The strong running coupling at $τ$ and $Z_0$ mass scales from lattice QCD

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 $\ams(m_τ^2)$ and $\ams(m_Z^2)$ in very good agreement with experimental results. Including a dynamical c quark makes safer the needed running of $\ams$.

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