Contribution from Duality Violations to the theoretical error on alpha_s

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.