Updated determination of $\alpha_s(m_\tau^2)$ from tau decays

Abstract

Using the most recent release of the ALEPH $\tau$ decay data, we present a very detailed phenomenological update of the $\alpha_s(m_\tau^2)$ determination. We have exploited the sensitivity to the strong coupling in many different ways, exploring several complementary methodologies. All determinations turn out to be in excellent agreement, allowing us to extract a very reliable value of the strong coupling. We find $\alpha_{s}^{(n_f=3)}(m_\tau^2) = 0.328 \pm 0.012$ which implies $\alpha_{s}^{(n_f=5)}(M_Z^{2}) = 0.1197\pm 0.0014$. We critically revise previous work, and point out the problems flawing some recent analyses which claim slightly smaller values.