Higher-order QCD corrections to hadronic τ decays from Padé approximants

The mathematical method of Pade approximants is put forward to reconstruct the Borel transformed series of the Adler function and extract higher-order corrections in a model-independent way. The use of the D-log Pade approximants provides valuable information to its analytic structure and yields, together with the standard Pade approximants, reliable model-independent predictions of the higher-order coefficients, as for example, c 5 , 1 = 277 ± 51 . Such reconstruction strongly favours the use of fixed-order perturbation theory (FOPT) for the renormalization-scale setting.