{"title":"重夸克的辐射轻子衰变* * 国家自然科学基金资助项目(12247119,12042507)","authors":"Junle Pei, Xinchou Lou, Yaquan Fang, Jinfei Wu, Manqi Ruan","doi":"10.1088/1674-1137/ad6552","DOIUrl":null,"url":null,"abstract":"In this study, the properties of heavy quarkonia <italic toggle=\"yes\">X</italic> are examined by treating them as bound states of <italic toggle=\"yes\">Q</italic> and <inline-formula>\n<tex-math><?CDATA $ \\bar{Q} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M1.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> at the leading-order level within the non-relativistic quantum chromodynamics (NRQCD) framework, where <italic toggle=\"yes\">Q</italic> represents either a charm or bottom quark. The branching ratios for the radiative leptonic decays <inline-formula>\n<tex-math><?CDATA $ X\\rightarrow \\gamma l^{+} l^{-} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M2.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> are revisited, and the angular and energy/momentum distributions of the final state particles are analyzed in the rest frame of <italic toggle=\"yes\">X</italic>. Furthermore, we apply Lorentz transformations from the rest frame of <italic toggle=\"yes\">X</italic> to the center-of-mass frame of <inline-formula>\n<tex-math><?CDATA $ l^+ l^- $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M3.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> to establish the connection between the widths <inline-formula>\n<tex-math><?CDATA $ {\\Gamma_{X \\rightarrow \\gamma l^{+} l^{-}}} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M4.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> and <inline-formula>\n<tex-math><?CDATA $ {\\Gamma_{X \\rightarrow l^{+} l^{-}}} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M5.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>. The comparison of the connection to those documented in literature (divided by <inline-formula>\n<tex-math><?CDATA $ 2\\pi $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M6.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>) for various <italic toggle=\"yes\">X</italic> states, such as <inline-formula>\n<tex-math><?CDATA $ J/\\Psi $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M7.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ \\Psi(2S) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M8.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ \\Upsilon(1S) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M9.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, and <inline-formula>\n<tex-math><?CDATA $ \\Upsilon(2S) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M10.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, shows relative differences typically around or below 10%, comparable to the next-to-leading order corrections of <inline-formula>\n<tex-math><?CDATA $ O(\\alpha) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M11.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> and <inline-formula>\n<tex-math><?CDATA $ O(v^4) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M12.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>. However, we observe a significant disparity in the ratio between <inline-formula>\n<tex-math><?CDATA $ {\\Gamma_{\\Psi(2S) \\to \\gamma \\tau^+ \\tau^-}} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M13.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> and <inline-formula>\n<tex-math><?CDATA $ {\\Gamma_{\\Psi(2S) \\to \\tau^+ \\tau^-}} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_10_103108_M14.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, with our prediction being four times larger than those in literature. The outcomes derived from this study have practical implications in describing the quantum electrodynamics radiative processes and contribute to the investigation of QCD processes associated with the decays of heavy quarkonia and searches for new physics.","PeriodicalId":10250,"journal":{"name":"中国物理C","volume":"6 1","pages":""},"PeriodicalIF":3.6000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Radiative leptonic decay of heavy quarkonia* * Supported by the National Natural Science Foundation of China (12247119, 12042507)\",\"authors\":\"Junle Pei, Xinchou Lou, Yaquan Fang, Jinfei Wu, Manqi Ruan\",\"doi\":\"10.1088/1674-1137/ad6552\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, the properties of heavy quarkonia <italic toggle=\\\"yes\\\">X</italic> are examined by treating them as bound states of <italic toggle=\\\"yes\\\">Q</italic> and <inline-formula>\\n<tex-math><?CDATA $ \\\\bar{Q} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M1.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> at the leading-order level within the non-relativistic quantum chromodynamics (NRQCD) framework, where <italic toggle=\\\"yes\\\">Q</italic> represents either a charm or bottom quark. The branching ratios for the radiative leptonic decays <inline-formula>\\n<tex-math><?CDATA $ X\\\\rightarrow \\\\gamma l^{+} l^{-} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M2.