UC Berkeley

Collinear fields in soft collinear effective theory (SCET) can be made invariant under collinear gauge transformations by multiplying them with collinear Wilson lines. We discuss how we can quantize SCET directly in terms of these gauge invariant fields, allowing to directly calculate S matrix elements using the gauge invariant collinear fields. We also show how for each collinear direction SCET can be written in terms of fields whose interactions are given by the usual QCD Lagrangian, and how external operators coupling these different directions can be constructed.

Using SCET, which provides a unified framework for factorization, resummation of logarithms, and incorporation of universal nonperturbative functions in hard-scattering QCD cross-sections, we present a new prediction of angularity distributions in e⁺e^- annihilation. Angularities τ_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. We calculate angularity distributions for all a<1 to first order in the strong coupling α_s and resum large logarithms in these distributions to next-to-leading logarithmic (NLL) accuracy. Our expressions for the next-to-leading order (NLO) O(α_s) partonic jet and soft functions in the factorization theorem for angularity distributions are given for the first time. We employ a model for the nonperturbative soft function with a gap parameter which cancels the renormalon ambiguity in the partonic soft function. We explore the relation between the SCET approach to resummation and past approaches in QCD, and discuss the advantages of the effective theory approach. In addition, we draw from the NLO calculations of the jet and soft functions an intuitive lesson about how factorization breaks down in the effective theory as a → 1.

A matching calculation for SCET is performed using exotic external states, which mimic the topology of Drell-Yan amplitude. It is found that for the consistency of effective theory, more specifically for the fact that the matching coefficient C₂ is independent of external states involved in the matching, a new mode needs to be added to SCET, which is the Glauber mode. Connections with Coleman-Norton theorem and Landau equations are discussed.