The Pentabox Master Integrals with the Simplified Differential Equations approach

TL;DR

This work computes massless two-loop Master Integrals for five-point amplitudes with one off-shell leg, deriving the complete set of planar five-point on-shell MIs via the Simplified Differential Equations approach. By parameterizing external momenta with a single variable x, the authors obtain a differential system that is transformed into a Fuchsian, ε-dominated form and solved in terms of Goncharov polylogarithms, with boundary conditions fixed through expansion by regions and known limits. The 74 MIs in the planar pentabox family P1 are provided analytically (and cross-checked numerically), illustrating the feasibility of a larger eight-denominator MI library needed for NNLO automation. The results advance NNLO QCD calculations for multi-jet and vector/Higgs plus jets processes at the LHC and point to future work on canonical DE forms, massive propagators, and improved numerics.

Abstract

We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many $2\to 3$ amplitudes of interest at the LHC, as for instance three jet production, $γ, V, H +2$ jets etc., based on the Simplified Differential Equations approach.

Figures (4)

• Figure 1: The three planar pentaboxes of the families $P_1$ (left), $P_2$ (middle) and $P_3$ (right) with one external massive leg.
• Figure 2: The five non-planar families with one external massive leg.
• Figure 3: The five-point Feynman diagrams, besides the pentabox itself in Figure \ref{['fig:param-P']}, that are contained in the family $P_1$. All external momenta are incoming.
• Figure 4: The parametrization of external momenta in terms of $x$ for the planar pentabox of the family $P_1$. All external momenta are incoming.