high energy physics; algebraic geometry; quantum field theory
Larsen Kasper, Bosma Jorrit, Zhang Yang (2018), Differential equations for loop integrals without squared propagators, in Loops and Legs in Quantum Field Theory
, St. Goar, GermanyLoops and Legs in Quantum Field Theory, St. Goar, Germany.
Böhm Janko, Georgoudis Alessandro, Larsen Kasper J., Schönemann Hans, Zhang Yang (2018), Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections, in Journal of High Energy Physics
, 2018(9), 24-24.
Böhm Janko, Georgoudis Alessandro, Larsen Kasper J., Schulze Mathias, Zhang Yang (2018), Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals, in Physical Review D
, 98(2), 025023-025023.
Bosma Jorrit, Larsen Kasper J., Zhang Yang (2018), Differential equations for loop integrals in Baikov representation, in Physical Review D
, 97(10), 105014-105014.
Jorrit Bosma, Mads Sogaard, Yang Zhang (2017), Maximal cuts in arbitrary dimension, in Journal of High Energy Physics
Zhang Yang (2016), Scattering amplitudes via computational algebtraic geometry, in Computeralgebra-Rundbrief
, 58, 9-13.
Bosma Jorrit, Søgaard Mads, Zhang Yang (2016), The Polynomial Form of the Scattering Equations is an H-Basis, in Phys. Rev.
, D94(4), 041701-041701.
Larsen Kasper J., Zhang Yang (2015), Integration-by-parts reductions from unitarity cuts and algebraic geometry, in Phys. Rev.
, D93(4), 041701-041701.
Søgaard Mads, Zhang Yang (2015), Scattering Equations and Global Duality of Residues, in Phys. Rev.
, D93(10), 105009-105009.
Georgoudis Alessandro, Zhang Yang (2015), Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves, in JHEP
, 12, 086-086.
Alessandro Georgoudis, Kasper J. Larsen, and Yang Zhang, Azurite: An algebraic geometry based package for finding bases of loop integrals, in Computer Physics Communications
Larsen Kasper, Zhang Yang, Integration-by-parts reductions from the viewpoint of computational algebraic geometry, in PoS
, LL2016, 29.
I work with the support of Ambizione grant from Swiss national science foundation, on the research project “Multi-loop Scattering Amplitudes via Algebraic Geometry”, which aims at developing new highly efficient methods for calculating the particle scattering processes in high energy physics, especially for Large Hadron Collider (LHC). The key of my idea is to apply the new mathematical method, computational algebraic geometry.The goal of high energy physics is to find new particles and new physical laws in the high energy regime, which is reached experimentally by particle scattering processes on colliders. Scattering processes are quantitatively characterized by scattering amplitudes in quantum physics. On colliders, possible new physics signals are hidden in the dominating Standard Model (SM) background, hence to extract signals of new physics, we have to theoretically calculate the SM scattering amplitudes to high precision.Traditionally, scattering amplitudes are calculated by Feynman diagrams. However, the method becomes obscure in the multi-loop orders. Some SM scattering amplitudes, crucial for LHC Run II, are untouchable from Feynman diagram approach.In my viewpoint, the difficulty of Feynman diagram approach originates from the large number of complex variables for high-loop scattering processes. I believe that the powerful mathematical method, algebraic geometry, which is the ideal tool for multivariate complex analysis, will lead to highly efficient scattering amplitude calculation methods. In this research project, I will apply the mathematical tools of algebraic geometry, like multivariate complex analysis, Gröbner basis, Riemann-Roch theorem, differential Galois theory, etc, to study two-loop and three-loop amplitudes thoroughly, and to evaluate several important multi-loop amplitudes for LHC Run II. I am also going to publish multi-loop amplitude public codes, to automate the amplitude calculation via algebraic geometry.