{"title":"短程动力学在D(*)D¯(*)和B(*)B¯(*)强子分子形成中的作用","authors":"Nijiati Yalikun, Xiang-Kun Dong, Ulf-G. Meißner","doi":"10.1103/physrevd.111.094036","DOIUrl":null,"url":null,"abstract":"We investigate potential hadronic molecular states in the D</a:mi>(</a:mo>*</a:mo>)</a:mo></a:mrow></a:msup>D</a:mi>¯</a:mo></a:mover>(</a:mo>*</a:mo>)</a:mo></a:mrow></a:msup></a:math> and <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:mo stretchy=\"false\">(</i:mo><i:mo>*</i:mo><i:mo stretchy=\"false\">)</i:mo></i:mrow></i:msup><i:msup><i:mrow><i:mover accent=\"true\"><i:mrow><i:mi>B</i:mi></i:mrow><i:mrow><i:mo stretchy=\"false\">¯</i:mo></i:mrow></i:mover></i:mrow><i:mrow><i:mo>*</i:mo></i:mrow></i:msup></i:mrow></i:math> systems using light meson exchange interactions. Our analysis focuses on coupled-channel systems with spin-parity quantum numbers <o:math xmlns:o=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><o:msup><o:mi>J</o:mi><o:mrow><o:mi>P</o:mi><o:mi>C</o:mi></o:mrow></o:msup><o:mo>=</o:mo><o:msup><o:mn>0</o:mn><o:mrow><o:mo>+</o:mo><o:mo>+</o:mo></o:mrow></o:msup></o:math>, <q:math xmlns:q=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><q:msup><q:mn>1</q:mn><q:mrow><q:mo>+</q:mo><q:mo>±</q:mo></q:mrow></q:msup></q:math>, and <s:math xmlns:s=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><s:msup><s:mn>2</s:mn><s:mrow><s:mo>+</s:mo><s:mo>+</s:mo></s:mrow></s:msup></s:math>, examining how the <u:math xmlns:u=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><u:mi>δ</u:mi><u:mo stretchy=\"false\">(</u:mo><u:mi mathvariant=\"bold-italic\">r</u:mi><u:mo stretchy=\"false\">)</u:mo></u:math> potential affects states near threshold. Using coupled-channel analysis, we reproduce the <z:math xmlns:z=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><z:mi>X</z:mi><z:mo stretchy=\"false\">(</z:mo><z:mn>3872</z:mn><z:mo stretchy=\"false\">)</z:mo></z:math> mass with a given cutoff for the <db:math xmlns:db=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><db:mo stretchy=\"false\">(</db:mo><db:mi>I</db:mi><db:mo stretchy=\"false\">)</db:mo><db:msup><db:mi>J</db:mi><db:mrow><db:mi>P</db:mi><db:mi>C</db:mi></db:mrow></db:msup><db:mo>=</db:mo><db:mo stretchy=\"false\">(</db:mo><db:mn>0</db:mn><db:mo stretchy=\"false\">)</db:mo><db:msup><db:mn>1</db:mn><db:mrow><db:mo>+</db:mo><db:mo>+</db:mo></db:mrow></db:msup></db:math> state, finding a minimal impact from the <jb:math xmlns:jb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><jb:mi>δ</jb:mi><jb:mo stretchy=\"false\">(</jb:mo><jb:mi mathvariant=\"bold-italic\">r</jb:mi><jb:mo stretchy=\"false\">)</jb:mo></jb:math> term. At this cutoff, both the <ob:math xmlns:ob=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><ob:mo stretchy=\"false\">(</ob:mo><ob:mn>0</ob:mn><ob:mo stretchy=\"false\">)</ob:mo><ob:msup><ob:mn>0</ob:mn><ob:mrow><ob:mo>+</ob:mo><ob:mo>+</ob:mo></ob:mrow></ob:msup></ob:math> state near the <sb:math xmlns:sb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><sb:mi>D</sb:mi><sb:mover accent=\"true\"><sb:mi>D</sb:mi><sb:mo stretchy=\"false\">¯</sb:mo></sb:mover></sb:math> threshold and the <wb:math xmlns:wb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><wb:mo