\begin{document}$\hat\alpha(k^2)$\end{document}. Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, \begin{document}$m_0= 0.43(1)\;$\end{document}GeV, this coupling saturates at infrared momenta: \begin{document}$\hat\alpha(0)/\pi=0.97(4)$\end{document}. Amongst other things: \begin{document}$\hat\alpha(k^2)$\end{document} is almost identical to the process-dependent (PD) effective charge defined via the Bjorken sum rule; and also that PD charge which, employed in the one-loop evolution equations, delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment. The diversity of unifying roles played by \begin{document}$\hat\alpha(k^2)$\end{document} suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale; and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions."> Effective charge from lattice QCD -
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