Inequalities on heavy quark-antiquark systems

We obtain inequalities and estimates on the radii and kinetic energies of heavy quark-antiquark systems in the framework of non-relativistic quantum mechanics. We also establish theorems on the mass dependence of the kinetic energy. These are used to derive bounds on the mass difference between the c quark and the b quark from experimental data on the J/ψ and Y systems. We also obtain tight upper and lower bounds on the masses of mixed flavour systems, on the mass of the toponium as a function of the t mass, and on the energy gap between a hidden flavour mass and the threshold for flavour pair production.