Kaon Decays in the Standard Model

Abstract

A comprehensive overview of kaon decays is presented. The Standard Model predictions are discussed in detail, covering both the underlying short-distance electroweak dynamics and the important interplay of QCD at long distances. Chiral perturbation theory provides a universal framework for treating leptonic, semileptonic and nonleptonic decays including rare and radiative modes. All allowed decay modes with branching ratios of at least 10^(-11) are analyzed. Some decays with even smaller rates are also included. Decays that are strictly forbidden in the Standard Model are not considered in this review. The present experimental status and the prospects for future improvements are reviewed.

53 pages, 21 figures. Typos corrected, references updated, content matches the version published in Rev. Mod. Phys. 84 (2012) 399

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• K_L to π^+ π^- e^+ e^-
• Violation of Time Reversal Invariance in the Decays K_L -> pi^+ pi^- gamma and K_L -> pi^+ pi^- e^+ e^-
• $B_K$ and Explicit Chiral Symmetry Breaking
• Dispersive analysis of K_{L mu3} and K_{L e3} scalar and vector form factors using KTeV data
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• Radiative Ke3 decays revisited
• Isospin Breaking in $K\to 3\pi$ Decays II: Radiative Corrections
• Search for the Decay K+ -> pi+ pi0 nu nubar
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• Isospin Breaking in $K\to 3\pi$ Decays I: Strong Isospin Breaking
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• Search for the K(S) --> e+e- decay with the KLOE detector at DAFNE
• Search for the K_S -> e+e- decay with the KLOE detector
• Reanalysis of pion pion phase shifts from K -> pi pi decays
• Measurements of the Decay KL->e+e-mu+mu-
• Measurements of the rare decay K_{L} -> e^{+} e^{-} e^{+} e^{-}
• K->pipie+e- decays and chiral low-energy constants
• Radiative Four--Meson Amplitudes in Chiral Perturbation Theory
• Unitarity corrections to K+ -> pi+ gamma l+l-
• A Measurement of the K0 Charge Radius and a CP Violating Asymmetry Together with a Search for CP Violating E1 Direct Photon Emission in the Rare Decay KL->pi+pi-e+e-
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• The decays $K\to \pi \pi \nu \overline{\nu }$ within the standard model
• The Physics of $K^0-{\bar{K}}^0$ Mixing: ${\hat{B}}_K$ and $\Delta M_{LS}$ in the Chiral Quark Model
• The $B_K$ Kaon Parameter in the Chiral Limit
• A joint analysis of the S-wave in the pi+pi- and pi0pi0 data
• A 1996 Analysis of the CP Violating Ratio epsilon'/epsilon
• Comment on `Analysis of O(p^2) Corrections to <2pi|Q_{7,8}|K>'
• Generating Functional for Strong and Nonleptonic Weak Interactions
• K_{L,S} \to ππν\barν Decays Within and Beyond the Standard Model
• Constructing CP-Odd Observables
• Calculating ${\epsilon }^{\prime }/\epsilon$ using HYP staggered fermions
• Improving the phenomenology of K_{l3} form factors with analyticity and unitarity
• Empirical parameterization of the K+- -> pi+- pi0 pi0 decay Dalitz plot
• Measurement of the K_L \to πμνform factor parameters with the KLOE detector
• Electromagnetic penguin operators and direct CP violation in K --> pi l^+ l^-
• Dispersive representation of K -> 3 pi amplitudes and cusps
• A New Measurement of the Radiative Ke3 Branching Ratio and Photon Spectrum
• Isospin Breaking in $K_{\ell 4}$ Decays of the Neutral Kaon
• Splitting Strong and Electromagnetic Interactions in K(L4) Decays
• A phenomenological description of $K\to \pi \pi \gamma$ magnetic transitions
• Reanalysis of CP Violation in K_L -> pi^+ pi^- gamma
• $K_L\to \gamma \nu \bar{\nu }$ in the Light Front Model
• First observation of the KS->pi0 gamma gamma decay
• Time Evolution of Decay Spectrum in K^0, K^0 bar -> pi^+ pi^- e^+ e^-
• Form factor in K+ --> pi+ pi0 gamma: interference versus direct emission
• Measurement of the Radiative Ke3 Branching Ratio
• The chiral logs of the K -> pi pi amplitude
• A Measurement of the Branching Ratio of $K_L\to e^{+}{e}^{-}\gamma \gamma$
• $K_{e5}$ Decays in Chiral Perturbation Theory
• Measurement of $K^{+}\to {\pi }^0{\pi }^0{e}^{+}\nu$ ($K_{e4}^{00}$) decay using stopped positive kaons
• Analysis of K_L -> pi^+ pi^- gamma in Chiral Perturbation Theory
• The CP-violating asymmetry in K_L -> pi+ pi- e+ e-
• $K^0$ Decays into Three Photons
• Hadronic Matrix Elements for Kaons
• Observation of the Decay $K_L\to {\mu }^{+}{\mu }^{-}\gamma \gamma$
• Measurements of the Decay $K_L\to e^{+}{e}^{-}\gamma$
• Measurement of Direct Emission in the KL->pi+pi-gamma Decay Mode
• $K\to (\pi \pi {)}_{I=2}$ decays and twisted boundary conditions
• Size of Isospin Breaking in Charged K(L4) Decay
• Measurement of the Decay KL -> pi0 e+ e- gamma
• Chiral predictions for K_L -> pi0 gamma mu+ mu-
• Charge asymmetry in K+- --> π+-γγinduced by the electromagnetic penguin operators
• Measurement of the Branching Ratio and Form Factors for the Decay \boldmath $K_L\toπ^{\pm}π^0e^{\mp}ν_e(\barν_e)
• Search for the decay $K_L^0\to 3\gamma$
• A Study of the Radiative Ke3 Decay and Search for Direct Photon Emission with the KLOE Detector
• Analysis of $K_L\to \gamma \nu \bar{\nu }$
• Search for the Rare Decay K_{L}\toπ^{0}π^{0}γ
• PEN experiment: a precise measurement of the pi+ -> e+ nu decay branching fraction
• Kaon Decay into Three Photons Revisited
• SU(3) and Nonet Breaking Effects in $K_L\to \gamma \gamma$ Induced by $s\to d+2gluon$ due to Anomaly
• $K_L\to \gamma \nu >\bar{\nu }$ decay beyond the standard model
• On V_ud determination from kaon decays

