Charm sea effects on charmonium decay constants and heavy meson masses

TL;DR

This study investigates the impact of charm quarks in the sea on charmonium decay constants and heavy meson masses using lattice QCD, finding effects below 1% and confirming charm decoupling up to 500 MeV.

Contribution

The paper provides a quantitative estimate of charm sea quark effects on meson properties, demonstrating that these effects are negligible below 1%, and clarifies the decoupling behavior of charm quarks in lattice QCD.

Findings

Charm sea effects are below 1% for charmonium decay constants.

Decoupling of charm quarks is effective up to about 500 MeV.

Sea effects on heavy meson mass ratios are approximately 0.1%.

Abstract

We estimate the effects on the decay constants of charmonium and on heavy meson masses due to the charm quark in the sea. Our goal is to understand whether for these quantities $N_f=2+1$ lattice QCD simulations provide results that can be compared with experiments or whether $N_f=2+1+1$ QCD including the charm quark in the sea needs to be simulated. We consider two theories, $N_f=0$ QCD and QCD with $N_f=2$ charm quarks in the sea. The charm sea effects (due to two charm quarks) are estimated comparing the results obtained in these two theories, after matching them and taking the continuum limit. The absence of light quarks allows us to simulate the $N_f=2$ theory at lattice spacings down to $0.023$ fm that are crucial for reliable continuum extrapolations. We find that sea charm quark effects are below $1\%$ for the decay constants of charmonium. Our results show that decoupling of charm works well up to energies of about $500$ MeV. We also compute the derivatives of the decay constants and meson masses with respect to the charm mass. For these quantities we again do not see a significant dynamical charm quark effect, albeit with a lower precision. For mesons made of a charm quark and a heavy antiquark, whose mass is twice that of the charm quark, sea effects are only about $0.1\%$ in the ratio of vector to pseudoscalar masses.