On the low-energy limit of one-loop photon–graviton amplitudes

F Bastianelli,O Corradini,J.M Dávila,C Schubert

doi:10.1016/j.physletb.2012.08.030

Abstract

We present first results of a systematic study of the structure of the low-energy limit of the one-loop photon–graviton amplitudes induced by massive scalars and spinors. Our main objective is the search of KLT-type relations where effectively two photons merge into a graviton. We find such a relation at the graviton–photon–photon level. We also derive the diffeomorphism Ward identity for the 1PI one-graviton–N-photon amplitudes.

Highlights

Graviton amplitudes are presently not of phenomenological relevance, their structure has been studied in parallel with the more important Yang-Mills amplitudes
We have shown here that, in the low energy limit, the one-loop gravitonphoton-photon amplitudes in Einstein-Maxwell theory coupled to scalars or spinors relate to a coincidence limit of the QED four photon amplitudes
This provides a new example of a KLT-like factorization in field theory at the loop level, and agrees with an identity found in [21] at the tree level in superstring theory

Summary

Introduction

Graviton amplitudes are presently not of phenomenological relevance, their structure has been studied in parallel with the more important Yang-Mills amplitudes. We will present first results of a systematic study of the structure of the mixed photon-graviton amplitudes with a massive loop in the low energy limit, and of the search for KLT-like relations for such amplitudes. In [45] the EHL (1.1) and its scalar analogue were generalized to the effective actions corresponding to the low energy one graviton - N photon amplitudes Those were obtained in [45] in terms of two-parameter integrals (a similar result was found in [46]). We will use the above effective actions at the RF 2 level to compute the low energy limits of the one graviton - two photon amplitudes with a scalar and spinor loop, and show that they relate to the four photon amplitudes in a KLT - like way. As a preparation for the study of the higher-point cases we will derive the Ward identities for the one graviton - N photon 1PI amplitudes in general

Ward identities for the 1PI one graviton – N photon amplitudes

The graviton-photon-photon amplitude

Conclusions