New Techniques for High Orders in Scattering Amplitudes - JOSEPH STRONG (2022)
This thesis uses four-dimensional unitarity and augmented recursion to calculate a selection of Yang-Mills amplitudes. This selection consists of the full-colour, two-loop, all-plus helicity amplitudes for ﬁve- and six-points; a conjecture for an n-point sub-subleading in colour two-loop amplitude; calculation of the cut-constructible piece of the full-colour, two-loop, all-plus helicity n-point amplitude. A new technique for calculating the cut constructible part of the leading in colour two-loop, ﬁve-point, single-minus helicity amplitude is presented. The correct infrared divergent piece of this single-minus amplitude was calculated, as well as the correct transcendental two pieces at ﬁnite order. Logarithms containing Mandelstam variables including only positive helicity legs were unable to be correctly calculated, but the calculation of this ﬁnal amplitude uncovered many new relations involving generalised hypergeometric functions such as the Appell functions.