Charmonium andϒsystems with small hyperfine splittings

The parameters of the simple Coulomb plus linear effective potential with lowest-order relativistic corrections are determined by the charmonium states other than the ¹S₀ states and by the leptonic decay widths of Jψ and ψ^'. The effective coupling constant αₛ is found to be 0.21. Within this framework the hyperfine splittings are small and so are the consequent $M1$ transitions (well below the experimental upper limit of 1.2 keV). The ¹S₀ partners of ψ and ψ^' are predicted to be ηc(3020) and ηc^'(3638) and are not to be identified with the experimentally uncertain $X(2830)$ and χ(3450). The same effective potential, chainging only the constituent quark mass, gives a good description of the Υ system. The spin-independent relativistic corrections play an important role in obtaining the equality m_Υ^'-m_Υ≈m_ψ^'-m_ψ.