{"title":"ρ介子纵向前旋分布振幅重访与D→ρ半轻子衰变* * 部分受国家自然科学基金（12265009, 12265010, 12147102）、贵州省科技厅项目（ZK[2021]024, ZK[2023]142）、贵州省教育厅项目（KY[2021]030）和重庆市研究生科研创新基金（ydstd1912）资助","authors":"Tao Zhong, Ya-Hong Dai, Hai-Bing Fu","doi":"10.1088/1674-1137/ad34be","DOIUrl":null,"url":null,"abstract":"Motivated by our previous study [Phys. Rev. D 104(1), 016021 (2021)] on the pionic leading-twist distribution amplitude (DA), we revisit the <italic toggle=\"yes\">ρ</italic>-meson leading-twist longitudinal DA <inline-formula>\n<tex-math><?CDATA $ \\phi_{2;\\rho}^\\|(x,\\mu) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M1.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> in this study. A model proposed by Chang based on the Dyson-Schwinger equations is adopted to describe the behavior of <inline-formula>\n<tex-math><?CDATA $ \\phi_{2;\\rho}^\\|(x,\\mu) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M2.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>. However, the <italic toggle=\"yes\">ξ</italic>-moments of <inline-formula>\n<tex-math><?CDATA $ \\phi_{2;\\rho}^\\|(x,\\mu) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M3.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> are calculated with the QCD sum rules in the framework of the background field theory. The sum rule formulas for these moments are improved. More accurate values for the first five nonzero <italic toggle=\"yes\">ξ</italic>-moments at the typical scale <inline-formula>\n<tex-math><?CDATA $ \\mu = (1.0, 1.4, 2.0, 3.0)\\; {\\rm GeV} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M4.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> are given, e.g., at <inline-formula>\n<tex-math><?CDATA $ \\mu = 1\\; {\\rm GeV} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M5.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ \\langle\\xi^2\\rangle_{2;\\rho}^\\| = 0.220(6) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M6.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ \\langle\\xi^4\\rangle_{2;\\rho}^\\| = 0.103(4) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M7.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ \\langle\\xi^6\\rangle_{2;\\rho}^\\| = 0.066(5) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M8.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ \\langle\\xi^8\\rangle_{2;\\rho}^\\| = 0.046(4) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M9.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> , and <inline-formula>\n<tex-math><?CDATA $ \\langle\\xi^{10}\\rangle_{2;\\rho}^\\| = 0.035(3) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M10.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>. By fitting these values with the least squares method, the DSE model for <inline-formula>\n<tex-math><?CDATA $ \\phi_{2;\\rho}^\\|(x,\\mu) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M11.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> is determined. By taking the left-handed current light-cone sum rule approach, we obtain the transition form factor in the large recoil region, <italic toggle=\"yes\">i.e.</italic>, <inline-formula>\n<tex-math><?CDATA $ A_1(0) = 0.498^{+0.014}_{-0.012} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M12.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ A_2(0)=0.460^{+0.055}_{-0.047} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M13.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, and <inline-formula>\n<tex-math><?CDATA $ V(0) = 0.800^{+0.015}_{-0.014} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M14.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, and the ratio <inline-formula>\n<tex-math><?CDATA $ r_2 = 0.923^{+0.133}_{-0.119} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M15.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ r_V = 1.607^{+0.071}_{-0.071} $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M16.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>. After extrapolating with a rapidly converging series based on <inline-formula>\n<tex-math><?CDATA $ z(t) $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M17.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>-expansion, we present the <inline-formula>\n<tex-math><?CDATA $ |V_{cd}| $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M18.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>-independent decay width for the semileptonic decays <inline-formula>\n<tex-math><?CDATA $ D\\to\\rho\\ell^+\\nu_\\ell $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M19.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>. Finally, the branching fractions are <inline-formula>\n<tex-math><?CDATA $ \\mathcal{B}(D^0\\to \\rho^- e^+ \\nu_e) = 1.825^{+0.170}_{-0.162}\\pm 0.004 $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M20.