{"title":"Mixing angle between P13 and P11 states in heavy axial vector mesons within the QCD sum rules framework","authors":"T. M. Aliev, S. Bilmis, M. Savci","doi":"10.1103/physrevd.111.014005","DOIUrl":null,"url":null,"abstract":"In this study, we calculate the mixing angles between the axial-vector mesons D</a:mi></a:mrow>1</a:mn>(</a:mo>s</a:mi>1</a:mn>)</a:mo></a:mrow></a:msub>−</a:mo>D</a:mi></a:mrow>1</a:mn>(</a:mo>s</a:mi>1</a:mn>)</a:mo></a:mrow>′</a:mo></a:mrow></a:msubsup></a:mrow></a:math> and <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><g:mrow><g:msub><g:mrow><g:mi>B</g:mi></g:mrow><g:mrow><g:mn>1</g:mn><g:mo stretchy=\"false\">(</g:mo><g:mi>s</g:mi><g:mn>1</g:mn><g:mo stretchy=\"false\">)</g:mo></g:mrow></g:msub><g:mo>−</g:mo><g:msubsup><g:mrow><g:mi>B</g:mi></g:mrow><g:mrow><g:mn>1</g:mn><g:mo stretchy=\"false\">(</g:mo><g:mi>s</g:mi><g:mn>1</g:mn><g:mo stretchy=\"false\">)</g:mo></g:mrow><g:mrow><g:mo>′</g:mo></g:mrow></g:msubsup></g:mrow></g:math> using the QCD sum rules approach. Our results are <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><m:mrow><m:msub><m:mrow><m:mi>θ</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub><m:mo>=</m:mo><m:mn>28.2</m:mn><m:mo>±</m:mo><m:mn>0.6</m:mn><m:mi>°</m:mi></m:mrow></m:math>, <o:math xmlns:o=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><o:mrow><o:msub><o:mrow><o:mi>θ</o:mi></o:mrow><o:mrow><o:mn>2</o:mn></o:mrow></o:msub><o:mo>=</o:mo><o:mn>26.6</o:mn><o:mo>±</o:mo><o:mn>0.6</o:mn><o:mi>°</o:mi></o:mrow></o:math>, <q:math xmlns:q=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><q:msub><q:mi>θ</q:mi><q:mn>3</q:mn></q:msub><q:mo>=</q:mo><q:mn>38.6</q:mn><q:mo>±</q:mo><q:mn>0.1</q:mn><q:mi>°</q:mi></q:math>, and <s:math xmlns:s=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><s:mrow><s:msub><s:mrow><s:mi>θ</s:mi></s:mrow><s:mrow><s:mn>4</s:mn></s:mrow></s:msub><s:mo>=</s:mo><s:mn>38.5</s:mn><s:mo>±</s:mo><s:mn>0.1</s:mn><s:mi>°</s:mi></s:mrow></s:math>. These values are in good agreement with the predictions of heavy quark effective theory, particularly for the mixing angle <u:math xmlns:u=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><u:mi>θ</u:mi><u:mo>=</u:mo><u:mn>35.3</u:mn><u:mi>°</u:mi></u:math>, and are compatible with several existing results in the literature. The predicted mixing angles can be tested through the analysis of semileptonic decays such as <w:math xmlns:w=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><w:msub><w:mi>B</w:mi><w:mi>c</w:mi></w:msub><w:mo stretchy=\"false\">→</w:mo><w:msub><w:mi>B</w:mi><w:mn>1</w:mn></w:msub><w:mo>ℓ</w:mo><w:mi>ν</w:mi></w:math>, <z:math xmlns:z=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><z:mrow><z:msub><z:mrow><z:mi>B</z:mi></z:mrow><z:mrow><z:mi>c</z:mi></z:mrow></z:msub><z:mo stretchy=\"false\">→</z:mo><z:msubsup><z:mrow><z:mi>B</z:mi></z:mrow><z:mrow><z:mi>s</z:mi><z:mn>1</z:mn></z:mrow><z:mrow><z:mn>0</z:mn></z:mrow></z:msubsup><z:mo>ℓ</z:mo><z:mi>ν</z:mi></z:mrow></z:math>, <cb:math xmlns:cb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><cb:mrow><cb:msub><cb:mrow><cb:mi>B</cb:mi></cb:mrow><cb:mrow><cb:mi>s</cb:mi></cb:mrow></cb:msub><cb:mo stretchy=\"false\">→</cb:mo><cb:msub><cb:mrow><cb:mi>D</cb:mi></cb:mrow><cb:mrow><cb:mi>s</cb:mi><cb:mn>1</cb:mn></cb:mrow></cb:msub><cb:mo>ℓ</cb:mo><cb:mi>ν</cb:mi></cb:mrow></cb:math>, and <fb:math xmlns:fb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><fb:mrow><fb:msub><fb:mrow><fb:mi>B</fb:mi></fb:mrow><fb:mrow><fb:mi>s</fb:mi></fb:mrow></fb:msub><fb:mo stretchy=\"false\">→</fb:mo><fb:msubsup><fb:mrow><fb:mi>D</fb:mi></fb:mrow><fb:mrow><fb:mi>s</fb:mi><fb:mn>1</fb:mn></fb:mrow><fb:mrow><fb:mo>′</fb:mo></fb:mrow></fb:msubsup><fb:mo>ℓ</fb:mo><fb:mi>ν</fb:mi></fb:mrow></fb:math>, which can be investigated at experimental facilities such as LHCb and Belle II. <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":"28 1","pages":""},"PeriodicalIF":5.0000,"publicationDate":"2025-01-08","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.111.014005","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}
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Abstract
In this study, we calculate the mixing angles between the axial-vector mesons D1(s1)−D1(s1)′ and B1(s1)−B1(s1)′ using the QCD sum rules approach. Our results are θ1=28.2±0.6°, θ2=26.6±0.6°, θ3=38.6±0.1°, and θ4=38.5±0.1°. These values are in good agreement with the predictions of heavy quark effective theory, particularly for the mixing angle θ=35.3°, and are compatible with several existing results in the literature. The predicted mixing angles can be tested through the analysis of semileptonic decays such as Bc→B1ℓν, Bc→Bs10ℓν, Bs→Ds1ℓν, and Bs→Ds1′ℓν, which can be investigated at experimental facilities such as LHCb and Belle II. Published by the American Physical Society2025
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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.
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