Reduction of Feynman integrals in the parametric representation

• Published in: The journal of high energy physics Vol. 2020; no. 2; pp. 1 - 11
• Main Author: Chen, Wen
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2020; Springer Nature B.V; SpringerOpen
• Subjects: 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; NLO Computations; QCD Phenomenology
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2020)115

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.