The rational parts of one-loop QCD amplitudes III: The six-gluon case

Abstract

The rational parts of 6-gluon one-loop amplitudes with scalars circulating in the loop are computed by using the newly developed method for computing the rational parts directly from Feynman integrals. We present the analytic results for the two MHV helicity configurations: (1 − 2 + 3 + 4 − 5 + 6 + ) and (1 − 2 + 3 − 4 + 5 + 6 + ), and the two NMHV helicity configurations: (1 − 2 − 3 + 4 − 5 + 6 + ) and (1 − 2 + 3 − 4 + 5 − 6 + ). Combined with the previously computed results for the cut-constructible part, our results are the last missing pieces for the complete partial helicity amplitudes of the 6-gluon one-loop QCD amplitude. *

The rational parts of one-loop QCD amplitudes I: The general formalism

“…These results are all the ingredients for computing up to the 6-gluon one-loop amplitudes in QCD. We will compute the (rational parts of the) 5-gluon and 6-gluon amplitudes in [68] and [69] respectively. By using the recursive relations it is straightforward to derive the rational terms of the 3-mass and 4-mass (tensor) box integrals.…”

“…To make more effective use of this trick, we have purposely chosen the reference momenta to make the tensor reduction simple. See [69] for further details about the specific choices of the reference momenta and the tensor reductions involved in the computation of (the rational parts of) the 6-gluon amplitudes.…”

“…Luckily we are able to avoid using them directly for tensor reduction with 5-and 6-point diagrams by a judicious choice of reference momenta for all the polarization vectors. The details will be given in [69]. For two-mass-hard box integrals, we must use the above general tensor reduction in order to obtain comparatively compact analytic expressions.…”

“…In [69], we will present the results for the rational parts of the 6-gluon amplitudes for the two MHV and two NMHV helicity configurations. The rational parts of the 6-gluon amplitudes for the "split helicity" configurations are known already [34,17].…”

“…Recently all one-loop maximally helicity violating gluonic amplitudes were computed by Berger, Bern, Dixon, Forde and Kosower [70]. We refer the reader to [70,69] for details about the explicit analytic results and comparisons. This paper is organized as follows: in Sect.…”