Reduction of Feynman integrals in the parametric representation
A bstract In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum space. Tensor integrals can directly be parametrized without performing tensor reductions. The...
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| Published in | The journal of high energy physics Vol. 2020; no. 2; pp. 1 - 11 |
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| Format | Journal Article |
| Language | English |
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| Abstract | A
bstract
In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum space. Tensor integrals can directly be parametrized without performing tensor reductions. The integrands of parametric integrals are functions of Lorentz scalars, instead of four momenta. The complexity of a calculation is determined by the number of propagators that are present rather than the number of all the linearly independent propagators. Furthermore, the symmetries of Feynman integrals under permutations of indices are transparent in the parametric representation. Since all the indices of the propagators are nonnegative, an algorithm to solve those identities can easily be developed, which can be used for automatic calculations. |
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| AbstractList | In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum space. Tensor integrals can directly be parametrized without performing tensor reductions. The integrands of parametric integrals are functions of Lorentz scalars, instead of four momenta. The complexity of a calculation is determined by the number of propagators that are present rather than the number of all the linearly independent propagators. Furthermore, the symmetries of Feynman integrals under permutations of indices are transparent in the parametric representation. Since all the indices of the propagators are nonnegative, an algorithm to solve those identities can easily be developed, which can be used for automatic calculations. A bstract In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum space. Tensor integrals can directly be parametrized without performing tensor reductions. The integrands of parametric integrals are functions of Lorentz scalars, instead of four momenta. The complexity of a calculation is determined by the number of propagators that are present rather than the number of all the linearly independent propagators. Furthermore, the symmetries of Feynman integrals under permutations of indices are transparent in the parametric representation. Since all the indices of the propagators are nonnegative, an algorithm to solve those identities can easily be developed, which can be used for automatic calculations. Abstract In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum space. Tensor integrals can directly be parametrized without performing tensor reductions. The integrands of parametric integrals are functions of Lorentz scalars, instead of four momenta. The complexity of a calculation is determined by the number of propagators that are present rather than the number of all the linearly independent propagators. Furthermore, the symmetries of Feynman integrals under permutations of indices are transparent in the parametric representation. Since all the indices of the propagators are nonnegative, an algorithm to solve those identities can easily be developed, which can be used for automatic calculations. |
| ArticleNumber | 115 |
| Author | Chen, Wen |
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| References_xml | – reference: SmirnovAVAlgorithm FIRE — Feynman Integral REductionJHEP2008101072008JHEP...10..107S10.1088/1126-6708/2008/10/107[arXiv:0807.3243] [INSPIRE] – reference: BöhmJGeorgoudisALarsenKJSchulzeMZhangYComplete sets of logarithmic vector fields for integration-by-parts identities of Feynman integralsPhys. Rev.2018D 982018PhRvD..98b5023B3924092[arXiv:1712.09737] [INSPIRE] – reference: von ManteuffelASchabingerRMQuark and gluon form factors to four-loop order in QCD: theNf3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {N}_f^3 $$\end{document}contributionsPhys. Rev.2017D 952017PhRvD..95c4030V[arXiv:1611.00795] [INSPIRE] – reference: P.A. Baikov, Explicit solutions of the multiloop integral recurrence relations and its application, Nucl. Instrum. Meth.A 389 (1997) 347 [hep-ph/9611449] [INSPIRE]. – reference: T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys.B 580 (2000) 485 [hep-ph/9912329] [INSPIRE]. – reference: TarasovOVConnection between Feynman integrals having different values of the space-time dimensionPhys. Rev.1996D 5464791996PhRvD..54.6479T14235860925.81121[hep-th/9606018] [INSPIRE] – reference: KantPFinding Linear Dependencies in Integration-By-Parts Equations: A Monte Carlo ApproachComput. Phys. Commun.201418514732014CoPhC.185.1473K10.1016/j.cpc.2014.01.017[arXiv:1309.7287] [INSPIRE] – reference: StuderusCReduze-Feynman Integral Reduction in C++Comput. Phys. Commun.201018112932010CoPhC.181.1293S264497110.1016/j.cpc.2010.03.012[arXiv:0912.2546] [INSPIRE] – reference: R.N. 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Phys.20191094972019LMaPh.109..497B391013410.1007/s11005-018-1114-8[arXiv:1712.09215] [INSPIRE] – reference: BöhmJGeorgoudisALarsenKJSchönemannHZhangYComplete integration-by-parts reductions of the non-planar hexagon-box via module intersectionsJHEP2018090242018JHEP...09..024B387127510.1007/JHEP09(2018)024[arXiv:1805.01873] [INSPIRE] – reference: NakanishiNGeneral Integral Formula of Perturbation Term in the Quantized Field TheoryProg. Theor. Phys.1957174011957PThPh..17..401N8438310.1143/PTP.17.401 – reference: W. 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bstract
In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the... In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the... Abstract In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the... |
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| SubjectTerms | Algorithms Classical and Quantum Gravitation Elementary Particles High energy physics Identities Integrals Mathematical analysis NLO Computations Permutations Physics Physics and Astronomy QCD Phenomenology Quantum Field Theories Quantum Field Theory Quantum Physics Reduction Regular Article - Theoretical Physics Relativity Theory Representations Scalars String Theory Tensors |
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