{"title":"张量状态bcb¯c¯的性质","authors":"S. S. Agaev, K. Azizi, H. Sundu","doi":"10.1103/physrevd.111.074025","DOIUrl":null,"url":null,"abstract":"Spectroscopic parameters and decays of the exotic tensor meson T</a:mi></a:math> with content <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mi>b</c:mi><c:mi>c</c:mi><c:mover accent=\"true\"><c:mi>b</c:mi><c:mo stretchy=\"false\">¯</c:mo></c:mover><c:mover accent=\"true\"><c:mi>c</c:mi><c:mo stretchy=\"false\">¯</c:mo></c:mover></c:math> are explored in the context of the diquark-antidiquark model. We treat it as a state built of axial-vector diquark <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><i:mrow><i:msup><i:mrow><i:mi>b</i:mi></i:mrow><i:mrow><i:mi>T</i:mi></i:mrow></i:msup><i:mi>C</i:mi><i:msub><i:mrow><i:mi>γ</i:mi></i:mrow><i:mrow><i:mi>μ</i:mi></i:mrow></i:msub><i:mi>c</i:mi></i:mrow></i:math> and antidiquark <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><k:mrow><k:mover accent=\"true\"><k:mrow><k:mi>b</k:mi></k:mrow><k:mrow><k:mo stretchy=\"false\">¯</k:mo></k:mrow></k:mover><k:msub><k:mrow><k:mi>γ</k:mi></k:mrow><k:mrow><k:mi>ν</k:mi></k:mrow></k:msub><k:mi>C</k:mi><k:msup><k:mrow><k:mover accent=\"true\"><k:mrow><k:mi>c</k:mi></k:mrow><k:mrow><k:mo stretchy=\"false\">¯</k:mo></k:mrow></k:mover></k:mrow><k:mrow><k:mi>T</k:mi></k:mrow></k:msup></k:mrow></k:math>, where <q:math xmlns:q=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><q:mi>C</q:mi></q:math> is the charge conjugation matrix. The mass <s:math xmlns:s=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><s:mi>m</s:mi></s:math> and current coupling <u:math xmlns:u=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><u:mi mathvariant=\"normal\">Λ</u:mi></u:math> of this tetraquark are extracted from two-point sum rules. Our result for <x:math xmlns:x=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><x:mrow><x:mi>m</x:mi><x:mo>=</x:mo><x:mo stretchy=\"false\">(</x:mo><x:mn>12.70</x:mn><x:mo>±</x:mo><x:mn>0.09</x:mn><x:mo stretchy=\"false\">)</x:mo><x:mtext> </x:mtext><x:mtext> </x:mtext><x:mi>GeV</x:mi></x:mrow></x:math> proves that <bb:math xmlns:bb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><bb:mi>T</bb:mi></bb:math> is unstable against strong dissociations to two-meson final states. Its dominant decay channels are processes <db:math xmlns:db=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><db:mrow><db:mi>T</db:mi><db:mo stretchy=\"false\">→</db:mo><db:mi>J</db:mi><db:mo>/</db:mo><db:mi>ψ</db:mi><db:mi mathvariant=\"normal\">ϒ</db:mi></db:mrow></db:math>, <hb:math xmlns:hb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><hb:mrow><hb:msub><hb:mrow><hb:mi>η</hb:mi></hb:mrow><hb:mrow><hb:mi>b</hb:mi></hb:mrow></hb:msub><hb:msub><hb:mrow><hb:mi>η</hb:mi></hb:mrow><hb:mrow><hb:mi>c</hb:mi></hb:mrow></hb:msub></hb:mrow></hb:math>, and <jb:math xmlns:jb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><jb:mrow><jb:msubsup><jb:mrow><jb:mi>B</jb:mi></jb:mrow><jb:mrow><jb:mi>c</jb:mi></jb:mrow><jb:mrow><jb:mo stretchy=\"false\">(</jb:mo><jb:mo>*</jb:mo><jb:mo stretchy=\"false\">)</jb:mo><jb:mo>+</jb:mo></jb:mrow></jb:msubsup><jb:msubsup><jb:mrow><jb:mi>B</jb:mi></jb:mrow><jb:mrow><jb:mi>c</jb:mi></jb:mrow><jb:mrow><jb:mo stretchy=\"false\">(</jb:mo><jb:mo>*</jb:mo><jb:mo stretchy=\"false\">)</jb:mo><jb:mo>−</jb:mo></jb:mrow></jb:msubsup></jb:mrow></jb:math>. Kinematically allowed transformations of <pb:math