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> are revisited, and the angular and energy/momentum distributions of the final state particles are analyzed in the rest frame of <italic toggle=\\\"yes\\\">X</italic>. Furthermore, we apply Lorentz transformations from the rest frame of <italic toggle=\\\"yes\\\">X</italic> to the center-of-mass frame of <inline-formula>\\n<tex-math><?CDATA $ l^+ l^- $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M3.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> to establish the connection between the widths <inline-formula>\\n<tex-math><?CDATA $ {\\\\Gamma_{X \\\\rightarrow \\\\gamma l^{+} l^{-}}} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M4.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> and <inline-formula>\\n<tex-math><?CDATA $ {\\\\Gamma_{X \\\\rightarrow l^{+} l^{-}}} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M5.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>. The comparison of the connection to those documented in literature (divided by <inline-formula>\\n<tex-math><?CDATA $ 2\\\\pi $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M6.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>) for various <italic toggle=\\\"yes\\\">X</italic> states, such as <inline-formula>\\n<tex-math><?CDATA $ J/\\\\Psi $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M7.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ \\\\Psi(2S) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M8.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ \\\\Upsilon(1S) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M9.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, and <inline-formula>\\n<tex-math><?CDATA $ \\\\Upsilon(2S) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M10.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, shows relative differences typically around or below 10%, comparable to the next-to-leading order corrections of <inline-formula>\\n<tex-math><?CDATA $ O(\\\\alpha) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M11.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> and <inline-formula>\\n<tex-math><?CDATA $ O(v^4) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M12.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>. However, we observe a significant disparity in the ratio between <inline-formula>\\n<tex-math><?CDATA $ {\\\\Gamma_{\\\\Psi(2S) \\\\to \\\\gamma \\\\tau^+ \\\\tau^-}} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M13.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> and <inline-formula>\\n<tex-math><?CDATA $ {\\\\Gamma_{\\\\Psi(2S) \\\\to \\\\tau^+ \\\\tau^-}} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_10_103108_M14.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, with our prediction being four times larger than those in literature. The outcomes derived from this study have practical implications in describing the quantum electrodynamics radiative processes and contribute to the investigation of QCD processes associated with the decays of heavy quarkonia and searches for new physics.\",\"PeriodicalId\":10250,\"journal\":{\"name\":\"中国物理C\",\"volume\":\"6 1\",\"pages\":\"\"},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2024-10-01\",\"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/ad6552\",\"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/ad6552","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}
引用次数: 0
摘要
在本研究中,通过把重夸克态 X 视为 Q 的束缚态,并在非相对论量子色动力学(NRQCD)框架内的先导阶水平(其中 Q 代表粲夸克或底夸克),研究了重夸克态 X 的性质。我们重新研究了辐射轻子衰变的分支比,并在 X 的静止帧中分析了终态粒子的角分布和能量/动量分布。与文献中对各种 X 状态(如 、 、 和 )的连接(除以 )进行比较,发现相对差异通常在 10%左右或以下,与 和 的次先导阶修正相当。 然而,我们观察到和 之间的比率存在显著差异,我们的预测比文献中的预测大四倍。这项研究得出的结果对描述量子电动力学辐射过程具有实际意义,并有助于研究与重夸克衰变相关的 QCD 过程和寻找新物理。
Radiative leptonic decay of heavy quarkonia* * Supported by the National Natural Science Foundation of China (12247119, 12042507)
In this study, the properties of heavy quarkonia X are examined by treating them as bound states of Q and at the leading-order level within the non-relativistic quantum chromodynamics (NRQCD) framework, where Q represents either a charm or bottom quark. The branching ratios for the radiative leptonic decays are revisited, and the angular and energy/momentum distributions of the final state particles are analyzed in the rest frame of X. Furthermore, we apply Lorentz transformations from the rest frame of X to the center-of-mass frame of to establish the connection between the widths and . The comparison of the connection to those documented in literature (divided by ) for various X states, such as , , , and , shows relative differences typically around or below 10%, comparable to the next-to-leading order corrections of and . However, we observe a significant disparity in the ratio between and , with our prediction being four times larger than those in literature. The outcomes derived from this study have practical implications in describing the quantum electrodynamics radiative processes and contribute to the investigation of QCD processes associated with the decays of heavy quarkonia and searches for new physics.
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.