Non-perturbative renormalization by decoupling

Abstract

We propose a new strategy for the determination of the QCD coupling. It relies on a coupling computed in QCD with $N_{\mathrm{f}}\ge 3$ degenerate heavy quarks at a low energy scale $\hat{I}{¼}_{\mathrm{dec}}$, together with a non-perturbative determination of the ratio $\hat{I}›/\hat{I}{¼}_{\mathrm{dec}}$ in the pure gauge theory. We explore this idea using a finite volume renormalization scheme for the case of $N_{\mathrm{f}}=3$ QCD, demonstrating that a precise value of the strong coupling $\hat{I}{\pm }_s$ can be obtained. The idea is quite general and can be applied to solve other renormalization problems, using finite or infinite volume intermediate renormalization schemes.

LaTeX, 6 pages, 2 figures