Spectral function sum rules for tensor currents and the ϱ-meson electromagnetic mass difference

Abstract

From the va;idity of equal-time commutation relations of the vector and the antisymmetric tensor currents, spectral function sum rules are derived which relate the spectral functions of vector currents to the spectral functions of the antisymmetric tensor currents. Saturation of these sum rules with single particle states is discussed. These sum rules are then used to calculate the electromagnetic mass splitting of the ρ-meson, with the result that ρ 0 is predicted to be heavier than ρ ±.