Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilation
Abstract The planar two-loop scalar Feynman integrals contributing to the massive NNLO QCD corrections for W-boson pair production via quark-antiquark annihilation can be classified into three family branches, each of which is reduced to a distinct set of master integrals (MIs), totaling 27, 45 and...
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| Format: | Article |
| Language: | English |
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2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)136 |
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| author | Wen-Jie He Ren-You Zhang Liang Han Yi Jiang Zhe Li Xiao-Feng Wang Shu-Xiang Li Pan-Feng Li Qing-hai Wang |
| author_facet | Wen-Jie He Ren-You Zhang Liang Han Yi Jiang Zhe Li Xiao-Feng Wang Shu-Xiang Li Pan-Feng Li Qing-hai Wang |
| author_sort | Wen-Jie He |
| collection | DOAJ |
| description | Abstract The planar two-loop scalar Feynman integrals contributing to the massive NNLO QCD corrections for W-boson pair production via quark-antiquark annihilation can be classified into three family branches, each of which is reduced to a distinct set of master integrals (MIs), totaling 27, 45 and 15, respectively. These MIs are analytically calculated using the method of differential equations, with solutions expanded as Taylor series in the dimensional regulator ϵ. For the first two family branches, the differential systems can be successfully transformed into canonical form by adopting appropriate bases of MIs. This enables the MIs of these family branches to be expressed either as Goncharov polylogarithms (GPLs) or as one-fold integrals over GPLs, up to O $$ \mathcal{O} $$ (ϵ 4). In contrast, the differential system for the third family branch can only be cast into a form linear in ϵ due to the presence of elliptic integrals. The solution to this linear-form differential system is expressed in an iterated form owing to the strictly lower-triangular structure of the coefficient matrices at ϵ = 0. Our analytic expressions for these MIs are verified with high accuracy against the numerical results from the AMFlow package. |
| format | Article |
| id | doaj-art-e24660992c1b4248a7bd8572387e34a7 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-e24660992c1b4248a7bd8572387e34a72025-01-05T12:06:19ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241214010.1007/JHEP12(2024)136Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilationWen-Jie He0Ren-You Zhang1Liang Han2Yi Jiang3Zhe Li4Xiao-Feng Wang5Shu-Xiang Li6Pan-Feng Li7Qing-hai Wang8State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of ChinaState Key Laboratory of Particle Detection and Electronics, University of Science and Technology of ChinaState Key Laboratory of Particle Detection and Electronics, University of Science and Technology of ChinaState Key Laboratory of Particle Detection and Electronics, University of Science and Technology of ChinaState Key Laboratory of Particle Detection and Electronics, University of Science and Technology of ChinaState Key Laboratory of Particle Detection and Electronics, University of Science and Technology of ChinaState Key Laboratory of Particle Detection and Electronics, University of Science and Technology of ChinaState Key Laboratory of Particle Detection and Electronics, University of Science and Technology of ChinaDepartment of Physics, National University of SingaporeAbstract The planar two-loop scalar Feynman integrals contributing to the massive NNLO QCD corrections for W-boson pair production via quark-antiquark annihilation can be classified into three family branches, each of which is reduced to a distinct set of master integrals (MIs), totaling 27, 45 and 15, respectively. These MIs are analytically calculated using the method of differential equations, with solutions expanded as Taylor series in the dimensional regulator ϵ. For the first two family branches, the differential systems can be successfully transformed into canonical form by adopting appropriate bases of MIs. This enables the MIs of these family branches to be expressed either as Goncharov polylogarithms (GPLs) or as one-fold integrals over GPLs, up to O $$ \mathcal{O} $$ (ϵ 4). In contrast, the differential system for the third family branch can only be cast into a form linear in ϵ due to the presence of elliptic integrals. The solution to this linear-form differential system is expressed in an iterated form owing to the strictly lower-triangular structure of the coefficient matrices at ϵ = 0. Our analytic expressions for these MIs are verified with high accuracy against the numerical results from the AMFlow package.https://doi.org/10.1007/JHEP12(2024)136Electroweak Precision PhysicsHigher-Order Perturbative Calculations |
| spellingShingle | Wen-Jie He Ren-You Zhang Liang Han Yi Jiang Zhe Li Xiao-Feng Wang Shu-Xiang Li Pan-Feng Li Qing-hai Wang Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilation Journal of High Energy Physics Electroweak Precision Physics Higher-Order Perturbative Calculations |
| title | Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilation |
| title_full | Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilation |
| title_fullStr | Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilation |
| title_full_unstemmed | Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilation |
| title_short | Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilation |
| title_sort | two loop planar master integrals for nnlo qcd corrections to w pair production in quark antiquark annihilation |
| topic | Electroweak Precision Physics Higher-Order Perturbative Calculations |
| url | https://doi.org/10.1007/JHEP12(2024)136 |
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