The semihadronic tau decay width allows a clean extraction of the strong coupling constant at low energies. We present a modification of the standard “contour-improved” method based on a derivative expansion of the Adler function. The new approach has some advantages compared to contour-improved perturbation theory. The renormalization scale dependence is weaker by more than a factor of 2 and the last term of the expansion is reduced by about 10%, while the renormalization scheme dependence remains approximately equal. The extracted QCD coupling at the tau mass scale is by 2% lower than the contour-improved value. We find ${\mathrm{\alpha \_\{s\}}}^{}\left({\mathrm{M\_\{Z\}^\{2\}}}^{}\right)=0.1211\pm 0.0010$.

G. Cvetič, M. Loewe, C. Martinez and C. Valenzuela, Phys. Rev. D 82, 093007. DOI: https://doi.org/10.1103/PhysRevD.82.093007

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.82.093007