QCD amplitudes with 2 initial spacelike legs via generalised BCFW recursion

Abstract

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 → 2 matrix elements as functions of the differences in rapidity and azimuthal angle of the final state particles.

Four-dimensional ambitwistor strings and form factors of local and Wilson line operators

“…The general practice when studying form factors is to consider the case of local gauge invariant color singlet operators. However, one may also consider gauge invariant (the representation under global gauge transformation is not necessary singlet) non-local operators, for example Wilson loops (lines) or their products [53][54][55][56][57][58][59][60][61][62][63][64][65]. An insertion of Wilson line operator will then correspond to the off-shell or reggeized gluon in such formulation.…”

“…An insertion of Wilson line operator will then correspond to the off-shell or reggeized gluon in such formulation. These objects should be more familiar to the reader as gauge invariant off-shell amplitudes [53][54][55][56][57][58][59][60][61][62] (also known as reggeon amplitudes in the framework of Lipatov's effective lagrangian), which appear within the context of k T or high-energy factorization [66][67][68][69] as well as in the study of processes at multi-regge kinematics.…”

“…Form factors of Wilson line operators are generally used to describe gauge invariant offshell or reggeon amplitudes [53][54][55][56][57][58][59][60][61][62]. The Wilson line operators used to describe off-shell reggeized gluons are defined as [60]:…”

Pgg TMD splitting function in kT factorization

“…In order to calculateP gg splitting we needed to extend formalism of [3,4] to the gluon case. This was achieved in [1] by generalizing definition of projector operators and defining appropriate generalized 3-gluon vertex that is gauge invariant in the presence of the off-shell momentum k. Definition of the generalized vertex follows from application of the spinor helicity methods to the high-energy factorization [28][29][30][31][32][33] and can be obtained by summing the diagrams of Fig. 2, giving:…”

The all-loop conjecture for integrands of reggeon amplitudes in $$ \mathcal{N}=4 $$ SYM

“…Wilson lines are non-local gauge invariant operators and are interesting objects not only from pure theoretical but also from phenomenological point of view. They appear, for example, in the description of reggeon amplitudes in the framework of Lipatov's effective QCD lagrangian 2 [22,[46][47][48][49][50][51][52][53][54][55][56], within the context of k T or high-energy factorization [57][58][59][60] as well as in the study of processes at multi-Regge kinematics. The Wilson line operators play the role of sources for the reggeized gluons, while their form factors are directly related to amplitudes with reggeized gluons in such framework.…”