Strong running coupling at $\tau$ and $Z_0$ mass scales from lattice QCD
Résumé
This letter reports on the first computation, from data obtained in lattice QCD with $u,d,s$ and $c$ quarks in the sea, of the running strong coupling via the ghost-gluon coupling renormalized in the MOM Taylor scheme. We provide with estimates of $\alpha_{\bar{\rm MS}}(m_\tau^2)$ and $\alpha_{\bar{\rm MS}}(m_Z^2)$ (for which the inclusion of the dynamical charm quark makes the running much safer) in very good agreement with experimental results.