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

Abstract

We present a direct computation of the full color two-loop five-point all-plus Yang-Mills amplitude using four dimensional unitarity and recursion. We present the SU (N c ) amplitudes in compact analytic forms. Our results match the explicit expressions previously computed but do not require full two-loop integral methods.

Conformal invariance of the one-loop all-plus helicity scattering amplitudes

“…It is natural to expect the same to hold for the non-planar contributions. Indeed, in the recently computed full two-loop fivegluon all-plus amplitude [15,16], the polylogarithmic part contains the same conformally invariant rational factors which appear in our formula for the one-loop amplitude.…”

“…Although the reverse is not true, it is still very interesting that the remarkably compact expressions for the subleading-colour components presented in Ref. [16] were proven to be conformally invariant for arbitrary n in Ref. [30].…”

Full color two-loop six-gluon all-plus helicity amplitude

“…1 using an axial gauge formalism [29,30], 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 [11,15,16,23], we labelled this process augmented recursion. We then color-dress fig.…”

“…Augmented recursion was reviewed in [23] and shown to work for a full color amplitude. We will outline the steps here.…”

“…This process is detailed in [16] and applied to the full color case in [23]. The U(N c ) color decomposition of dΛ c contains a common kinematic factor so we have the color decompositions…”