We will describe two different strategies for the precise extraction of the strong coupling, alpha_s, using data for hadronic tau decays and cross sections for e+e- to hadrons.
In the first one, we determine the strong coupling using finite-energy sum rules combined
(i) with a new tau-based vector spectral function and
(ii) with a recent compilation of the hadronic R-ratio from available data for e+e- to hadrons below the charm threshold.
These determinations are performed at relatively low-energies, with three active flavours (n_f=3) . We will also present a new strategy for the determination of the strong coupling with n_f=4 and n_f=5 from ratios of moments of the charm- and bottom-quark vector correlators, which can also be extracted from e^+e^- to hadrons cross sections. I will discuss the perturbative behaviour of these recently introduced moments and their relation to moments employed in charm- and bottom-mass extractions.
