Fragmentation to a jet in the large z limit

We consider the fragmentation of a parton into a jet with small radius R in the large z limit, where z is the ratio of the jet energy to the mother parton energy. In this region of phase space, large logarithms of both R and 1-z can appear, requiring resummation in order to have a well-defined perturbative expansion. Using the soft-collinear effective theory, we study the fragmentation function to a jet in this end-point region. We derive a factorization theorem for this object, separating collinear and collinear-soft modes. This allows for the resummation using renormalization group evolution of the logarithms lnR and ln(1-z) simultaneously. We show results valid to next-to-leading logarithmic order for the global Sudakov logarithms. We also discuss the possibility of nonglobal logarithms that should appear at two loops and give an estimate of their size.