Jet shapes and jet algorithms in SCET

Jet shapes are weighted sums over the four-momenta of the constituents of a and reveal details of its internal structure, potentially allowing discrimination of its partonic. In this work we make predictions for quark and gluon jet shape distributions N-jet final states in e(+)e(-) collisions, de fined with a cone or recombination algorithm, we measure some jet shape observable on a subset of these jets. Using the framework Soft-Collinear Effective Theory, we prove a factorization theorem for jet shape distriand demonstrate the consistent renormalization-group running of the functions in factorization theorem for any number of measured and unmeasured jets, any number quark and gluon jets, and any angular size R of the jets, as long as R is much smaller the angular separation between jets. We calculate the jet and soft functions for angujet shapes T-a to one-loop order (O(alpha(s))) and resum a subset of the large logarithms of needed for next-to-leading logarithmic (NLL) accuracy for both cone and k(T)-type jets. We compare our predictions for the resummed T-a jet final state in e(+)e(-) annihilation to the output of a Monte Carlo event generator and find that the dependence on a R is very similar.