Two-Loop N=4 Supersymmetric Amplitudes and QCD

Two-loop four-gluonN = 4 susy amplitudes are evaluated via cutting techniques as a testing ground for QCD. A conjecture for four-point amplitudes to all loop orders is described. We also present a new conjecture for the leadingcolor part of the two-loop five-gluon amplitudes. INTRODUCTION Over the years there have been a number of rather impressive Feynman diagram calculations at two and higher loops. (For one recent example see ref. [1]). However, a number of important computations remain to be performed. Two examples of computations which are required for analysis of experiments but have not been carried out are two-loop contributions to e e → 3 jets and to Altarelli-Parisi splitting functions. More generally, no computations have appeared at two and higher loops which involve more than a single kinemtic variable. In contrast, at one-loop, recent years have seen improvements in the calculational techniques for scattering amplitudes [2]. In this talk we discuss initial steps taken to apply some of these techniques to twoand higher-loop amplitudes. In particular, we apply the recent developments in cutting techniques for obtaining complete amplitudes with no ambiguities or subtractions. These cutting techniques have been used for obtaining infinite sequences of one-loop supersymmetric amplitudes [3] and for the calculations performed in refs. [4] of the one-loop helicity amplitudes for e e → 4 jets and deeply inelastic scattering in association with three jets. Other approaches for efficiently calculating higher-loop amplitudes taken by various authors include string theory [5], first quantized [6] and recursive [7] approaches. (Further references are contained in ref. [2].) 1) This work was supported by the DOE under contract DE-FG03-91ER40662 and by the Alfred P. Sloan Foundation under grant BR-3222. 2) Presenter at 5th International Workshop on Deep Inelastic Scattering and QCD, April, 1997 c © 1995 American Institute of Physics 1