Two-loop Master Integrals with the Simplified Differential Equations approach

TL;DR

This work computes the complete set of two-loop master integrals for diboson production with two off-shell legs and massless propagators using the Simplified Differential Equations (SDE) framework. By introducing a dimensionless parameter $x$ to drive the differential equations, the authors express all integrals in terms of Goncharov polylogarithms and solve the system in a bottom-up manner, with boundary contributions automatically captured at $x=0$. They provide explicit $x$-parametrizations that unify planar and non-planar double-box families and deliver full analytic results (in terms of $GP$) with numerical validations against SecDec and prior analytic results in the physical region. The results enable efficient, automated NNLO QCD calculations for diboson processes at the LHC and pave the way for extensions to more complex integral topologies and massive internal lines.

Abstract

We calculate the complete set of two-loop Master Integrals with two off mass-shell legs with massless internal propagators, that contribute to amplitudes of diboson $V_1V_2$ production at the LHC. This is done with the Simplified Differential Equations approach to Master Integrals, which was recently proposed by one of the authors.

Figures (4)

• Figure 1: General graphs represented by (\ref{['eq:loopgen']}) on the left and (\ref{['eq:loopgenx']}) on the right.
• Figure 2: Required parametrization for off mass-shell triangles after possible pinching of internal line(s).
• Figure 3: The parametrization of external momenta for the three planar double boxes of the families $P_{12}$ (left), $P_{13}$ (middle) and $P_{23}$ (right) contributing to pair production at the LHC. All external momenta are incoming.
• Figure 4: The parametrization of external momenta for the three non-planar double boxes of the families $N_{12}$ (left), $N_{13}$ (middle) and $N_{34}$ (right) contributing to pair production at the LHC. All external momenta are incoming.