# Meson Particle Listings

## K$^{\pm}$

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>0.736</td><td>±0.014</td><td>±0.012</td><td>33k</td><td>BATUSOV</td><td>98</td><td>SPEC</td><td>+</td></tr><tr><td>0.582</td><td>±0.021</td><td></td><td>43k</td><td>BOLOTOV</td><td>86</td><td>CALO</td><td>-</td></tr><tr><td>0.670</td><td>±0.054</td><td></td><td>3263</td><td>BRAUN</td><td>76b</td><td>HLBC</td><td>+</td></tr><tr><td>0.630</td><td>±0.038</td><td></td><td>5635</td><td>SHEAFF</td><td>75</td><td>HLBC</td><td>+</td></tr><tr><td>0.510</td><td>±0.060</td><td></td><td>27k</td><td>SMITH</td><td>75</td><td>WIRE</td><td>+</td></tr><tr><td>0.67</td><td>±0.06</td><td></td><td>1365</td><td>AUBERT</td><td>72</td><td>HLBC</td><td>+</td></tr><tr><td>0.544</td><td>±0.048</td><td></td><td>4048</td><td>DAVISION</td><td>69</td><td>HLBC</td><td>+</td></tr></table>

Also emulsion

¹Measured using in-flight decays of the 25 GeV negative secondary beam.

²They form new world averages $g_{-} = (0.617 \pm 0.018)$ and $g_{+} = (0.684 \pm 0.033)$ which give $\Delta g_{\tau'} = 0.051 \pm 0.028$.

## QUADRATIC COEFFICIENT h FOR $K^{\pm} \to \pi^{\pm} \pi^{0} \pi^{0}$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.052 ±0.008</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>0.0551 ±0.0044 ±0.0086</td><td>493k</td><td>AKOPDZHAN..05B</td><td>TNF</td><td>±</td><td></td></tr><tr><td>0.046 ±0.004 ±0.012</td><td>252k</td><td>1 AJINENKO</td><td>03B</td><td>ISTR</td><td>-</td></tr><tr><td colspan="6"><strong>• • • We do not use the following data for averages, fits, limits, etc. • • •</strong></td></tr><tr><td>0.128 ±0.015 ±0.024</td><td>33k</td><td>BATUSOV</td><td>98</td><td>SPEC</td><td>+</td></tr><tr><td>0.037 ±0.024</td><td>43k</td><td>BOLOTOV</td><td>86</td><td>CALO</td><td>-</td></tr><tr><td>0.152 ±0.082</td><td>3263</td><td>BRAUN</td><td>76b</td><td>HLBC</td><td>+</td></tr><tr><td>0.041 ±0.030</td><td>5635</td><td>SHEAFF</td><td>75</td><td>HLBC</td><td>+</td></tr><tr><td>0.009 ±0.040</td><td>27k</td><td>SMITH</td><td>75</td><td>WIRE</td><td>+</td></tr><tr><td>-0.01 ±0.08</td><td>1365</td><td>AUBERT</td><td>72</td><td>HLBC</td><td>+</td></tr><tr><td>0.026 ±0.050</td><td>4048</td><td>DAVISION</td><td>69</td><td>HLBC</td><td>+</td></tr></tbody></table>

Also emulsion

¹Measured using in-flight decays of the 25 GeV negative secondary beam.

## QUADRATIC COEFFICIENT k FOR $K^{\pm} \to \pi^{\pm} \pi^{0} \pi^{0}$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td><strong>0.0054 ±0.0035</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>0.0082 ±0.0011 ±0.0014</td><td>493k</td><td>AKOPDZHAN..05B</td><td>TNF</td><td>±</td></tr><tr><td>0.001 ±0.001 ±0.002</td><td>252k</td><td>1 AJINENKO</td><td>03B</td><td>ISTR</td><td>-</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>0.0197 ±0.0045 ±0.0029</td><td>33k</td><td>BATUSOV</td><td>98</td><td>SPEC</td><td>+</td></tr></table>

¹Measured using in-flight decays of the 25 GeV negative secondary beam.

## $(g_{+} - g_{-}) / (g_{+} + g_{-})$ FOR $K^{\pm} \to \pi^{\pm} \pi^{0} \pi^{0}$

A nonzero value for this quantity indicates CP violation.

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>1.8 ± 1.8</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td></tr><tr><td>1.8 ± 1.7 ± 0.6</td><td>91.3M</td><td>1 BATLEY</td><td>07E</td><td>NA48</td></tr><tr><td>2 ± 18 ± 5</td><td>619k</td><td>2 AKOPDZHAN..05</td><td>03B</td><td>ISTR</td><td>TNF</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>1.8 ± 2.2 ± 1.3</td><td>47M</td><td>3 BATLEY</td><td>06A</td><td>NA48</td><td></td></tr></table>

¹BATLEY 07E includes data from BATLEY 06A. Uses quadratic parametrization and PDG 06 value $g = 0.626 \pm 0.007$ to obtain $g_{+} - g_{-} = (2.2 \pm 2.1 \pm 0.7) \times 10^{-4}$. Neglects any possible charge asymmetries in higher order slope parameters $h$ or $k$.

²Asymmetry obtained assuming that $g_{+} + g_{-} = 2 \times 0.652$ (PDG 02) and that asymmetries in $h$ and $k$ are zero.

³Linear and quadratic slopes from PDG 04 are used. Any possible charge asymmetries in higher order slope parameters $h$ or $k$ are neglected.

## ALTERNATIVE PARAMETRIZATIONS OF $K^{\pm} \to \pi^{\pm} \pi^{0} \pi^{0}$ DALITZ PLOT

The following functional form for the matrix element suggested by $\pi\pi$ rescattering in $K^{+} \to \pi^{+} \pi^{+} \pi^{-} \to \pi^{+} \pi^{0} \pi^{0}$ is used for this fit (CABIBBO 04A, CABIBBO 05): Matrix element $M = M_{0} + M_{1}$ where $M_{0} = 1 + (1/2)g_{0}u + (1/2)h' u^{2} + (1/2)k_{0}v^{2}$ with $u = (s_{3}-s_{5})/(m_{\pi+})^{2}$, $v = (s_{2}-s_{1})/(m_{\pi+})^{2}$ and where $M_{1}$ takes into account the non-analytic piece due to $\pi i$ rescattering amplitudes $a_{0}$ and $a_{2}$; The parameters $g_{0}$ and $h'$ are related to the parameters $g$ and $h$ of the matrix element squared given in the previous section by the approximations $g_{0} \sim g^{\text{PDG}}$ and $h' \sim h^{\text{PDG}} - (g/2)^{2}$ and $k_{0} \sim k^{\text{PDG}}$.

In addition, we also consider the effective field theory framework of COLANGELO 06A and BISSEGGER 09 to extract $g_{BB}$ and $h'_{BB}$.

## LINEAR COEFFICIENT $g_{0}$ FOR $K^{\pm} \to \pi^{\pm} \pi^{0} \pi^{0}$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td><strong>0.6525 ±0.0009 ±0.0033</strong></td><td><strong>60M</strong></td><td><strong>1 BATLEY</strong></td><td><strong>09A</strong></td><td><strong>NA48</strong></td><td><strong>±</strong></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>0.645 ±0.004 ±0.009</td><td>23M</td><td>2 BATLEY</td><td>06B</td><td>NA48</td><td>±</td></tr></table>

¹This fit is obtained with the CABIBBO 05 matrix element in the $2\pi^{0}$ invariant mass squared range $0.074094 < m_{2\pi^{0}}^{2} < 0.104244 \text{ GeV}^{2}$. Electromagnetic corrections and CHPT constraints for $\pi\pi$ phase shifts $(a_{0}$ and $a_{2})$ have been used. Also measured $(a_{0} - a_{2}) m_{\pi^{+}} = 0.2646 \pm 0.0021 \pm 0.0023$, where $k_{0}$ was kept fixed in the fit at $-0.0099$.

²Superseded by BATLEY 09A. This fit is obtained with the CABIBBO 05 matrix element in the $2\pi^{0}$ invariant mass squared range $0.074 \text{ GeV}^{2} < m_{2\pi^{0}}^{2} < 0.097 \text{ GeV}^{2}$, assuming $k = 0$ (no term proportional to $(s_{2} - s_{1})^{2}$) and excluding the kinematic region around the cusp $(m_{2\pi^{0}}^{2} = (2m_{\pi^{+}})^{2} \pm 0.000525 \text{ GeV}^{2})$. Also $\pi\pi$ phase shifts $a_{0}$ and $a_{2}$ are measured: $(a_{0} - a_{2}) m_{\pi^{+}} = 0.268 \pm 0.010 \pm 0.004 \pm 0.013(\text{external})$ and $a_{2} m_{\pi^{+}} = -0.041 \pm 0.022 \pm 0.014$.

## QUADRATIC COEFFICIENT $h'$ FOR $K^{\pm} \to \pi^{\pm} \pi^{0} \pi^{0}$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td><strong>-0.0433 ±0.0008 ±0.0026</strong></td><td><strong>60M</strong></td><td><strong>1 BATLEY</strong></td><td><strong>09A</strong></td><td><strong>NA48</strong></td><td><strong>±</strong></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>-0.047 ±0.012 ±0.011</td><td>23M</td><td>2 BATLEY</td><td>06B</td><td>NA48</td><td>±</td></tr></table>

¹This fit is obtained with the CABIBBO 05 matrix element in the $2\pi^{0}$ invariant mass squared range $0.074094 < m_{2\pi^{0}}^{2} < 0.104244 \text{ GeV}^{2}$. Electromagnetic corrections and CHPT constraints for $\pi\pi$ phase shifts $(a_{0}$ and $a_{2})$ have been used. Also measured $(a_{0} - a_{2}) m_{\pi^{+}} = 0.2646 \pm 0.0021 \pm 0.0023$, where $k_{0}$ was kept fixed in the fit at $-0.0099$.

²Superseded by BATLEY 09A. This fit is obtained with the CABIBBO 05 matrix element in the $2\pi^{0}$ invariant mass squared range $0.074 \text{ GeV}^{2} < m_{2\pi^{0}}^{2} < 0.097 \text{ GeV}^{2}$, assuming $k = 0$ (no term proportional to $(s_{2} - s_{1})^{2}$) and excluding the kinematic region around the cusp $(m_{2\pi^{0}}^{2} = (2m_{\pi^{+}})^{2} \pm 0.000525 \text{ GeV}^{2})$. Also $\pi\pi$ phase shifts $a_{0}$ and $a_{2}$ are measured: $(a_{0} - a_{2}) m_{\pi^{+}} = 0.268 \pm 0.010 \pm 0.004 \pm 0.013(\text{external})$ and $a_{2} m_{\pi^{+}} = -0.041 \pm 0.022 \pm 0.014$.

## QUADRATIC COEFFICIENT $k_{0}$ FOR $K^{\pm} \to \pi^{\pm} \pi^{0} \pi^{0}$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td><strong>0.0095 ±0.00017 ±0.00048</strong></td><td><strong>60M</strong></td><td><strong>1 BATLEY</strong></td><td><strong>09A</strong></td><td><strong>NA48</strong></td><td><strong>±</strong></td></tr></tbody></table>

¹Assumed $a_{2} m_{\pi^{+}} = -0.0044$ in the fit.

