Λ Parameter of the SU(3) Yang-Mills Theory from the Continuous Β Function

Nonperturbative determinations of the renormalization group beta function are essential to connect lattice results to perturbative predictions of strongly coupled gauge theories and to determine the. parameter or the strong coupling constant. The continuous beta function is very well suited for this task because it is applicable both in the weakly coupled deconfined regime as well as the strongly coupled confined regime. Here we report on our results for the beta function of the pure gauge SU(3) Yang-Mills theory in the gradient flow scheme. Our calculations cover the renormalized coupling range g(GF)(2) similar to 1.2-27, allowing for a direct determination of root 8t(0)Lambda((MS) over bar) in this system. Our prediction, root 8t(0)Lambda((MS) over bar) = 0.622(10), is in good agreement with recent direct determinations of this quantity.