The quark jet function for k T -like variables in NNLO QCD

The precise description of jet processes requires observables capable of efficiently capturing the dynamics of the energy flow in hadronic final states. We consider a class of transverse-momentum like resolution variables that smoothly describe the $n+1$ to n jet transition in multi-jet processes. We discuss a general method for the computation of the corresponding quark jet function at next-to-next-to-leading order in perturbative QCD. Rapidity divergences are regulated by using a time-like auxiliary vector. We present explicit results for a variant of $y_{23}$ in the E-scheme and in the WTA scheme.