Fine structure of the P states in heavy quarkonium and the nature of the spin-dependent potential

The failure of existing theories to agree with the experimental measurements of the fine structure of the Χ states of the bb-bar and cc-bar systems is discussed. Various possible explanations, such as mixing of the 2P triplet with the 1F triplet are ruled out. The fact is used that the spin-independent potential is well-determined in the relevant range to extract accurate determinations of expectation values of the spin-dependent potentials, providing tests for future theories. It is found that the usual ansatz that the qq-bar interaction has effective vector and scalar contributions only is very unlikely to be sufficient to explain the fine structure of the 3P levels and to accommodate the recent measurement of the mass of the 1P state in charmonium. (author) 22 refs.; 3 figs.; 3 tabs