{"title":"向量夸克子强子衰变的O(αsv2)修正","authors":"Wen-Long Sang, F. Feng, Yu Jia","doi":"10.1103/physrevd.102.094021","DOIUrl":null,"url":null,"abstract":"Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the ${\\mathcal O}(\\alpha_s v^2)$ corrections to the hadronic decay rate of vector quarkonia, exemplified by $J/\\psi$ and $\\Upsilon$. Setting both the renormalization and NRQCD factorization scales to be $m_Q$, we obtain $\\Gamma(J/\\psi\\to {\\rm LH})= 0.0716\\frac{\\alpha_s^3}{m_c^2} \\langle \\mathcal{O}_1({}^3S_1)\\rangle_{J/\\psi} [1-1.19\\alpha_s+(-5.32+3.03\\alpha_s)\\langle v^2\\rangle_{J/\\psi}]$ and $\\Gamma(\\Upsilon\\to {\\rm LH})= 0.0716\\frac{\\alpha_s^3}{m_b^2}\\langle\\mathcal{O}_1({}^3S_1)\\rangle_{\\Upsilon}[1-1.56\\alpha_s+(-5.32+4.61\\alpha_s)\\langle v^2\\rangle_{\\Upsilon}]$. We confirm the previous calculation of $\\mathcal{O}(\\alpha_s)$ corrections on a diagram-by-diagram basis, with the accuracy significantly improved. For $J/\\psi$ hadronic decay, we find that the ${\\mathcal O}(\\alpha_sv^2)$ corrections are moderate and positive, nevertheless unable to counterbalance the huge negative corrections. On the other hand, the effect of ${\\mathcal O}(\\alpha_sv^2)$ corrections for $\\Upsilon(nS)$ is sensitive to the $\\mathcal{O}(v^2)$ NRQCD matrix elements. With the appropriate choice of the NRQCD matrix elements, our theoretical predictions for the decay rates may be consistent with the experimental data for $\\Upsilon(1S,2S)\\to {\\rm LH}$. As a byproduct, we also present the theoretical predictions for the branching ratio of $J/\\psi(\\Upsilon)\\to 3\\gamma$ accurate up to $\\mathcal{O}(\\alpha_s v^2)$.","PeriodicalId":8457,"journal":{"name":"arXiv: High Energy Physics - Phenomenology","volume":"48 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"O(αsv2)\\n corrections to the hadronic decay of vector quarkonia\",\"authors\":\"Wen-Long Sang, F. Feng, Yu Jia\",\"doi\":\"10.1103/physrevd.102.094021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the ${\\\\mathcal O}(\\\\alpha_s v^2)$ corrections to the hadronic decay rate of vector quarkonia, exemplified by $J/\\\\psi$ and $\\\\Upsilon$. Setting both the renormalization and NRQCD factorization scales to be $m_Q$, we obtain $\\\\Gamma(J/\\\\psi\\\\to {\\\\rm LH})= 0.0716\\\\frac{\\\\alpha_s^3}{m_c^2} \\\\langle \\\\mathcal{O}_1({}^3S_1)\\\\rangle_{J/\\\\psi} [1-1.19\\\\alpha_s+(-5.32+3.03\\\\alpha_s)\\\\langle v^2\\\\rangle_{J/\\\\psi}]$ and $\\\\Gamma(\\\\Upsilon\\\\to {\\\\rm LH})= 0.0716\\\\frac{\\\\alpha_s^3}{m_b^2}\\\\langle\\\\mathcal{O}_1({}^3S_1)\\\\rangle_{\\\\Upsilon}[1-1.56\\\\alpha_s+(-5.32+4.61\\\\alpha_s)\\\\langle v^2\\\\rangle_{\\\\Upsilon}]$. We confirm the previous calculation of $\\\\mathcal{O}(\\\\alpha_s)$ corrections on a diagram-by-diagram basis, with the accuracy significantly improved. For $J/\\\\psi$ hadronic decay, we find that the ${\\\\mathcal O}(\\\\alpha_sv^2)$ corrections are moderate and positive, nevertheless unable to counterbalance the huge negative corrections. On the other hand, the effect of ${\\\\mathcal O}(\\\\alpha_sv^2)$ corrections for $\\\\Upsilon(nS)$ is sensitive to the $\\\\mathcal{O}(v^2)$ NRQCD matrix elements. With the appropriate choice of the NRQCD matrix elements, our theoretical predictions for the decay rates may be consistent with the experimental data for $\\\\Upsilon(1S,2S)\\\\to {\\\\rm LH}$. As a byproduct, we also present the theoretical predictions for the branching ratio of $J/\\\\psi(\\\\Upsilon)\\\\to 3\\\\gamma$ accurate up to $\\\\mathcal{O}(\\\\alpha_s v^2)$.\",\"PeriodicalId\":8457,\"journal\":{\"name\":\"arXiv: High Energy Physics - Phenomenology\",\"volume\":\"48 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-10-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: High Energy Physics - Phenomenology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevd.102.094021\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: High Energy Physics - Phenomenology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1103/physrevd.102.094021","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
O(αsv2)
corrections to the hadronic decay of vector quarkonia
Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the ${\mathcal O}(\alpha_s v^2)$ corrections to the hadronic decay rate of vector quarkonia, exemplified by $J/\psi$ and $\Upsilon$. Setting both the renormalization and NRQCD factorization scales to be $m_Q$, we obtain $\Gamma(J/\psi\to {\rm LH})= 0.0716\frac{\alpha_s^3}{m_c^2} \langle \mathcal{O}_1({}^3S_1)\rangle_{J/\psi} [1-1.19\alpha_s+(-5.32+3.03\alpha_s)\langle v^2\rangle_{J/\psi}]$ and $\Gamma(\Upsilon\to {\rm LH})= 0.0716\frac{\alpha_s^3}{m_b^2}\langle\mathcal{O}_1({}^3S_1)\rangle_{\Upsilon}[1-1.56\alpha_s+(-5.32+4.61\alpha_s)\langle v^2\rangle_{\Upsilon}]$. We confirm the previous calculation of $\mathcal{O}(\alpha_s)$ corrections on a diagram-by-diagram basis, with the accuracy significantly improved. For $J/\psi$ hadronic decay, we find that the ${\mathcal O}(\alpha_sv^2)$ corrections are moderate and positive, nevertheless unable to counterbalance the huge negative corrections. On the other hand, the effect of ${\mathcal O}(\alpha_sv^2)$ corrections for $\Upsilon(nS)$ is sensitive to the $\mathcal{O}(v^2)$ NRQCD matrix elements. With the appropriate choice of the NRQCD matrix elements, our theoretical predictions for the decay rates may be consistent with the experimental data for $\Upsilon(1S,2S)\to {\rm LH}$. As a byproduct, we also present the theoretical predictions for the branching ratio of $J/\psi(\Upsilon)\to 3\gamma$ accurate up to $\mathcal{O}(\alpha_s v^2)$.