Three-gluon running coupling from lattice QCD at $N_f=2+1+1$: a consistency check of the OPE approach

We present a lattice calculation of the renormalized running coupling constant in symmetric (MOM) and asymmetric ($\widetilde{\mathrm{M}\mathrm{O}\mathrm{M}}$) momentum substraction schemes including $u$, $d$, $s$ and $c$ quarks in the sea. An Operator Product Expansion dominated by the dimension-two $⟨A^2⟩$ condensate is used to fit the running of the coupling. We argue that the agreement in the predicted $⟨A^2⟩$ condensate for both schemes is a strong support for the validity of the OPE approach and the effect of this non-gauge invariant condensate over the running of the strong coupling.