$e^+ e^-$ 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.