QCD amplitudes with 2 initial spacelike legs via generalised BCFW recursion

TL;DR

This paper extends BCFW recursion to off-shell cases in QCD, enabling computation of tree-level amplitudes with off-shell initial partons, crucial for high-energy factorization, and provides explicit results for up to four-point amplitudes.

Contribution

It generalizes BCFW recursion to off-shell initial states in QCD, including explicit calculations for two off-shell legs and non-recursive four-fermion amplitudes.

Findings

Explicit formulas for 2 off-shell leg amplitudes up to 4 points

Diagrammatic computation for non-recursive 4-fermion amplitudes

Analysis of matrix element behavior in rapidity and azimuthal angle differences

Abstract

We complete the generalisation of the BCFW recursion relation to the off-shell case, allowing for the computation of tree level scattering amplitudes for full High Energy Factorisation (HEF), i.e. with both incoming partons having a non-vanishing transverse momentum. We provide explicit results for color-ordered amplitudes with two off-shell legs in massless QCD up to 4 point, continuing the program begun in two previous papers. For the 4-fermion amplitudes, which are not BCFW-recursible, we perform a diagrammatic computation, so as to offer a complete set of expressions. We explicitly show and discuss some plots of the squared $2 \rightarrow 2$ matrix elements as functions of the differences in rapidity and azimuthal angle of the final state particles.