Abstract
We present all two-loop five-parton leading-colour finite remainders in the spinor-helicity formalism by analysing numerical evaluations of their known expressions in terms of Mandelstam invariants. Recasting them in terms of spinor-helicity variables allows us to obtain expressions which are more compact, faster to evaluate, numerically more stable and manifestly free from poles of higher order than necessary. At the same time, due to the better scaling of our reconstruction strategy with the complexity of the input, we required one order of magnitude fewer numerical samples to complete the analytical reconstruction than were needed by the authors of ref. [1], albeit using higher numerical working precision. This places our reconstruction technique as an alternative to the finite-field single-numerator reconstruction for future applications.
Highlights
Analysing the singularity structure of the coefficients and performing the reconstruction in terms of spinor-helicity variables as proposed in ref. [23] the obtained analytical expressions are more compact, faster to evaluate and numerically more stable
E-mail: giuseppe.de.laurentis@physik.uni-freiburg.de, daniel.maitre@durham.ac.uk Abstract: We present all two-loop five-parton leading-colour finite remainders in the spinor-helicity formalism by analysing numerical evaluations of their known expressions in terms of Mandelstam invariants
We compare three aspects of our results compared to those we used as an input. We compare their complexity in terms of the leaf count of the finite remainder expressions, that is in terms of the number of nodes in their abstract syntax trees
Summary
The original calculation in ref. [1] was performed via numerical D-dimensional generalised unitarity in the leading-colour approximation, more precisely in the limit of large number of colours Nc while keeping the ratio to the number of flavours Nf fixed. The full amplitudes A are stripped of their dependence on the gauge-group factors by colour-ordering decompositions [24, 25] in terms of color-ordered sub-amplitudes A. Their expansion in terms of the bare QCD coupling α0 reads. Each loop amplitude can be further expanded in the ratio Nf /Nc as. A(R1) = I([n1])( )A(R0) + O( 0) , A(R2) = I([n2])( )A(R0) + I([n1])( )A(R1) + O( 0) The latter equation can be rearranged to obtain the definition of the so-called finite remainders, which contain the genuine two-loop information. The rational coefficients ri are the subject of the present study
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