New color decompositions for gauge amplitudes at tree and loop level

Recently, a color decomposition using structure constants was introduced fo r purely gluonic tree amplitudes, in a compact form involving only the line arly independent subamplitudes. We give two proofs that this decomposition holds for an arbitrary number of gluons, We also present and prove similar decompositions at one loop, both for purl gluon amplitudes and for amplitud es with an external quark-antiquark pair. (C) 2000 Elsevier Science B.V. Al l rights reserved.