## LINEAR COEFFICIENT $g_{BB}$ FOR $K^{\pm} \to \pi^{\pm} \pi^{0} \pi^{0}$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td><strong>0.6219 ±0.0009 ±0.0033</strong></td><td><strong>60M</strong></td><td><strong>1 BATLEY</strong></td><td><strong>09A</strong></td><td><strong>NA48</strong></td><td><strong>±</strong></td></tr></tbody></table>

¹This fit is obtained using parametrizations of COLANGELO 06A and BISSEGGER 09 in the $2\pi^{0}$ invariant mass squared range $0.074094 < m_{2\pi^{0}}^{2} < 0.104244 \text{ GeV}^{2}$. Electromagnetic corrections and CHPT constraints for $\pi\pi$ phase shifts $(a_{0}$ and $a_{2})$ have been used. Also measured $(a_{0} - a_{2}) m_{\pi^{+}} = 0.2633 \pm 0.0024 \pm 0.0024$, where $k_{0}$ was kept fixed in the fit at $0.0085$.

## QUADRATIC COEFFICIENT $h'_{BB}$ FOR $K^{\pm} \to \pi^{\pm} \pi^{0} \pi^{0}$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td><strong>-0.0520 ±0.0009 ±0.0026</strong></td><td><strong>60M</strong></td><td><strong>1 BATLEY</strong></td><td><strong>09A</strong></td><td><strong>NA48</strong></td><td><strong>±</strong></td></tr></tbody></table>

¹This fit is obtained using parametrizations of COLANGELO 06A and BISSEGGER 09 in the $2\pi^{0}$ invariant mass squared range $0.074094 < m_{2\pi^{0}}^{2} < 0.104244 \text{ GeV}^{2}$. Electromagnetic corrections and CHPT constraints for $\pi\pi$ phase shifts $(a_{0}$ and $a_{2})$ have been used. Also measured $(a_{0} - a_{2}) m_{\pi^{+}} = 0.2633 \pm 0.0024 \pm 0.0024$, where $k_{0}$ was kept fixed in the fit at $0.0085$.

## $K_{\pm 3}$ FORM FACTORS

In the form factor comments, the following symbols are used.

$f_{+}$ and $f_{-}$ are form factors for the vector matrix element.

$f_{S}$ and $f_{T}$ refer to the scalar and tensor term.

$$f_0 = f_+ + f_- t / (m_{K^+}^2 - m_{\pi^0}^2).$$

$t$ = momentum transfer to the $\pi$.

$\lambda_{+}$ and $\lambda_{0}$ are the linear expansion coefficients of $f_{+}$ and $f_{0}$:

$$f_{+}(t) = f_{+}(0) (1 + \lambda_{+} t / m_{\pi^{+}}^{2}).$$

For quadratic expansion

$$f_{+}(t) = f_{+}(0) \left(1 + \lambda'_{+} t / m_{\pi^{+}}^{2} + \frac{\lambda''_{+} t^{2}}{m_{\pi^{+}}^{4}}\right)$$

as used by KTeV. If there is a non-vanishing quadratic term, then $\lambda_{+}$

represents an average slope, which is then different from $\lambda'_{+}$.

NA48/2 and OKA quadratic expansion coefficients are converted with $\lambda'_{+} \text{PDG} = \lambda'_{+} \text{NA48/2}$ and $\lambda''_{+} \text{PDG} = 2 \lambda''_{+} \text{NA48/2}$

$$\lambda'_{+} \text{PDG} = \left(\frac{m_{\pi^{+}}}{m_{\pi^{0}}}\right)^2 \lambda'_{+} \text{OKA} \text{ and}$$

$$\lambda''_{+} \text{PDG} = 2 \left(\frac{m_{\pi^{+}}}{m_{\pi^{0}}}\right)^4 \lambda''_{+} \text{OKA}$$

OKA linear expansion coefficients are converted with

$$\lambda_{+} \text{PDG} = \left(\frac{m_{\pi^{+}}}{m_{\pi^{0}}}\right)^2 \lambda_{+} \text{OKA} \text{ and } \lambda_{0} \text{PDG} = \left(\frac{m_{\pi^{+}}}{m_{\pi^{0}}}\right)^2 \lambda_{0} \text{OKA}$$

The pole parametrization is

$$f_{+}(t) = f_{+}(0) \left(\frac{M_{V}^{2}}{M_{V}^{2} - t}\right)$$

$$f_{0}(t) = f_{0}(0) \left(\frac{M_{S}^{2}}{M_{S}^{2} - t}\right)$$

where $M_{V}$ and $M_{S}$ are the vector and scalar pole masses.

The following abbreviations are used:

DP = Dalitz plot analysis.

PI = $\pi$ spectrum analysis.

MU = $\mu$ spectrum analysis.

POL = $\mu$ polarization analysis.

BR = $K_{\mu 3}^{\pm} / K_{e 3}^{\pm}$ branching ratio analysis.

E = positron or electron spectrum analysis.

RC = radiative corrections.

For previous $\lambda'_{+}$ and $\lambda''_{+}$, parametrizations used by NA48 (e.g. LAI 07A) and ISTRA (e.g. YUSHCHENKO 04B) see PDG 18.
# Meson Particle Listings

## K±

### $|f_S/f_+|$ FOR $K_{e3}^{\pm}$ DECAY

Ratio of scalar to $f_+$ couplings.

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="7" style="text-align: center; font-weight: bold;">-0.008 <sup>+0.34</sup><sub>-0.40</sub> OUR AVERAGE</td></tr><tr><td>0.01 <sup>+0.38</sup><sub>-0.46</sub></td><td>5.25M</td><td>YUSHCHENKO18</td><td>OKA</td><td>+</td><td>λ'<sub>+</sub>, λ''<sub>+</sub>, f<sub>S</sub> fit</td><td></td></tr><tr><td>-0.37 <sup>+0.66</sup><sub>-0.56</sub> ± 0.41</td><td>919k</td><td>YUSHCHENKO04B</td><td>ISTR</td><td>-</td><td>λ'<sub>+</sub>, λ''<sub>+</sub>, f<sub>S</sub> fit</td><td></td></tr><tr><td>0.2 ± 2.6 ± 1.4</td><td>41k</td><td>SHIMIZU</td><td>00</td><td>SPEC</td><td>+</td><td>λ<sub>+</sub>, f<sub>S</sub>, f<sub>T</sub> fit</td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">• • • We do not use the following data for averages, fits, limits, etc.</td></tr><tr><td>0.2 <sup>+2.0</sup><sub>-2.2</sub> ± 0.3</td><td>550k</td><td>1 AJINENKO</td><td>03C</td><td>ISTR</td><td>-</td><td>λ<sub>+</sub>, f<sub>S</sub>, f<sub>T</sub> fit</td></tr><tr><td>-1.9 <sup>+2.5</sup><sub>-1.6</sub></td><td>130k</td><td>1 AJINENKO</td><td>02</td><td>SPEC</td><td></td><td>λ<sub>+</sub>, f<sub>S</sub> fit</td></tr><tr><td>7.0 ± 1.6 ± 1.6</td><td>32k</td><td>AKIMENKO</td><td>91</td><td>SPEC</td><td></td><td>λ<sub>+</sub>, f<sub>S</sub>, f<sub>T</sub>, φ fit</td></tr><tr><td>0 ± 10</td><td>2827</td><td>2 BRAUN</td><td>75</td><td>HLBC</td><td>+</td><td></td></tr><tr><td>&lt; 13</td><td>90</td><td>4017</td><td></td><td></td><td></td><td></td></tr><tr><td>14 <sup>+3</sup><sub>-4</sub></td><td>2707</td><td>2 STEINER</td><td>71</td><td>HLBC</td><td>+</td><td>λ<sub>+</sub>, f<sub>S</sub>, f<sub>T</sub>, φ fit</td></tr><tr><td>&lt; 23</td><td>90</td><td>BOTTERILL</td><td>68C</td><td>ASPK</td><td></td><td></td></tr><tr><td>&lt; 18</td><td>90</td><td>BELLOTTI</td><td>67B</td><td>HLBC</td><td></td><td></td></tr><tr><td>&lt; 30</td><td>95</td><td>KALMUS</td><td>67</td><td>HLBC</td><td></td><td></td></tr></tbody></table>

¹Superseded by YUSHCHENKO 04B.

²Statistical errors only.

### $|f_T/f_+|$ FOR $K_{e3}^{\pm}$ DECAY

Ratio of tensor to $f_+$ couplings.

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="6" style="text-align: center; font-weight: bold;">- 1.2 <sup>+ 1.3</sup><sub>- 1.1</sub> OUR AVERAGE</td></tr><tr><td>- 1.24 <sup>+ 1.6</sup><sub>- 1.3</sub></td><td>5.25M</td><td>YUSHCHENKO18</td><td>OKA</td><td>+</td><td>λ'<sub>+</sub>, λ''<sub>+</sub>, f<sub>T</sub> fit</td></tr><tr><td>- 1.2 ± 2.1 ± 1.1</td><td>919k</td><td>YUSHCHENKO04B</td><td>ISTR</td><td>-</td><td>λ'<sub>+</sub>, λ''<sub>+</sub>, f<sub>T</sub> fit</td></tr><tr><td>1 ± 14 ± 9</td><td>41k</td><td>SHIMIZU</td><td>00</td><td>SPEC</td><td>+</td><td>λ<sub>+</sub>, f<sub>S</sub>, f<sub>T</sub> fit</td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">• • • We do not use the following data for averages, fits, limits, etc.</td></tr><tr><td>2.1 <sup>+ 6.4</sup><sub>- 7.5</sub> ± 2.6</td><td>550k</td><td>1 AJINENKO</td><td>03C</td><td>ISTR</td><td>-</td><td>λ<sub>+</sub>, f<sub>S</sub>, f<sub>T</sub> fit</td></tr><tr><td>- 4.5 <sup>+ 6.0</sup><sub>- 5.7</sub></td><td>130k</td><td>1 AJINENKO</td><td>02</td><td>SPEC</td><td></td><td>λ<sub>+</sub>, f<sub>T</sub> fit</td></tr><tr><td>53 <sup>+ 9</sup><sub>- 10</sub> ± 10</td><td>32k</td><td>AKIMENKO</td><td>91</td><td>SPEC</td><td></td><td>λ<sub>+</sub>, f<sub>S</sub>, f<sub>T</sub>, φ fit</td></tr></tbody></table>

¹Superseded by YUSHCHENKO 04B.

### $f_S/f_+$ FOR $K_{\mu3}^{\pm}$ DECAY

Ratio of scalar to $f_+$ couplings.

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.17 ± 0.14 ± 0.54</td><td>540k</td><td>1 YUSHCHENKO04</td><td>ISTR</td><td>-</td><td>DP</td></tr><tr><td colspan="6" style="text-align: center; font-weight: bold;">• • • We do not use the following data for averages, fits, limits, etc.</td></tr><tr><td>0.4 ± 0.5 ± 0.5</td><td>112k</td><td>2 AJINENKO</td><td>03</td><td>ISTR</td><td>-</td><td>DP</td></tr></tbody></table>

¹The second error is the theoretical error from the uncertainty in the chiral perturbation theory prediction for $\lambda_0$, ±0.0053, combined in quadrature with the systematic error ±0.0009.

²The second error is the theoretical error from the uncertainty in the chiral perturbation theory prediction for $\lambda_0$. Superseded by YUSHCHENKO 04.

### $f_T/f_+$ FOR $K_{\mu3}^{\pm}$ DECAY

Ratio of tensor to $f_+$ couplings.

