[Paper Review] Determination of |Vus| from tau Decays

Ian Michael Nugent|arXiv (Cornell University)|Jan 3, 2013

Quantum Chromodynamics and Particle Interactions9 references3 citations

TL;DR

This paper evaluates three precision methods for determining the CKM matrix element |Vus| using hadronic tau decays, with the most accurate approach relying on the ratio of branching fractions for τ→Kν and τ→πν. The FESR-based method shows a 3.4σ deviation from unitarity, suggesting potential theoretical or experimental inconsistencies, while other methods align with unitarity within uncertainties.

ABSTRACT

The weak interaction between the first and second generation of quarks, the Cabibbo-Kobayashi-Maskawa matrix (CKM) element |Vus|, can be probed using hadronic tau decays. In this paper, we present the recent measurements of hadronic tau decays from BELLE and BABAR and the improvements in the determination of |Vus| from tau decays.

Motivation & Objective

• To determine |Vus| with high precision using hadronic tau decays as a complementary probe to kaon decays.
• To assess the consistency of |Vus| extracted from tau decays with the unitarity condition of the CKM matrix.
• To investigate potential discrepancies between tau decay measurements and kaon decay measurements that could signal new physics.
• To evaluate the impact of experimental and theoretical uncertainties, particularly from lattice QCD and SU(3) breaking corrections.
• To identify whether the observed 3.4σ deviation in the FESR method arises from missing decay modes or theoretical convergence issues.

Proposed method

• Uses Finite Energy Sum Rules (FESR) to extract |Vus| from the flavor-breaking difference between strange and non-strange hadronic tau decay widths.
• Applies the ratio of branching fractions B(τ→Kν)/B(τ→πν) to determine |Vus|, normalized by the known fK/fπ ratio and phase-space factors.
• Employs the absolute branching fraction B(τ→Kν) with theoretical corrections for electroweak effects and phase space.
• Relies on experimental data from B-factory experiments BABAR and BELLE to measure branching fractions and spectral functions.
• Incorporates lattice QCD inputs for fK/fπ and fK, with associated uncertainties, and includes long-distance corrections δLD.
• Uses the HFAG average of branching fractions and applies theoretical corrections to extract |Vus| with minimal model dependence.

Experimental results

Research questions

• RQ1 What is the current precision of |Vus| extracted from tau decays using the FESR, branching fraction ratio, and absolute branching fraction methods?
• RQ2 How do the results from tau decays compare with the unitarity constraint and kaon decay measurements of |Vus|?
• RQ3 What is the origin of the 3.4σ deviation observed in the FESR-based |Vus| determination from unitarity?
• RQ4 To what extent do missing decay modes or experimental systematics contribute to the observed discrepancy in the FESR method?
• RQ5 Are the theoretical uncertainties in the FESR method, particularly from OPE weights and SU(3) breaking, sufficient to explain the deviation?

Key findings

• The FESR-based determination of |Vus| deviates from unitarity by 3.4σ, indicating a significant tension not yet explained by current uncertainties.
• The branching fraction ratio method (B(τ→Kν)/B(τ→πν)) yields a |Vus| value consistent with unitarity and dominated by the BABAR measurement.
• The absolute branching fraction method for τ→Kν provides a competitive |Vus| determination, with uncertainties primarily from lattice QCD inputs.
• Updated measurements from BABAR and BELLE show systematic discrepancies with previous world averages, possibly due to mode definition differences or incomplete branching fraction updates.
• The possibility that missing decay modes account for the FESR deviation is now considered less likely due to recent upper limits on unmeasured modes.
• Theoretical uncertainties in the FESR method, particularly from OPE weight convergence, may not be fully accounted for, suggesting a potential source of the observed tension.