DOUBLE UNRESOLVED APPROXIMATIONS TO MULTIPARTON SCATTERING-AMPLITUDES

We present approximations to tree-level multiparton scattering amplitu des which are appropriate when two partons are unresolved. These appro ximations are required for the analytic isolation of infrared singular ities of n + 2 parton scattering processes contributing to the next-to -next-to-leading order corrections to n jet cross sections. In each ca se the colour ordered matrix elements factorise and yield a function c ontaining the singular factors multiplying the n-parton amplitudes. Wh en the unresolved particles are colour unconnected, the approximations are simple products of the familiar eikonal and Altarelli-Parisi spli tting functions used to describe single unresolved emission. However, when the unresolved particles are colour connected the factorisation i s more complicated and we introduce new and general functions to descr ibe the triple collinear and soft/collinear limits in addition to the known double soft gluon limits of Berends and Giele. As expected the t riple collinear splitting functions obey an N = 1 SUSY identity. To il lustrate the use of these double unresolved approximations, we have ex amined the singular limits of the tree-level matrix elements for e(+)e (-) --> 5 partons when only three partons are resolved. When integrate d over the unresolved regions of phase space, these expressions will b e of use in evaluating the O(alpha(s)(3)) corrections to the three-jet rate in electron-positron annihilation. (C) 1998 Elsevier Science B.V .