$\alpha_s$ in 2016 from the (revised) ALEPH data for $\tau$ decay

Abstract

We summarize a comparison of the two strategies which are currently available in the literature for determining the value of $\alpha_s(m_\tau)$. We will refer to these as the truncated Operator Product Expansion model and the Duality Violation model. After describing the main features of both approaches, we explain why the former fails to pass crucial tests. The latter, on the other hand, passes all the tests known up to date and, therefore, should be currently considered the only reliable method.