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Precision tests of the Standard Model with leptonic and semileptonic kaon decays

FlaviaNet Working Group, M. Antonelli, V. Cirigliano, P. Franzini, S. Glazov, R. Hill, G. Isidori, F. Mescia, M. Moulson, M. Palutan, E. Passemar, M. Piccini, M. Veltri, O. Yushchenko, R. Wanke

TL;DR

This work provides a comprehensive, high-precision test of the Standard Model through leptonic and semileptonic kaon decays by combining world data on branching ratios and lifetimes with robust, model-independent form-factor constraints. It extracts $|V_{us}|$ via $K_{\ell 3}$ and $K_{\ell 2}$ channels, using both dispersive and $z$-expansion form-factor parametrizations and incorporating lattice QCD inputs for $f_+(0)$ and $f_K/f_\pi$. Callan–Treiman tests and lattice comparisons offer stringent cross-checks of hadronic inputs, while CKM unitarity and lepton-flavor universality are probed with sub-percent precision, substantially constraining new-physics scenarios such as charged-Higgs and right-handed currents. The results reinforce the SM framework, constrain the scale of possible new physics, and demonstrate the power of kaon decays as precision probes of fundamental couplings and symmetries.

Abstract

We present a global analysis of leptonic and semileptonic kaon decays data, including all recent results by BNL-E865, KLOE, KTeV, ISTRA+, and NA48. Experimental results are critically reviewed and combined, taking into account theoretical (both analytical and numerical) constraints on the semileptonic kaon form factors. This analysis leads to a very accurate determination of Vus and allows us to perform several stringent tests of the Standard Model.

Precision tests of the Standard Model with leptonic and semileptonic kaon decays

TL;DR

This work provides a comprehensive, high-precision test of the Standard Model through leptonic and semileptonic kaon decays by combining world data on branching ratios and lifetimes with robust, model-independent form-factor constraints. It extracts via and channels, using both dispersive and -expansion form-factor parametrizations and incorporating lattice QCD inputs for and . Callan–Treiman tests and lattice comparisons offer stringent cross-checks of hadronic inputs, while CKM unitarity and lepton-flavor universality are probed with sub-percent precision, substantially constraining new-physics scenarios such as charged-Higgs and right-handed currents. The results reinforce the SM framework, constrain the scale of possible new physics, and demonstrate the power of kaon decays as precision probes of fundamental couplings and symmetries.

Abstract

We present a global analysis of leptonic and semileptonic kaon decays data, including all recent results by BNL-E865, KLOE, KTeV, ISTRA+, and NA48. Experimental results are critically reviewed and combined, taking into account theoretical (both analytical and numerical) constraints on the semileptonic kaon form factors. This analysis leads to a very accurate determination of Vus and allows us to perform several stringent tests of the Standard Model.

Paper Structure

This paper contains 44 sections, 81 equations, 12 figures, 15 tables.

Table of Contents

  1. Introduction
  2. Theoretical framework
  3. $K_{\ell3}$ and $K_{\ell2}$ rates within the SM
  4. Parametrization of $K_{\ell 3 }$ form factors
  5. Dispersive constraints
  6. Analyticity and improved series expansion
  7. $K_{\ell3}$ and $K_{\ell2}$ decays beyond the SM
  8. The $s\rightarrow u$ effective Hamiltonian
  9. $K_{\ell 2}$ rates
  10. $K_{\ell 3}$ rates and kinematical distributions
  11. Data Analysis
  12. $K_L$ leading branching ratios and $\tau_L$
  13. $K_S$ leading branching ratios and $\tau_S$
  14. $K^\pm$ leading branching ratios and $\tau^\pm$
  15. Measurement of BR($K_{e2})$/BR($K_{\mu2}$)
  16. ...and 29 more sections

Figures (12)

  • Figure 1: Evolution of average values for main $K_L$ BRs.
  • Figure 2: Evolution of average values for main $K^\pm$ BRs.
  • Figure 3: 1-$\sigma$ contours for $\lambda_+'$, $\lambda_+"$, $\lambda_0$ determinations from ISTRA+(pink ellipse), KLOE(blue ellipse), KTeV(red ellipse), NA48(green ellipse), and world average with(filled yellow ellipse) and without(filled cyan ellipse) the NA48 $K_{\mu3}$ result.
  • Figure 4: Display of $\vert V_{us}\vert\times$$f_{+}(0)$ for all channels.
  • Figure 5: Present determinations of $f_+(0)\equiv f_+^{K^0\pi^-}(0)$ from lattice QCD and analytical or semi-analytical approaches LRrbcf0milcf0f0.
  • ...and 7 more figures