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 ${10}^{\ensuremath{-}11}$ 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

Kaon Decays in the Standard Model

The structure of the ${K}_{l4}$ decay spectrum is displayed in its full generality as a function of a complete set of five kinematic variables; polarization effects are in part similarly described. The nontrivial dynamical aspects of ${K}_{l4}$ decay reside in certain form factors, which depend on only three of the variables. It is shown that, with large cuts at the two remaining variables, the measurement of the decay spectrum alone suffices to overdetermine the form factors. On certain standard assumptions, these form factors carry information relating to the phase shifts for pion-pion scattering. It is an important practical matter to extract something of this information under conditions of limited statistics, where the spectra have to be treated in partially integrated form. We find that this can be accomplished, with surprising economy, for the energy-dependent phase-shift difference ${\ensuremath{\delta}}_{s}\ensuremath{-}{\ensuremath{\delta}}_{p}$, on the single additional assumption that the dipion system is produced chiefly in $s$- and $p$-wave states. The information emerges from the intensity spectrum for ${K}_{e4}$ decay, and again from the polarization spectrum for ${K}_{\ensuremath{\mu}4}$ decay, the spectra being treated as functions of only three variables. Moreover, the structure in two of these variables is simple and therefore relatively undemanding in a statistical sense.

Pion Phase-Shift Information from K l 4 Decays

K ℓ4 form-factors and π - π scattering

The $F$ and $G$ form-factors of $K_{\ell4}$ and the quark condensates are calculated to ${\cal O}(p^6)$ in Chiral Perturbation Theory (CHPT). Full formulas are presented as much as possible. A full refit of most of the ${\cal O}(p^4)$ CHPT parameters is done with a discussion of all inputs and underlying assumptions. We discuss the consequences for the vacuum expectation values, decay constants, pseudoscalar masses and $\pi$-$\pi$ scattering.

$K_{\ell 4}$ Form-Factors and $\pi$-$\pi$ Scattering

A study of 13.3\ifmmode\times\else\texttimes\fi{}${10}^{6}$ stopped ${K}^{+}$ in a heavy-liquid bubble chamber yielded 269 ${K}_{e4}$ decays of the type ${e}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\nu}$, a total greater by a factor of 4 than the number found in a previous experiment. No examples of ${e}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}\overline{\ensuremath{\nu}}$ were found. With 95% confidence, the upper limit for the decay rate of ${K}_{e4}({e}^{\ensuremath{-}})$ was found to be 56 ${\mathrm{sec}}^{\ensuremath{-}1}$. The rate for ${K}_{e4}({e}^{+})$ was found to be (2.60\ifmmode\pm\else\textpm\fi{}0.30)\ifmmode\times\else\texttimes\fi{}${10}^{3}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. The angular distributions and the dipion invariant-mass plot have been fitted by varying the form factors ${f}_{s}$, ${f}_{p}$, $g$, and $h$, and the difference between $s$- and $p$-wave $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ phase shift. Two acceptable solutions have been found. Both agree that the vector form factor $h$ is significantly nonzero and that its sign is negative with respect to that of ${f}_{g}$. Also, it has been found necessary to include ${f}_{p}$ in order to obtain a good fit. Although both solutions give the magnitude of the phase difference to be 25\ifmmode\pm\else\textpm\fi{}9 deg, the two estimates have opposite sign. No evidence of a $\ensuremath{\sigma}$ resonance is seen. The angular distributions are found to be consistent with time-reversal invariance, and with the locality of lepton production.

Study of K e 4 Decays

${K}_{l4}$ decay is formulated in a way which allows the extraction of form factors and $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ phase-shift differences from data with limited statistics. The only assumptions required are $T$ invariance and a restriction to $S$ and $P$ waves in the final state, no other dynamical assumptions being required. It is shown that the assumption of the $\ensuremath{\Delta}I=\frac{1}{2}$ rule is not necessary if all ${K}_{l4}$ decays are taken into account. When the existing available data are analyzed in the simple extension of the Cabibbo-Maksymowicz approach in which all $P$-wave contributions are taken into account, there is a sign ambiguity in the $S$-wave $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ phase shift. This ambiguity is fundamental to this approach and can be solved only by means of another angular distribution. Such a distribution could be obtained from the existing data.

THEORETICAL STUDY OF K/sub l4/ DECAY.

Analysis of Ke4 decay, evidence for a vector current and its consequences

A note on the Ke4 and Kμ4 decay rates

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THEORETICAL STUDY OF K/sub l4/ DECAY.

Analysis of Ke4 decay, evidence for a vector current and its consequences

A note on the Ke4 and Kμ4 decay rates