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>-0.07 ± 0.71 ± 0.20</td><td>540k</td><td>YUSHCHENKO04</td><td>ISTR</td><td>-</td><td>DP</td></tr><tr><td colspan="6" style="text-align: center; font-weight: bold;">• • • We do not use the following data for averages, fits, limits, etc.</td></tr><tr><td>-2.1 ± 2.8 ± 1.4</td><td>112k</td><td>1 AJINENKO</td><td>03</td><td>ISTR</td><td>-</td><td>DP</td></tr><tr><td>2 ± 12</td><td>1585</td><td>BRAUN</td><td>75</td><td>HLBC</td><td></td><td></td></tr></tbody></table>

¹The second error is the theoretical error from the uncertainty in the chiral perturbation theory prediction for $\lambda_0$. Superseded by YUSHCHENKO 04.

## $K_{e4}^{\pm}$ FORM FACTORS

Based on the parametrizations of AMOROS 99, the $K_{e4}^{\pm}$ form factors can be expressed as

$$F_S = f_S + f'_S q^2 + f''_S q^4 + f'_e S_e / 4m_{\pi}^2$$

$$F_P = f_P$$

$$G_p = g_p + g'_p q^2$$

$$H_p = h_p$$

where $q^2 = (S_\pi / 4m_{\pi}^2) - 1$, $S_\pi$ is the invariant mass squared of the dipion, and $S_e$ is the invariant mass squared of the dilepton.

### $f_S$ FOR $K^{\pm} \to \pi^+\pi^- e^{\pm} \nu$ DECAY

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>5.712 ± 0.032</td><td>OUR AVERAGE</td><td></td><td></td><td></td></tr><tr><td>5.705 ± 0.003 ± 0.035</td><td>1.1M</td><td>1 BATLEY</td><td>12</td><td>NA48 ±</td></tr><tr><td>5.75 ± 0.02 ± 0.08</td><td>400k</td><td>2 PISLAK</td><td>03</td><td>B865 ±</td></tr></tbody></table>

¹BATLEY 12 uses data collected in 2003–2004. The result is obtained from a measurement of $\Gamma(\pi^+\pi^- e\nu)/\Gamma(\pi^+\pi^- \pi^+) \text{ and } \text{assumed PDG 12 value of } \Gamma(\pi^+\pi^- \pi^+)/\Gamma = (5.59 \pm 0.04) \times 10^{-2}$.

²Radiative corrections included. Using Roy equations and not including isospin breaking, PISLAK 03 obtains the following $\pi\pi$ scattering lengths $a_0^0 = 0.228 \pm 0.012 \pm 0.004^{+0.012}_{-0.016}$ (theor.) and $a_0^2 = -0.0365 \pm 0.0023 \pm 0.0008^{+0.0031}_{-0.0026}$ (theor.).

### $f'_S/f_S$ FOR $K^{\pm} \to \pi^+\pi^- e^{\pm} \nu$ DECAY

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>15.2 ± 0.7 ± 0.5</td><td>1.13M</td><td>1 BATLEY</td><td>10C</td><td>NA48 ±</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">• • • We do not use the following data for averages, fits, limits, etc.</td></tr><tr><td>17.2 ± 0.9 ± 0.6</td><td>670k</td><td>2 BATLEY</td><td>08A</td><td>NA48 ±</td></tr></tbody></table>

¹Radiative corrections included. Using Roy equations and including isospin breaking, BATLEY 10C obtains the following scattering lengths $a_0^0 = 0.2220 \pm 0.0128 \pm 0.0050 \pm 0.0037$ (theor.), $a_0^2 = -0.0432 \pm 0.0086 \pm 0.0034 \pm 0.0028$ (theor.). The correlation with $f'_S/f_S = -0.954$ and with $f'_e/f_S = 0.080$. Supersedes BATLEY 08A.

²Radiative corrections included. Using Roy equations and not including isospin breaking, BATLEY 08A obtains the following $\pi\pi$ scattering length $a_0^0 = 0.233 \pm 0.016 \pm 0.007 \pm 0.004$.

### $f''_S/f_S$ FOR $K^{\pm} \to \pi^+\pi^- e^{\pm} \nu$ DECAY

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>-7.3 ± 0.7 ± 0.6</td><td>1.13M</td><td>1 BATLEY</td><td>10C</td><td>NA48 ±</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">• • • We do not use the following data for averages, fits, limits, etc.</td></tr><tr><td>-9.0 ± 0.9 ± 0.7</td><td>670k</td><td>2 BATLEY</td><td>08A</td><td>NA48 ±</td></tr></tbody></table>

¹Radiative corrections included. Using Roy equations and including isospin breaking, BATLEY 10C obtains the following scattering lengths $a_0^0 = 0.2220 \pm 0.0128 \pm 0.0050 \pm 0.0037$ (theor.), $a_0^2 = -0.0432 \pm 0.0086 \pm 0.0034 \pm 0.0028$ (theor.). The correlation with $f''_S/f_S = -0.954$ and with $f''_e/f_S = 0.019$. Supersedes BATLEY 08A.

²Radiative corrections included. Using Roy equations and not including isospin breaking, BATLEY 08A obtains the following $\pi\pi$ scattering length $a_0^0 = 0.233 \pm 0.016 \pm 0.007 \pm 0.004$.

### $f'_e/f_S$ FOR $K^{\pm} \to \pi^+\pi^- e^{\pm} \nu$ DECAY

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>6.8 ± 0.6 ± 0.7</td><td>1.13M</td><td>1 BATLEY</td><td>10C</td><td>NA48 ±</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">• • • We do not use the following data for averages, fits, limits, etc.</td></tr><tr><td>8.1 ± 0.8 ± 0.9</td><td>670k</td><td>2 BATLEY</td><td>08A</td><td>NA48 ±</td></tr></tbody></table>

¹Radiative corrections included. Using Roy equations and including isospin breaking, BATLEY 10C obtains the following scattering lengths $a_0^0 = 0.2220 \pm 0.0128 \pm 0.0050 \pm 0.0037$ (theor.), $a_0^2 = -0.0432 \pm 0.0086 \pm 0.0034 \pm 0.0028$ (theor.). The correlation with $f'_S/f_S = 0.080$ and with $f''_S/f_S = 0.019$. Supersedes BATLEY 08A.

²Radiative corrections included. Using Roy equations and not including isospin breaking, BATLEY 08A obtains the following $\pi\pi$ scattering length $a_0^0 = 0.233 \pm 0.016 \pm 0.007 \pm 0.004$.

### $f_p/f_S$ FOR $K^{\pm} \to \pi^+\pi^- e^{\pm} \nu$ DECAY

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>-4.8 ± 0.3 ± 0.4</td><td>1.13M</td><td>1 BATLEY</td><td>10C</td><td>NA48 ±</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">• • • We do not use the following data for averages, fits, limits, etc.</td></tr><tr><td>-4.8 ± 0.4 ± 0.4</td><td>670k</td><td>2 BATLEY</td><td>08A</td><td>NA48 ±</td></tr></tbody></table>

¹Radiative corrections included. Using Roy equations and including isospin breaking, BATLEY 10C obtains the following scattering lengths $a_0^0 = 0.2220 \pm 0.0128 \pm 0.0050 \pm 0.0037$ (theor.), $a_0^2 = -0.0432 \pm 0.0086 \pm 0.0034 \pm 0.0028$ (theor.). Supersedes BATLEY 08A.

²Radiative corrections included. Using Roy equations and not including isospin breaking, BATLEY 08A obtains the following $\pi\pi$ scattering length $a_0^0 = 0.233 \pm 0.016 \pm 0.007 \pm 0.004$.

### $g_p/f_S$ FOR $K^{\pm} \to \pi^+\pi^- e^{\pm} \nu$ DECAY

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>86.6 ± 1.0 ± 1.0</td><td>1.13M</td><td>1 BATLEY</td><td>10C</td><td>NA48 ±</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">• • • We do not use the following data for averages, fits, limits, etc.</td></tr><tr><td>87.3 ± 1.3 ± 1.2</td><td>670k</td><td>2 BATLEY</td><td>08A</td><td>NA48 ±</td></tr><tr><td>80.9 ± 0.9 ± 1.2</td><td>400k</td><td>3 PISLAK</td><td>03</td><td>B865 ±</td></tr></tbody></table>

¹Radiative corrections included. Using Roy equations and including isospin breaking, BATLEY 10C obtains the following scattering lengths $a_0^0 = 0.2220 \pm 0.0128 \pm 0.0050 \pm 0.0037$ (theor.), $a_0^2 = -0.0432 \pm 0.0086 \pm 0.0034 \pm 0.0028$ (theor.). Supersedes BATLEY 08A.

²Radiative corrections included. Using Roy equations and not including isospin breaking, BATLEY 08A obtains the following $\pi\pi$ scattering length $a_0^0 = 0.233 \pm 0.016 \pm 0.007 \pm 0.004$.

³Radiative corrections included. Using Roy equations PISLAK 03 obtains the following scattering lengths $a_0^0 = 0.203 \pm 0.033 \pm 0.004$, $a_0^2 = -0.055 \pm 0.023 \pm 0.003$.

### $g'_p/f_S$ FOR $K^{\pm} \to \pi^+\pi^- e^{\pm} \nu$ DECAY

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>8.9 ± 1.7 ± 1.3</td><td>1.13M</td><td>1 BATLEY</td><td>10C</td><td>NA48 ±</td></tr></tbody></table>
• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>8.1±2.2±1.5</td><td>670k</td><td><sup>2</sup> BATLEY</td><td>08A NA48</td><td>±</td></tr><tr><td>12.0±1.9±0.7</td><td>400k</td><td><sup>3</sup> PISLAK</td><td>03 B865</td><td>±</td></tr></table>

¹Radiative corrections included. Using Roy equations and including isospin breaking, BATLEY 10c obtains the following scattering lengths $a_0^0 = 0.2220 \pm 0.0128 \pm 0.0050 \pm 0.0037$ (theor.), $a_0^2 = -0.0432 \pm 0.0086 \pm 0.0034 \pm 0.0028$ (theor.). The correlation with $g_p/f_s = -0.914$. Supersedes BATLEY 08A.

²Radiative corrections included. Using Roy equations and not including isospin breaking, BATLEY 08A obtains the following $\pi\pi$ scattering length $a_0^0 = 0.233 \pm 0.016 \pm 0.007$ $a_0^2 = -0.0471 \pm 0.011 \pm 0.004$.

³Radiative corrections included. Using Roy equations PISLAK 03 obtains the following scattering lengths $a_0^0 = 0.203 \pm 0.033 \pm 0.004$, $a_0^2 = -0.055 \pm 0.023 \pm 0.003$.

$h_p/f_s$ FOR $K^{\pm} \rightarrow \pi^{+}\pi^{-}e^{\pm}\nu$ DECAY

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>-39.8±1.5±0.8</td><td>1.13M</td><td>1 BATLEY</td><td>10C NA48</td><td>±</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>-41.1±1.9±0.8</td><td>670k</td><td><sup>2</sup> BATLEY</td><td>08A NA48</td><td>±</td></tr><tr><td>-51.3±3.3±3.5</td><td>400k</td><td><sup>3</sup> PISLAK</td><td>03 B865</td><td>±</td></tr></table>

¹Radiative corrections included. Using Roy equations and including isospin breaking, BATLEY 10c obtains the following scattering lengths $a_0^0 = 0.2220 \pm 0.0128 \pm 0.0050 \pm 0.0037$ (theor.), $a_0^2 = -0.0432 \pm 0.0086 \pm 0.0034 \pm 0.0028$ (theor.). Supersedes BATLEY 08A.

²Radiative corrections included. Using Roy equations and not including isospin breaking, BATLEY 08A obtains the following $\pi\pi$ scattering length $a_0^0 = 0.233 \pm 0.016 \pm 0.007$ $a_0^2 = -0.0471 \pm 0.011 \pm 0.004$.

