{"title":"底介子 B 和 B* 的强顶点以及 bottomonia , ηb * * 国家自然科学基金（12175068）和河北省自然科学基金（A2018502124）资助","authors":"Jie Lu, Guo-Liang Yu, Zhi-Gang Wang, Bin Wu","doi":"10.1088/1674-1137/ad061d","DOIUrl":null,"url":null,"abstract":"In this study, the strong coupling constants of vertices <inline-formula>\n<tex-math><?CDATA $ BB\\Upsilon $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M3.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ BB^{*}\\Upsilon $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M4.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ B^{*}B^{*}\\Upsilon $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M5.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ BB^{*}\\eta_{b} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M6.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> , and <inline-formula>\n<tex-math><?CDATA $ B^{*}B^{*}\\eta_{b} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M7.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> are analyzed in the framework of QCD sum rules. All possible off-shell cases and the contributions of vacuum condensate terms including <inline-formula>\n<tex-math><?CDATA $ \\langle\\overline{q}q\\rangle $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M8.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ \\langle\\overline{q}g_{s}\\sigma Gq\\rangle $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M9.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ \\langle g_{s}^{2}G^{2}\\rangle $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M10.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ \\langle f^{3}G^{3}\\rangle $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M11.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> , and <inline-formula>\n<tex-math><?CDATA $ \\langle\\overline{q}q\\rangle\\langle g_{s}^{2}G^{2}\\rangle $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M12.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> are considered. The momentum dependent strong coupling constants are first calculated and then fitted into the analytical function <inline-formula>\n<tex-math><?CDATA $ g(Q^{2}) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M13.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, which is extrapolated to time-like regions to obtain the final values of strong coupling constants. The final results are <inline-formula>\n<tex-math><?CDATA $ g_{BB\\Upsilon}=40.67^{+7.55}_{-4.20} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M14.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ g_{BB^{*}\\Upsilon}=11.58^{+2.19}_{-1.09} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M15.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> GeV<inline-formula>\n<tex-math><?CDATA $ ^{-1} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M16.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ g_{B^{*}B^{*}\\Upsilon}=57.02^{+5.32}_{-5.31} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M17.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ g_{BB^{*}\\eta_{b}}=23.39^{+4.74}_{-2.30} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M18.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> , and <inline-formula>\n<tex-math><?CDATA $ g_{B^{*}B^{*}\\eta_{b}}=12.49^{+2.12}_{-1.35} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M19.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> GeV<inline-formula>\n<tex-math><?CDATA $ ^{-1} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_1_013102_M20.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>. These strong coupling constants are important input parameters that reflect the dynamic properties of the interactions among the mesons and quarkonia.","PeriodicalId":10250,"journal":{"name":"中国物理C","volume":"22 1","pages":""},"PeriodicalIF":3.6000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Strong vertices of bottom mesons B and B* and bottomonia , ηb * * Supported by the National Natural Science Foundation of China (12175068), and Natural Science Foundation of Hebei Province, China (A2018502124)\",\"authors\":\"Jie Lu, Guo-Liang Yu, Zhi-Gang Wang, Bin Wu\",\"doi\":\"10.1088/1674-1137/ad061d\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, the strong coupling constants of vertices <inline-formula>\\n<tex-math><?CDATA $ BB\\\\Upsilon $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M3.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ BB^{*}\\\\Upsilon $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M4.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ B^{*}B^{*}\\\\Upsilon $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M5.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ BB^{*}\\\\eta_{b} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M6.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> , and <inline-formula>\\n<tex-math><?CDATA $ B^{*}B^{*}\\\\eta_{b} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M7.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> are analyzed in the framework of QCD sum rules. All possible off-shell cases and the contributions of vacuum condensate terms including <inline-formula>\\n<tex-math><?CDATA $ \\\\langle\\\\overline{q}q\\\\rangle $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M8.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ \\\\langle\\\\overline{q}g_{s}\\\\sigma Gq\\\\rangle $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M9.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ \\\\langle g_{s}^{2}G^{2}\\\\rangle $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M10.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ \\\\langle f^{3}G^{3}\\\\rangle $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M11.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> , and <inline-formula>\\n<tex-math><?CDATA $ \\\\langle\\\\overline{q}q\\\\rangle\\\\langle g_{s}^{2}G^{2}\\\\rangle $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M12.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> are considered. The momentum dependent strong coupling constants are first calculated and then fitted into the analytical function <inline-formula>\\n<tex-math><?CDATA $ g(Q^{2}) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M13.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, which is extrapolated to time-like regions to obtain the final values of strong coupling constants. The final results are <inline-formula>\\n<tex-math><?CDATA $ g_{BB\\\\Upsilon}=40.67^{+7.55}_{-4.20} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M14.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ g_{BB^{*}\\\\Upsilon}=11.58^{+2.19}_{-1.09} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M15.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> GeV<inline-formula>\\n<tex-math><?CDATA $ ^{-1} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M16.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ g_{B^{*}B^{*}\\\\Upsilon}=57.02^{+5.32}_{-5.31} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M17.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ g_{BB^{*}\\\\eta_{b}}=23.39^{+4.74}_{-2.30} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M18.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> , and <inline-formula>\\n<tex-math><?CDATA $ g_{B^{*}B^{*}\\\\eta_{b}}=12.49^{+2.12}_{-1.35} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M19.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> GeV<inline-formula>\\n<tex-math><?CDATA $ ^{-1} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_1_013102_M20.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>. These strong coupling constants are important input parameters that reflect the dynamic properties of the interactions among the mesons and quarkonia.\",\"PeriodicalId\":10250,\"journal\":{\"name\":\"中国物理C\",\"volume\":\"22 1\",\"pages\":\"\"},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"中国物理C\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1674-1137/ad061d\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, NUCLEAR\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"中国物理C","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1674-1137/ad061d","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, NUCLEAR","Score":null,"Total":0}
Strong vertices of bottom mesons B and B* and bottomonia , ηb * * Supported by the National Natural Science Foundation of China (12175068), and Natural Science Foundation of Hebei Province, China (A2018502124)
In this study, the strong coupling constants of vertices , , , , and are analyzed in the framework of QCD sum rules. All possible off-shell cases and the contributions of vacuum condensate terms including , , , , and are considered. The momentum dependent strong coupling constants are first calculated and then fitted into the analytical function , which is extrapolated to time-like regions to obtain the final values of strong coupling constants. The final results are , GeV, , , and GeV. These strong coupling constants are important input parameters that reflect the dynamic properties of the interactions among the mesons and quarkonia.
期刊介绍：
Chinese Physics C covers the latest developments and achievements in the theory, experiment and applications of:
Particle physics;
Nuclear physics;
Particle and nuclear astrophysics;
Cosmology;
Accelerator physics.
The journal publishes original research papers, letters and reviews. The Letters section covers short reports on the latest important scientific results, published as quickly as possible. Such breakthrough research articles are a high priority for publication.
The Editorial Board is composed of about fifty distinguished physicists, who are responsible for the review of submitted papers and who ensure the scientific quality of the journal.
The journal has been awarded the Chinese Academy of Sciences ‘Excellent Journal’ award multiple times, and is recognized as one of China''s top one hundred key scientific periodicals by the General Administration of News and Publications.
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