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Preliminary Calculation of $α_s$ from Green Functions with Dynamical Quarks

We present preliminary results on the computation of the QCD running coupling constant in the $\widetilde{MOM}$ scheme and Landau gauge with two flavours of dynamical Wilson quarks. Gluon momenta range up to about 7 GeV ($β=$ 5.6, 5.8 and 6.0) with a constant dynamical-quark mass. This range already allows to exhibit some evidence for a sizable $1/μ^2$ correction to the asymptotic behaviour, as in the quenched approximation, although a fit without power corrections is still possible with a reasonable $χ^2$. Following the conclusions of our quenched study, we take into account $1/μ^2$ correction to the asymptotic behaviour. We find $Λ_{\rm \bar{MS}}^{N_f=2} = 264(27) {\rm MeV} \times [{a^{-1}(5.6,0.1560)}/{2.19 {\rm GeV}}] $, which leads to $α_s(M_Z) = 0.113(3)(4)$. The latter result has to be taken as a preliminary indication rather than a real prediction in view of the systematic errors still to be controlled. Still, being two sigmas below the experimental result makes it very encouraging.