Jet shapes and jet algorithms in SCET

Jet shapes are weighted sums over the four-momenta of the constituents of a jet and reveal details of its internal structure, potentially allowing discrimination of its partonic origin. In this work we make predictions for quark and gluon jet shape distributions in N-jet final states in e + e − collisions, defined with a cone or recombination algorithm, where we measure some jet shape observable on a subset of these jets. Using the framework of Soft-Collinear Effective Theory, we prove a factorization theorem for jet shape distributions and demonstrate the consistent renormalization-group running of the functions in the factorization 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. We calculate the jet and soft functions for angularity jet shapes τ α to one-loop order \( \left( {\mathcal{O}\left( {{\alpha_s}} \right)} \right) \) and resum a subset of the large logarithms of τ α needed for next-to-leading logarithmic (NLL) accuracy for both cone and kT-type jets. We compare our predictions for the resummed τ α distribution of a quark or a gluon jet produced in a 3-jet final state in e + e − annihilation to the output of a Monte Carlo event generator and find that the dependence on a and R is very similar.