Two-loop five-point massless QCD amplitudes within the integration-by-parts approach

Abstract

We solve the integration-by-parts (IBP) identities needed for the computation of any planar twoloop five-point massless amplitude in QCD. We also derive some new results for the most complicated non-planar topology with irreducible numerators of power as high as six. We do this by applying a new strategy for solving the IBP identities which scales better for problems with a large number of scales and/or master integrals. Our results are a proof of principle that the remaining non-planar contributions for all two-loop five-point massless QCD amplitudes can be computed in analytic form.

NNLO QCD corrections to three-photon production at the LHC

“…It cannot be currently derived since the required non-planar IBPs (topology B 2 from ref. [26]) are not yet known. The term M (f) is suppressed with respect to the leading color one by a single power 1/N c .…”

“…The non-planar contribution cannot be computed at present since the required IBP solutions (topologies B and C in the notation of ref. [26]) are not yet fully known.…”

“…The only ingredient for such calculations which is not readily available are the two-loop five-point amplitudes. Thanks to the development of various new methods [20][21][22][23][24][25][26][27][28][29][30][31][32][33], first results for selected helicities, color structures or kinematics (typically Euclidean) have started to appear. This includes 5-point amplitudes computed in QCD [34][35][36][37][38][39][40][41][42][43][44], in pure Yang-Mills [45][46][47], in supersymmetric theories [48][49][50][51] and in gravity [52][53][54].…”

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

“…The leading in color five-point amplitudes have been computed for the remaining helicities [9,10]. Full color amplitudes are significantly more complicated requiring a larger class of master integrals incorporating non-planar integrals [11,12]. In [13] the first full color five-point amplitude was presented in QCD.…”

n -point QCD two-loop amplitude

“…The leading in color five-point amplitudes have been computed for the remaining helicities [12,13]. Full color amplitudes are significantly more complicated requiring a larger class of master integrals incorporating non-planar integrals [14,15]. In [16] the first full color five-point amplitude was presented in QCD -for the case of all-plus helicities.…”