$n$-point amplitudes with a single negative-helicity graviton

TL;DR

This work addresses the computation of $n$-point one-loop graviton amplitudes with a single negative helicity leg using augmented recursion to overcome non-factorising (double-pole) contributions. The authors shift the negative helicity leg and decompose the amplitude into factorising parts and a non-factorising piece $\Delta_n$, invoking gravity currents built from KLT relations to construct the required leading and sub-leading pole terms. They provide an explicit recursive construction for the all-$n$ single-minus amplitude, validated up to $n=8$ and made available in explicit Mathematica form, with careful treatment of soft limits. The study finds that loop corrections modify the sub-sub-leading soft behaviour, confirming anomalies in the loop-level soft theorem for gravity and illustrating the power and limitations of augmented recursion for non-supersymmetric one-loop amplitudes.

Abstract

We construct an expression for the n-point one-loop graviton scattering amplitude with a single negative helicity external leg using an augmented recursion technique. We analyse the soft-limits of these amplitudes and demonstrate that they have soft behaviour beyond the conjectured universal behaviour.

Figures (8)

• Figure 1: Diagrams with an explicit pole.
• Figure 2: Diagrams with a pole from loop integration.
• Figure 3: Double poles may arise from these diagrams.
• Figure 4: Factorisations of type A. $\{ R\} \cup \{ \bar{R}\}=\{c,\cdots,n\}$ and both contain at least two elements.
• Figure 5: Factorisation of type B.