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.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)