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• Hunting down massless dark photons in kaon physics
• Comparison of lattice QCD+QED predictions for radiative leptonic decays of light mesons with experimental data
• Sterile neutrinos facing kaon physics experiments
• High-precision determination of the $K_{e3}$ radiative corrections
• ${\epsilon }^{\prime }/\epsilon$ in the Standard Model at the Dawn of the 2020s
• D-meson semileptonic decays to pseudoscalars from four-flavor lattice QCD
• Invisible $K_L$ decays as a probe of new physics
• Rare b hadron decays at the LHC
• Low Scale $U(1{)}_X$ Gauge Symmetry as an Origin of Dark Matter, Neutrino Mass and Flavour Anomalies
• New method for calculating electromagnetic effects in semileptonic beta-decays of mesons
• What can we learn about light-meson interactions at electron-positron colliders?
• Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses
• $K\to {\mu }^{+}{\mu }^{-}$ as a clean probe of short-distance physics
• Towards NNLO accuracy for ${\epsilon }^{\prime }/\epsilon$
• A New Theory Framework for the Electroweak Radiative Corrections in $K_{l3}$ Decays
• Radiative corrections to semileptonic beta decays: Progress and challenges
• Standard Model evaluation of ${\epsilon }_K$ using lattice QCD inputs for ${\hat{B}}_K$ and $V_{cb}$
• K^+ -> pi^+pi^0e^+e^-: a novel short-distance probe
• Dark matter and $B$-meson anomalies in a flavor dependent gauge symmetry
• The Large $N_c$ limit of QCD on the lattice
• A new search for the $K_L\to {\pi }^0\nu \overline{\nu }$ and $K_L\to {\pi }^0{X}^0$ decays
• Standard Model and New Physics contributions to $K_L$ and $K_S$ into four leptons
• Probing flavor constrained SMEFT operators through $tc$ production at the Muon collider
• ${\epsilon }_K^{\prime }/{\epsilon }_K$ and $K\to \pi \nu \bar{\nu }$ in a two-Higgs doublet model
• A symmetry preserving contact interaction treatment of the kaon
• Weakly-induced strong CP-violation
• Search for the $K_L\to {\pi }^0\nu \bar{\nu }$ Decay at the J-PARC KOTO Experiment
• New physics in $s\to d$ semileptonic transitions: rare hyperon vs. kaon decays
• Dark-sector physics in the search for the rare decays $K^{+}\to {\pi }^{+}\bar{\nu }\nu$ and $K_L\to {\pi }^0\bar{\nu }\nu$
• Final state interaction phases using data from CP asymmetries
• Anomalous $tqZ$ coupling effects in rare B- and K-meson decays
• On the amplitudes for the CP-conserving $K^{\pm }(K_S)\to {\pi }^{\pm }({\pi }^0){\ell }^{+}{\ell }^{-}$ rare decay modes
• Non-leptonic kaon decays at large $N_c$
• Methods for high-precision determinations of radiative-leptonic decay form factors using lattice QCD
• Comprehensive Analysis of Charged Lepton Flavour Violation in the Symmetry Protected Type-I Seesaw
• Lepton Flavour Violation in minimal grand-unified type II seesaw models
• Dark showers from Z-dark Z' mixing
• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• Impact of indirect CP violation on Br$(K_S\to {\mu }^{+}{\mu }^{-}{)}_{\ell =0}$
• Axiogenesis with a Heavy QCD Axion
• $B\to K+$invisible, dark matter, and $CP$ violation in hyperon decays
• Constraints on Scalar Leptoquark from Kaon Sector
• Measurement of the $K^{+}\to {\pi }^{+}\gamma \gamma$ decay
• Lattice QCD calculation of $K\to \ell {\nu }_{\ell }{\ell }^{\prime +}{\ell }^{\prime -}$ decay width
• Advancing the phenomenology of GeV-scale axion-like particles
• Sterile neutrino and leptonic decays of the pseudoscalar mesons
• openQ*D code: a versatile tool for QCD+QED simulations
• Beyond the Standard Model prospects for kaon physics at future experiments
• Portal Effective Theories: A framework for the model independent description of light hidden sector interactions
• New bounds on axion-like particles from MicroBooNE
• Radiative lepton flavor violating B, D, and K decays
• The 27-plet contributions to the CP-conserving $K\to \pi l^{+}{l}^{-}$ decays
• Three Exceptions to the Grossman-Nir Bound
