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

Abstract

In a previous paper we performed an analysis of asymptotic structure of perturbation theory series for semileptonic $τ$-lepton decays in massless limit. We extend our analysis to the Cabibbo suppressed $ΔS=1$ decay modes of the $τ$ lepton. In particular we address the problem of $m_s^2$ corrections to 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.