Analytic Properties of the QCD Running Coupling Constant and $τ$ Decay

Details Analytic Properties of the QCD Running Coupling Constant and $τ$ Decay Analytic Properties of the QCD Running Coupling Constant and $τ$ Decay

1995-06-19

arxiv.org/abs/hep-ph/9506358v1

Phys.Lett. B357 (1995) 441-445

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX, 11 pages

Scientific paper

10.1016/0370-2693(95)00914-7

A non-perturbative expansion method which gives a well-defined analytic continuation of the running coupling constant from the spacelike to the timelike region is applied to the inclusive semileptonic decay of the $\tau$--lepton. The method allows us to evaluate $R_{\tau}$ by integration over the non-perturbative physical region, rather than by using Cauchy's theorem, and hence to incorporate threshold effects in a very direct way. Within our framework the difference between the effective coupling constants in the timelike and spacelike domains can be substantial and is not simply a matter of the standard $\pi^2$ terms.

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