We compute the complete set of Feynman Rules producing the Rational Terms of kind R 2 needed to perform any QCD 1-loop calculation. We also explicitly check that in order to account for the entire R 2 contribution, even in case of processes with more than four external legs, only up to four-point vertices are needed. Our results are expressed both in the 't Hooft Veltman regularization scheme and in the Four Dimensional Helicity scheme, using explicit color configurations as well as the color connection language.
The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators, which compensates for the absence of the multiple-cut contributions that appear in the Feynman tree theorem. We rederive the duality theorem at one-loop order in a form that is more suitable for its iterative extension to higher-loop orders. We explicitly show its application to two-and three-loop scalar master integrals, and we discuss the structure of the occurring cuts and the ensuing results in detail.
A computational algorithm based on recursive equations is developed in order
to estimate multigluon production processes at high energy hadron colliders.
The partonic reactions gg->(n-2)g with n up to n=9 are studied and comparisons
with known approximations are presented.Comment: 12 pages, LaTe
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