Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit

In the high-energy limit, we compute the gauge-invariant three-parton forwa rd clusters, which in the BFKL theory constitute the tree parts of the NNLO impact factors. In the triple collinear limit, we obtain the polarized dou ble-splitting functions. For the unpolarized and the spin-correlated double -splitting functions, our results agree with the ones obtained by Campbell- Glover and Catani-Grazzini, respectively. In addition, we compute the four- gluon forward cluster, which in the BFKL theory forms the tree part of the NNNLO gluonic impact factor. In the quadruple collinear limit we obtain the unpolarized triple-splitting functions, while in the limit of a three-part on central cluster we derive the Lipatov vertex for the production of three gluons, relevant for the calculation of a BFKL ladder at NNLL accuracy. Fi nally, motivated by the reorganization of the color in the high-energy limi t, we introduce a color decomposition of the purely gluonic tree amplitudes in terms of the linearly independent subamplitudes only. (C) 2000 Elsevier Science B.V. All rights reserved.