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

TL;DR

This paper analyzes the asymptotic behavior of perturbative series for $ au$ lepton decay observables, focusing on $m_s^2$ corrections in Cabibbo suppressed decay modes, extending previous massless limit studies.

Contribution

It extends prior work on massless $ au$ decay series to include $m_s^2$ corrections in Cabibbo suppressed modes, analyzing their asymptotic properties.

Findings

Studied the asymptotic behavior of perturbation series for $m_s^2$ corrections.

Provided insights into the convergence properties of these series.

Enhanced understanding of theoretical predictions for $ au$ decay observables.

Abstract

In a previous paper we performed an analysis of asymptotic structure of perturbation theory series for semileptonic $\tau$-lepton decays in 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 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.