Effects of the disconnected flavor singlet corrections on the hyperfine splitting in charmonium

TL;DR

This paper investigates the impact of disconnected flavor singlet diagrams on the hyperfine splitting in charmonium, aiming to reconcile lattice results with experimental measurements by calculating these corrections on fine lattice configurations.

Contribution

It provides preliminary lattice QCD calculations of disconnected flavor singlet corrections to charmonium hyperfine splitting, a factor previously estimated roughly.

Findings

Disconnected flavor singlet corrections are significant for hyperfine splitting.

Results suggest corrections could account for the discrepancy between lattice and experimental values.

Preliminary results on fine lattices show potential for more accurate determinations.

Abstract

Experimentally the charmonium hyperfine splitting is $M_{J/\psi}-M_{\eta_c}=117$ MeV and current lattice results are generally below this value. The difference could be due to the effects of the disconnected flavor singlet diagrams which have not been included in these calculations. Previous attempts to determine the disconnected flavor singlet corrections have led just to rough estimates in the range of $\pm 20$ MeV. We present preliminary results for these corrections calculated on fine ($a\approx 0.09$ fm) Asqtad 2+1 flavor lattices provided by the MILC Collaboration.