The 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 N${}^3$LL${}^{\mathrm{\prime }}$. 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/slicing method at N${}^3$LO, which eventually may enable the calculation of fully-differential cross sections with a colorful final state at this order.