Jets in effective theory: Summing phase space logs

Abstract

We demonstrate how to resum phase space logarithms in the Sterman-Weinberg (SW) dijet decay rate within the context of soft collinear effective theory (SCET). An operator basis corresponding to two and three jet events is defined in SCET and renormalized. We obtain the renormalization group equation of the two and three jet operators and run the operators from the scale ${\ensuremath{\mu}}^{2}={Q}^{2}$ to the phase space scale ${\ensuremath{\mu}}_{\ensuremath{\delta}}^{2}={\ensuremath{\delta}}^{2}{Q}^{2}$. This phase space scale, where $\ensuremath{\delta}$ is the cone half angle of the jet, defines the angular region of the jet. At ${\ensuremath{\mu}}_{\ensuremath{\delta}}^{2}$ we determine the mixing of the three and two jet operators. We combine these results with the running of the two jet shape function, which we run down to an energy cut scale ${\ensuremath{\mu}}_{\ensuremath{\beta}}^{2}$. This defines the resummed SW dijet decay rate in the context of SCET. The approach outlined here demonstrates how to establish a jet definition in the context of SCET. This allows a program of systematically improving the theoretical precision of jet phenomenology to be carried out.