\"pages\":\"\"},\"PeriodicalIF\":5.3000,\"publicationDate\":\"2025-04-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review D\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevd.111.074023\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.111.074023","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
Nucleon and singly heavy baryons from the QCD instanton vacuum
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=359MeV. 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=1.2680GeV. 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=1.3853fm by using the self-consistent mean-field solution, which yields the Δ−N mass splitting MΔ−N=213.67MeV. 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=206.20MeV, 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. Published by the American Physical Society2025
期刊介绍:
Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics.
PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including:
Particle physics experiments,
Electroweak interactions,
Strong interactions,
Lattice field theories, lattice QCD,
Beyond the standard model physics,
Phenomenological aspects of field theory, general methods,
Gravity, cosmology, cosmic rays,
Astrophysics and astroparticle physics,
General relativity,
Formal aspects of field theory, field theory in curved space,
String theory, quantum gravity, gauge/gravity duality.