Elliptic multiscale Feynman integrals

• Applicant: Professor Dr. Stefan Weinzierl
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Mathematics
• Term: from 2015 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 274006707

The goal of this renewal proposal is to extend our knowledge of single-scale elliptic Feynman integrals towards multi-scale elliptic Feynman integrals.Feynman integrals are an indispensable tool for precision calculations in particle physics.There is a class of Feynman integrals, which evaluate to multiple polylogarithm and captures a significant part of integrals occurring in massless quantum field theories.However, for processes involving the Higgs boson, the top quark or $W$/$Z$-bosons we do not want to neglect the masses of the heavy particles.With non-zero internal masses we leave already at two loops the function space of multiple polylogarithms and have to consider elliptic generalisations.In the first funding period we studied successfully single-scale elliptic Feynman integrals.We now plan to extend our knowledge towards multi-scale elliptic Feynman integrals.The concrete goals of this renewal proposal are:(i) to provide a method for the algorithmic construction of a suitable basis of master integrals in the elliptic multi-scale setting.(ii) to study the integration kernels appearing in the differential equations for the master integrals as generalisations of modular forms.(iii) to provide a method for the numerical evaluation of the master integrals in the elliptic multi-scale setting.

• DFG Programme: Research Grants