Vus from Kℓ3 Decays

The slope and curvature parameters of the $K\pi$ vector form factor, $F_+^{K\pi}$, are fitted to the data on $\tauKpi$ and $K_{l3}$ decays yielding $\lambda_+'=(25.49 \pm 0.31) \times 10^{-3}$ and $\lambda_+"= (12.22 \pm 0.14) \times 10^{-4}$. The pole position of the $K^*(892)^\pm$ is found to be at $m_{K^*(892)^\pm}= 892.0\pm 0.5$ MeV and $\Gamma_{K^*(892)^\pm}= 46.5 \pm1.1$ MeV. The phase-space integrals relevant for $K_{l3}$ analyses and the $P$-wave isospin-1/2 $K\pi$ phase-shift threshold parameters are also calculated.

Eur Phys J C, 2004

We present a detailed numerical study of the K e3 decays to {\cal O}(p^6, (m_d-m_u)p^2, e^2 p^2) in chiral perturbation theory with virtual photons and leptons. We describe the extraction of the CKM matrix element |V us | from the experimental K e3 decay parameters. We propose a consistency check of the K + e3 and K 0 e3 data that is largely insensitive to the dominating theoretical uncertainties, in particular the contributions of {\cal O}(p^6). Our analysis is highly relevant in view of the recent high statistics measurement of the K + e3 branching ratio by E865 at Brookhaven which does not indicate any significant deviation from CKM unitarity but rather a discrepancy with the present K 0 e3 data.

Physical Review D, 2007

The estimation of rare K decay matrix-elements from K ℓ3 experimental data is extended beyond LO in Chiral Perturbation Theory. Isospin-breaking effects at NLO (and partially NNLO) in the ChPT expansion, as well as QED radiative corrections, are now accounted for. The analysis relies mainly on the cleanness of two specific ratios of form-factors, for which the theoretical control is excellent. As a result, the uncertainties on the K + → π + νν and K L → π 0 νν matrix-elements are reduced by a factor of about 7 and 4, respectively, and similarly for the direct CP-violating contributions to K L → π 0 e + e − and K L → π 0 µ + µ − . They could be reduced even further with better experimental data for the K ℓ3 slopes and the K + ℓ3 branching ratios. As a result, the non-parametric errors for B (K → πνν) and for the direct CP-violating contributions to B K L → π 0 ℓ + ℓ − are now completely dominated by those on the short-distance physics.

Journal of High Energy Physics, 2010

Dispersive representations of the Kπ vector and scalar form factors are used to fit the spectrum of τ → Kπν τ obtained by the Belle collaboration incorporating constraints from results for K l 3 decays. The slope and curvature of the vector form factor are obtained directly from the data through the use of a three-times-subtracted dispersion relation. We find λ ′ + = (25.49 ± 0.31) × 10 −3 and λ ′′ + = (12.22 ± 0.14) × 10 −4. From the pole position on the second Riemann sheet the mass and width of the K * (892) ± are found to be m K * (892) ± = 892.0 ± 0.5 MeV and Γ K * (892) ± = 46.5 ± 1.1 MeV. The phase-space integrals needed for K l 3 decays are calculated as well. Furthermore, the Kπ isospin-1/2 P-wave threshold parameters are derived from the phase of the vector form factor. For the scattering length and the effective range we find respectively a 1/2 1 = (0.166 ± 0.004) m −3 π and b 1/2 1 = (0.258 ± 0.009) m −5 π .

Journal of High Energy Physics, 2008

We study the radiative corrections to all K ℓ3 decay modes to leading non-trivial order in the chiral effective field theory, working with a fully inclusive prescription on real photon emission. We present new results for K µ3 modes and update previous results on K e3 modes. Our analysis provides important theoretical input for the extraction of the CKM element V us from K ℓ3 decays.

Journal of High Energy Physics, 2008

We study the radiative corrections to all K ℓ3 decay modes to leading non-trivial order in the chiral effective field theory, working with a fully inclusive prescription on real photon emission. We present new results for K µ3 modes and update previous results on K e3 modes. Our analysis provides important theoretical input for the extraction of the CKM element V us from K ℓ3 decays. * This work was supported in part by the EU Contract No. MRTN-CT-2006-035482, "FLAVIAnet". With the advent of precision measurements in Kaon physics (see and references therein), K ℓ3 decays offer the opportunity to probe charged current weak interactions at unprecedented levels. Most notably, with current experimental uncertainties, K ℓ3 decays allow one to access the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing angle V us at the subpercent level, and also provide competitive probes of lepton universality and the ratios of light quark masses. In order to fully exploit the amazing experimental achievements, it becomes mandatory to have theoretical control of these decays at the percent level or better. This requires quantitative understanding of the vector and scalar K → π form factors as well as the electromagnetic (EM) corrections. The framework to analyze the EM corrections is provided by Chiral Perturbation Theory (ChPT) [2], the low energy effective field theory (EFT) of QCD, extended to include the photon [3] and the light leptons [4] as active degrees of freedom. ChPT exploits the special role of π, K, η as Goldstone modes associated with the spontaneous breaking of chiral SU(3) L ×SU(3) R symmetry, and provides a systematic expansion of the amplitudes in powers of the masses of pseudoscalar mesons and charged leptons (p ∼ M π,K,ℓ /Λ χ with Λ χ ∼ 4πF π ∼ 1.2 GeV) and the electromagnetic coupling (e).

Physics Letters B, 1969

Physics Letters B, 2004

We present a new measurement of the branching ratio R of the decay KL→ π±e∓ ν, denoted as Ke3, relative to all charged KL decays with two tracks, based on data taken with the NA48 detector at the CERN SPS. We measure R= 0.4978±0.0035. From this we derive the Ke3 branching fraction and the weak coupling parameter| Vus| in the CKM matrix. We obtain| Vus| f+ (0)= 0.2146±0.0016, where f+ (0) is the vector form factor in the Ke3 decay.

2016

A subtracted dispersive representation of the Kπ vector form factor, F Kπ + , is used to fit the Belle spectrum of τ → Kπν τ decays incorporating constraints from results on K l3 decays. Through the use of three subtractions, the slope and curvature of F Kπ + are obtained directly from the data yielding λ ′ + = (25.49±0.31)×10 −3 and λ ′′ + = (12.22±0.14)×10 −4. The phase-space integrals relevant for K l3 analyses are calculated. Additionally, from the pole position on the second Riemann sheet the mass and width of the K * (892) ± are found to be m K * (892) ± = 892.0 ± 0.5 MeV and Γ K * (892) ± = 46.5 ± 1.1 MeV. Finally, we study the P-wave isospin-1/2 Kπ phase-shift and its threshold parameters.

Journal of Physics: Conference Series, 2008

The analysis made in 2000 indicated that the unitarity relation |V ud | 2 + |Vus| 2 + |V ub | 2 = 1 might be broken at the 2.3σ level. At that time, however, |Vus| was inferred from old experimental data. Since then, a great experimental and theoretical effort has been invested to understand the source of that discrepancy. Thanks to the new and improved measurements by BNL-E865, KLOE, KTeV, ISTRA+ and NA48, the old K ℓ3 decay rate got shifted so that the new |Vus| is now consistent with unitarity. On the theory side, much progress in the lattice QCD has been made in order to tame the systematic uncertainties related to the computation of the K ℓ3 form factors.