$e^{+}{e}^{-}$ angularity distributions at NNLL${}^{\prime }$ accuracy

Abstract

We present predictions for the $e^{+}{e}^{-}$ event shape angularities at NNLL${}^{\prime }$ resummed and $\mathcal{O}({\alpha }_s^2)$ matched accuracy and compare them to LEP data at center-of-mass energies $Q=91.2$ GeV and $Q=197$ GeV. We perform the resummation within the framework of Soft-Collinear Effective Theory, and make use of recent results for the two-loop angularity soft function. We determine the remaining NNLL${}^{\prime }$ and $\mathcal{O}({\alpha }_s^2)$ ingredients from a fit to the EVENT2 generator, and implement a shape function with a renormalon-free gap parameter to model non-perturbative effects. Using values of the strong coupling ${\alpha }_s(m_Z)$ and the universal non-perturbative shift parameter ${\Omega }_1$ that are consistent with those obtained in previous fits to the thrust and $C$-parameter distributions, we find excellent agreement between our predictions and the LEP data for all angularities with $a\in [-1,0.5]$. This provides a robust test of the predictions of QCD, factorization, and the universal scaling of the non-perturbative shift across different angularities. Promisingly, our results indicate that current degeneracies in the $\{{\alpha }_s(m_Z),{\Omega }_1\}$ parameter space could be be alleviated upon fitting these parameters to experimental data for the angularity distributions.

51 pages + appendices, 18 figures. v2: minor clarifications and corrections, references updated. v3: version published in JHEP

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