Resummation and NLO matching of event shapes with effective field theory

Abstract

The resummed differential thrust rate in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation is calculated using soft-collinear effective theory (SCET). The resulting distribution in the two-jet region ($T\ensuremath{\sim}1)$ is found to agree with the corresponding expression derived by the standard approach. A matching procedure to account for finite corrections at $Tl1$ 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 $p\ensuremath{\sim}Q\sqrt{(1\ensuremath{-}T)}$. 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 ${e}^{+}{e}^{\ensuremath{-}}$ cross section is reproduced from these finite parts without having to perform additional infrared regulation.