Sum rule analysis of vector and axial-vector spectral functions with excited states in vacuum

We simultaneously analyze vector and axial-vector spectral functions in vacuum using hadronic models constrained by experimental data and the requirement that Weinberg-type sum rules are satisfied. Upon explicit inclusion of an excited vector state, viz. ρ′, and the requirement that the perturbative continua are degenerate in vector and axial-vector channels, we deduce the existence of an excited axial-vector resonance state, , in order that the Weinberg sum rules are satisfied. The resulting spectral functions are further tested with QCD sum rules.