Renormalization group improved $m_s$ and $\vert V_{us}\vert$ determination from hadronic $\tau$ decays

TL;DR

This paper refines the determination of the strange quark mass and the CKM matrix element V_us from hadronic tau decays by improving theoretical models and using phenomenological parametrization, leading to more precise results.

Contribution

It introduces an improved analysis method replacing longitudinal contributions with phenomenological parametrization and employs RGSPT coefficients for better accuracy.

Findings

Determined $m_s(2\,\mathrm{GeV})=98\pm19\,\mathrm{MeV}$.

Measured $|V_{us}|=0.2191\pm0.0043$.

Enhanced precision over previous analyses.

Abstract

We determine the strange quark mass ($m_s$) and quark mixing element $\vert V_{us}\vert $, and their joint determination from the Cabibbo suppressed hadronic $\tau$ decays in various perturbative schemes. Compared to the previous analysis based on the optimal renormalization or the renormalization group summed perturbation theory (RGSPT) scheme, we have improved this analysis by replacing the theoretical longitudinal contributions with phenomenological parametrization, and the RGSPT coefficients are used for the dimension-4 Adler functions. The improved analysis results in the extraction of $m_s(2\,\mathrm{GeV})=98\pm19\,\mathrm{MeV}$ and $\vert V_{us}\vert=0.2191\pm0.0043$ from the RGSPT scheme.