A non-perturbative determination of $b_{\rm g}$

Author:

Mattia Dalla Brida, Roman Höllwieser, Francesco Knechtli, Tomasz Korzec, Alberto Ramos, Stefan Sint, Rainer Sommer

Keyword:

High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat)

journal:

date:

2024-01-11 00:00:00

Abstract

Close to the continuum limit, lattice QCD with mass-degenerate Wilson quarks can be described by Symanzik's effective continuum action, which contains the dimension 5 operator, $m\,{\rm tr}(F_{\mu\nu}F_{\mu\nu})$. Its effect can be eliminated by an O($am_{\rm q}$) rescaling of the bare lattice coupling constant. Until recently, the corresponding improvement coefficient, $b_{\rm g}$, was only known perturbatively to 1-loop order and an estimate of the remaining uncertainty is the dominant systematic error in the ALPHA collaboration's recent determination of $\alpha_s(m_Z)$ with the decoupling method. To remove this error we have determined $b_{\rm g}$ non-perturbatively for the corresponding parameter range. We here briefly review improvement conditions for $b_{\rm g}$, perform a perturbative test and report on our non-perturbative results for $b_{\rm g}$.

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