Novel $|V_{us}|$ Determination Using Inclusive Strange $\tau$ Decay and Lattice HVPs

TL;DR

This paper introduces a novel method to determine |V_{us}| by combining dispersion relations with lattice QCD HVPs, reducing experimental uncertainties and aligning well with existing measurements.

Contribution

The paper presents a new approach that uses dispersion relations with specific weight functions to relate strange tau decay data to lattice HVPs, improving precision in |V_{us}| determination.

Findings

|V_{us}| agrees with CKM unitarity and kaon decay results

Method suppresses regions with large experimental errors

Accurate lattice HVP combinations are achievable

Abstract

We propose and apply a new approach to determining $|V_{us}|$ using dispersion relations with weight functions having poles at Euclidean (space-like) momentum which relate strange hadronic $\tau$ decay distributions to hadronic vacuum polarization functions (HVPs) obtained from lattice QCD. We show examples where spectral integral contributions from the region where experimental data have large errors or do not exist are strongly suppressed but accurate determinations of the relevant lattice HVP combinations remain possible. The resulting $|V_{us}|$ agrees well with determinations from $K$ physics and 3-family CKM unitarity. Advantages of this new approach over the conventional hadronic $\tau$ decay determination employing flavor-breaking sum rules are also discussed.