stretchy=\"false\">(</wb:mo><wb:mn>0</wb:mn><wb:mo stretchy=\"false\">)</wb:mo><wb:msup><wb:mn>1</wb:mn><wb:mrow><wb:mo>+</wb:mo><wb:mo>−</wb:mo></wb:mrow></wb:msup></wb:math> state near the D</ac:mi>D</ac:mi>¯</ac:mo></ac:mover>*</ac:mo></ac:msup></ac:math> threshold show less sensitivity to the <ec:math xmlns:ec=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><ec:mi>δ</ec:mi><ec:mo stretchy=\"false\">(</ec:mo><ec:mi mathvariant=\"bold-italic\">r</ec:mi><ec:mo stretchy=\"false\">)</ec:mo></ec:math> term compared to the three states–<jc:math xmlns:jc=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><jc:mo stretchy=\"false\">(</jc:mo><jc:mn>0</jc:mn><jc:mo stretchy=\"false\">)</jc:mo><jc:msup><jc:mn>0</jc:mn><jc:mrow><jc:mo>+</jc:mo><jc:mo>+</jc:mo></jc:mrow></jc:msup></jc:math>, <nc:math xmlns:nc=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><nc:mo stretchy=\"false\">(</nc:mo><nc:mn>0</nc:mn><nc:mo stretchy=\"false\">)</nc:mo><nc:msup><nc:mn>1</nc:mn><nc:mrow><nc:mo>+</nc:mo><nc:mo>−</nc:mo></nc:mrow></nc:msup></nc:math>, and <rc:math xmlns:rc=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><rc:mo stretchy=\"false\">(</rc:mo><rc:mn>0</rc:mn><rc:mo stretchy=\"false\">)</rc:mo><rc:msup><rc:mn>2</rc:mn><rc:mrow><rc:mo>+</rc:mo><rc:mo>+</rc:mo></rc:mrow></rc:msup></rc:math>–near the <vc:math xmlns:vc=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><vc:msup><vc:mi>D</vc:mi><vc:mo>*</vc:mo></vc:msup><vc:msup><vc:mover accent=\"true\"><vc:mi>D</vc:mi><vc:mo stretchy=\"false\">¯</vc:mo></vc:mover><vc:mo>*</vc:mo></vc:msup></vc:math> threshold. As anticipated, the <zc:math xmlns:zc=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><zc:msup><zc:mi>B</zc:mi><zc:mrow><zc:mo stretchy=\"false\">(</zc:mo><zc:mo>*</zc:mo><zc:mo stretchy=\"false\">)</zc:mo></zc:mrow></zc:msup><zc:msup><zc:mover accent=\"true\"><zc:mi>B</zc:mi><zc:mo stretchy=\"false\">¯</zc:mo></zc:mover><zc:mo>*</zc:mo></zc:msup></zc:math> systems exhibit similar behavior but with stronger binding due to their larger reduced mass. These findings suggest promising directions for future experimental searches, particularly in the isoscalar sector, which could substantially advance our understanding of exotic tetraquark states. <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":"35 1","pages":""},"PeriodicalIF":5.3000,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Role of the short-range dynamics in the formation of D(*)D¯(*) and B(*)B¯(*) hadronic molecules\",\"authors\":\"Nijiati Yalikun, Xiang-Kun Dong, Ulf-G. Meißner\",\"doi\":\"10.1103/physrevd.111.094036\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate potential hadronic molecular states in the D</a:mi>(</a:mo>*</a:mo>)</a:mo></a:mrow></a:msup>D</a:mi>¯</a:mo></a:mover>(</a:mo>*</a:mo>)</a:mo></a:mrow></a:msup></a:math> and <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:mo stretchy=\\\"false\\\">(</i:mo><i:mo>*</i:mo><i:mo stretchy=\\\"false\\\">)</i:mo></i:mrow></i:msup><i:msup><i:mrow><i:mover accent=\\\"true\\\"><i:mrow><i:mi>B</i:mi></i:mrow><i:mrow><i:mo stretchy=\\\"false\\\">¯</i:mo></i:mrow></i:mover></i:mrow><i:mrow><i:mo>*</i:mo></i:mrow></i:msup></i:mrow></i:math> systems