xmlns:pb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><pb:mi>T</pb:mi></pb:math> include also decays <rb:math xmlns:rb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><rb:mrow><rb:mi>T</rb:mi><rb:mo stretchy=\"false\">→</rb:mo><rb:msup><rb:mrow><rb:mi>D</rb:mi></rb:mrow><rb:mrow><rb:mo stretchy=\"false\">(</rb:mo><rb:mo>*</rb:mo><rb:mo stretchy=\"false\">)</rb:mo><rb:mo>+</rb:mo></rb:mrow></rb:msup><rb:msup><rb:mrow><rb:mi>D</rb:mi></rb:mrow><rb:mrow><rb:mo stretchy=\"false\">(</rb:mo><rb:mo>*</rb:mo><rb:mo stretchy=\"false\">)</rb:mo><rb:mo>−</rb:mo></rb:mrow></rb:msup></rb:mrow></rb:math> and <yb:math xmlns:yb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><yb:mrow><yb:msup><yb:mrow><yb:mi>D</yb:mi></yb:mrow><yb:mrow><yb:mo stretchy=\"false\">(</yb:mo><yb:mo>*</yb:mo><yb:mo stretchy=\"false\">)</yb:mo><yb:mn>0</yb:mn></yb:mrow></yb:msup><yb:msup><yb:mrow><yb:mover accent=\"true\"><yb:mrow><yb:mi>D</yb:mi></yb:mrow><yb:mrow><yb:mo stretchy=\"false\">¯</yb:mo></yb:mrow></yb:mover></yb:mrow><yb:mrow><yb:mo stretchy=\"false\">(</yb:mo><yb:mo>*</yb:mo><yb:mo stretchy=\"false\">)</yb:mo><yb:mn>0</yb:mn></yb:mrow></yb:msup></yb:mrow></yb:math>, which are generated by <gc:math xmlns:gc=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><gc:mi>b</gc:mi><gc:mover accent=\"true\"><gc:mi>b</gc:mi><gc:mo stretchy=\"false\">¯</gc:mo></gc:mover></gc:math> annihilation inside of <kc:math xmlns:kc=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><kc:mi>T</kc:mi></kc:math>. The full width of <mc:math xmlns:mc=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mc:mi>T</mc:mi></mc:math> is estimated by considering all of these channels. Their partial widths are calculated by invoking methods of three-point sum rule approach, which are required to evaluate strong couplings at corresponding tetraquark-meson-meson vertices. Our predictions for the mass and width <oc:math xmlns:oc=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><oc:mrow><oc:msub><oc:mrow><oc:mi mathvariant=\"normal\">Γ</oc:mi></oc:mrow><oc:mrow><oc:mi>T</oc:mi></oc:mrow></oc:msub><oc:mo>=</oc:mo><oc:mo stretchy=\"false\">(</oc:mo><oc:mn>117.4</oc:mn><oc:mo>±</oc:mo><oc:mn>15.9</oc:mn><oc:mo stretchy=\"false\">)</oc:mo><oc:mtext> </oc:mtext><oc:mtext> </oc:mtext><oc:mi>MeV</oc:mi></oc:mrow></oc:math> of the tensor state <tc:math xmlns:tc=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><tc:mi>T</tc:mi></tc:math> provide useful information for experimental studies of fully heavy four-quark exotic structures. <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":"31 1","pages":""},"PeriodicalIF":5.3000,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Properties of the tensor state bcb¯c¯\",\"authors\":\"S. S. Agaev, K. Azizi, H. Sundu\",\"doi\":\"10.1103/physrevd.111.074025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Spectroscopic parameters and decays of the exotic tensor meson T</a:mi></a:math> with content <c:math xmlns:c=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><c:mi>b</c:mi><c:mi>c</c:mi><c:mover accent=\\\"true\\\"><c:mi>b</c:mi><c:mo stretchy=\\\"false\\\">¯</c:mo></c:mover><c:mover accent=\\\"true\\\"><c:mi>c</c:mi><c:mo stretchy=\\\"false\\\">¯</c:mo></c:mover></c:math> are explored in the context of the diquark-antidiquark model. We treat it as a state built of axial-vector diquark <i:math