Perturbative versus non-perturbative decoupling of heavy quarks

TL;DR

This paper investigates how heavy quarks decouple at low energies by comparing non-perturbative lattice simulation results with perturbative predictions for certain mass ratios.

Contribution

It provides the first detailed comparison between non-perturbative lattice results and perturbative predictions for heavy quark decoupling in a theory with two heavy quarks.

Findings

Ratios like t_0(M)/t_0(0) match perturbative predictions at large M

Decoupling behavior is consistent with effective theory expectations

Results validate the leading order factorization formula in 1/M

Abstract

We simulate a theory with $N_f=2$ heavy quarks of mass $M$. At energies much smaller than $M$ the heavy quarks decouple and the theory can be described by an effective theory which is a pure gauge theory to leading order in $1/M$. We present results for the mass dependence of ratios such as $t_0(M)/t_0(0)$. We compute these ratios from simulations and compare them to the perturbative prediction. The latter relies on a factorisation formula for the ratios which is valid to leading order in $1/M$.