Recursion relations and scattering amplitudes in the light-front formalism

TL;DR

This paper explores how light-front perturbation theory leads to recursion relations for scattering amplitudes, connecting off-shell and on-shell amplitudes, and providing exact solutions within this framework.

Contribution

It introduces light-front analogs of Berends-Giele recursion relations and demonstrates their exact solvability, linking off-shell and on-shell scattering amplitudes.

Findings

Recursion relations for light-front off-shell amplitudes are derived.

Exact solutions express off-shell amplitudes as linear combinations of on-shell amplitudes.

On-shell limits recover known scattering amplitudes from the literature.

Abstract

The fragmentation functions and scattering amplitudes are investigated in the framework of light-front perturbation theory. It is demonstrated that, the factorization property of the fragmentation functions implies the recursion relations for the off-shell scattering amplitudes which are light-front analogs of the Berends-Giele relations. These recursion relations on the light-front can be solved exactly by induction and it is shown that the expressions for the off-shell light-front amplitudes are represented as a linear combinations of the on-shell amplitudes. By putting external particles on-shell we recover the scattering amplitudes previously derived in the literature.