Global Determination of $|V_{us}|$

Abstract

In light of ongoing issues with the first-row unitarity test of the CKM matrix, we showcase a global fit to measurements of $K\to \ell \nu$, $K\to \pi \ell \nu$, $\tau \to K\nu$, and $\tau \to K\pi \nu$ decays for the first time. Fitting the semileptonic and 3-body $\tau$ decay data simultaneously becomes computationally feasible because we employ a simple form factor parametrisation for the $K\pi$ form factor that manifestly connects the semileptonic and pair-production regions. We find good agreement with the data and use our analyses to infer $|V_{us}|$ and the parameters for the $K\pi$ form factors. Our result for $|V_{us}|$ sits close to the results extracted from exclusive $K_{\ell 2}$ and somewhat above the $K_{\ell 3}$ decay and inclusive $\tau$ decay result. Moreover, our results for the $K\to \pi$ vector form factor at zero momentum transfer are compatible with lattice QCD determinations, despite not using lattice QCD inputs for this quantity in our fit of the hadronic matrix elements. We are further able to determine some of the pole parameters of the individual scalar and vector $K\pi$ resonances with masses below the $\tau$ mass. We caution that our results account only for short-distance electromagnetic corrections but not long-distance contributions; this is due to the lack of a consistent description of long-distance corrections to the $K\pi$ matrix elements both above and below threshold for an arbitrary model of the form factors.

19 pages + references, 4 figures

References in corpus (50)

• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• Domain wall QCD with physical quark masses
• Model-independent description of $B\to \pi l\nu$ decays and a determination of $|V_{ub}|$
• Dynamic nested sampling: an improved algorithm for parameter estimation and evidence calculation
• High Precision determination of the pi, K, D and D_s decay constants from lattice QCD
• Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks
• Comment on form factor shape and extraction of |V_ub| from B --> pi l nu
• Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks
• V_us and m_s from hadronic tau decays
• WCxf: an exchange format for Wilson coefficients beyond the Standard Model
• Study of tau- -> K_S pi- nu_tau decay at Belle
• Leptonic decay constants fK, fD and fDs with Nf = 2+1+1 twisted-mass lattice QCD
• Theory determination of $\bar{B}\to D^{(\ast )}{\ell }^{-}\bar{\nu }$ form factors at $\mathcal{O}(1/m_c^2)$
• Determination of m_s and |V_us| from hadronic tau decays
• Heavy-Quark Expansion for ${\bar{B}}_s\to D_s^{(\ast )}$ Form Factors and Unitarity Bounds beyond the $SU(3{)}_F$ Limit
• Topological amplitudes in $D$ decays to two pseudoscalars: a global analysis with linear $SU(3{)}_F$ breaking
• Spectral distribution for the decay tau -> nu_tau K pi
• $K\to \pi$ semileptonic form factors with $N_f=2+1+1$ Twisted Mass fermions
• FLAG Review 2024
• Dispersive representation and shape of the Kl3 form factors: robustness
• Scrutinizing CKM unitarity with a new measurement of the $K_{\mu 3}/K_{\mu 2}$ branching fraction
• Measurements of the Absolute Branching Ratios for the Dominant KL Decays, the KL Lifetime, and Vus with the KLOE Detector
• K pi vector form factor, dispersive constraints and tau -> nu_tau K pi decays
• The Fermi constant from muon decay versus electroweak fits and CKM unitarity
• What can be learned from the Belle spectrum for the decay tau- -> nu_tau K_S pi-
• Electromagnetic effects in Kl3 decays
• On the Statistical Treatment of the Cabibbo Angle Anomaly
• K pi vector form factor constrained by tau ---> K pi nu_tau and K_l3 decays
• EOS -- A Software for Flavor Physics Phenomenology
• Measurement of the tau- --> K- pi0 nu_tau Branching Fraction
• Measurements of Branching Fractions of $\tau$ Lepton Decays with one or more $K_S^0$
• First-Generation New Physics in Simplified Models: From Low-Energy Parity Violation to the LHC
• Measurement of the Strange Spectral Function in Hadronic tau Decays
• Measurements of KL Branching Fractions and the CP Violation Parameter |eta+-|
• $|V_{us}|$ from $K_{\ell 3}$ decay and four-flavor lattice QCD
• Measurement of the Absolute Branching Ratio for the K+ -> mu+ nu(gamma) Decay with the KLOE Detector
• Global Fit of Modified Quark Couplings to EW Gauge Bosons and Vector-Like Quarks in Light of the Cabibbo Angle Anomaly
• Constraints on the form factors for K --> pi l nu and implications for V_us
• Predicting the tau strange branching ratios and implications for V_{us}
• Ratio of kaon and pion leptonic decay constants with $N_f=2+1+1$ Wilson-clover twisted-mass fermions
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2023
• Measurement of the charged kaon lifetime with the KLOE detector
• Measurement of the branching fraction for the decay KS --> pi e nu
• Measurement of the branching fraction for the decay $K_S\to \pi \mu \nu$ with the KLOE detector
• Tau decays with neutral kaons
• A Study of One-Prong Tau Decays with a Charged Kaon
• Model Independent Electromagnetic corrections in hadronic $\tau$ decays
• A Simple Parametrisation of the Pion Form Factor
• Cabibbo-Kobayashi-Maskawa unitarity deficit reduction via finite nuclear size
• Advanced parametrisations for hadronic form factors