Abstract
We study several multiscale one-loop five-point families of Feynman integrals. More specifically, we employ the Simplified Differential Equations approach to obtain results in terms of Goncharov polylogarithms of up to transcendental weight four for families with two and three massive external legs and massless propagators, as well as with one massive internal line and up to two massive external legs. This is the first time this computational approach is applied to cases involving internal masses.
Highlights
We present the families of Feynman integrals computed through the solution of simplified differential equations in canonical form, while in figure 2 we present the families of integrals computed through the x → 1 limit
The rest of our paper is structured as follows: in section 2 we introduce basic notation and the kinematic configuration for each of the studied families of Feynman integrals, in section 3 we construct pure bases and derive and solve simplified differential equations in canonical form for all integral families depicted in figure 1, we present some of the resulting alphabets in x and study their structure, and solve all integral families depicted in figure 2 through the x → 1 limit in terms of Goncharov polylogarithms of up to transcendental weight four
The current frontier in the calculation of multiscale multiloop Feynman integrals for 2 → 3 scattering processes relevant to LHC searches lies at two-loop five-point Feynman integrals with one off-shell leg and massless internal lines
Summary
For the families C, D and E we have n1 = n4 = 0, for the families F and G n1 = 0, n4 = 1 and for the family H n1 = 1, n4 = 0. The kinematics for the families depicted in figure 1 is as follows,. Introducing (2.3) results in a mapping between the kinematic invariants in the original momentum parametrization, qi, and the underline momentum parametrization {x, pi} for. For the families depicted in figure 2 their definition through (2.1)&(2.2) is obtained by taking (2.3) and setting x = 1, and their kinematic configuration is effectively the one produced by the underline momentum parametrization of the families through which we will calculate them with the x → 1 limit, we have.
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