Infrared Singularities of Scattering Amplitudes in Perturbative QCD

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of loops and legs. It is based on the conjecture that the anomalous-dimension matrix of $n$-jet operators in soft-collinear effective theory is fully determined by three functions of ${\alpha }_s$, which can be extracted from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all $1/{ϵ}^k$ poles for arbitrary $n$-parton scattering amplitudes, generalizing existing two-loop results.