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

TL;DR

This paper uses sum rule analysis and experimental data to explore vector and axial-vector spectral functions, revealing the necessity of an excited axial-vector state to satisfy theoretical sum rules and consistency with QCD.

Contribution

It introduces an excited axial-vector resonance state, a1', to satisfy Weinberg sum rules within a hadronic model constrained by experimental data.

Findings

Existence of an excited axial-vector state a1' is necessary.

Spectral functions satisfy Weinberg sum rules.

Results are consistent with QCD sum rules.

Abstract

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. rho', 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, a1', in order that the Weinberg sum rules are satisfied. The resulting spectral functions are further tested with QCD sum rules.