Hyperfine splittings in the image system

Recent measurements of the image, the ground state of the image system, show the splitting between it and the image to be image, larger than lattice QCD and potential model predictions, including recent calculations published by us. The models seem unable to incorporate such a large hyperfine splitting within the context of a consistent description of the energy spectrum and decays. We investigate whether a perturbative treatment of our potential model (described below) can lead to such a consistent description, including the measured hyperfine splitting, by not softening the delta function terms in the hyperfine potential. With this modification, we calculate the 1S hyperfine splitting to be 67.5 MeV, with little effect on the overall fit of our model results. We also present predictions for the 2S and 3S hyperfine splittings.