Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2003-11-21
Nucl.Phys.B682:265-288,2004
Physics
High Energy Physics
High Energy Physics - Phenomenology
19 pages, LaTeX
Scientific paper
10.1016/j.nuclphysb.2004.01.023
The inclusive four-particle phase space integral of any $1\to 4$ matrix element in massless QCD contains divergences due to the soft and collinear emission of up to two particles in the final state. We show that any term appearing in this phase space integral can be expressed as linear combination of only four master integrals. These four master integrals are all computed in dimensional regularisation up to their fourth order terms, relevant to next-to-next-to-leading order jet calculations, both in an analytic form and purely numerically. New analytical and numerical techniques are developed in this context. We introduce the tripole parametrisation of the four-parton phase space. Furthermore, we exploit unitarity relations between multi-parton phase space integrals and multi-loop integrals. For the numerical calculation, the iterated sector decomposition of loop integrals is extended to phase space integrals. The results in this paper lead to infrared subtraction terms needed for the double real radiation contributions to jet physics in $e^+e^-$ annihilation at the next-to-next-to-leading order.
Gehrmann Thomas
Heinrich Georg
Ridder Aude Gehrmann--De
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