# On-shell recursion relations for generic integrands

@article{Boels2016OnshellRR, title={On-shell recursion relations for generic integrands}, author={Rutger H. Boels and Hui Luo}, journal={arXiv: High Energy Physics - Theory}, year={2016} }

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…

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## References

SHOWING 1-10 OF 56 REFERENCES

Loops and trees

- Physics
- 2011

We investigate relations between loop and tree amplitudes in quantum field theory that involve putting on-shell some loop propagators. This generalizes the so-called Feynman tree theorem which is…

An introduction to on-shell recursion relations

- Physics
- 2012

This article provides an introduction to on-shell recursion relations for calculations of tree-level amplitudes. Starting with the basics, such as spinor notations and color decompositions, we expose…

One-loop amplitudes on the Riemann sphere

- Mathematics
- 2015

A bstractThe scattering equations provide a powerful framework for the study of scattering amplitudes in a variety of theories. Their derivation from ambitwistor string theory led to proposals for…

On BCFW shifts of integrands and integrals

- Mathematics
- 2010

In this article a first step is made towards the extension of Britto-Cachazo-Feng-Witten (BCFW) tree level on-shell recursion relations to integrands and integrals of scattering amplitudes to…

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM

- Mathematics
- 2010

We give an explicit recursive formula for the all ℓ-loop integrand for scattering amplitudes in $ \mathcal{N} = 4 $ SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This…

From trees to loops and back

- Physics
- 2006

We argue that generic one-loop scattering amplitudes in supersymmetric Yang-Mills theories can be computed equivalently with MHV diagrams or with Feynman diagrams. We first present a general proof of…

New Representations of the Perturbative S Matrix.

- PhysicsPhysical review letters
- 2016

A new framework to represent the perturbative S matrix is proposed, constructed from tree-level amplitudes and integrable term by term, derived from the Feynman expansion through a series of partial fraction identities, discarding terms that vanish upon integration.

On-shell diagrammatics and the perturbative structure of planar gauge theories

- Mathematics
- 2015

We discuss the on-shell diagrammatic representation of theories less special than maximally supersymmetric Yang-Mills. In particular, we focus on planar $\mathcal{N}\,\le\,2$ gauge theories,…

One-loop corrections from higher dimensional tree amplitudes

- Mathematics
- 2015

A bstractWe show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level…