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $\\mathcal{B}(D^+ \\to \\rho^0 e^+ \\nu_e) = $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M21.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>\n<inline-formula>\n<tex-math><?CDATA $ 2.299^{+0.214}_{-0.204}\\pm 0.011$?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M21-1.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $ \\mathcal{B}(D^0\\to \\rho^- \\mu^+ \\nu_\\mu) = 1.816^{+0.168}_{-0.160}\\pm 0.004 $?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M22.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, and <inline-formula>\n<tex-math><?CDATA $\\mathcal{B}(D^+ \\to \\rho^0 \\mu^+ \\nu_\\mu) =2.288^{+0.212}_{-0.201} \\pm 0.011$?></tex-math>\n<inline-graphic xlink:href=\"cpc_48_6_063108_M23.jpg\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>.","PeriodicalId":10250,"journal":{"name":"Chinese Physics C","volume":null,"pages":null},"PeriodicalIF":3.6000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ρ-meson longitudinal leading-twist distribution amplitude revisited and the D→ρ semileptonic decay* * Supported in part by the National Natural Science Foundation of China (12265009, 12265010, 12147102), the Project of Guizhou Provincial Department of Science and Technology (ZK[2021]024, ZK[2023]142), the Project of Guizhou Provincial Department of Education (KY[2021]030) and the Chongqing Graduate Research and Innovation Foundation (ydstd1912)\",\"authors\":\"Tao Zhong, Ya-Hong Dai, Hai-Bing Fu\",\"doi\":\"10.1088/1674-1137/ad34be\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Motivated by our previous study [Phys. Rev. D 104(1), 016021 (2021)] on the pionic leading-twist distribution amplitude (DA), we revisit the <italic toggle=\\\"yes\\\">ρ</italic>-meson leading-twist longitudinal DA <inline-formula>\\n<tex-math><?CDATA $ \\\\phi_{2;\\\\rho}^\\\\|(x,\\\\mu) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M1.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> in this study. A model proposed by Chang based on the Dyson-Schwinger equations is adopted to describe the behavior of <inline-formula>\\n<tex-math><?CDATA $ \\\\phi_{2;\\\\rho}^\\\\|(x,\\\\mu) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M2.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>. However, the <italic toggle=\\\"yes\\\">ξ</italic>-moments of <inline-formula>\\n<tex-math><?CDATA $ \\\\phi_{2;\\\\rho}^\\\\|(x,\\\\mu) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M3.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> are calculated with the QCD sum rules in the framework of the background field theory. The sum rule formulas for these moments are improved. More accurate values for the first five nonzero <italic toggle=\\\"yes\\\">ξ</italic>-moments at the typical scale <inline-formula>\\n<tex-math><?CDATA $ \\\\mu = (1.0, 1.4, 2.0, 3.0)\\\\; {\\\\rm GeV} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M4.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> are given, e.g., at <inline-formula>\\n<tex-math><?CDATA $ \\\\mu = 1\\\\; {\\\\rm GeV} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M5.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ \\\\langle\\\\xi^2\\\\rangle_{2;\\\\rho}^\\\\| = 0.220(6) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M6.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ \\\\langle\\\\xi^4\\\\rangle_{2;\\\\rho}^\\\\| = 0.103(4) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M7.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ \\\\langle\\\\xi^6\\\\rangle_{2;\\\\rho}^\\\\| = 0.066(5) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M8.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ \\\\langle\\\\xi^8\\\\rangle_{2;\\\\rho}^\\\\| = 0.046(4) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M9.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> , and <inline-formula>\\n<tex-math><?CDATA $ \\\\langle\\\\xi^{10}\\\\rangle_{2;\\\\rho}^\\\\| = 0.035(3) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M10.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>. By fitting these values with the least squares method, the DSE model for <inline-formula>\\n<tex-math><?CDATA $ \\\\phi_{2;\\\\rho}^\\\\|(x,\\\\mu) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M11.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> is determined. By taking the left-handed current light-cone sum rule approach, we obtain the transition form factor in the large recoil region, <italic toggle=\\\"yes\\\">i.e.