Mass scaling inequalities for quarkonium energy levels

Abstract

Inequalities are derived which constrain the mass variation of the difference of energy levels of a quark-antiquark system when the binding potential is assumed to be independent of the quark mass and to have the form, V(r)= ∫ β 1 β 2 ρ(β)r β d(β) − ∫ β 3 β 4 σ(β)r β dβ with β 2⩾ β 1⩾0, 0> β 4⩾ β 3>−2 and ρ( β), σ( β)⩾0. Applications are made to bound the p-wave ground state of the γ family of heavy mesons.