Three-Loop Quark Jet Function.

We calculate the massless quark jet function to three-loop order. The quark jet function is a universal ingredient in SCET factorization for many collider and decay processes with quark initiated final state jets. Our three-loop result contributes to the resummation for observables probing the invariant mass of final state quark jets at primed next-to-next-to-next-to-leading-logarithmic accuracy. It represents the first complete three-loop result for a factorization ingredient describing collinear radiation. Furthermore it constitutes a major component of the N-jettiness subtraction method at next-to-next-to-next-to-leading order accuracy, which eventually may enable the calculation of fully differential cross sections with a colorful final state at this order.