Duality violations in tau hadronic spectral moments

TL;DR

This paper emphasizes the importance of including duality violations in spectral function analyses for precise alpha_s determination from tau decay, proposing a physically motivated model and fitting strategy.

Contribution

It introduces a new ansatz for duality violations in spectral functions and demonstrates its application in fitting spectral moments with various weights.

Findings

Duality violations significantly impact spectral moment analyses.

Preliminary fits show the model's potential to improve alpha_s extraction.

Further work needed to incorporate covariance matrix updates.

Abstract

Evidence is presented for the necessity of including duality violations in a consistent description of spectral function moments employed in the precision determination of $\alpha_s$ from $\tau$ decay. A physically motivated ansatz for duality violations in the spectral functions enables us to perform fits to spectral moments employing both pinched and unpinched weights. We describe our analysis strategy and provide some preliminary findings. Final numerical results await completion of an ongoing re-determination of the ALEPH covariance matrices incorporating correlations due to the unfolding procedure which are absent from the currently posted versions. To what extent this issue affects existing analyses and our own work will require further study.