{"title":"标准模型中的电弱单极子-反单极子对","authors":"Dan Zhu, Khai-Ming Wong, Guo-Quan Wong","doi":"10.1088/1572-9494/ad23dd","DOIUrl":null,"url":null,"abstract":"We present the first numerical solution that corresponds to a pair of Cho–Maison monopoles and antimonopoles (MAPs) in the SU(2) × U(1) Weinberg–Salam (WS) theory. The monopoles are finitely separated, while each pole carries a magnetic charge ±4<italic toggle=\"yes\">π</italic>/<italic toggle=\"yes\">e</italic>. The positive pole is situated in the upper hemisphere, whereas the negative pole is in the lower hemisphere. The Cho–Maison MAP is investigated for a range of Weinberg angles, <inline-formula>\n<tex-math>\n<?CDATA $0.4675\\leqslant \\tan {\\theta }_{{\\rm{W}}}\\leqslant 10$?>\n</tex-math>\n<mml:math overflow=\"scroll\"><mml:mn>0.4675</mml:mn><mml:mo>≤</mml:mo><mml:mi>tan</mml:mi><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">W</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mn>10</mml:mn></mml:math>\n<inline-graphic xlink:href=\"ctpad23ddieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, and Higgs self-coupling, 0 ≤ <italic toggle=\"yes\">β</italic> ≤ 1.7704. The magnetic dipole moment (<italic toggle=\"yes\">μ</italic>\n<sub>m</sub>) and pole separation (<italic toggle=\"yes\">d</italic>\n<sub>\n<italic toggle=\"yes\">z</italic>\n</sub>) of the numerical solutions are calculated and analyzed. The total energy of the system, however, is infinite due to point singularities at the locations of monopoles.","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The electroweak monopole–antimonopole pair in the standard model\",\"authors\":\"Dan Zhu, Khai-Ming Wong, Guo-Quan Wong\",\"doi\":\"10.1088/1572-9494/ad23dd\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present the first numerical solution that corresponds to a pair of Cho–Maison monopoles and antimonopoles (MAPs) in the SU(2) × U(1) Weinberg–Salam (WS) theory. The monopoles are finitely separated, while each pole carries a magnetic charge ±4<italic toggle=\\\"yes\\\">π</italic>/<italic toggle=\\\"yes\\\">e</italic>. The positive pole is situated in the upper hemisphere, whereas the negative pole is in the lower hemisphere. The Cho–Maison MAP is investigated for a range of Weinberg angles, <inline-formula>\\n<tex-math>\\n<?CDATA $0.4675\\\\leqslant \\\\tan {\\\\theta }_{{\\\\rm{W}}}\\\\leqslant 10$?>\\n</tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mn>0.4675</mml:mn><mml:mo>≤</mml:mo><mml:mi>tan</mml:mi><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\\\"normal\\\">W</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mn>10</mml:mn></mml:math>\\n<inline-graphic xlink:href=\\\"ctpad23ddieqn1.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, and Higgs self-coupling, 0 ≤ <italic toggle=\\\"yes\\\">β</italic> ≤ 1.7704. The magnetic dipole moment (<italic toggle=\\\"yes\\\">μ</italic>\\n<sub>m</sub>) and pole separation (<italic toggle=\\\"yes\\\">d</italic>\\n<sub>\\n<italic toggle=\\\"yes\\\">z</italic>\\n</sub>) of the numerical solutions are calculated and analyzed. The total energy of the system, however, is infinite due to point singularities at the locations of monopoles.\",\"PeriodicalId\":10641,\"journal\":{\"name\":\"Communications in Theoretical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Theoretical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1572-9494/ad23dd\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1572-9494/ad23dd","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
The electroweak monopole–antimonopole pair in the standard model
We present the first numerical solution that corresponds to a pair of Cho–Maison monopoles and antimonopoles (MAPs) in the SU(2) × U(1) Weinberg–Salam (WS) theory. The monopoles are finitely separated, while each pole carries a magnetic charge ±4π/e. The positive pole is situated in the upper hemisphere, whereas the negative pole is in the lower hemisphere. The Cho–Maison MAP is investigated for a range of Weinberg angles, 0.4675≤tanθW≤10, and Higgs self-coupling, 0 ≤ β ≤ 1.7704. The magnetic dipole moment (μm) and pole separation (dz) of the numerical solutions are calculated and analyzed. The total energy of the system, however, is infinite due to point singularities at the locations of monopoles.
期刊介绍：
Communications in Theoretical Physics is devoted to reporting important new developments in the area of theoretical physics. Papers cover the fields of:
mathematical physics
quantum physics and quantum information
particle physics and quantum field theory
nuclear physics
gravitation theory, astrophysics and cosmology
atomic, molecular, optics (AMO) and plasma physics, chemical physics
statistical physics, soft matter and biophysics
condensed matter theory
others
Certain new interdisciplinary subjects are also incorporated.
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