using light meson exchange interactions. Our analysis focuses on coupled-channel systems with spin-parity quantum numbers <o:math xmlns:o=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><o:msup><o:mi>J</o:mi><o:mrow><o:mi>P</o:mi><o:mi>C</o:mi></o:mrow></o:msup><o:mo>=</o:mo><o:msup><o:mn>0</o:mn><o:mrow><o:mo>+</o:mo><o:mo>+</o:mo></o:mrow></o:msup></o:math>, <q:math xmlns:q=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><q:msup><q:mn>1</q:mn><q:mrow><q:mo>+</q:mo><q:mo>±</q:mo></q:mrow></q:msup></q:math>, and <s:math xmlns:s=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><s:msup><s:mn>2</s:mn><s:mrow><s:mo>+</s:mo><s:mo>+</s:mo></s:mrow></s:msup></s:math>, examining how the <u:math xmlns:u=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><u:mi>δ</u:mi><u:mo stretchy=\\\"false\\\">(</u:mo><u:mi mathvariant=\\\"bold-italic\\\">r</u:mi><u:mo stretchy=\\\"false\\\">)</u:mo></u:math> potential affects states near threshold. Using coupled-channel analysis, we reproduce the <z:math xmlns:z=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><z:mi>X</z:mi><z:mo stretchy=\\\"false\\\">(</z:mo><z:mn>3872</z:mn><z:mo stretchy=\\\"false\\\">)</z:mo></z:math> mass with a given cutoff for the <db:math xmlns:db=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><db:mo stretchy=\\\"false\\\">(</db:mo><db:mi>I</db:mi><db:mo stretchy=\\\"false\\\">)</db:mo><db:msup><db:mi>J</db:mi><db:mrow><db:mi>P</db:mi><db:mi>C</db:mi></db:mrow></db:msup><db:mo>=</db:mo><db:mo stretchy=\\\"false\\\">(</db:mo><db:mn>0</db:mn><db:mo stretchy=\\\"false\\\">)</db:mo><db:msup><db:mn>1</db:mn><db:mrow><db:mo>+</db:mo><db:mo>+</db:mo></db:mrow></db:msup></db:math> state, finding a minimal impact from the <jb:math xmlns:jb=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><jb:mi>δ</jb:mi><jb:mo stretchy=\\\"false\\\">(</jb:mo><jb:mi mathvariant=\\\"bold-italic\\\">r</jb:mi><jb:mo stretchy=\\\"false\\\">)</jb:mo></jb:math> term. At this cutoff, both the <ob:math xmlns:ob=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><ob:mo stretchy=\\\"false\\\">(</ob:mo><ob:mn>0</ob:mn><ob:mo stretchy=\\\"false\\\">)</ob:mo><ob:msup><ob:mn>0</ob:mn><ob:mrow><ob:mo>+</ob:mo><ob:mo>+</ob:mo></ob:mrow></ob:msup></ob:math> state near the <sb:math xmlns:sb=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><sb:mi>D</sb:mi><sb:mover accent=\\\"true\\\"><sb:mi>D</sb:mi><sb:mo stretchy=\\\"false\\\">¯</sb:mo></sb:mover></sb:math> threshold and the <wb:math xmlns:wb=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><wb:mo stretchy=\\\"false\\\">(</wb:mo><wb:mn>0</wb:mn><wb:mo stretchy=\\\"false\\\">)</wb:mo><wb:msup><wb:mn>1</wb:mn><wb:mrow><wb:mo>+</wb:mo><wb:mo>−</wb:mo></wb:mrow></wb:msup></wb:math> state near the D</ac:mi>D</ac:mi>¯</ac:mo></ac:mover>*</ac:mo></ac:msup></ac:math> threshold show less sensitivity to the <ec:math xmlns:ec=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><ec:mi>δ</ec:mi><ec:mo stretchy=\\\"false\\\">(</ec:mo><ec:mi mathvariant=\\\"bold-italic\\\">r</ec:mi><ec:mo stretchy=\\\"false\\\">)</ec:mo></ec:math> term compared to the three states–<jc:math