Asymptotic structure of perturbative series for $\tau$ lepton decay observables: $m_s^2$ corrections

Abstract

In a previous paper [1] we performed an analysis of the asymptotic structure of the perturbation theory series for semileptonic $\tau$ lepton decays in the massless limit. We extend our analysis to the Cabibbo suppressed $\Delta S=1$ decay modes of the $\tau$ lepton. In particular we address the problem of $m_s^2$ corrections to the theoretical formulas. The properties of the asymptotic behavior of the finite order perturbation theory series for the coefficient functions of the $m_s^2$ corrections are studied.