³Radiative corrections included. Using Roy equations PISLAK 03 obtains the following scattering lengths $a_0^0 = 0.203 \pm 0.033 \pm 0.004$, $a_0^2 = -0.055 \pm 0.023 \pm 0.003$.

DECAY FORM FACTOR FOR $K^{\pm} \rightarrow \pi^0\pi^0 e^{\pm}\nu$

Given in BOLOTOV 86B, BARMIN 88B, and SHIMIZU 04.

$K^{\pm} \rightarrow \ell^{\pm}\nu\gamma$ FORM FACTORS

For definitions of the axial-vector $F_A$ and vector $F_V$ form factor, see the "Note on $\pi^{\pm} \rightarrow \ell^{\pm}\nu\gamma$ and $K^{\pm} \rightarrow \ell^{\pm}\nu\gamma$ Form Factors" in the $\pi^{\pm}$ section. In the kaon literature, often different definitions $a_K = F_A/m_K$ and $v_K = F_V/m_K$ are used.

$F_A + F_V$, SUM OF AXIAL-VECTOR AND VECTOR FORM FACTOR FOR

$K \rightarrow e\nu e\gamma$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.133±0.008</strong> OUR AVERAGE</td><td></td><td></td><td></td><td>See the ideogram below.</td></tr><tr><td>0.125±0.007±0.001</td><td>1.4k</td><td>1 AMBROSINO</td><td>09E KLOE</td><td>E<sub>γ</sub> in 10-250 MeV,<br>p<sub>e</sub> > 200 MeV/c</td></tr><tr><td>0.147±0.011</td><td>51</td><td>2 HEINTZE</td><td>79 SPEC</td><td></td></tr><tr><td>0.150<sup>+</sup>±0.018</td><td>56</td><td>3 HEARD</td><td>75 SPEC</td><td></td></tr></tbody></table>

¹AMBROSINO 09E measures the absolute value $|F_A + F_V|$ which is parametrized as $|F_A + F_V| = F_V (1 + \lambda(1-x)) + F_A \cdot x = 2E_γ/m_K$. ($F_A + F_V$) and $\lambda$ are fit parameters. The fitted value of $\lambda = 0.38 \pm 0.20 \pm 0.02$ with a correlation of $-0.93$ between ($F_A + F_V$) and $\lambda$.

²HEINTZE 79 quotes absolute value of $|F_A + F_V| \sin\theta_C$. We use $\sin\theta_C = V_{US} = 0.2205$.

³HEARD 75 quotes absolute value of $|F_A + F_V| \sin\theta_C$. We use $\sin\theta_C = V_{US} = 0.2205$.

WEIGHTED AVERAGE
0.133±0.008 (Error scaled by 1.3)

<figure><img src="image_509.png" /></figure>

$F_A + F_V$, SUM OF AXIAL-VECTOR AND VECTOR FORM FACTOR FOR $K \rightarrow e\nu e\gamma$

$F_A + F_V$, SUM OF AXIAL-VECTOR AND VECTOR FORM FACTOR FOR

$K \rightarrow \mu\nu\mu\gamma$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td><strong>0.165±0.007±0.011</strong></td><td></td><td>2588</td><td>1 ADLER</td><td>00B B787</td><td>+</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>-1.2</td><td>to 1.1</td><td>90</td><td>DEMIDOV</td><td>90 XEBC</td></tr><tr><td>&lt; 0.23</td><td></td><td>90</td><td>1 AKIBA</td><td>85 SPEC</td></tr></table>

¹Quotes absolute value. Sign not determined.

$F_A - F_V$, DIFFERENCE OF AXIAL-VECTOR AND VECTOR FORM FACTOR

FOR $K \rightarrow e\nu e\gamma$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td><strong>&lt;0.49</strong></td><td></td><td>90</td><td>1 HEINTZE</td><td>79 SPEC</td><td></td></tr></tbody></table>

¹HEINTZE 79 quotes $|F_A - F_V| < \sqrt{11} |F_A + F_V|$.

$F_A - F_V$, DIFFERENCE OF AXIAL-VECTOR AND VECTOR FORM FACTOR

FOR $K \rightarrow \mu\nu\mu\gamma$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td><strong>-0.153±0.033</strong> OUR AVERAGE</td><td></td><td></td><td></td><td></td><td>Error includes scale factor of 1.1.</td></tr><tr><td>-0.134±0.021±0.027</td><td>95k</td><td>KRAVTSOV</td><td>19 OKA</td><td>+</td><td></td></tr><tr><td>-0.21 ± 0.06</td><td>22k</td><td>DUK</td><td>11 ISTR</td><td>-</td><td></td></tr><tr><td>-0.24 to 0.04</td><td>90</td><td>ADLER</td><td>00B B787</td><td>+</td><td></td></tr><tr><td>-2.2 to 0.6</td><td>90</td><td>DEMIDOV</td><td>90 XEBC</td><td></td><td></td></tr><tr><td>-2.5 to 0.3</td><td>90</td><td>AKIBA</td><td>85 SPEC</td><td></td><td></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$K^{\pm}$ CHARGE RADIUS

<table><thead><tr><th>VALUE (fm)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.560±0.031</strong> OUR AVERAGE</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.580±0.040</td><td></td><td>AMENDOLIA</td><td>86 SPEC</td><td>+</td><td></td></tr><tr><td>0.530±0.050</td><td></td><td>DALLY</td><td>80 K<sub>e</sub> → K<sub>e</sub></td><td></td><td></td></tr><tr><td>0.620±0.037</td><td></td><td>BLATNIK</td><td>79 VMD + dispersion relations</td><td></td><td></td></tr></tbody></table>

$K^{\pm}$ LONGITUDINAL POLARIZATION OF EMITTED $\mu^{+}$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;0.990</strong></td><td></td><td>90</td><td>1 AOKI</td><td>94 SPEC</td><td>+</td></tr><tr><td>&lt;0.990</td><td></td><td>90</td><td>IMAZATO</td><td>92 SPEC</td><td>+</td></tr><tr><td>-0.970±0.047</td><td></td><td>2 YAMANAKA</td><td>86 SPEC</td><td>+</td><td>Repl. by AOKI 94</td></tr><tr><td>-1.0 ± 0.1</td><td></td><td>2 CUTTS</td><td>69 SPRK</td><td>+</td><td></td></tr><tr><td>-0.96 ± 0.12</td><td></td><td>2 COOMBES</td><td>57 CNTR</td><td>+</td><td></td></tr></tbody></table>

¹AOKI 94 measures $\xi P_{\mu\mu} = -0.9996 \pm 0.0030 \pm 0.0048$. The above limit is obtained by summing the statistical and systematic errors in quadrature, normalizing to the physically significant region ($|\xi P_{\mu\mu}| < 1$) and assuming that $\xi=1$, its maximum value.

²Assumes $\xi=1$.

FORWARD-BACKWARD ASYMMETRY IN $K^{\pm}$ DECAYS

$A_{FB}(K^{\pm}\pi\mu\mu) = \frac{\Gamma(\cos\theta_{K\mu})>0}{\Gamma(\cos\theta_{K\mu})<0} = \frac{\Gamma(\cos\theta_{K\mu})>0}{\Gamma(\cos\theta_{K\mu})<0} + \frac{\Gamma(\cos\theta_{K\mu})<0}{\Gamma(\cos\theta_{K\mu})<0}$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;0.9 × 10<sup>-2</sup></strong></td><td></td><td>90</td><td>1 CORTINA-GIL 22A</td><td>NA62 2017-18 data</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>&lt;2.3 × 10<sup>-2</sup></td><td>90</td><td>2 BATLEY</td><td>11A NA48</td></tr></table>

¹CORTINA-GIL 22A measured the asymmetry $A_{FB} = (0.0 \pm 0.7) \times 10^{-2}$. The quoted 90% C.L. was obtained via private communication and also presented at the Morion 2023 conference. The authors will publish this limit in an addendum to the publication.

²BATLEY 11A gives a corresponding value of the asymmetry $A_{FB} = (-2.4 \pm 1.8) \times 10^{-2}$.

$K^{\pm}$ REFERENCES

<table><tr><td>CORTINA-GIL</td><td>23</td><td>PL B838 137679</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>23B</td><td>PL B846 138193</td><td>E. Cortina-Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>23D</td><td>JHEP 2309 040</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>KOBAYASHI</td><td>23</td><td>PL B843 138020</td><td>A. Kobayashi et al.</td><td>(J-PARC E36 Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>22</td><td>PL B830 137172</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>22A</td><td>JHEP 2211 011</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>ITO</td><td>22</td><td>PL B826 136913</td><td>H. Ito et al.</td><td>(J-PARC E36 Collab.)</td></tr><tr><td>ALIBERTI</td><td>21</td><td>PRL 127 131802</td><td>R. Alberti et al.</td><td>(NA62 Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>21</td><td>PL B816 136259</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>21B</td><td>JHEP 2106 093</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>POLYARUSH</td><td>21</td><td>EJ P C61 161</td><td>A.Yu. Polyarush et al.</td><td>(OKA Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>20C</td><td>JHEP 2011 042</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>BATLEY</td><td>19</td><td>PL B788 552</td><td>J.R. Batley et al.</td><td>(NA48/2 Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>19A</td><td>PL B797 134794</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>19B</td><td>PL B791 156</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>KRAVTSOV</td><td>19</td><td>EJ P C79 635</td><td>V.I. Kravtsov et al.</td><td>(OKA Collab.)</td></tr><tr><td>SHAPKIN</td><td>19</td><td>EJ P C79 296</td><td>M.M. Shapkin et al.</td><td>(OKA Collab.)</td></tr><tr><td>BATLEY</td><td>18</td><td>JHEP 1810 150</td><td>J.R. Batley et al.</td><td>(NA48/2 Collab.)</td></tr><tr><td>PDG</td><td>18</td><td>PR D98 030001</td><td>M. Tanabashi et al.</td><td>(PDG Collab.)</td></tr><tr><td>YUSHCHENKO</td><td>18</td><td>JETPL 107 139</td><td>O.P. Yushchenko et al.</td><td>(OKA Collab.)</td></tr><tr><td>BATLEY</td><td>17</td><td>PL B769 67</td><td>J.R. Batley et al.</td><td>(NA48/2 Collab.)</td></tr><tr><td>ARTAMONOV</td><td>16</td><td>PR D94 032012</td><td>A.V. Artamonov et al.</td><td>(BNL E949 Collab.)</td></tr><tr><td>BABUSCI</td><td>14B</td><td>PL B738 128</td><td>D. Babusci et al.</td><td>(KLOE and KLOE-2 Collab.)</td></tr><tr><td>BATLEY</td><td>14</td><td>PL B730 141</td><td>J.R. Batley et al.</td><td>(CERN NA48/2 Collab.)</td></tr><tr><td>BATLEY</td><td>14A</td><td>JHEP 1408 159</td><td>J.R. Batley et al.</td><td>(CERN NA48/2 Collab.)</td></tr><tr><td>LAZZERONI</td><td>14</td><td>PL B732 65</td><td>C. Lazzeroni et al.</td><td>(CERN NA62 Collab.)</td></tr><tr><td>UVAROV</td><td>14</td><td>PAN 77 725</td><td>V.A. Uvarov et al.</td><td>(ISTRA+ Collab.)</td></tr></table>
# Meson Particle Listings

