Centre d'études et d'expertise sur les risques, l'environnement, la mobilité et l'aménagement

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For the case of n-jet production at next-to-next-to-leading order in the QCD coupling, in the infrared divergent corners of phase space where particles are collinear or soft, one must evaluate (n + 1)-parton final-state one-loop amplitudes through O(ǫ 2 ), where ǫ is the dimensional regularization parameter. For the case of gluons, we present to all orders in ǫ the required universal functions which describe the behavior of one-loop amplitudes in the soft and collinear regions of phase space. An explicit example is discussed for three-parton production in multi-Regge kinematics that has applications to the next-to-leading logarithmic corrections to the BFKL equation.

We present universal factorization formulas describing the behavior of one-loop QCD amplitudes as external momenta become either soft or collinear. Our results are valid to all orders in the dimensional regularization parameter, ǫ. Terms through O(ǫ 2 ) can contribute in infrared divergent phase space integrals associated with next-to-next-to-leading order jet cross-sections.