Resummation and NLO Matching of Event Shapes with Effective Field Theory

Abstract

The resummed differential thrust rate in \(e^+e^-\) annihilation is calculated using Soft-Collinear Effective Theory (SCET). The resulting distribution in the two-jet region \((T \sim 1)\) is found to agree with the corresponding expression derived by the standard approach. A matching procedure to account for finite corrections at \(T < 1\) is then described. There are two important advantages of the SCET approach. First, SCET manifests a dynamical seesaw scale \(q = p^2/Q\) in addition to the center-of-mass energy \(Q\) and the jet mass scale \(p \sim Q\sqrt{(1 - T)}\). Thus, the resummation of logs of \(p/q\) can be cleanly distinguished from the resummation of logs of \(Q/p\). Second, finite parts of loop amplitudes appear in specific places in the perturbative distribution: in the matching to the hard function, at the scale \(Q\), in matching to the jet function, at the scale p, and in matching to the soft function, at the scale \(q\). This allows for a consistent merger of fixed order corrections and resummation. In particular, the total NLO \(e^+e^-\) cross section is reproduced from these finite parts without having to perform additional infrared regulation.