Infrared structure of e⁺e⁻ → 3 jets at NNLO

We describe the calculation of the next-to-next-to-leading order (NNLO) QCD corrections to three-jet production and related event shape observables in electron-positron annihilation. Infrared singularities due to double real radiation at tree level and single real radiation at one loop are subtracted from the full QCD matrix elements using antenna functions, which are then integrated analytically and added to the two loop contribution. Using this antenna subtraction method, we obtain numerically finite contributions from five-parton and four-parton processes, and observe an explicit analytic cancellation of infrared poles in the four-parton and three-parton contributions. All contributions are implemented in a flexible parton-level event generator programme, allowing the numerical computation of any infrared-safe observable related to three-jet final states to NNLO accuracy.