## K⁺

<table><thead><tr><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>LAZZERONI</td><td>13</td><td>PL B719 326</td><td>C. Lazzeroni et al. (CERN NA62 Collab.)</td></tr><tr><td>BATLEY</td><td>12</td><td>PL B715 105</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>PDG</td><td>12</td><td>PR D86 010001</td><td>PL B697 107 (PDG Collab.)</td></tr><tr><td>BATLEY</td><td>11A</td><td>PL B695 59</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>DUK</td><td>11</td><td>PL B695 59</td><td>V.A. Duk et al. (CERN NA62 Collab.)</td></tr><tr><td>LAZZERONI</td><td>11</td><td>PL B698 105</td><td>C. Lazzeroni et al. (BNL E787 Collab.)</td></tr><tr><td>ADLER</td><td>10</td><td>PL B921 092001</td><td>S. Adler et al. (CERN NA48/2 Collab.)</td></tr><tr><td>BATLEY</td><td>10A</td><td>EPJ C68 75</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>BATLEY</td><td>10C</td><td>EPJ C70 635</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>PDG</td><td>10</td><td>K G37 075021</td><td>K. Nakamura et al. (PDG Collab.)</td></tr><tr><td>PISLAK</td><td>10A</td><td>PRL 105 019901E</td><td>S. Pislak et al. (BNL E865 Collab.)</td></tr><tr><td>AKOPDZANOV</td><td>09</td><td>PAN 71 2074<br>Translated from YAF 71</td><td>G.A. Akopdzanov et al. (IHEP)</td></tr><tr><td>AMBROSINO</td><td>09E</td><td>EPJ C64 627</td><td>F. Ambrosino et al. (KLOE Collab.)</td></tr><tr><td>Also</td><td>09</td><td>EPJ C65 703 (errat.)</td><td>F. Ambrosino et al. (KLOE Collab.)</td></tr><tr><td>BATLEY</td><td>09</td><td>PL B677 246</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>BATLEY</td><td>09A</td><td>EPJ C68 589</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>BISSEGER</td><td>09A</td><td>PR N806 178</td><td>M. Bissegger et al. (KLOE Collab.)</td></tr><tr><td>AMBROSINO</td><td>08</td><td>JHEP 0801 073</td><td>F. Ambrosino et al. (KLOE Collab.)</td></tr><tr><td>AMBROSINO</td><td>08A</td><td>JHEP 0802 098</td><td>F. Ambrosino et al. (KLOE Collab.)</td></tr><tr><td>AMBROSINO</td><td>08E</td><td>PL B666 305</td><td>A.V. Artamonov et al. (BNL E947 Collab.)</td></tr><tr><td>ARTAMONOV</td><td>08E</td><td>PL 101 191802</td><td>A.V. Artamonov et al. (BNL E947 Collab.)</td></tr><tr><td>Also</td><td>08</td><td>PR D79 092004</td><td>A.V. Artamonov et al. (CERN NA48/2 Collab.)</td></tr><tr><td>BATLEY</td><td>08</td><td>PL B659 493</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>BATLEY</td><td>08A</td><td>EPJ C54 411</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>AKIMENKO</td><td>07</td><td>PAN 70 702<br>Translated from YAF 734</td><td>S.A. Akimenko et al. (ISTRA+ Collab.)</td></tr><tr><td>ANDRE</td><td>07</td><td>ANP 322 2518</td><td>T. Andre (EHI)</td></tr><tr><td>BATLEY</td><td>07A</td><td>EPJ C50 329</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>Also</td><td>07</td><td>EPJ C52 1021 (errat.)</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>BATLEY</td><td>07B</td><td>PL B649 349</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>BATLEY</td><td>07E</td><td>PL B649 875</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>LAI</td><td>07A</td><td>PL B647 341</td><td>A. Lai et al. (CERN NA48/2 Collab.) (ISTRA+ Collab.)</td></tr><tr><td>TCHIKILEV</td><td>07</td><td>EPN 70 29</td><td>O.G. Tchikilev et al. (KLOE Collab.)</td></tr><tr><td>ALIEV</td><td>06</td><td>JP C64 46</td><td>M.A. Aliev et al. (KEK E470 Collab.)</td></tr><tr><td>AMBROSINO</td><td>06A</td><td>PL B632 76</td><td>F. Ambrosino et al. (KLOE Collab.)</td></tr><tr><td>BATLEY</td><td>06A</td><td>PL B634 474</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>BATLEY</td><td>06B</td><td>PL B638 22</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>Also</td><td>06B</td><td>PL B640 297 (errat.)</td><td>J.R. Batley et al. (CERN NA48/2 Collab.)</td></tr><tr><td>COLANGELO</td><td>06A</td><td>PL B638 187</td><td>G. Colangelo et al. (BNL E865 Collab.)</td></tr><tr><td>MA</td><td>06</td><td>PR D73 037101</td><td>H. Ma et al. (PDG Collab.)</td></tr><tr><td>PDG</td><td>06</td><td>W D73 037101</td><td>W. Yao et al. (PDG Collab.)</td></tr><tr><td>SHIMIZU</td><td>06</td><td>PL B639 190</td><td>S. Shimizu et al. (KEK E470 Collab.) (ISTRA+ Collab.)</td></tr><tr><td>UVARAN</td><td>06</td><td>PL AN 69 26</td><td>V.A. Varvar et al. (IHEP)</td></tr><tr><td>AKOPDZHAN...</td><td>05</td><td>EPJ C40 343</td><td>G.A. Akopdzanov et al. (IHEP)</td></tr><tr><td>Also</td><td>05</td><td>PL B68 948</td><td>A. Akopdzanov et al. (IHEP)</td></tr><tr><td>AKOPDZHAN...</td><td>05B</td><td>JETPL 82 675<br>Translated from ZETF 82 771</td><td>G.A. Akopdzanov et al. (IHEP)</td></tr><tr><td>ARTAMONOV</td><td>05</td><td>PL B623 192</td><td>A.V. Artamonov et al. (BNL E949 Collab.)</td></tr><tr><td>CABIBBO</td><td>05</td><td>PL D73 05021</td><td>N. Cabbibo, G. Idsorli (CERN ROMAI, FRAS)</td></tr><tr><td>SHER</td><td>05</td><td>PR D72 012005</td><td>A. Sher et al. (BNL E865 Collab.)</td></tr><tr><td>ABE</td><td>04F</td><td>PR L93 131601</td><td>M. Abe et al. (KEK E246 Collab.)</td></tr><tr><td>Also</td><td>04</td><td>PR L93 072005</td><td>M. Abe et al. (KEK E246 Collab.)</td></tr><tr><td>ADLER</td><td>04A</td><td>PR D70 037102</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>ALDISIO</td><td>04A</td><td>PL B597 139</td><td>A. Aloisio et al. (KLOE Collab.)</td></tr><tr><td>ANISIMOVSK...</td><td>04</td><td>PL B93 031801</td><td>V.V. Anisimovsky et al. (BNL E949 Collab.)</td></tr><tr><td>Also</td><td>04</td><td>PR D77 052003</td><td>S. Adler et al. (BNL E949 Collab.)</td></tr><tr><td>CABIBBO</td><td>04A</td><td>PL B93 121801</td><td>N. Cabibbo (CERN, ROMAI)</td></tr><tr><td>CIRIGLIANO</td><td>04</td><td>EPJ C35 53</td><td>V. Cirigliano, H. Neufeld, H. Pichl (CIT, VALE+)</td></tr><tr><td>PDG</td><td>04</td><td>PL B621 1</td><td>S. Eidelman et al. (PDG Collab.)</td></tr><tr><td>SHIMIZU</td><td>04</td><td>PR D70 037101</td><td>S. Shimizu et al. (KEK E470 Collab.) (INRM, INRM)</td></tr><tr><td>YUSHCHENKO</td><td>04</td><td>PL B581 31</td><td>O.P. Yushchenko et al. (INRM, INRM)</td></tr><tr><td>YUSHCHENKO</td><td>04B</td><td>PL B589 111</td><td>O.P. Yushchenko et al. (INRM)</td></tr><tr><td>AJINENKO</td><td>03</td><td>PAN 66 105<br>Translated from YAF 66</td><td>I.V. Ajinenko et al. (IHEP, INRM)</td></tr><tr><td>AJINENKO</td><td>03B</td><td>PL B567 159</td><td>I.V. Ajinenko et al. (IHEP, INRM)</td></tr><tr><td>AJINENKO</td><td>03C</td><td>PL B574 14</td><td>I.V. Ajinenko et al. (IHEP, INRM)</td></tr><tr><td>ALIEV</td><td>03</td><td>PL B554 7</td><td>M.A. Aliev et al. (KEK E470 Collab.)</td></tr><tr><td>ANISIMOVSK...</td><td>03</td><td>PL B562 166</td><td>V.V. Anisimovsky et al. (BNL E865 Collab.)</td></tr><tr><td>PISLAK</td><td>03</td><td>PL B67 072004</td><td>S. Pislak et al. (BNL E865 Collab.)</td></tr><tr><td>Also</td><td>03</td><td>PR B81 119903E</td><td>S. Pislak et al. (BNL E865 Collab.)</td></tr><tr><td>SHER</td><td>03</td><td>PR L91 261802</td><td>A. Sher et al. (BNL E865 Collab.)</td></tr><tr><td>ADLER</td><td>02B</td><td>PR L84 081403</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>ADLER</td><td>02B</td><td>PR D65 052009</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>ADLER</td><td>02C</td><td>PL B537 211</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>AJINENKO</td><td>02</td><td>PAN 65 2064<br>Translated from YAF 65</td><td>I.V. Ajinenko et al. (IHEP, INRM)</td></tr><tr><td>CIRIGLIANO</td><td>02</td><td>PL B23 1215</td><td>V. Cirigliano et al. (VIEN, VALE, MARS)</td></tr><tr><td>PARK</td><td>02</td><td>PR L88 111801</td><td>H.K. Park et al. (FNAL HyperCP Collab.)</td></tr><tr><td>PDG</td><td>02</td><td>PR D70 010001</td><td>M.S. Iwara et al. (BNL E865 Collab.)</td></tr><tr><td>POBLAGUEV</td><td>02</td><td>PL B81 061003</td><td>A.A. Plobaguev et al. (BNL E865 Collab.)</td></tr><tr><td>ADLER</td><td>01</td><td>PR D63 032004</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>HORIE</td><td>01</td><td>PR B513 311</td><td>K. Horie et al. (KEK E426 Collab.)</td></tr><tr><td>PISLAK</td><td>01</td><td>PR L87 221801</td><td>S. Pislak et al. (BNL E865 Collab.)</td></tr><tr><td>Also</td><td>01</td><td>PR D67 072004</td><td>S. Pislak et al. (BNL E865 Collab.)</td></tr><tr><td>Also</td><td>01</td><td>PR D70 019901E</td><td>S. Pislak et al. (BNL E865 Collab.)</td></tr><tr><td>ADLER</td><td>00</td><td>PR L84 3768</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>ADLER</td><td>00B</td><td>PR L85 2256</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>ADLER</td><td>00C</td><td>PR L85 4856</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>APPEL</td><td>00</td><td>PR L85 2450</td><td>R. Appel et al. (BNL E865 Collab.)</td></tr><tr><td>Also</td><td>00</td><td>Thesis, Yale Univ.</td><td>Thesis, Yale Univ. (BNL E865 Collab.)</td></tr><tr><td>APPEL</td><td>00B</td><td>PR L85 2877</td><td>R. Appel et al. (BNL E865 Collab.)</td></tr><tr><td>MA</td><td>00</td><td>PR L84 2580</td><td>H. Ma et al. (BNL E865 Collab.)</td></tr><tr><td>PDG</td><td>00</td><td>EPJ C15 1</td><td>D.E. Groom et al. (PDG Collab.)</td></tr><tr><td>SHIMIZU</td><td>00</td><td>PL B70 233</td><td>M. Abe et al. (KEK E246 Collab.)</td></tr><tr><td>ABE</td><td>99S</td><td>PR L83 4253</td><td>G. Amoros, J. Blijens (LUND, HELS)</td></tr><tr><td>AMOROS</td><td>99</td><td>JP G25 1607</td><td>R. Appel et al. (BNL E865 Collab.)</td></tr><tr><td>APPEL</td><td>99</td><td>PR L83 4482</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>ADLER</td><td>99</td><td>PR D58 012003</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>BATUSOV</td><td>98A</td><td>NP B516 3</td><td>V.V. Batusov et al. (BNL E865 Collab.)</td></tr><tr><td>AKOBROSIO</td><td>98</td><td>PL B69 0004</td><td>D'Ambrosio et al. (BNL E787 Collab.)</td></tr><tr><td>ADLER</td><td>97</td><td>PR L7 2204</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>ADLER</td><td>97C</td><td>PR L7 4756</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>BERGMAN</td><td>97</td><td>Thesis, Yale Univ.</td><td>D.R. Bergman</td></tr><tr><td>KITCHING</td><td>97</td><td>PR L79 4079</td><td>P. Kitching et al. (BNL E787 Collab.)</td></tr><tr><td>PISLAK</td><td>97</td><td>Thesis, Univ. Zurich</td><td>S. Pislak</td></tr><tr><td>ADLER</td><td>96</td><td>PR L76 1421</td><td>S. Adler et al. (BNL E787 Collab.)</td></tr><tr><td>KOPEV</td><td>95</td><td>JETPL 61 877<br>Translated from ZETF 61 865</td><td>V.P. Koptev et al. (PNPI)</td></tr><tr><td>AOKI</td><td>94</td><td>PR D50 69</td><td>M. Aoki et al. (INUS, KEK, TOKMS)</td></tr><tr><td>ATIYA</td><td>93</td><td>PR L7 2521</td><td>M.S. Atiya et al. (BNL E787 Collab.)</td></tr><tr><td>Also</td><td>93</td><td>PR L71 305 (errat.)</td><td>M.S. Atiya et al. (BNL E787 Collab.)</td></tr><tr><td>ATIYA</td><td>93B</td><td>PR D48 1</td><td>M.S. Atiya et al. (BNL E787 Collab.)</td></tr><tr><td>ALLIEGRO</td><td>92</td><td>PR B68 278</td><td>A. Alliego et al. (BNL, FNAL, PSI+)</td></tr><tr><td>BARMIN</td><td>92</td><td>SJNP 55 547<br>Translated from YAF 55</td><td>V.V. Barmin et al. (ITEP)</td></tr><tr><td>IMAZATO</td><td>92</td><td>PR L69 877</td><td>J. Imazato et al. (Erratum.)</td></tr><tr><td>IVANOV</td><td>92</td><td>THESES</td><td>Yu.M. Ivanov (PNPI)</td></tr><tr><td>LITTENBERG</td><td>92</td><td>PR D68 443</td><td>L.S. Littenberg, R.E. Shrock (BNL, STON)</td></tr><tr><td>USHER</td><td>92</td><td>PR D45 3961</td><td>T. Usher et al. (UCI)</td></tr></tbody></table>

