# Optimal renormalization and the extraction of strange quark mass from semi-leptonic $\tau$-decay

## TL;DR

This paper uses optimal renormalization group techniques to analyze semi-leptonic tau decay data, providing a precise extraction of the strange quark mass with reduced scale dependence.

## Contribution

It introduces an optimal renormalization group method to improve the accuracy of strange quark mass extraction from tau decay measurements.

## Key findings

- Strange quark mass from ALEPH data: 106.70 ± 9.36 MeV
- Strange quark mass from OPAL data: 74.47 ± 7.77 MeV
- Reduced scale dependence in the mass determination

## Abstract

We employ optimal renormalization group analysis to semi-leptonic $\tau$-decay polarization functions and extract the strange quark mass from their moments measured by the ALEPH and OPAL collaborations. The optimal renormalization group makes use of the renormalization group equation of a given perturbation series which then leads to closed form sum of all the renormalization group-accessible logarithms which have reduced scale dependence. Using the latest theoretical inputs we find $m_s(2{\rm GeV}) = 106.70 \pm 9.36~{\rm MeV}$ and $m_s(2{\rm GeV}) = 74.47 \pm 7.77~{\rm MeV}$ for ALEPH and OPAL data respectively.