Evaluation of Multi-loop Feynman Integrals using Modern methods

Abstract

Multi-loop Feynman integrals have been a significant roadblock in the journey of precision in collider physics and calculations in perturbative gravity. The search for New Physics amplifies the need to compute multi-loop integrals effectively. In the first half of the project, we understand the developments in analytical calculation of multi-loop integrals using modern methods such as IBP reduction and the differential equations method for the master integrals. In the second half of the project, we study the idea of obtaining a generalized boundary condition for the differential equations by adding an auxiliary mass to the master integrals. We then extend the idea by solving the differential equations of master integrals w.r.t. eta using the techniques of series expansions and analytical continuation, and obtain the numerical solutions of the master integrals for one-loop and two-loop integrals, including the possibilities of having complex mass in the integrals.