Abstract
We present analytic expressions in terms of polylogarithmic functions for all three families of planar two-loop five-point Master Integrals with one off-shell leg. The calculation is based on the Simplified Differential Equations approach. The results are relevant to the study of many 2 → 3 scattering processes of interest at the LHC, especially for the leading-color W + 2 jets production.
Highlights
Remarkable contradistinction with the NLO case is that the basis of Master Integrals at two loops is still far from complete
In this paper we have presented analytic expressions in terms of poly-logarithmic functions, Goncharov Polylogarithms, of all planar two-loop five-point integrals with a massive external leg
This has been achieved by using the Simplified Differential Equations approach and the data for the canonical basis provided in reference [44]
Summary
There are three families of Master Integrals, labelled as P1, P2 and P3, see figure 1, associated to planar two-loop five-point amplitudes with one off-shell leg. We adopt the definition of the scattering kinematics following [44], where external momenta qi, i = 1 . The set of independent invariants is given by {S12, S23, S34, S45, S51, x}, with Sij := (pi + pj). As usual the x = 1 limit corresponds to the on-shell kinematics. For P2 and P3 the corresponding numbers are 75 and 86. This can be verified using standard IBP reduction software, such as FIRE6 [45] and Kira [46, 47].
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