</italic>, <inline-formula>\\n<tex-math><?CDATA $ A_1(0) = 0.498^{+0.014}_{-0.012} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M12.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ A_2(0)=0.460^{+0.055}_{-0.047} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M13.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, and <inline-formula>\\n<tex-math><?CDATA $ V(0) = 0.800^{+0.015}_{-0.014} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M14.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, and the ratio <inline-formula>\\n<tex-math><?CDATA $ r_2 = 0.923^{+0.133}_{-0.119} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M15.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ r_V = 1.607^{+0.071}_{-0.071} $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M16.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>. After extrapolating with a rapidly converging series based on <inline-formula>\\n<tex-math><?CDATA $ z(t) $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M17.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>-expansion, we present the <inline-formula>\\n<tex-math><?CDATA $ |V_{cd}| $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M18.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>-independent decay width for the semileptonic decays <inline-formula>\\n<tex-math><?CDATA $ D\\\\to\\\\rho\\\\ell^+\\\\nu_\\\\ell $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M19.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>. Finally, the branching fractions are <inline-formula>\\n<tex-math><?CDATA $ \\\\mathcal{B}(D^0\\\\to \\\\rho^- e^+ \\\\nu_e) = 1.825^{+0.170}_{-0.162}\\\\pm 0.004 $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M20.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $\\\\mathcal{B}(D^+ \\\\to \\\\rho^0 e^+ \\\\nu_e) = $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M21.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>\\n<inline-formula>\\n<tex-math><?CDATA $ 2.299^{+0.214}_{-0.204}\\\\pm 0.011$?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M21-1.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $ \\\\mathcal{B}(D^0\\\\to \\\\rho^- \\\\mu^+ \\\\nu_\\\\mu) = 1.816^{+0.168}_{-0.160}\\\\pm 0.004 $?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M22.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, and <inline-formula>\\n<tex-math><?CDATA $\\\\mathcal{B}(D^+ \\\\to \\\\rho^0 \\\\mu^+ \\\\nu_\\\\mu) =2.288^{+0.212}_{-0.201} \\\\pm 0.011$?></tex-math>\\n<inline-graphic xlink:href=\\\"cpc_48_6_063108_M23.jpg\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>.\",\"PeriodicalId\":10250,\"journal\":{\"name\":\"Chinese Physics C\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2024-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chinese Physics C\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1674-1137/ad34be\",\"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":"Chinese Physics C","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1674-1137/ad34be","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}
ρ-meson longitudinal leading-twist distribution amplitude revisited and the D→ρ semileptonic decay* * Supported in part by the National Natural Science Foundation of China (12265009, 12265010, 12147102), the Project of Guizhou Provincial Department of Science and Technology (ZK[2021]024, ZK[2023]142), the Project of Guizhou Provincial Department of Education (KY[2021]030) and the Chongqing Graduate Research and Innovation Foundation (ydstd1912)
Motivated by our previous study [Phys. Rev. D 104(1), 016021 (2021)] on the pionic leading-twist distribution amplitude (DA), we revisit the ρ-meson leading-twist longitudinal DA in this study. A model proposed by Chang based on the Dyson-Schwinger equations is adopted to describe the behavior of . However, the ξ-moments of are calculated with the QCD sum rules in the framework of the background field theory. The sum rule formulas for these moments are improved. More accurate values for the first five nonzero ξ-moments at the typical scale are given, e.g., at , , , , , and . By fitting these values with the least squares method, the DSE model for is determined. By taking the left-handed current light-cone sum rule approach, we obtain the transition form factor in the large recoil region, i.e., , , and , and the ratio , . After extrapolating with a rapidly converging series based on -expansion, we present the -independent decay width for the semileptonic decays . Finally, the branching fractions are , , , and .
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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