Weinberg like sum rules revisited

TL;DR

This paper revisits generalized Weinberg sum rules involving vector and axial-vector spectral functions, analyzing their consistency with various theoretical models and experimental data to deepen understanding of hadronic spectral properties.

Contribution

It provides a comprehensive review of the status of generalized Weinberg sum rules and evaluates their agreement with multiple phenomenological and theoretical frameworks.

Findings

Sum rules are consistent with certain phenomenological models.

Discrepancies observed with some experimental data.

Parity doubling and string models offer partial explanations.

Abstract

The generalized Weinberg sum rules containing the difference of isovector vector and axial-vector spectral functions saturated by both finite and infinite number of narrow resonances are considered. We summarize the status of these sum rules and analyze their overall agreement with phenomenological Lagrangians, low-energy relations, parity doubling, hadron string models, and experimental data.