Finite energy chiral sum rules in QCD

TL;DR

This paper tests well-known chiral sum rules in QCD against experimental tau decay data, finding that modified sum rules with specific weight factors are better saturated than the traditional ones.

Contribution

It introduces modified chiral sum rules with weight factors that improve saturation with experimental data compared to traditional sum rules.

Findings

Standard sum rules are not well saturated by data.

Modified sum rules with vanishing weight factors are highly saturated.

The results suggest new approaches to understanding QCD spectral functions.

Abstract

A set of well known chiral sum rules, expected to be valid in QCD, is confronted with experimental data on the vector and axial-vector hadronic spectral functions, obtained from tau-lepton decay by the ALEPH collaboration. The Das-Mathur-Okubo sum rule, the first and second Weinberg sum rules, and the electromagnetic pion mass difference sum rule are not well saturated by the data. Instead, a modified set of sum rules having additional weight factors that vanish at the end of the integration range on the real axis, is found to be precociously saturated by the data to a remarkable extent.