Testing the Concept of Quark–Hadron Duality with the ALEPH τ Decay Data

摘要

We propose a modified procedure for extracting the numerical value for the strong coupling constant α _s from the τ lepton hadronic decay rate into non-strange particles in the vector channel. We employ the concept of the quark–hadron duality specifically, introducing a boundary energy squared s _p > 0, the onset of the perturbative QCD continuum in Minkowski space (Bertlmann et al. in Nucl Phys B 250:61, 1985; de Rafael in An introduction to sum rules in QCD. In: Lectures at the Les Houches Summer School. arXiv: 9802448 [hep-ph], 1997; Peris et al. in JHEP 9805:011, 1998). To approximate the hadronic spectral function in the region s > s _p, we use analytic perturbation theory (APT) up to the fifth order. A new feature of our procedure is that it enables us to extract from the data simultaneously the QCD scale parameter L<sub>[`(MS)]</sub>{Lambda_{overline{rm MS}}} and the boundary energy squared s <sub>p</sub>. We carefully determine the experimental errors on these parameters which come from the errors on the invariant mass squared distribution. For the [`(MS)]{overline{rm MS}} scheme coupling constant, we obtain a_s(m2_t)=0.3204±0.0159_exp.{alpha_s(m^{2}_{tau})=0.3204pm 0.0159_{exp.}}. We show that our numerical analysis is much more stable against higher-order corrections than the standard one. Additionally, we recalculate the “experimental” Adler function in the infrared region using final ALEPH results. The uncertainty on this function is also determined.