Contributor info: Dr Konstantinos Papadopoulos

D. Canko, A. Kardos, C. G. Papadopoulos, A. V Smirnov, N. Syrrakos, C. Wever

SciPost Phys. Proc. 7, 037 (2022) · published 21 June 2022 | Toggle abstract · pdf

Analytic expressions in terms of polylogarithmic functions for all three families of planar two-loop five-point Master Integrals with one off-shell leg are presented. The Simplified Differential Equations approach is the only known way to fulfil this task due to its unique factorisation property of the symbols of the canonical differential equation. The results are relevant to the study of many $2\to 3$ scattering processes of interest at the LHC.

Dhimiter D. Canko, Costas G. Papadopoulos, Nikolaos Syrrakos

SciPost Phys. Proc. 7, 030 (2022) · published 21 June 2022 | Toggle abstract · pdf

We present analytical results for one-loop five-point master integrals with up to three off-shell legs. The method of canonical differential equations along with the Simplified Differential Equations approach is employed. All necessary boundary terms are given in closed form, resulting to solutions in terms of Goncharov Polylogarithms of arbitrary weight. Explicit results up to weight six will be presented.

Dhimiter D. Canko, Federico Gasparotto, Luca Mattiazzi, Costas G. Papadopoulos, Nikolaos Syrrakos

SciPost Phys. Proc. 7, 028 (2022) · published 21 June 2022 | Toggle abstract · pdf

We present the computation of the massless three-loop ladder-box family with one external off-shell leg using the Simplified Differential Equations (SDE) approach. We also discuss the methods we used for finding a canonical differential equation for the two tennis-court families with one off-shell leg, and the application of the SDE approach on these two families.