• First Observation and Study of the $K^{\pm }\to {\pi }^{\pm }{\pi }^0{e}^{+}{e}^{-}$ Decay
• Theoretical status of ${\epsilon }^{\prime }/\epsilon$
• ${\epsilon }_K$ and ${\epsilon }^{\prime }/\epsilon$ in a diquark model
• Interference effect in lepton number violating and conserving meson decays for a left-right symmetric model
• Dispersive treatment of $K_S\to \gamma \gamma$ and $K_S\to \gamma {\ell }^{+}{\ell }^{-}$
• A Precision Relation between $\Gamma (K\to {\mu }^{+}{\mu }^{-})(t)$ and $\mathcal{B}(K_L\to {\mu }^{+}{\mu }^{-})/\mathcal{B}(K_L\to \gamma \gamma )$
• Improved Standard-Model prediction for $K_L\to {\ell }^{+}{\ell }^{-}$
• $K\to \pi {\ell }^{+}{\ell }^{-}$ form factor in the Large-N${}_c$ and cut-off regularization method
• Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory
• Probing new physics with the kaon decays $K\to \pi \pi /E$
• Long-distance weak annihilation contribution to the $B^{\pm }\to ({\pi }^{\pm },K^{\pm }){\ell }^{+}{\ell }^{-}$ decays
• Twisted finite-volume corrections to $K_{l3}$ decays with partially-quenched and rooted-staggered quarks
• TAU2012 Summary
• Vector and Axial-vector form factors in radiative kaon decay and flavor SU(3) symmetry breaking
• Towards a discovery of BSM physics from the Cabibbo angle anomaly
• Recent progress in applying lattice QCD to kaon physics
• $S$-wave contribution to rare $D^0\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ decays in the Standard Model and sensitivity to New Physics
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Light scalar beyond the Higgs mixing limit
• Strange processes in general two Higgs doublet model
• Updated Standard Model Prediction for ${\epsilon }^{\prime }/\epsilon$
• Facets of chiral perturbation theory
• Measurements of the absolute branching fractions of ${\Omega }^{-}$ decays and test of the $\Delta I=1/2$ rule
• Towards a unified treatment of $\Delta S=0$ parity violation in low-energy nuclear processes
• CP violation in the hyperon decays $\Sigma \to N\pi$
• Exploring the role of the charm quark in the $\Delta I=1/2$ rule
• Workshop summary -- Kaons@CERN 2023
• Experimental Status of the CKM Matrix
• ${\Sigma }^{+}\to p{\ell }^{+}{\ell }^{-}$ decays within the standard model and beyond
• New determination of the branching ratio of the structure dependent radiative $K^{+}\to e^{+}{\nu }_e\gamma$ decay
• Quantum pions
• On the three-point order parameters of chiral symmetry breaking
• The Light Sgoldstino Phenomenology: Explanations for the Muon $(g-2)$ Deviation and KOTO Anomaly
• Explaining the $b\to s{\ell }^{+}{\ell }^{-}$ anomalies in $Z^{\prime }$ scenarios with top-FCNC couplings
• Improved $K_{e3}$ radiative corrections sharpen the $K_{\mu 2}$--$K_{l3}$ discrepancy
• Hidden physics in pion and some other meson decays
• First Order Electroweak Phase Transition from Weakly Coupled sub-GeV Physics and Possible Connection to Fermion Flavor
• Leading Chiral Logarithms of $K_S\to \gamma \gamma$ and $K_S\to \gamma l^{+}{l}^{-}$ at two Loops
• Efficient lattice QCD computation of radiative-leptonic-decay form factors at multiple positive and negative photon virtualities
• Factorizing Hidden Particle Production Rates
• Theoretical overview of kaon decays
• New Limits on Light Dark Matter-Nucleon Scattering
• ${\epsilon }^{\prime }/\epsilon$ in and beyond the Standard Model
• Radiative modes $K^{+}\to {\pi }^{+}{\gamma }^{\ast }{\gamma }^{(\ast )}$ and the $K^{+}\to {\pi }^{+}4e$ decay
• Consistency tests of AMPCALCULATOR and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial based approach
• CP violation in $K\to {\mu }^{+}{\mu }^{-}$ with and without time dependence through a tagged analysis
• Isospin-breaking contributions to ${\epsilon }^{\prime }/\epsilon$
• Non-leptonic kaon decays at large $N_c$
• Confronting hadronic tau decays with non-leptonic kaon decays
• Flavor Physics and Lattice QCD
• The Optimal Strategy for ${\epsilon }^{\prime }/\epsilon$ in the SM: 2019