Computational Solutions of Feynman Integrals for One-Loop Five-Point Processes

We present the computation of the canonical form for the differential equations for the master integrals of three one-loop five-point integrals. The integrals of interest are the one-loop one-mass five-point, the one-loop two non-adjacent mass five-point, and the one-loop two adjacent mass five-point. Integrals such as these are important for the calculation of scattering amplitudes in high energy collider physics. A brief overview of Feynman integrals and their properties is given, along with the concept of IBPs, master integrals, and the development of a pure basis for the master integrals. We also discuss the derivation of the canonical form of the differential equations for the master integrals in the pure basis. In our work, we compute the master integrals associated with each one-loop five-point integral, and discuss how to cast the master integrals into a pure basis. We compute the exact form of the differential equations in this pure basis, this is done using the associated symbol alphabet. Computational work is aided by the Mathematica package LiteRed, which computes IBPs, master integrals and derivatives. The possible applications of these integrals, along with plans for the computation of other one-loop five-point integrals are discussed.