Resummation and NLO matching of event shapes with effective field theory
Matthew D. Schwartz

\vspace{0.2cm} 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 calculated in perturbative QCD. Matching procedures to account for finite corrections at $T &lt 1$ in the two theories are then described. There are two important differences between the SCET and QCD approaches. 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.

© 2008 The American Physical Society.