A resolution of the inclusive flavor-breaking $\tau$ $|V_{us}|$ puzzle

Abstract

We revisit the puzzle of $|V_{us}|$ values obtained from the conventional implementation of hadronic-$\tau$-decay-based flavor-breaking finite-energy sum rules lying $>3\sigma$ below the expectations of three-family unitarity. Significant unphysical dependences of $|V_{us}|$ on the choice of weight, w, and upper limit, $s_0$, of the experimental spectral integrals entering the analysis are confirmed, and a breakdown of assumptions made in estimating higher dimension, $D>4$, OPE contributions is identified as the main source of these problems. A combination of continuum and lattice results is shown to suggest a new implementation of the flavor-breaking sum rule approach in which not only $|V_{us}|$, but also $D>4$ effective condensates, are fit to data. Lattice results are also used to clarify how to reliably treat the slowly converging D=2 OPE series. The new sum rule implementation is shown to cure the problems of the unphysical w- and $s_0$-dependence of $|V_{us}|$ and to produce results $\sim 0.0020$ higher than those of the conventional implementation. With B-factory input, and using, in addition, dispersively constrained results for the $K\pi$ branching fractions, we find $|V_{us}|=0.2231(27{)}_{exp}(4{)}_{th}$, in excellent agreement with the result from $K_{\ell 3}$, and compatible within errors with the expectations of three-family unitarity, thus resolving the long-standing inclusive $\tau$ $|V_{us}|$ puzzle.

arXiv comment15 pages, 4 figures. Updated treatment of strange hadronic tau decay data; expanded discussion of the breakdown of the conventional implementation approach. Final version to appear in Physics Letters B

References in corpus (29)

• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• Superallowed 0+ --> 0+ nuclear beta decays: 2014 critical survey, with precise results for Vud and CKM unitarity
• S-wave Kpi scattering in chiral perturbation theory with resonances
• Strangeness-changing scalar form factors
• Update of the ALEPH non-strange spectral functions from hadronic $\tau$ decays
• Renormalization group analysis of the tau-lepton decay within QCD
• V_us and m_s from hadronic tau decays
• Study of tau- -> K_S pi- nu_tau decay at Belle
• Scalar K pi form factor and light quark masses
• Direct determination of the strange and light quark condensates from full lattice QCD
• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• An updated determination of α_s from tau decays
• Constraints on Hadronic Spectral Functions From Continuous Families of Finite Energy Sum Rules
• Alpha_s(M_Z) from hadronic tau decays
• Exclusive branching fraction measurements of semileptonic tau decays into three charged hadrons, ${\tau }^{-}\to \varphi {\pi }^{-}{\nu }_{\tau }$ and ${\tau }^{-}\to \varphi K^{-}{\nu }_{\tau }$
• Decay constants, light quark masses and quark mass bounds from light quark pseudoscalar sum rules
• The Strange Quark Mass From Flavor Breaking in Hadronic Tau Decays
• Strange Quark Mass from Tau Lepton Decays with O(alpha_s^3) Accuracy
• Measurement of the tau- --> K- pi0 nu_tau Branching Fraction
• Measurements of Branching Fractions of $\tau$ Lepton Decays with one or more $K_S^0$
• Mass Corrections to the Tau Decay Rate
• Chiral sum rules and duality in QCD
• Measurement of the branching fractions and the invariant mass distributions for tau^- -> h^-h^+h^-nu_tau decays
• Parameterization of the statistical rate function for select superallowed transitions
• V_us From Hadronin Tau Decays
• V_us From Hadronic Tau Decays
• Status of the Hadronic tau Decay Determination of |V_{us}|
• A critical look at V_us determinations from hadronic tau decay data
• Joint Extraction of m_s and V_us from Hadronic Tau Decays

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• FLAG Review 2019
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• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2018
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2021
• 50 Years of Quantum Chromodynamics
• $|V_{us}|$ from $K_{\ell 3}$ decay and four-flavor lattice QCD
• Semileptonic tau decays beyond the Standard Model
• Global Fit of Modified Quark Couplings to EW Gauge Bosons and Vector-Like Quarks in Light of the Cabibbo Angle Anomaly
• The strong coupling from $e^{+}{e}^{-}\to$ hadrons below charm
• Exclusive hadronic tau decays as probes of non-SM interactions
• Precision physics with inclusive QCD processes
• Determination of the quark condensate from heavy-light current-current correlators in full lattice QCD
• Evidence against naive truncations of the OPE from $e^{+}{e}^{-}\to$ hadrons below charm
• Renormalization group improved $m_s$ and $|V_{us}|$ determination from hadronic $\tau$ decays
• Status and progress of the HFLAV-Tau group activities
• Theoretical point of view on Cabibbo angle anomaly
• Spectral sum of current correlators from lattice QCD
• Confronting hadronic tau decays with non-leptonic kaon decays