2016/12/31 by Humberto Gomez, Sebastian Mizera, Guojun Zhang · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Amplitude #Black Holes and Theoretical Physics #Combinatorics #Cosmology and Gravitation Theories #Feynman diagram #Holomorphic function #Loop (graph theory) #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Philosophy #Physics #Pure mathematics #Quantum mechanics #Scattering amplitude #Simple (philosophy) #hep-th
paper · pdf · doi:10.1007/jhep03(2017)092
30+12 pages, notation modified and references added
arxiv created 2017/03/01 · openalex publication_date 2017/03/01 · arxiv updated 2017/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Recently, the Cachazo-He-Yuan (CHY) approach for calculating scattering amplitudes has been extended beyond tree level. In this paper, we introduce a way of constructing CHY integrands for Φ3 theory up to two loops from holomorphic forms on Riemann surfaces. We give simple rules for translating Feynman diagrams into the corresponding CHY integrands. As a complementary result, we extend the Λ-algorithm, originally introduced in arXiv:1604.05373 , to two loops. Using this approach, we are able to analytically verify our prescription for the CHY integrands up to seven external particles at two loops. In addition, it gives a natural way of extending to higher-loop orders.