The three-loop beta-fuction of QCD with the clover action

TL;DR

This paper computes the three-loop perturbative beta-function of lattice QCD with the clover action, providing key relations between bare and renormalized couplings and the lattice Lambda parameter, crucial for scaling tests.

Contribution

It presents the first three-loop calculation of the lattice QCD beta-function with the clover action, including explicit dependence on parameters and relations to continuum schemes.

Findings

Three-loop beta-function explicitly calculated.

Two-loop relation between bare and MS-bar coupling derived.

Three-loop correction to Lambda-parameter relation found to be significant.

Abstract

We calculate, to 3 loops in perturbation theory, the bare $\beta$-function of QCD, formulated on the lattice with the clover fermionic action. The dependence of our result on the number of colors $N$, the number of fermionic flavors $N_f$, as well as the clover parameter $c_{SW}$, is shown explicitly. A direct outcome of our calculation is the two-loop relation between the bare coupling constant $g_0$ and the one renormalized in the MS-bar scheme. Further, we can immediately derive the three-loop correction to the relation between the lattice $\Lambda$-parameter and $g_0$, which is important in checks of asymptotic scaling. For typical values of $c_{SW}$, this correction is found to be very pronounced.