Power corrections from decoupling of the charm quark

Abstract

Decoupling of heavy quarks at low energies can be described by means of an effective theory as shown by S. Weinberg in Ref. [1]. We study the decoupling of the charm quark by lattice simulations. We simulate a model, QCD with two degenerate charm quarks. In this case the leading order term in the effective theory is a pure gauge theory. The higher order terms are proportional to inverse powers of the charm quark mass $M$ starting at $M^{-2}$. Ratios of hadronic scales are equal to their value in the pure gauge theory up to power corrections. We show, by precise measurements of ratios of scales defined from the Wilson flow, that these corrections are very small and that they can be described by a term proportional to $M^{-2}$ down to masses in the region of the charm quark mass.

20 pages, 3 figures, 3 tables, v2: Introduction and Conclusions expanded, new fits added to Figure 2 and 3, References updated

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Cited by in corpus (11)

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• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Static force from generalized Wilson loops on the lattice using the gradient flow
• Charmonium and exotics from lattice QCD
• Precision Determination of ${\alpha }_s$ from Lattice QCD
• The determination of potential scales in 2+1 flavor QCD
• Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence
• Memory efficient finite volume schemes with twisted boundary conditions