n-point amplitudes with a single negative-helicity graviton

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.

Two-loopn-point all-plus helicity amplitude

“…While this has proved possible for some amplitudes [19][20][21][22], we have not yet been able to obtain the rational part of the n-point amplitude in closed form.…”

Color dressed unitarity and recursion for Yang-Mills two-loop all-plus amplitudes

“…4 using an axial gauge formalism, we can determine the full pole structure of the rational piece, including the nonfactorising simple poles. We have used this approach previously to compute one-loop [31][32][33] and two-loop amplitudes [6][7][8], we labelled this process augmented recursion. In axial gauge formalism helicity labels can be assigned to internal off-shell legs and vertices expressed in terms of nullified momenta [34,35], where q is a reference momentum.…”

Two-loop five-point all-plus helicity Yang-Mills amplitude

“…The existence of double poles means we must determine the sub-leading contributions which are not captured by the naive factorisation. These pole under the pole contributions have been determined for a number of one-loop amplitudes using augmented recursion [26][27][28][29]. The contribution from this channel can be computed using axial gauge techniques [30][31][32] by considering diagrams of the form shown in fig.…”