Contribution from Duality Violations to the theoretical error on alpha_s

TL;DR

This paper quantifies the impact of Duality Violations on the theoretical uncertainty in determining alpha_s from tau decay data, highlighting that DVs are a significant source of error previously neglected.

Contribution

It introduces a physically motivated ansatz to estimate Duality Violations in tau data, providing a quantitative assessment of their effect on alpha_s determination.

Findings

DVs contribute an additional error of about 0.003-0.010 to alpha_s(m_tau).

The fit to spectral functions with the ansatz is better than expected.

The 1st Weinberg sum rule does not eliminate DVs.

Abstract

Duality Violations (DVs) is a nickname for the failure of the Operator Product Expansion to describe QCD correlators on the physical axis. Using a physically motivated ansatz, a fit to the spectral functions allows us to get a quantitative estimate for the amount of DVs present in tau data. The quality of the fit turns out to be better than expected. Since DVs have not been included in the past in the determination of alpha_s, they amount to an additional theoretical error which we estimate could be \delta alpha_s(m_{tau}) \sim 0.003-0.010 . Our ansatz satisfies, in particular, the 1st Weinberg sum rule, which shows that this sum rule is not enough to force DVs to vanish.