Summation of the perturbation expansion and the QCD corrections to τ decay

The problem of summation of the perturbation expansion in QCD is discussed. It is argued that this expansion is summable by a modified Borel method. The QCD corrections to the semileptonic width of a heavy lepton are considered as an example. The possible differences between the predictions from the resummed expansion and the truncated expansion are illustrated. It is shown that the use of a Borel-type approximant may eliminate certain discrepancy between the theoretical prediction for the τ lepton and experiment