The case for duality violations in the analysis of hadronic $\tau$ decays

TL;DR

This paper argues that neglecting duality violations and higher-dimension condensates in analyzing hadronic tau decays introduces significant systematic errors, challenging previous assumptions and highlighting the importance of accounting for duality violations in alpha_s determinations.

Contribution

It demonstrates that duality violations are significant and cannot be ignored, questioning the validity of common assumptions in tau decay analyses.

Findings

Duality violations affect alpha_s extraction from tau decays.

Pinched weights do not fully suppress duality violations.

Evidence supports the presence of duality violations in experimental data.

Abstract

We discuss why, in the determination of $\alpha_s(m_{\tau}^2)$ from hadronic $\tau$ decays, two important assumptions made in most of previous analyses, namely the neglect of higher-dimension condensates and of Duality Violations (DVs), have introduced uncontrolled systematic errors into this determination. Although the use of pinched weights is usually offered as a justification of these assumptions, we explain why it is not possible to simultaneously suppress these two contributions; particularly since the Operator Product Expansion is expected to be an asymptotic, rather than a convergent expansion. There is not only experimental and theoretical evidence for DVs, but they also affect the extraction of $\alpha_s(m_{\tau}^2)$.