Renormalization scheme dependence and the problem of determination of alpha_s and the condensates from the semileptonic tau decays

Abstract

The QCD corrections to the moments of the invariant mass distribution in the semileptonic $τ$ decays are considered. The effect of the renormalization scheme dependence on the fitted values of alpha_s(m^2_tau) and the condensates is discussed, using a simplified approach where the nonperturbative contributions are approximated by the dimension six condensates. The fits in the vector and the axial-vector channel are investigated in the next-to-leading and the next-to-next-to-leading order. The next-to-next-to-leading order results are found to be relatively stable with respect to change of the renormalization scheme. A change from the MS-bar scheme to the minimal sensitivity scheme results in the reduction of the extracted value of alpha_s(m^2_tau) by 0.01.