A Precise Determination of ${\alpha }_s$ from the C-parameter Distribution

Abstract

We present a global fit for ${\alpha }_s(m_Z)$, 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${}^{\prime }$ + $\mathcal{O}({\alpha }_s^3)$ + ${\Omega }_1$ 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 ${\Omega }_1$, which is defined in a scheme which eliminates the $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ renormalon ambiguity. The resummation region plays a dominant role in the C-parameter spectrum, and in this region a fit for ${\alpha }_s(m_Z)$ and ${\Omega }_1$ is sufficient. We find ${\alpha }_s(m_Z)=0.1123\pm 0.0015$ and ${\Omega }_1=0.421\pm 0.063\mathrm{GeV}$ with ${\chi }^2/\mathrm{dof}=0.988$ for $404$ bins of data. These results agree with the prediction of universality for ${\Omega }_1$ between thrust and C-parameter within 1-$\sigma$.

Comments: 24 pages, 19 figures