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)

IF 3.6 2区物理与天体物理 Q1 PHYSICS, NUCLEAR 中国物理C Pub Date : 2024-06-01 DOI:10.1088/1674-1137/ad34be

Tao Zhong, Ya-Hong Dai, Hai-Bing Fu

{"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":"中国物理C","volume":"59 1","pages":""},"PeriodicalIF":3.6000,"publicationDate":"2024-06-01","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/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}

引用次数: 0

Abstract

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

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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

受我们之前关于先驱前旋分布振幅（DA）的研究[Phys. Rev. D 104(1), 016021 (2021)]的启发，我们在本研究中重新审视了ρ介子前旋纵向分布振幅。我们采用了张建国提出的基于戴森-施温格方程的模型来描述ρ介子的行为。然而，ρ介子的ξ矩是在背景场理论框架下用QCD和则计算出来的。这些矩的和则公式得到了改进。给出了典型尺度下前五个非零ξ矩的更精确值，例如在、、、和。用最小二乘法拟合这些值，就可以确定的 DSE 模型。通过采用左手电流光锥和规则的方法，我们得到了大反冲区的转变形式因子，即、、和，以及比值、。在利用基于-展开的快速收敛数列进行外推之后，我们给出了与-无关的半轻子衰变宽度。最后，分支分数分别为、、和。

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来源期刊

中国物理C 物理-物理：核物理

CiteScore

6.50

自引率

8.30%

发文量

8976

审稿时长

1.3 months

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.