Tau-decay hadronic spectral functions: probing quark-hadron duality

TL;DR

This paper uses ALEPH tau-decay spectral functions and finite energy QCD sum rules with pinched kernels to investigate quark-hadron duality violations, finding no significant evidence for such violations within experimental uncertainties.

Contribution

It introduces a pinched kernel method in FESR to extend analysis beyond tau decay limits and tests duality violations without needing explicit models.

Findings

Good agreement between data and FESR results

No evidence for significant duality violations within uncertainties

Pinched kernels reduce free parameters in analysis

Abstract

The vector and axial-vector ALEPH hadronic spectral functions from $\tau$-decay are used to probe potential quark-hadron duality violations (DV). This is done in the framework of finite energy QCD sum rules (FESR). A pinched integration kernel is introduced in the FESR in order to (a) quench potential duality violations on the real axis in the complex squared energy $s$-plane, and (b) effectively extend the analysis well beyond the kinematical $\tau$-decay end-point where there is no longer data, i.e.\ in the range $s = 3 - 10 \,{\mbox{GeV}}^2$. In the vector channel this procedure is supplemented with actual data from $e^+ e^-$-annihilation into hadrons, above the tau-decay kinematical end-point, with results fully supporting this extension. Very good agreement is obtained between data and two specific pinched FESR. Results from this analysis are confronted with those from a specific model of DV. As the sum rules are well satisfied in both cases within experimental errors, we conclude that possible DV must be buried under the experimental uncertainties. In other words, there seems to be no need for explicit models of DV in this case. Pinched kernels work as well, but with far less free parameters.