Simplicity in the Structure of QED and Gravity Amplitudes

Simon Badger (1) , N. E. J. Bjerrum-Bohr (2) , P. Vanhove (3, 4)

1 DESY - Deutsches Elektronen-Synchrotron [Zeuthen]
2 IAS - Institute of Advanced Studies
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681
4 IHES - Institut des Hautes Études Scientifiques

We investigate generic properties of one-loop amplitudes in unordered gauge theories in four dimensions. For such theories the organisation of amplitudes in manifestly crossing symmetric expressions poses restrictions on their structure and results in remarkable cancellations. We show that one-loop multi-photon amplitudes in QED with at least eight external photons are given only by scalar box integral functions. This QED `no-triangle' property is true for all helicity configurations and has similarities to the `no-triangle' property found in the case of maximal N = 8 supergravity. Results are derived both via a world-line formalism as well as using on-shell unitarity methods. We show that the simple structure of the loop amplitude originates from the extremely good BCFW scaling behaviour of the QED tree-amplitude.

Domaines: Physique des Hautes Energies - Phénoménologie [hep-ph]; Physique des Hautes Energies - Théorie [hep-th]

Simon Badger, N. E. J. Bjerrum-Bohr, P. Vanhove. Simplicity in the Structure of QED and Gravity Amplitudes. 2008. ⟨hal-00340801⟩