Non-perturbative tests of continuum HQET through small-volume two-flavour QCD

TL;DR

This study tests the validity of continuum Heavy Quark Effective Theory (HQET) by comparing lattice QCD results for heavy-light meson observables across a range of quark masses, including the static limit.

Contribution

It provides a non-perturbative verification of HQET's effectiveness in describing QCD for heavy quarks in a small-volume setting, extending previous perturbative analyses.

Findings

Good agreement between QCD and HQET predictions at the few-percent level.

Less convincing results for the pseudoscalar decay constant when perturbative matching is used.

Successful extrapolation to the infinite-mass limit from charm to beyond bottom quark masses.

Abstract

We study the heavy quark mass dependence of selected observables constructed from heavy-light meson correlation functions in small-volume two-flavour lattice QCD after taking the continuum limit. The light quark mass is tuned to zero, whereas the range of available heavy quark masses $m_h$ covers a region extending from around the charm to beyond the bottom quark mass scale. This allows entering the asymptotic mass-scaling regime as $1/m_h \to 0$ and performing well-controlled extrapolations to the infinite-mass limit. Our results are then compared to predictions obtained in the static limit of continuum Heavy Quark Effective Theory (HQET), in order to verify non-perturbatively that HQET is an effective theory of QCD. While in general we observe a nice agreement at the few-% level, we find it to be less convincing for the small-volume pseudoscalar decay constant when perturbative matching is involved.