Charm sea effects on charmonium decay constants and heavy meson masses

Salvatore Calì; Kevin Eckert; Jochen Heitger; Francesco Knechtli; Tomasz Korzec

doi:10.1140/epjc/s10052-021-09520-y

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 733
https://doi.org/10.1140/epjc/s10052-021-09520-y

Regular Article - Theoretical Physics

ALPHA Collaboration

Salvatore Calì¹^,2^a, Kevin Eckert³, Jochen Heitger³, Francesco Knechtli⁴ and Tomasz Korzec⁴

¹ Center for Theoretical Physics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA
² Institute of Theoretical Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348, Kraków, Poland
³ Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 9, 48149, Münster, Germany
⁴ Department of Physics, Bergische Universität Wuppertal, Gaußstr. 20, 42119, Wuppertal, Germany

^a calis@mit.edu

Received: 18 June 2021
Accepted: 1 August 2021
Published online: 14 August 2021

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 $N_{f} = 2 + 1$ ${N_\mathrm{f}}=2+1$ lattice QCD simulations provide results that can be compared with experiments or whether $N_{f} = 2 + 1 + 1$ ${N_\mathrm{f}}=2+1+1$ QCD including the charm quark in the sea needs to be simulated. We consider two theories, $N_{f} = 0$ ${N_\mathrm{f}}=0$ QCD and QCD with $N_{f} = 2$ ${N_\mathrm{f}}=2$ 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 $N_{f} = 2$ ${N_\mathrm{f}}=2$ 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 1‰ in the ratio of vector to pseudoscalar masses.

© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.