Factorization is the central ingredient in any theoretical prediction for collider experiments. I introduce a factorization formalism that can be applied to any desired observable, like event shapes or jet observables, for any number of jets and a wide range of jet algorithms in leptonic or hadronic collisions. This is achieved by using soft-collinear effective theory to prove the formal factorization of a generic fully-differential cross section in terms of a hard coefficient, and generic jet and soft functions. The factorization formula for any such observable immediately follows from our general result, including the precise definition of the functions appropriate for the observable in question.
As a first application, I present a new prediction of angularity distributions in e+e- annihilation. Angularities tau_a are an infinite class of event shapes which vary in their sensitivity to the substructure of jets in the final state, controlled by a continuous parameter a < 2. I calculate angularity distributions for all a < 1 to first order in the strong coupling alpha_s and resum large logarithms in these distributions to next-to-leading logarithmic (NLL) accuracy.
I then apply SCET to the more exclusive case of jet shapes. In particular, I make predic- tions for quark and gluon jet shape distributions in N-jet final states in e+e- collisions, defined with a cone or recombination algorithm, where I measure some jet shape observable on a subset of these jets. I demonstrate the consistent renormalization-group running of the functions in the factoriza- tion theorem for any number of measured and unmeasured jets, any number of quark and gluon jets, and any angular size R of the jets, as long as R is much smaller than the angular separation between jets. I calculate the jet and soft functions for angularity jet shapes tau_a to next-to-leading order (NLO) in alpha_s and resum large logarithms of tau_a to next-to-leading logarithmic (NLL) accuracy for both cone and kT -type jets.
Finally, I apply SCET to the case of threshold resummmation at hadron colliders. Factor- ization theorems for processes at hadron colliders near the hadronic endpoint have largely focused on simple final states with either no jets (e.g., Drell-Yan) or one inclusive jet (e.g., deep inelastic scattering and prompt photon production). Factorization for the former type of process gives rise to a soft function that depends on timelike momenta whereas the soft function for the latter type depends on null momenta. I derive a factorization theorem that allows for an arbitrary number of jets, where the jets are defined with respect to a jet algorithm, together with any number of non- strongly interacting particles. I find the soft function in general depends on the null components of the soft momenta inside the jets and on the timelike component of the soft momentum outside of the jets. This generalizes and interpolates between the soft functions for the cases of no jets and one inclusive jet.
