A Precise Determination of $α_s$ from the C-parameter Distribution

We present a global fit for $α_s(m_Z)$, analyzing the available C-parameter data measured at center-of-mass energies between $Q=35$ and $207$ GeV. The experimental data is compared to a N$^3$LL$^\prime$ + $\mathcal{O}(α_s^3)$ + $Ω_1$ theoretical prediction (up to the missing 4-loop cusp anomalous dimension), which includes power corrections coming from a field theoretical nonperturbative soft function. The dominant hadronic parameter is its first moment $Ω_1$, which is defined in a scheme which eliminates the $\mathcal{O}(Λ_{\rm QCD})$ renormalon ambiguity. The resummation region plays a dominant role in the C-parameter spectrum, and in this region a fit for $α_s(m_Z)$ and $Ω_1$ is sufficient. We find $α_s(m_Z)=0.1123\pm 0.0015$ and $Ω_1=0.421\pm 0.063\,{\rm GeV}$ with $χ^2/\rm{dof}=0.988$ for $404$ bins of data. These results agree with the prediction of universality for $Ω_1$ between thrust and C-parameter within 1-$σ$.

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