<table><thead><tr><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>AKIMENKO</td><td>91</td><td>PL B259 225</td><td>S.A. Akimenko et al. (SERP, JINR, TBIL+)</td></tr><tr><td>BARMIN</td><td>91</td><td>SJNP 53 606</td><td>V.V. Barmin et al. (ITEP)</td></tr><tr><td>ENISOV</td><td>91</td><td>JETPL 54 558<br>THESIS</td><td>A.S. Denisov et al. (PNPI)</td></tr><tr><td>ATIYA</td><td>90</td><td>PRL 64 21</td><td>M.S. Atiya et al. (BNL E787 Collab.)</td></tr><tr><td>ATIYA</td><td>90B</td><td>PRL 65 1188</td><td>M.S. Atiya et al. (BNL E787 Collab.)</td></tr><tr><td>DEMIDOV</td><td>90</td><td>SJNP 52 1006</td><td>V.S. Demidov et al. (ITEP)</td></tr><tr><td>LEE</td><td>90</td><td>PRL 64 165</td><td>A.M. Lee et al. (BNL, FNAL, VILL, WASH+)</td></tr><tr><td>ATIYA</td><td>89</td><td>PRL 63 2177</td><td>M.S. Atiya et al. (BNL E787 Collab.)</td></tr><tr><td>BARMIN</td><td>89</td><td>SJNP 50 421</td><td>V.V. Barmin et al. (ITEP)</td></tr><tr><td>BARMIN</td><td>88</td><td>Translated from YAF 50 679</td><td>V.V. Barmin et al. (ITEP)</td></tr><tr><td>GALL</td><td>88</td><td>SJNP 47 643</td><td>V.V. Barmin et al. (ITEP)</td></tr><tr><td>BARMIN</td><td>88B</td><td>Translated from YAF 47 1011</td><td>V.V. Barmin et al. (ITEP)</td></tr><tr><td>BOLOTOV</td><td>88</td><td>SJNP 48 1032</td><td>V.V. Barmin et al. (ITEP)</td></tr><tr><td>BOLOTOV</td><td>88</td><td>JETPL 47 7<br>Translated from ZETF 47 8</td><td>V.N. Bolotov et al. (ASCI)</td></tr><tr><td>GALL</td><td>88</td><td>PRL 60 186</td><td>K.P. Gall et al. (BOST, MIT, WILL, CIT+)</td></tr><tr><td>BARMIN</td><td>87</td><td>SJNP 45 62</td><td>V.V. Barmin et al. (ITEP)</td></tr><tr><td>BOLOTOV</td><td>86B</td><td>Translated from YAF 45 957</td><td>V.N. Bolotov et al. (INRM)</td></tr><tr><td>AMENDOLIA</td><td>86B</td><td>PR L178 435</td><td>S.R. Amendola et al. (CERN NA7 Collab.)</td></tr><tr><td>BOLOTOV</td><td>86</td><td>SJNP 44 73</td><td>V.N. Bolotov et al. (INRM)</td></tr><tr><td>BOLOTOV</td><td>86B</td><td>Translated from YAF 44 117</td><td>V.N. Bolotov et al. (INRM)</td></tr><tr><td>YAMANAKA</td><td>86</td><td>PR D34 85</td><td>T. Yamanaoka et al. (KEK, TOKY)</td></tr><tr><td>Also</td><td>86</td><td>PR L32 329</td><td>R.S. Hayano et al. (TOKY, KEK)</td></tr><tr><td>AKIBA</td><td>85</td><td>PR D32 2911</td><td>Y. Akiba et al. (TOKY, TINT, TSUK, KEK)</td></tr><tr><td>BOLOTOV</td><td>85</td><td>JETPL 42 481<br>Translated from ZETF 42 390</td><td>V.N. Bolotov et al. (INRM)</td></tr><tr><td>ASANO</td><td>82</td><td>PL 113B 195</td><td>Y. Asano et al. (KEK, TOKY, INUS, OSAK)</td></tr><tr><td>COOPER</td><td>82</td><td>PR L122 97</td><td>A.M. Cooper et al. (RL)</td></tr><tr><td>PDG</td><td>82B</td><td>PL 111B 70</td><td>M. Roos et al. (HELS, CIT, CERN)</td></tr><tr><td>ASANO</td><td>81B</td><td>PL 107B 159</td><td>Y. Asano et al. (KEK, TOKY, INUS, OSAK)</td></tr><tr><td>CAMPBELL</td><td>81</td><td>PR 47 1032</td><td>M.K. Campbell et al. (YALE, BNL)</td></tr><tr><td>Also</td><td>81</td><td>S.R. Blatt et al.</td><td>S.R. Blatt et al. (YALE, BNL)</td></tr><tr><td>LUM</td><td>81</td><td>PR D27 1056</td><td>G.K. Lut et al. (LBL, NBS+)</td></tr><tr><td>LYONS</td><td>81</td><td>ZPHY C10 215</td><td>L. Lyons, C. Albarja, G. Myatt (OXF)</td></tr><tr><td>DALLY</td><td>80</td><td>PR L32 432</td><td>E.B. Dally et al. (UCLA+)</td></tr><tr><td>BARKOV</td><td>79</td><td>NP B148 53</td><td>L. Barkov et al. (NOVO, LEK)</td></tr><tr><td>BLATNIK</td><td>79</td><td>LNC 24 59</td><td>S. Blatnik, J. Stahov, C.B. Lang (TUZL, GRAZ)</td></tr><tr><td>HEINTZE</td><td>79</td><td>PL 114 327</td><td>J. Heintze et al. (HEIDP, CERN)</td></tr><tr><td>ABRAMS</td><td>77</td><td>PR D15 22</td><td>R.J. Abrams et al. (BNL)</td></tr><tr><td>DEVAUX</td><td>77</td><td>PR N812 11</td><td>B. Devaux et al. (SACL, GEVA)</td></tr><tr><td>HEINTZE</td><td>77</td><td>PL D70 482</td><td>J. Heintze et al. (HEIDP, CERN)</td></tr><tr><td>ROSELET</td><td>77</td><td>PL D15 574</td><td>L. Rosselet et al. (GEVA, SACL)</td></tr><tr><td>BLOCH</td><td>77</td><td>PL 60B 393</td><td>P. Bloch et al. (GEVA, SACL)</td></tr><tr><td>BRAUN</td><td>76B</td><td>LNC 17 521</td><td>H.M. Braun et al. (AACH3, BARI, BELG+)</td></tr><tr><td>DIAMANT...</td><td>76</td><td>PL 62B 485</td><td>A.M. Diamant-Berger et al. (SACL, GEVA)</td></tr><tr><td>HEINTZE</td><td>76</td><td>PL 60B 302</td><td>J. Heintze et al. (HEIDP)</td></tr><tr><td>SMITH</td><td>76</td><td>NP B109 173</td><td>A.O. Weissenberg et al. (ITEP, LEBD)</td></tr><tr><td>WEISSENBE...</td><td>76</td><td>PR N115 55</td><td>P. Bloch et al. (SACL, GEVA)</td></tr><tr><td>BLOCH</td><td>75</td><td>PL 56B 201</td><td>H.M. Braun et al. (AACH3, BARI, BRUX+)</td></tr><tr><td>BRUN</td><td>75</td><td>PL B89 210</td><td>S.C. Cheng et al. (COLU, YALE)</td></tr><tr><td>CHENG</td><td>75</td><td>NP A254 381</td><td>K.S. Heard et al. (CERN, HEIDH)</td></tr><tr><td>HEARD</td><td>75</td><td>PL 55B 324</td><td>K.S. Heard et al. (CERN, HEIDH)</td></tr><tr><td>HEARD</td><td>75B</td><td>PL 55B 327</td><td>M. Sheaff (WISC)</td></tr><tr><td>SHEAFF</td><td>75</td><td>PR D12 2570</td><td>K.M. Smith et al. (GLAS, LIVP, OXF+)</td></tr><tr><td>SMITH</td><td>75</td><td>PR B91 45</td><td>A.O. Weissenberg et al. (ITEP, LEBD)</td></tr><tr><td>WEISSENBE...</td><td>74</td><td>PL 48B 474</td><td>P. Bloch et al. (SACL, GEVA)</td></tr><tr><td>ABRAMS</td><td>73B</td><td>PL 30 500</td><td>H.M. Braun et al. (AACH3, BARI, BRUX+)</td></tr><tr><td>BACKENST...</td><td>73</td><td>PL 43B 431</td><td>G. Backenstoss et al. (CERN, KARLK, KARLE+)</td></tr><tr><td>LJUNG</td><td>73</td><td>PR D8 1307</td><td>D. Ljung, D. Cline (WISC)</td></tr><tr><td>Also</td><td>73</td><td>PR L28 523</td><td>D. Ljung (WISC)</td></tr><tr><td>Also</td><td>73</td><td>PR L28 1287</td><td>D. Cline, D. Ljung (WISC)</td></tr><tr><td>Also</td><td>73</td><td>PL D23 326</td><td>U. Camerini et al. (WISC)</td></tr><tr><td>LUCAS</td><td>73</td><td>PR D8 719</td><td>P.W. Lucas, H.D. Taft, W.J. Willis (YALE)</td></tr><tr><td>LUCAS</td><td>73B</td><td>PR D8 727</td><td>P.W. Lucas, H.D. Taft, W.J. Willis (YALE)</td></tr><tr><td>PANG</td><td>73</td><td>PR D8 1989</td><td>C.Y. Pang et al. (EFI, ARIZ, LBL)</td></tr><tr><td>Also</td><td>73</td><td>PL 40B 699</td><td>G.D. Cable et al. (EFI, LBL)</td></tr><tr><td>SMITH</td><td>73</td><td>PR B60 411</td><td>K.M. Smith et al. (GLAS, LIVP, OXF+)</td></tr><tr><td>ABRAMS</td><td>72</td><td>PR L29 1118</td><td>R.J. Abrams et al. (BNL)</td></tr><tr><td>ABRAMS</td><td>72</td><td>PR D12 1209</td><td>B. Aubert et al. (ORSAY, BRUX, EPL+)</td></tr><tr><td>CHIANG</td><td>71</td><td>PR D6 1254</td><td>I.H. Chang et al. (ROCH, WISC)</td></tr><tr><td>CLARK</td><td>72</td><td>PL 29 1274</td><td>A.R. Clark et al. (PLR)</td></tr><tr><td>FORD</td><td>72</td><td>PR 38B 335</td><td>W.T. Ford et al. (PRIN)</td></tr><tr><td>HOFFMASTER</td><td>72</td><td>NP B36 1</td><td>S. Hoffmaster et al. (STEV, SETO, LEHI)</td></tr><tr><td>BOURQUIN</td><td>71</td><td>PL 36B 615</td><td>M.H. Bourquin et al. (GEVA, SACL)</td></tr><tr><td>HAIDT</td><td>71</td><td>PR D3 10</td><td>D. Haidt (AACH, BARI, CERN, EPOL, NJM+)</td></tr><tr><td>Also</td><td>71</td><td>PL 29B 691</td><td>D. Haidt et al. (AACH, BARI, CERN, EPOL+)</td></tr><tr><td>KLEMS</td><td>74</td><td>PR D4 66</td><td>J.H. Klems, R.H. Hildebrand, R. Stiening (CHIC+)</td></tr><tr><td>Also</td><td>74</td><td>PR L24 1086</td><td>J.H. Klems, R.H. Hildebrand, R. Stiening (LRL+)</td></tr><tr><td>Also</td><td>74</td><td>PR D2 473</td><td>J.H. Klems, R.H. Hildebrand, R. Stiening (LRL+)</td></tr><tr><td>OTT</td><td>71</td><td>PR D3 52</td><td>R.J. Ott, L.W. Pritchard (LOQM)</td></tr><tr><td>ROMANO</td><td>71</td><td>PL 36B 525</td><td>F. Romano et al. (BARI, CERN, ORSAY)</td></tr><tr><td>SWEINBE...</td><td>71</td><td>PL 36B 246</td><td>W. Schweinberger (AACH, BELG, CERN, NJM+)</td></tr><tr><td>STEINER</td><td>71</td><td>PL 36B 521</td><td>H.J. Steiner (AACH, BARI, CERN, EPOL, ORSAY+)</td></tr><tr><td>BARDIN</td><td>70</td><td>PL 32B 121</td><td>D.Y. Bardin, S.N. Bilenky, B.M. Pontecorvo (JINR)</td></tr><tr><td>BECERRAWY</td><td>70</td><td>PR D1 1452</td><td>T. Becerrawy (ROCH)</td></tr><tr><td>FORD</td><td>70</td><td>PR 25 1370</td><td>W.T. Ford et al. (PRIN)</td></tr><tr><td>GAILLARD</td><td>70</td><td>CERN 70-14</td><td>J.M. Gaillard, L.M. Chouet (CERN)</td></tr><tr><td>GRAUMAN</td><td>70</td><td>PR D1 1277</td><td>J. Grauman et al. (STEV, SETO, LEHI)</td></tr><tr><td>Also</td><td>70</td><td>PR L23 737</td><td>J.U. Grauman et al. (STEV, SETO, LEHI)</td></tr><tr><td>PANDOLLAS</td><td>70</td><td>PR D2 1205</td><td>D. Pandolas et al. (STEV, LEHI)</td></tr><tr><td>CUTTS</td><td>69</td><td>PR 184 1380</td><td>D. Cutts et al. (LRL, MIT)</td></tr><tr><td>Also</td><td>69</td><td>PR 20 955</td><td>D. Cutts et al. (LRL, MIT)</td></tr><tr><td>DAVISON</td><td>69</td><td>PR 180 1333</td><td>D.C. Davison et al. (UCR)</td></tr><tr><td>ELY</td><td>69</td><td>PR 180 1319</td><td>R.P.J. Ely et al. (LOUC, WISC, LRL)</td></tr><tr><td>HERZO</td><td>69</td><td>PR 186 1403</td><td>D. Herzo et al. (LRL)</td></tr><tr><td>LOBKOWICZ</td><td>69</td><td>PR 185 576</td><td>F. Lobkowicz et al. (ROCH, BNL)</td></tr><tr><td>Also</td><td>69</td><td>PR L7 548</td><td>T.S. Mast et al. (LRL)</td></tr><tr><td>MAST</td><td>69</td><td>PR 183 1200</td><td>F. Selleli</td></tr><tr><td>SELLERI</td><td>69</td><td>PR NC 60A 291</td><td>M.E. Zeller et al. (UCLA, LRL)</td></tr><tr><td>ZELLER</td><td>69B</td><td>PR 182 1420</td><td>D.R. Botterill et al. (OXF)</td></tr><tr><td>BOTTERILL</td><td>68C</td><td>PR 174 1566</td><td>D.R. Botterill et al. (OXF)</td></tr><tr><td>BOTTERILL</td><td>68C</td><td>PR 174 1661</td><td>W.D. Butler et al. (LRL)</td></tr><tr><td>BUTLER</td><td>68</td><td>UCRL 18420</td><td>C.Y. Chang et al. (UMD, RUTG)</td></tr><tr><td>CHANG</td><td>68</td><td>PR 20 510</td><td>M. Chen et al. (LRL, MIT)</td></tr><tr><td>CHEN</td><td>68</td><td>PR L20 73</td><td>M. Chen et al. (LRL, MIT)</td></tr><tr><td>EICHTEN</td><td>68</td><td>PR L27B 586</td><td>P.T. Eschtrich et al. (AACH, BARI, CERN, EPOL, OXF+)</td></tr><tr><td>ESCHSTRUTH</td><td>68</td><td>PR 165 1487</td><td>P.T. Eschtrich et al. (PRIN, PENN)</td></tr><tr><td>GARLAND</td><td>68</td><td>PR 167 1225</td><td>R. Garland et al. (COLU, RUTG, WISC)</td></tr><tr><td>MOSCOSO</td><td>68</td><td>PR 155 1505</td><td>L. Moscoso et al. (ORSAY)</td></tr><tr><td>AUERBACH</td><td>67</td><td>PR D9 3216</td><td>L.B. Auerbach et al. (PENN, PRIN)</td></tr><tr><td>Also</td><td>67</td><td>Heidelberg Conf.</td><td>L.B. Auerbach et al. (MILA)</td></tr><tr><td>BELLOTTI</td><td>67B</td><td>NC 52A 1287</td><td>E. Bellotti, E. Pullia (MILA)</td></tr><tr><td>BELLOTTI</td><td>67B</td><td>PL 20 690</td><td>E. Bellotti, E. Fiorini, A. Pullia (MILA)</td></tr><tr><td>Also</td><td>67B</td><td></td><td>E. Bellotti et al. (MILA)</td></tr></tbody></table>
### T-VIOLATION PARAMETER IN $K^{0}$-$\bar{K}^{0}$ MIXING