xmlns:i=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><i:mrow><i:msup><i:mrow><i:mi>b</i:mi></i:mrow><i:mrow><i:mi>T</i:mi></i:mrow></i:msup><i:mi>C</i:mi><i:msub><i:mrow><i:mi>γ</i:mi></i:mrow><i:mrow><i:mi>μ</i:mi></i:mrow></i:msub><i:mi>c</i:mi></i:mrow></i:math> and antidiquark <k:math xmlns:k=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><k:mrow><k:mover accent=\\\"true\\\"><k:mrow><k:mi>b</k:mi></k:mrow><k:mrow><k:mo stretchy=\\\"false\\\">¯</k:mo></k:mrow></k:mover><k:msub><k:mrow><k:mi>γ</k:mi></k:mrow><k:mrow><k:mi>ν</k:mi></k:mrow></k:msub><k:mi>C</k:mi><k:msup><k:mrow><k:mover accent=\\\"true\\\"><k:mrow><k:mi>c</k:mi></k:mrow><k:mrow><k:mo stretchy=\\\"false\\\">¯</k:mo></k:mrow></k:mover></k:mrow><k:mrow><k:mi>T</k:mi></k:mrow></k:msup></k:mrow></k:math>, where <q:math xmlns:q=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><q:mi>C</q:mi></q:math> is the charge conjugation matrix. The mass <s:math xmlns:s=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><s:mi>m</s:mi></s:math> and current coupling <u:math xmlns:u=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><u:mi mathvariant=\\\"normal\\\">Λ</u:mi></u:math> of this tetraquark are extracted from two-point sum rules. Our result for <x:math xmlns:x=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><x:mrow><x:mi>m</x:mi><x:mo>=</x:mo><x:mo stretchy=\\\"false\\\">(</x:mo><x:mn>12.70</x:mn><x:mo>±</x:mo><x:mn>0.09</x:mn><x:mo stretchy=\\\"false\\\">)</x:mo><x:mtext> </x:mtext><x:mtext> </x:mtext><x:mi>GeV</x:mi></x:mrow></x:math> proves that <bb:math xmlns:bb=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><bb:mi>T</bb:mi></bb:math> is unstable against strong dissociations to two-meson final states. Its dominant decay channels are processes <db:math xmlns:db=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><db:mrow><db:mi>T</db:mi><db:mo stretchy=\\\"false\\\">→</db:mo><db:mi>J</db:mi><db:mo>/</db:mo><db:mi>ψ</db:mi><db:mi mathvariant=\\\"normal\\\">ϒ</db:mi></db:mrow></db:math>, <hb:math xmlns:hb=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><hb:mrow><hb:msub><hb:mrow><hb:mi>η</hb:mi></hb:mrow><hb:mrow><hb:mi>b</hb:mi></hb:mrow></hb:msub><hb:msub><hb:mrow><hb:mi>η</hb:mi></hb:mrow><hb:mrow><hb:mi>c</hb:mi></hb:mrow></hb:msub></hb:mrow></hb:math>, and <jb:math xmlns:jb=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><jb:mrow><jb:msubsup><jb:mrow><jb:mi>B</jb:mi></jb:mrow><jb:mrow><jb:mi>c</jb:mi></jb:mrow><jb:mrow><jb:mo stretchy=\\\"false\\\">(</jb:mo><jb:mo>*</jb:mo><jb:mo stretchy=\\\"false\\\">)</jb:mo><jb:mo>+</jb:mo></jb:mrow></jb:msubsup><jb:msubsup><jb:mrow><jb:mi>B</jb:mi></jb:mrow><jb:mrow><jb:mi>c</jb:mi></jb:mrow><jb:mrow><jb:mo stretchy=\\\"false\\\">(</jb:mo><jb:mo>*</jb:mo><jb:mo stretchy=\\\"false\\\">)</jb:mo><jb:mo>−</jb:mo></jb:mrow></jb:msubsup></jb:mrow></jb:math>. Kinematically allowed transformations of <pb:math xmlns:pb=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><pb:mi>T</pb:mi></pb:math> include also decays <rb:math xmlns:rb=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><rb:mrow><rb:mi>T</rb:mi><rb:mo stretchy=\\\"false\\\">→</rb:mo><rb:msup><rb:mrow><rb:mi>D</rb:mi></rb:mrow><rb:mrow><rb:mo stretchy=\\\"false\\\">(</rb:mo><rb:mo>*</rb:mo><rb:mo stretchy=\\\"false\\\">)</rb:mo><rb:mo>+</rb:mo></rb:mrow></rb:msup><rb:msup><rb:mrow><rb:mi>D</rb:mi></rb:mrow><rb:mrow><rb:mo stretchy=\\\"false\\\">(</rb:mo><rb:mo>*</rb:mo><rb:mo stretchy=\\\"false\\\">)</rb:mo><rb:mo>−</rb:mo></rb:mrow></rb:msup></rb:mrow></rb:math> and <yb:math xmlns:yb=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><yb:mrow><yb:msup><yb:mrow><yb:mi>D</yb:mi></yb:mrow><yb:mrow><yb:mo stretchy=\\\"false\\\">(</yb:mo><yb:mo>*</yb:mo><yb:mo stretchy=\\\"false\\\">)</yb:mo><yb:mn>0</yb:mn></yb:mrow></yb:msup><yb:msup><yb:mrow><yb:mover accent=\\\"true\\\"><yb:mrow><yb:mi>D</yb:mi></yb:mrow><yb:mrow><yb:mo stretchy=\\\"false\\\">¯</yb:mo></yb:mrow></yb:mover></yb:mrow><yb:mrow><yb:mo stretchy=\\\"false\\\">(</yb:mo><yb:mo>*</yb:mo><yb:mo stretchy=\\\"false\\\">)</yb:mo><yb:mn>0</yb:mn></yb:mrow></yb:msup></yb:mrow></yb:math>, which are generated by <gc:math xmlns:gc=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><gc:mi>b</gc:mi><gc:mover accent=\\\"true\\\"><gc:mi>b</gc:mi><gc:mo stretchy=\\\"false\\\">¯</gc:mo></gc:mover></gc:math> annihilation inside of <kc:math xmlns:kc=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><kc:mi>T</kc:mi></kc:math>. The full width of <mc:math xmlns:mc=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><mc:mi>T</mc:mi></mc:math> is estimated by considering all of these channels. Their partial widths are calculated by invoking methods of three-point sum rule approach, which are required to evaluate strong couplings at corresponding tetraquark-meson-meson vertices. Our predictions for the mass and width <oc:math xmlns:oc=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><oc:mrow><oc:msub><oc:mrow><oc:mi mathvariant=\\\"normal\\\">Γ</oc:mi></oc:mrow><oc:mrow><oc:mi>T</oc:mi></oc:mrow></oc:msub><oc:mo>=</oc:mo><oc:mo stretchy=\\\"false\\\">(</oc:mo><oc:mn>117.4</oc:mn><oc:mo>±</oc:mo><oc:mn>15.9</oc:mn><oc:mo stretchy=\\\"false\\\">)</oc:mo><oc:mtext> </oc:mtext><oc:mtext> </oc:mtext><oc:mi>MeV</oc:mi></oc:mrow></oc:math> of the tensor state <tc:math xmlns:tc=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><tc:mi>T</tc:mi></tc:math> provide useful information for experimental studies of fully heavy four-quark exotic structures. <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\":\"31 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.111.074025\",\"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.111.074025","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}
Spectroscopic parameters and decays of the exotic tensor meson T with content bcb¯c¯ are explored in the context of the diquark-antidiquark model. We treat it as a state built of axial-vector diquark bTCγμc and antidiquark b¯γνCc¯T, where C is the charge conjugation matrix. The mass m and current coupling Λ of this tetraquark are extracted from two-point sum rules. Our result for m=(12.70±0.09)GeV proves that T is unstable against strong dissociations to two-meson final states. Its dominant decay channels are processes T→J/ψϒ, ηbηc, and Bc(*)+Bc(*)−. Kinematically allowed transformations of T include also decays T→D(*)+D(*)− and D(*)0D¯(*)0, which are generated by bb¯ annihilation inside of T. The full width of T is estimated by considering all of these channels. Their partial widths are calculated by invoking methods of three-point sum rule approach, which are required to evaluate strong couplings at corresponding tetraquark-meson-meson vertices. Our predictions for the mass and width ΓT=(117.4±15.9)MeV of the tensor state T provide useful information for experimental studies of fully heavy four-quark exotic structures. 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.