Disentangling observable dependence in SCETI and SCETII anomalous dimensions: angularities at two loops

The resummation of radiative corrections to collider jet observables using soft collinear effective theory is encoded in differential renormalization group equations (RGEs), with anomalous dimensions depending on the observable under consideration. This observable dependence arises from the ultraviolet (UV) singular structure of real phase space integrals in the effective field theory. We show that the observable dependence of anomalous dimensions in SCETI problems can be disentangled by introducing a suitable UV regulator in real radiation integrals. Resummation in the presence of the new regulator can be performed by solving a two-dimensional system of RGEs in the collinear and soft sectors, and resembles many features of resummation in SCETII theories by means of the rapidity renormalization group. We study the properties of SCETI with the additional regulator and explore the connection with the system of RGEs in SCETII theories, highlighting some universal patterns that can be exploited in perturbative calculations. As an application, we compute the two-loop soft and jet anomalous dimensions for a family of recoil-free angularities and give new analytic results. This allows us to study the relations between the SCETI and SCETII limits for these observables. We also discuss how the extra UV regulator can be exploited to calculate anomalous dimensions numerically, and the prospects for numerical resummation.

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