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

Understand

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.