Abstract
Using loop-tree duality, we relate a renormalised $n$-point $l$-loop amplitude in a quantum field theory to a phase-space integral of a regularised $l$-fold forward limit of a UV-subtracted $(n+2l)$-point tree-amplitude-like object. We show that up to three loops the latter object is easily computable from recurrence relations. This defines an integrand of the loop amplitude with a global definition of the loop momenta. Field and mass renormalisation are performed in the on-shell scheme.
Highlights
Precision physics at the LHC requires next-to-next-toleading order (NNLO) calculations for various processes
We show that the integrand for the renormalized n-point l-loop amplitude within the loop-tree duality approach is related to the regularized l-fold forward limit of a UVsubtracted ðn þ 2lÞ-point tree-amplitude-like object, if field renormalization and mass renormalization are performed in the on-shell scheme
We present the equivalence between the renormalized npoint l-loop amplitude and the phase space integral of a regularized l-fold forward limit of a UV-subtracted ðn þ 2lÞ-point tree-amplitude-like object as a general property of quantum field theory
Summary
Precision physics at the LHC requires next-to-next-toleading order (NNLO) calculations for various processes. We show that the integrand for the renormalized n-point l-loop amplitude within the loop-tree duality approach is related to the regularized l-fold forward limit of a UVsubtracted ðn þ 2lÞ-point tree-amplitude-like object, if field renormalization and mass renormalization are performed in the on-shell scheme. The main result of this paper is given in Eq (99), which relates the renormalized n-point l-loop amplitude to a phase space integral of a regularized l-fold forward limit of a UVsubtracted ðn þ 2lÞ-point tree-amplitude-like object.
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