The infrared behavior of one-loop gluon amplitudes at next-to-next-to-leading order

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(ϵ2), where ϵ is the dimensional regularization parameter. For the case of gluons, we present to all orders in ϵ 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.