Study of tau decays involving kaons, spectral functions and determination of the strange quark mass

TL;DR

This paper analyzes tau decays involving kaons to extract spectral functions and determine the strange quark mass, combining experimental data with theoretical models to improve understanding of QCD parameters.

Contribution

It introduces a novel method to determine the strange quark mass from tau decay spectral functions, accounting for convergence issues in the hadronic component.

Findings

Measured strange tau decay branching ratio: (28.7±1.2)×10^{-3}

Determined strange quark mass: m_s(M_τ^2)=(176^{+46}_{-57}) MeV/c^2

Derived m_s(1 GeV^2) = (234^{+61}_{-76}) MeV/c^2

Abstract

All ALEPH measurements of branching ratios of tau decays involving kaons are summarized including a combination of results obtained with K^0_S and K^0_L detection. The decay dynamics are studied, leading to the determination of contributions from vector K^*(892) and K^{*}(1410), and axial-vector K_1(1270) and K_1(1400) resonances. Agreement with isospin symmetry is observed among the different final states. Under the hypothesis of the conserved vector current, the spectral function for the K\bar{K}\pi mode is compared with the corresponding cross section for low energy e^+e^- annihilation, yielding an axial-vector fraction of (94^{+6}_{-8})% for this mode. The branching ratio for tau decay into all strange final states is determined to be B(\tau^-\to X^-(S=-1)\nu_\tau)=(28.7\pm1.2)\times 10^{-3}. The measured mass spectra of the strange tau decay modes are exploited to derive the S=-1 spectral function. A combination of strange and nonstrange spectral functions is used to determine the strange quark mass and nonperturbative contributions to the strange hadronic width. A method is developed to avoid the bad convergence of the spin zero hadronic component, with the result m_s(M_\tau^2)=(176^{+46}_{-57}) MeV/c^2. The evolution down to 1 GeV gives m_s(1 {GeV}^2) = (234^{+61}_{-76}) MeV/c^2.