Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2005-08-31
JHEP 0509 (2005) 058
Physics
High Energy Physics
High Energy Physics - Phenomenology
20 pages, 5 eps-figures; discussion on scale and scheme dependence added as compared to published journal version JHEP 09 (200
Scientific paper
10.1088/1126-6708/2005/09/058
The hadronic decay rate of the tau lepton serves as one of the most precise determinations of the QCD coupling alpha_s. The dominant theoretical source of uncertainty at present resides in the seeming disparity of two approaches to improving the perturbative expansion with the help of the renormalisation group, namely fixed-order and contour-improved perturbation theory. In this work it is demonstrated that in fact both approaches yield compatible results. However, the fixed-order series is found to oscillate around the contour-improved result with an oscillation frequency of approximately six perturbative orders, approaching it until about the 30th order, after which the expansion reveals its asymptotic nature. Additionally, the renormalisation scale and scheme dependencies of the perturbative series for the tau hadronic width are investigated in detail.
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