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An evaluation of |Vus| and precise tests of the Standard Model from world data on leptonic and semileptonic kaon decays

M. Antonelli, V. Cirigliano, G. Isidori, F. Mescia, M. Moulson, H. Neufeld, E. Passemar, M. Palutan, B. Sciascia, M. Sozzi, R. Wanke, O. P. Yushchenko

TL;DR

The paper performs a comprehensive global analysis of leptonic and semileptonic kaon decays, integrating world experimental data with lattice QCD inputs to extract $|V_{us}|$ and test CKM unitarity and lepton universality. It relies on precise descriptions of $K_{ ext{l}2}$ and $K_{ ext{l}3}$ rates, including electromagnetic and isospin corrections, and employs dispersive and Taylor parameterizations for form factors, with Callan–Treiman constraints linking scalar form factors to $f_K/f_\\pi$ and $f_+(0)$. The results yield $|V_{us}|f_+(0)=0.2163(5)$ and $|V_{us}/V_{ud}| imes f_K/f_\\pi=0.2758(5)$, leading to a first-row CKM unitarity test $\, riangle_{CKM}=-0.0001(6)$ and a bound on new-physics scales around 11 TeV. The analysis also cross-validates lattice predictions for $f_+(0)$ and $f_K/f_\\pi$, confirms lepton universality at the permille level, and constrains beyond-SM contributions in a model-independent EFT framework. Overall, the work demonstrates that kaon decays provide a highly sensitive arena for precision SM tests and for probing high-energy new physics.

Abstract

We present a global analysis of leptonic and semileptonic kaon decay data, including all recent results published by the BNL-E865, KLOE, KTeV, ISTRA+ and NA48 experiments. This analysis, in conjunction with precise lattice calculations of the hadronic matrix elements now available, leads to a very precise determination of |Vus| and allows us to perform several stringent tests of the Standard Model.

An evaluation of |Vus| and precise tests of the Standard Model from world data on leptonic and semileptonic kaon decays

TL;DR

The paper performs a comprehensive global analysis of leptonic and semileptonic kaon decays, integrating world experimental data with lattice QCD inputs to extract and test CKM unitarity and lepton universality. It relies on precise descriptions of and rates, including electromagnetic and isospin corrections, and employs dispersive and Taylor parameterizations for form factors, with Callan–Treiman constraints linking scalar form factors to and . The results yield and , leading to a first-row CKM unitarity test and a bound on new-physics scales around 11 TeV. The analysis also cross-validates lattice predictions for and , confirms lepton universality at the permille level, and constrains beyond-SM contributions in a model-independent EFT framework. Overall, the work demonstrates that kaon decays provide a highly sensitive arena for precision SM tests and for probing high-energy new physics.

Abstract

We present a global analysis of leptonic and semileptonic kaon decay data, including all recent results published by the BNL-E865, KLOE, KTeV, ISTRA+ and NA48 experiments. This analysis, in conjunction with precise lattice calculations of the hadronic matrix elements now available, leads to a very precise determination of |Vus| and allows us to perform several stringent tests of the Standard Model.

Paper Structure

This paper contains 33 sections, 66 equations, 12 figures, 16 tables.

Table of Contents

  1. Introduction
  2. Phenomenological framework
  3. $K_{\ell2}$ rates in the Standard Model
  4. Theoretical determination of $f_K/f_\pi$
  5. $K_{\ell3}$ rates in the Standard Model
  6. Theoretical determination of $f_+(0)$
  7. Electromagnetic effects in $K_{\ell3}$ decays
  8. Isospin-breaking corrections in $K_{\ell3}$ decays
  9. Parameterization of the form factors
  10. Dispersive parameterization for the form factors
  11. $K_{\ell3}$ and $K_{\ell2}$ beyond the Standard Model
  12. Effective Lagrangian for semileptonic decays
  13. Phenomenology in the $\rm U(3)^5$ limit
  14. Beyond $\rm U(3)^5$
  15. Experimental inputs
  16. ...and 18 more sections

Figures (12)

  • Figure 1: Summary of lattice determinations of $f_K/f_\pi$Aoki:1999yrAliKhan:2001txAoki:2002ucAoki:2004htGockeler:2006nsBlossier:2007vvBlossier:2009bxAubin:2004fsBernard:2007psBazavov:2009fkBeane:2006kxAllton:2008pnMawhinney:2009jyAoki:2008smNoaki:2009skFollana:2007uvAubin:2008ieDurr:2010hr. The smallest lattice spacing $a$ (when available), lightest value of $m_\pi$ simulated, and type of lattice fermions used are listed in each case All results for which a value of $a$ is listed have been extrapolated by the authors to the contiunuum limit. Where two types of lattice fermions are listed (e.g. "DWF/Stag"), valence and sea quarks are discretized differently. Unpublished results are indicated by asterisks.
  • Figure 2: Present determinations of $f_+(0) \equiv f_+^{K^0\pi^-}(0)$ from analytical or semi-analytical approaches Leutwyler:1984jeBijnens:2003uyJamin:2004reCirigliano:2005xn and lattice QCD Becirevic:2004yaTsutsui:2005cjDawson:2006qcBrommel:2007wnLubicz:2009htBoyle:2007qeBoyle:2010bh. Unpublished results are indicated by asterisks.
  • Figure 3: Evolution of average values for main $K_L$ BRs.
  • Figure 4: Evolution of average values for main $K^\pm$ BRs.
  • Figure 5: Recent measurements of $K_{e3}$ vector form factor parameters. The yellow ellipse shows the result of a fit to all data.
  • ...and 7 more figures