Lattice calculation of $1\mathrm{/}{p}^2$ corrections to ${\alpha }_s$ and of ${\mathrm{\Lambda }}_{\mathrm{Q}\mathrm{C}\mathrm{D}}$ in the $\widetilde{MOM}$ scheme

We report on very strong evidence of the occurrence of power terms in $\text{as}(p)$, the QCD running coupling constant in the $\widetilde{MOM}$ scheme, by analyzing non-perturbative measurements from the lattice three-gluon vertex between 2.0 and 10.0 GeV at zero flavor. While putting forward the caveat that this definition of the coupling is a gauge dependent one, the general relevance of such an occurrence is discussed. We fit $\Lambda_{\bar{\rm MS}}^{(n_f=0)}= 237 \pm 3 ^{+ 0}{-10}$ MeV in perfect agreement with the result obtained by the ALPHA group with a totally different method. The power correction to $\text{as}(p)$ is fitted to $(0.63\pm 0.03 ^{+ 0.0}{- 0.13}) {\rm GeV}^2/p^2$.