On-shell recursion relations for generic integrands

TL;DR

This paper develops a new method for defining single cut contributions in on-shell recursion relations for scattering amplitude integrands, applicable to generic renormalisable theories including the Standard Model, with checks at one loop and initial steps toward gravity.

Contribution

It introduces a novel approach to on-shell recursion for integrands, integrating single cut contributions and relating them to unitarity cuts, applicable at any loop order.

Findings

Provides a diagrammatic construction for integrand recursion

Validates the method with one-loop box coefficient checks

Extends the approach to rational terms in Yang-Mills theory

Abstract

The quantum effects encapsulated in loop corrections are crucial in quantum field theory for a wide variety of formal and phenomenological applications. In this article we propose and check a definition of the so-called single cut contributions needed to complete on-shell recursion relations for the integrand of scattering amplitudes in generic power-counting renormalisable theories at conjecturally any loop order. Our proposal meshes well with standard dimensional regularisation and applies in particular directly to much of the standard model of particle physics. Apart from a diagrammatic construction, at one loop order we provide a direct cross-check for box coefficients. Interestingly, at one loop our proposal can be related to a specific subset of all double unitarity cuts as well as tree-level poles by iterated recursion. We focus in particular on demonstrating the method in rational-term one-loop examples in pure Yang-Mills theory. For the finite amplitudes we present all-order arguments. First steps toward gravity integrands are taken.