The asymmetry $A_T = \frac{\Gamma(\bar{K}^0 \to K^0) - \Gamma(\bar{K}^0 \to \bar{K}^0)}{\Gamma(\bar{K}^0 \to K^0) + \Gamma(\bar{K}^0 \to \bar{K}^0)}$ must vanish if

$T$ invariance holds.

### ASYMMETRY $A_T$ IN $K^0$-$\bar{K}^0$ MIXING

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>6.6&plusmn;1.3&plusmn;1.0</td><td>640k</td><td>1 ANGELOPO... 98E</td><td>CPLR</td></tr></tbody></table>

1 ANGELOPOULOS 98E measures the asymmetry $A_T = [\Gamma(\bar{K}^0_{t=0} \to e^+\pi^-\nu_{t=\tau}) - \Gamma(\bar{K}^0_{t=0} \to e^+\pi^+\nu_{t=\tau})]/[\Gamma(\bar{K}^0_{t=0} \to e^+\pi^-\nu_{t=\tau}) + \Gamma(\bar{K}^0_{t=0} \to e^+\pi^+\nu_{t=\tau})]$ as a function of the neutral-kaon eigentime $\tau$. The initial strangeness of the neutral kaon is tagged by the charge of the accompanying charged kaon in the reactions $p\bar{p} \to K^+\pi^+K^0$ and $p\bar{p} \to K^+\pi^-\bar{K}^0$. The strangeness at the time of the decay is tagged by the lepton charge. The reported result is the average value of $A_T$ over the interval $1\tau_S < \tau < 20\tau_S$. From this value of $A_T$ ANGELOPOULOS 01B, assuming $CPT$ invariance in the $e^+\pi^-\nu$ decay amplitude, determine the $T$-violating as $\Delta S=\Delta S$ conserving parameter (for its definition, see Review below) $4\Re(\epsilon) = (6.2 \pm 1.4 \pm 1.0) \times 10^{-3}$.

