The Two-Loop QCD Matrix Element for $e^+e^- \to 3$ Jets

Details The Two-Loop QCD Matrix Element for $e^+e^- \to 3$ Jets The Two-Loop QCD Matrix Element for $e^+e^- \to 3$ Jets

2001-12-05

arxiv.org/abs/hep-ph/0112081v1

Nucl.Phys.B627:107-188,2002

Physics

High Energy Physics

High Energy Physics - Phenomenology

52 pages, LaTeX

Scientific paper

10.1016/S0550-3213(02)00057-3

We compute the ${\cal O}(\alpha_s^3)$ virtual QCD corrections to the $\gamma^*\to q\bar q g$ matrix element arising from the interference of the two-loop with the tree-level amplitude and from the self-interference of the one-loop amplitude. The calculation is performed by reducing all loop integrals appearing in the two-loop amplitude to a small set of known master integrals. Infrared and ultraviolet divergences are both regularized using conventional dimensional regularization, and the ultraviolet renormalization is performed in the $\bar{MS}$ scheme. The infrared pole structure of the matrix elements agrees with the prediction made by Catani using an infrared factorization formula. The analytic result for the finite terms of both matrix elements is expressed in terms of one- and two-dimensional harmonic polylogarithms.

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