# Power corrections from decoupling of the charm quark

## TL;DR

This study uses lattice simulations to analyze how the decoupling of the charm quark affects low-energy QCD, showing that power corrections are minimal and well-described by inverse square mass terms.

## Contribution

It provides the first lattice simulation evidence that charm quark decoupling introduces small, quantifiable power corrections consistent with effective theory predictions.

## Key findings

- Power corrections are very small at charm quark mass.
- Ratios of hadronic scales match pure gauge theory up to $M^{-2}$ corrections.
- Decoupling effects can be accurately described by inverse square mass terms.

## 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.