Energy level inequalities in a “wrinkled” quarkonium potential

Abstract

The “concave” downward property of the standard static qq- potentials leads to the energy level inequalities En+2-En+1 < En+1-En in the quarkonium mass spectrum. However, this inequality is experimentally observed to be reversed for n=2 in charmonium and n=3 in bottomonium, a fact that is inexplicable in terms of any known concave downward potential. We attempt to explain this by allowing for the violation of the concavity condition in a small interval, i.e., a “wrinkle” in some recently proposed quarkonium potentials. © 1996 The American Physical Society.