Strong Coupling Constant from Hadronic τ Decays within the Dispersive Treatment

摘要

We extract numerical values for the strong coupling constant α_s from the revised ALEPH τ decay data for the non-strange vector hadronic spectral function. The distinguished feature of our procedure is that we employ the global quark-hadron duality in the bounded below region, s_c≤s≤m_τ~2, where s_c is the onset of the perturbative QCD continuum. On this interval, we construct the modified Finite Energy Sum Rules (FESRs) using the "spectral weights" w_(kl)(s) (k,l=1,2..) associated with the spectral moments of the invariant mass distribution. These sum rules are used in conjunction with the dimension-two sum rule valid in the chiral limit. We have performed several determinations of the strong coupling constant α_s and the continuum threshold s_e, combining different w_(kl) based FESRs with the dimension-two FESR. The numerical values for the strong coupling constant from different determinations are found to be in good agreement. We obtain, in the MS scheme, the values α_s (m_τ~2) = 0.322 ±0.011_(ex) using a dispersive modification of Contour Improved Perturbation Theory and α_s (m_τ~2) = 0.298 ± 0.012_(ex) using Fixed Order Perturbation Theory.