Abstract
We calculate one loop scattering amplitudes for arbitrary number of positive helicity on-shell gluons and one off-shell gluon treated within the quasi-multi Regge kinematics. The result is fully gauge invariant and possesses the correct on-shell limit. Our method is based on embedding the off-shell process, together with contributions needed to retain gauge invariance, in a bigger fully on-shell process with auxiliary quark or gluon line.
Highlights
In this appendix we detail the calculation that leads to eq (5.7) which implies the correct on-shell limit for the n-point off-shell amplitude we presented in eq (4.8)
We focus on the first term in the sum over j, since it is the term that leads to U3∗ when applying the Λ prescription
The first equality is obtained by momentum conservation on the index l and the second one by momentum conservation, on the index i this time
Summary
The method to obtain the off-shell amplitudes we are about to use has been developed in [53]. The auxiliary quark and antiquark spinors are decoupled ensuring gauge invariance of the off-shell amplitude. In order to use the helicity method, we need to express kTμ in terms of spinors. It can be decomposed as follows kTμ = −κeμ − κ∗eμ∗ ,. We shall call the above kinematics (together with taking the limit Λ → ∞) the “Λ prescription” Applying it to an amplitude with auxiliary partons gives the gauge invariant off-shell amplitude. The color decomposition for (n − 2)-gluon amplitude with a quark-antiquark pair is given by. We will see here that the same holds at one loop for the all-plus amplitudes
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