Two-Jet Rate in $e^{+}{e}^{-}$ at Next-to-Next-to-Leading-Logarithmic Order

We present the first next-to-next-to-leading-logarithmic resummation for the two-jet rate in $e^{+}{e}^{-}$ annihilation in the Durham and Cambridge algorithms. The results are obtained by extending the ares method to observables involving any global, recursively infrared and collinear safe jet algorithm in $e^{+}{e}^{-}$ collisions. As opposed to other methods, this approach does not require a factorization theorem for the observables. We present predictions matched to next-to-next-to-leading order and a comparison to LEP data.

Figure 1

Differential distributions for the three-jet resolution in the Durham (left) and Cambridge (right) algorithms. The plots show both the $\mathrm{NLL}+\mathrm{NNLO}$ (blue, solid band) and the $\mathrm{NNLL}+\mathrm{NNLO}$ (red, hatched band) results.

Figure 2

Comparison of $\mathrm{NNLL}+\mathrm{NNLO}$ predictions for the two-jet rates to data from the L3 Collaboration [30].