Fragmentation in Jets: Cone and Threshold Effects

We study the fragmentation of (light) quarks and gluons to hadrons inside a jet of cone size R. This allows for a more exclusive analysis of fragmentation than is currently the case. The shape of semi-inclusive cross sections in the hadron energy fraction z is described by fragmenting jet functions (FJFs), which we calculate in terms of R and the jet energy E. We introduce a new joint resummation to sum the double logarithms of R and 1-z in the FJFs, which may similarly be applied to initial-state radiation at hadron colliders. Our results at next-to-leading logarithmic order indicate that the resummation of the threshold logarithms of 1-z is already important for z > 0.5 and improves the convergence of perturbation theory. Our framework may be used to analyze LHC and RHIC data and to test and tune Monte Carlo event generators.