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

A. Bode·H. Panagopoulos
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Abstract

We calculate, to 3 loops in perturbation theory, the bare $β$-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 $Λ$-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.

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A. Bode, H. Panagopoulos. 2001-10-29. The three-loop beta-fuction of QCD with the clover action. https://doi.org/10.1016/s0550-3213(02)00012-3

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