# How much do charm sea quarks affect the charmonium spectrum?

## TL;DR

This study assesses the influence of charm sea quarks on the charmonium spectrum and related properties using lattice QCD with two degenerate charm quarks, finding effects below 5% and emphasizing the need for fine lattice spacings.

## Contribution

It provides the first detailed lattice QCD analysis of charm sea quark effects on charmonium, including mass shifts and content, in a model with two degenerate charm quarks.

## Key findings

- Charm sea quarks affect hyperfine splitting below 2%.
- Charm quark mass is influenced by about 5%.
- Charm content of eta_c changes by approximately 3%.

## Abstract

The properties of charmonium states are or will be intensively studied by the B-factories Belle II and BESIII, the LHCb and PANDA experiments and at a future Super-c-tau Factory. Precise lattice calculations provide valuable input and several results have been obtained by simulating up, down and strange quarks in the sea. We investigate the impact of a charm quark in the sea on the charmonium spectrum, the renormalization group invariant charm-quark mass and the scalar charm-quark content of charmonium. The latter is obtained by the direct computation of the mass-derivatives of the charmonium masses. We do this investigation in a model, QCD with two degenerate charm quarks. The absence of light quarks allows us to reach very small lattice spacings down to 0.023 fm. By comparing to pure gauge theory we find that charm quarks in the sea affect the hyperfine splitting at a level below 2%. The most significant effects are 5% in the quark mass and 3% in the value of the charm quark content of the eta_c meson. Given that we simulate two charm quarks these estimates are upper bounds for the contribution of a single charm quark. We show that lattice spacings <0.06 fm are needed for safe continuum extrapolations of the charmonium spectrum with O(a) improved Wilson quarks. A useful relation for the projection to the desired parity of operators in two-point functions computed with twisted mass fermions is proven.