Efficient Analytic Computation of Higher-order Qcd Amplitudes * 1. Total Quantum-number Management

We review techniques simplifying the analytic calculation of one-loop QCD amplitudes with many external legs, for use in next-to-leading-order corrections to multi-jet processes. Particularly useful are the constraints imposed by perturba-tive unitarity, collinear singularities and a supersymmetry-inspired organization of helicity amplitudes. Certain sequences of one-loop helicity amplitudes with an arbitrary number of external gluons have been obtained using these constraints. The calculation of one-loop QCD amplitudes with many external quarks and glu-ons is a bottleneck that must be navigated in order to obtain next-to-leading-order (NLO) corrections to multijet processes, for precision comparison with collider experiments. The full correction has a real (bremsstrahlung) part as well as a virtual part. Efficient techniques for computing the tree amplitudes entering the real part have been available for several years 2 ; however, significant numerical work is required to combine these parts into a finite answer. In this talk we ignore the numerical subtleties a , and focus on techniques for computing analytically the one-loop amplitudes entering the virtual part. a Such subtleties have recently been discussed for the energy-energy correlation in e + e − annihilation 1 .