Where are the 1 1P1 states in heavy quarkonia?

It is shown that for heavy quark-antiquark systems described by the generalized Fermi-Breit hamiltonian with a static nonrelativistic potential satisfying only a concavity condition derived from lattice QCD, a fit of the triplet 1 3Pj states implies tight bounds for the singlet P state. In particular, the candidate for υ(1 1P1) proposed by the CLEO Collaboration some years ago can be excluded on the basis of these inequalities. If, in addition, the vector exchange potential satisfies the condition of asymptotic freedom, then the singlet state must be very close to the centre of gravity of the triplet state. (orig.)