Large logarithm behavior of $e^+ e^-$ jet cross-sections and event shape distributions in $\mathcal O (\alpha_s^2)$

Abstract

We have calculated the leading and next-to-leading logarithm coefficients of $\mathcal O(\alpha_s^2)$ $e^+e^-$ annihilation jet cross sections, thrust distribution and energy-energy correlation in the two-jet limit when the jet resolution and the event shape variables vanish. We have compared our results with expectations based on leading logarithm approximations used to resum the pertubative cross sections where this is possible. There is good agreement for the leading and next-to-leading coefficients of jet cross sections in the Durham scheme. Also for the thrust distribution and energy-energy correlation we find results which are consistent with the leading logarithm predictions