Resummation analysis of the $τ$ decay width using the four-loop $β$-function

Details Resummation analysis of the $τ$ decay width using the four-loop $β$-function Resummation analysis of the $τ$ decay width using the four-loop $β$-function

1997-03-07

arxiv.org/abs/hep-ph/9703268v2

Mod.Phys.Lett. A13 (1998) 637-650

Physics

High Energy Physics

High Energy Physics - Phenomenology

12 pages, LaTeX, more detailed explanation of the analysis done for the determination of the convergence radius, one PostScrip

Scientific paper

10.1142/S0217732398000693

We extract the strong coupling constant $\alpha_s(m_\tau^2)$ from the semileptonic $\tau$ decay width taking into account resummation effects from the running of the strong coupling constant. In the $\overline{\rm MS}$ scheme the result reads $\alpha_s=0.375\pm 0.007$ to third order and $\alpha_s=0.378\pm 0.007$ to fourth order in the $\beta$-function, respectively, where we use the recently computed four-loop coefficient $\beta_3$. These values for the coupling constant have to be compared with the value $\alpha_s=0.354\pm 0.005$ derived from a third order analysis of $\tau$ decays. We determine the exact value of the convergence radius of the perturbation series by analyzing the singularity structure of the complex coupling constant plane.

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