Remarks on the determination of the Landau gauge OPE for the Asymmetric three gluon vertex

We compute a compact OPE formula describing power corrections to the perturbative expression for the asymmetric $\widetilde{MOM}$-renormalized running coupling constant up to the leading logarithm. By the use of the phenomelogical hypothesis leading to the factorization of the condensates through a perturbative vacuum insertion, the only relevant condensate in the game is $<A^2>$. The validity of the OPE formula is tested by searching for a good-quality coherent description of previous lattice evaluations of $\widetilde{MOM}$-renormalized gluon propagator and running coupling.