The recent determination of the $\beta$--function of the QCD running coupling $\alpha_{ \overline{ MS}}(Q^2)$ to 5-loops{ \color{ blue},} provides a verification of the convergence of a novel method for determining the fundamental QCD parameter $\Lambda_s$ based on the Light-Front Holographic approach to nonperturbative QCD. The new 5-loop analysis, together with improvements in determining the holographic QCD nonperturbative scale parameter $\kappa$ from hadronic spectroscopy, leads to an improved precision of the value of $\Lambda_s$ in the ${ \overline{ MS}}$ scheme close to a factor of two; we find $\Lambda^{ (3)}_{ \overline{ MS}}=0.339\pm0.019$ GeV for $n_{ f}=3$, in excellent agreement with the world average, $\Lambda_{ \overline{ MS}}^{ (3)}=0.332\pm0.017$ GeV. We also discuss the constraints imposed on the scale dependence of the strong coupling in the nonperturbative domain by superconformal quantum mechanics and its holographic embedding in anti-de Sitter space.
Categories: hep-ph