xmlns:jc=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><jc:mo stretchy=\\\"false\\\">(</jc:mo><jc:mn>0</jc:mn><jc:mo stretchy=\\\"false\\\">)</jc:mo><jc:msup><jc:mn>0</jc:mn><jc:mrow><jc:mo>+</jc:mo><jc:mo>+</jc:mo></jc:mrow></jc:msup></jc:math>, <nc:math xmlns:nc=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><nc:mo stretchy=\\\"false\\\">(</nc:mo><nc:mn>0</nc:mn><nc:mo stretchy=\\\"false\\\">)</nc:mo><nc:msup><nc:mn>1</nc:mn><nc:mrow><nc:mo>+</nc:mo><nc:mo>−</nc:mo></nc:mrow></nc:msup></nc:math>, and <rc:math xmlns:rc=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><rc:mo stretchy=\\\"false\\\">(</rc:mo><rc:mn>0</rc:mn><rc:mo stretchy=\\\"false\\\">)</rc:mo><rc:msup><rc:mn>2</rc:mn><rc:mrow><rc:mo>+</rc:mo><rc:mo>+</rc:mo></rc:mrow></rc:msup></rc:math>–near the <vc:math xmlns:vc=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><vc:msup><vc:mi>D</vc:mi><vc:mo>*</vc:mo></vc:msup><vc:msup><vc:mover accent=\\\"true\\\"><vc:mi>D</vc:mi><vc:mo stretchy=\\\"false\\\">¯</vc:mo></vc:mover><vc:mo>*</vc:mo></vc:msup></vc:math> threshold. As anticipated, the <zc:math xmlns:zc=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><zc:msup><zc:mi>B</zc:mi><zc:mrow><zc:mo stretchy=\\\"false\\\">(</zc:mo><zc:mo>*</zc:mo><zc:mo stretchy=\\\"false\\\">)</zc:mo></zc:mrow></zc:msup><zc:msup><zc:mover accent=\\\"true\\\"><zc:mi>B</zc:mi><zc:mo stretchy=\\\"false\\\">¯</zc:mo></zc:mover><zc:mo>*</zc:mo></zc:msup></zc:math> systems exhibit similar behavior but with stronger binding due to their larger reduced mass. These findings suggest promising directions for future experimental searches, particularly in the isoscalar sector, which could substantially advance our understanding of exotic tetraquark states. <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\":\"35 1\",\"pages\":\"\"},\"PeriodicalIF\":5.3000,\"publicationDate\":\"2025-05-27\",\"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.111.094036\",\"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.111.094036","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}
Role of the short-range dynamics in the formation of D(*)D¯(*) and B(*)B¯(*) hadronic molecules
We investigate potential hadronic molecular states in the D(*)D¯(*) and B(*)B¯* systems using light meson exchange interactions. Our analysis focuses on coupled-channel systems with spin-parity quantum numbers JPC=0++, 1+±, and 2++, examining how the δ(r) potential affects states near threshold. Using coupled-channel analysis, we reproduce the X(3872) mass with a given cutoff for the (I)JPC=(0)1++ state, finding a minimal impact from the δ(r) term. At this cutoff, both the (0)0++ state near the DD¯ threshold and the (0)1+− state near the DD¯* threshold show less sensitivity to the δ(r) term compared to the three states–(0)0++, (0)1+−, and (0)2++–near the D*D¯* threshold. As anticipated, the B(*)B¯* systems exhibit similar behavior but with stronger binding due to their larger reduced mass. These findings suggest promising directions for future experimental searches, particularly in the isoscalar sector, which could substantially advance our understanding of exotic tetraquark states. 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.