One-loop off-shell amplitudes from classical equations of motion

TL;DR

This paper introduces a recursive method to compute one-loop off-shell amplitudes in colored quantum field theories, leveraging classical equations of motion and an extended perturbiner approach.

Contribution

It generalizes the perturbiner method to off-shell amplitudes and develops a sewing procedure for iterative one-loop integrand computation, including gauge symmetry considerations.

Findings

Provides a recursive framework for one-loop off-shell amplitude calculation.

Extends to theories with gauge symmetries and ghosts.

Applicable to certain non-Lagrangian field theories.

Abstract

In this letter we present a recursive method for computing one-loop off-shell amplitudes in colored quantum field theories. First, we generalize the perturbiner method by recasting the multiparticle currents as generators of off-shell tree level amplitudes. After, by taking advantage of the underlying color structure, we define a consistent sewing procedure to iteratively compute the one-loop integrands. When gauge symmetries are involved, the whole procedure is extended to multiparticle solutions involving ghosts, which can then be accounted for in the full loop computation. Since the required input here is equations of motion and gauge symmetry, our framework naturally extends to one-loop computations in certain non-Lagrangian field theories.