<table><tbody><tr><td>BISI</td><td>67</td><td>PL 25B 572</td><td>V. Bisi et al.</td><td>(TORI)</td></tr><tr><td>FLETCHER</td><td>67</td><td>PRL 19 98</td><td>C.R. Fletcher et al.</td><td>(ILL)</td></tr><tr><td>FORD</td><td>67</td><td>PRL 18 1214</td><td>W.T. Ford et al.</td><td>(PRIN)</td></tr><tr><td>GINSBERG</td><td>67</td><td>PR 162 1570</td><td>E.S. Ginsberg</td><td>(MASB)</td></tr><tr><td>KALMUS</td><td>67</td><td>PR 159 1187</td><td>G.E. Kalmus, A. Kernan</td><td>(LRL)</td></tr><tr><td>ZINCHENKO</td><td>67</td><td>Thesis Rutgers</td><td>A.I. Zinchenko</td><td>(RUTG)</td></tr><tr><td>CALLAHAN</td><td>66</td><td>NC 44A 90</td><td>A.C. Callahan</td><td>(WISC)</td></tr><tr><td>CALLAHAN</td><td>66B</td><td>PR 150 1153</td><td>A.C. Callahan</td><td>(WISC, LRL, UCR+)</td></tr><tr><td>CESTER</td><td>66</td><td>PL 21 343</td><td>R. Cester et al.</td><td>(PPA)</td></tr><tr><td colspan="4">See footnote 1 in</td></tr><tr><td></td><td></td><td>AUERBACH 67.</td><td></td><td></td></tr><tr><td></td><td></td><td>PR 155 1505</td><td></td><td></td></tr><tr><td>BIRGE</td><td>65</td><td>PR 139 B1600</td><td>L.B. Averbuch et al.</td><td>(PENN, PRIN)</td></tr><tr><td>BISI</td><td>65</td><td>PR 139 B1600</td><td>R.W. Birge et al.</td><td>(LRL, WISC)</td></tr><tr><td>BISI</td><td>65B</td><td>PR 139 B1606</td><td>V. Bisi et al.</td><td>(TORI)</td></tr><tr><td>CALLAHAN</td><td>65</td><td>PRL 15 129</td><td>V. Bisi et al.</td><td>(TORI)</td></tr><tr><td>CLINE</td><td>65</td><td>PL 15 293</td><td>A. Callahan, D. Cline</td><td>(WISC)</td></tr><tr><td>DEMARCO</td><td>65</td><td>PL 140 B1430</td><td>D. Cline, W.F. Fry</td><td>(WISC)</td></tr><tr><td>FITCH</td><td>65B</td><td>PR 140 B1088</td><td>A. de Marco, C. Grosso, G. Rinaudo</td><td>(TORI, CERN)</td></tr><tr><td>STAMER</td><td>65</td><td>PR 138 B440</td><td>V.L. Fitch, C.A. Quarles, H.C. Wilkins</td><td>(PRIN+)</td></tr><tr><td>YOUNG</td><td>65</td><td>Thesis UCRL 16362</td><td>P. Stamer et al.</td><td>(STEV)</td></tr><tr><td>Also</td><td>65</td><td>PR 156 1464</td><td>P.S. Young</td><td>(LRL)</td></tr><tr><td>BOREANI</td><td>64</td><td>PL 12 123</td><td>P.S. Young, W.Z. Osborne, W.H. Barkas</td><td>(LRL)</td></tr><tr><td>CALLAHAN</td><td>64</td><td>PR 136 B1463</td><td>G. Borreani, G. Rinaudo, A.E. Werbrock</td><td>(LRL)</td></tr><tr><td>GREINER</td><td>64</td><td>PRL 13 284</td><td>A. de Marco, C. Grosso, G. Rinaudo</td><td>(WISC)</td></tr><tr><td>SHAKLEE</td><td>64</td><td>PR 136 B1423</td><td>D.E. Greiner, W.Z. Osborne, W.H. Barkas</td><td>(LRL)</td></tr><tr><td>BOYARSKI</td><td>62</td><td>PR 128 2398</td><td>F.S. Shaklee et al.</td><td>(MICH)</td></tr><tr><td>FERRO-LUZZI</td><td>61</td><td>NC 22 1087</td><td>A.M. Boyarski et al.</td><td>(MIT)</td></tr><tr><td>ROE</td><td>61</td><td>PL 7 346</td><td>M. Ferro-Luzzi et al.</td><td>(LRL)</td></tr><tr><td>TAYLOR</td><td>59</td><td>PR 114 359</td><td>B.P. Roe et al.</td><td>(MICH, LRL)</td></tr><tr><td>COOMBES</td><td>57</td><td>PR 108 1348</td><td>S. Taylor et al.</td><td>(COLU)</td></tr><tr><td></td><td></td><td></td><td>C.A. Coombes et al.</td><td>(LBL)</td></tr></tbody></table>

### OTHER RELATED PAPERS

<table><tbody><tr><td>LITTENBERG</td><td>93</td><td>ARNPS 43 729</td><td>L.S. Littenberg, G. Valencia</td><td>(BNL, FNAL)</td></tr><tr><td>RITCHIE</td><td>93</td><td>Rare and Radiative Kaon Decays</td><td>J.L. Ritchie, S.G. Wojcicki</td><td></td></tr><tr><td colspan="4">"Rare K Decays"</td></tr><tr><td>BATTISTON</td><td>92</td><td>PRPL 214 293</td><td>R. Battiston et al.</td><td>(PGIA, CERN, TRSTT)</td></tr><tr><td colspan="4">Status and Perspectives of K Decay Physics</td></tr><tr><td>BRYMAN</td><td>89</td><td>UJP A4 79</td><td>D.A. Bryman</td><td>(TRIU)</td></tr><tr><td colspan="4">"Rare Kaon Decays"</td></tr><tr><td>CHOUET</td><td>72</td><td>PRPL 4L 199</td><td>L.M. Chouet, J.M. Gaillard, M.K. Gaillard (ORSAY+)</td><td></td></tr><tr><td>FEARING</td><td>70</td><td>PR D2 542</td><td>H.W. Fearing, E. Fischbach, J. Smith (STON, BOHR)</td><td></td></tr><tr><td>HAIDT</td><td>69B</td><td>PL 29B 696</td><td>D. Haidt et al.</td><td>(AACH, BARI, CERN, EPL+)</td></tr><tr><td>CRONIN</td><td>68B</td><td>Vienna Conf. 241</td><td>J.W. Cronin</td><td>(PRIN)</td></tr><tr><td colspan="4">Rapporteur talk.</td></tr><tr><td>WILLIS</td><td>67</td><td>Heidelberg Conf. 273</td><td>W.J. Willis</td><td>(YALE)</td></tr><tr><td colspan="4">Rapporteur talk.</td></tr><tr><td>CABIBBO</td><td>66</td><td>Berkeley Conf. 33</td><td>N. Cabibbo</td><td>(CERN)</td></tr><tr><td>ADAIR</td><td>64</td><td>PL 12 67</td><td>R.K. Adair, L.B. Leipuner</td><td>(YALE, BNL)</td></tr><tr><td>CABIBBO</td><td>64</td><td>PL 9 352</td><td>N. Cabibbo, A. Maksymowicz</td><td>(CERN)</td></tr><tr><td>Also</td><td></td><td>PL 11 360</td><td>N. Cabibbo, A. Maksymowicz</td><td>(CERN)</td></tr><tr><td>Also</td><td></td><td>PL 14 72</td><td>N. Cabibbo, A. Maksymowicz</td><td>(CERN)</td></tr><tr><td>BIRGE</td><td>63</td><td>PRL 11 35</td><td>R.W. Birge et al.</td><td>(LRL, WISC, BARI)</td></tr><tr><td>BLOCK</td><td>62B</td><td>CERN Conf. 371</td><td>M.M. Block, L. Lendinara, L. Monari (NWES, BGNA)</td><td></td></tr><tr><td> BRENE</td><td>61</td><td>NP 22 553</td><td>N. Brene, L. Egardt, B. Qvist</td><td>(NORD)</td></tr></tbody></table>

$K^0$

$$I(J^P) = \frac{1}{2}(0^-)$$

$K^0$ MASS

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="6"><strong>497.611&plusmn;0.013 OUR FIT</strong> Error includes scale factor of 1.2.</td></tr><tr><td colspan="6"><strong>497.611&plusmn;0.013 OUR AVERAGE</strong> Error includes scale factor of 1.2.</td></tr><tr><td>497.607&plusmn;0.007&plusmn;0.015</td><td>261k</td><td>1 TOMARADZE 14</td><td>ψ(2S) &rarr; K<sub>S</sub><sup>0</sup>X</td><td></td><td></td></tr><tr><td>497.583&plusmn;0.005&plusmn;0.020</td><td>35k</td><td>AMBROSINO</td><td>07B KLOE</td><td>e<sup>+</sup>e<sup>-</sup> &rarr; K<sub>L</sub><sup>0</sup>K<sub>S</sub><sup>0</sup></td><td></td></tr><tr><td>497.625&plusmn;0.001&plusmn;0.031</td><td>655k</td><td>LAI</td><td>02 NA48</td><td>K<sub>L</sub><sup>0</sup> beam</td><td></td></tr><tr><td>497.661&plusmn;0.033</td><td>3713</td><td>BARKOV</td><td>87B CMD</td><td>e<sup>+</sup>e<sup>-</sup> &rarr; K<sub>S</sub><sup>0</sup>K<sub>S</sub><sup>0</sup></td><td></td></tr><tr><td>497.742&plusmn;0.085</td><td>780</td><td>BARKOV</td><td>85B CMD</td><td>e<sup>+</sup>e<sup>-</sup> &rarr; K<sub>S</sub><sup>0</sup>K<sub>S</sub><sup>0</sup></td><td></td></tr><tr><td colspan="6">&bull; &bull; &bull; We do not use the following data for averages, fits, limits, etc. &bull; &bull; &bull;</td></tr><tr><td>497.44&plusmn;0.50</td><td></td><td>FITCH</td><td>67 OSPK</td><td></td><td></td></tr><tr><td>498.9 &plusmn; 0.5</td><td>4500</td><td>BALTAY</td><td>66 HBC</td><td>K<sub>S</sub><sup>0</sup> from p<span style="text-decoration: overline">p</span></td><td></td></tr><tr><td>497.44 &plusmn; 0.33</td><td>2223</td><td>KIM</td><td>65B HBC</td><td>K<sub>S</sub><sup>0</sup> from p<span style="text-decoration: overline">p</span></td><td></td></tr><tr><td>498.1 &plusmn; 0.4</td><td></td><td>CHRISTENS...</td><td>64 OSPK</td><td></td><td></td></tr></tbody></table>

1 Obtained by analyzing CLEO-c data but not authored by the CLEO Collaboration.

$$m_{K^0} - m_{K^\pm}$$

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="6"><strong>3.934&plusmn;0.020 OUR FIT</strong> Error includes scale factor of 1.6.</td></tr><tr><td colspan="6">&bull; &bull; &bull; We do not use the following data for averages, fits, limits, etc. &bull; &bull; &bull;</td></tr><tr><td>3.95 &plusmn; 0.21</td><td>417</td><td>HILL</td><td>68B DBC</td><td>+</td><td>K<sup>+</sup>d &rarr; K<sup>0</sup>pp</td></tr><tr><td>3.90 &plusmn; 0.25</td><td>9</td><td>BURNSTEIN</td><td>65 HBC</td><td>-</td><td></td></tr><tr><td>3.71 &plusmn; 0.35</td><td>7</td><td>KIM</td><td>65B HBC</td><td>-</td><td>K<sup>-</sup>p &rarr; nK<sup>0</sup></td></tr><tr><td>5.4 &plusmn; 1.1</td><td></td><td>CRAWFORD</td><td>59 HBC</td><td>+</td><td></td></tr><tr><td>3.9 &plusmn; 0.6</td><td></td><td>ROSENFELD</td><td>59 HBC</td><td>-</td><td></td></tr></tbody></table>

$K^0$ MEAN SQUARE CHARGE RADIUS

<table><thead><tr><th>VALUE (m<sup>2</sup><sub>0</sub>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>-0.077&plusmn;0.010 OUR AVERAGE</strong></td></tr><tr><td>-0.077&plusmn;0.007&plusmn;0.011</td><td>5037</td><td>ABOUZAID</td><td>06 KTEV</td><td>K<sub>S</sub><sup>0</sup> &rarr; &pi;<sup>+</sup>&pi;<sup>-</sup>e<sup>+</sup>e<sup>-</sup></td></tr><tr><td>-0.090&plusmn;0.021</td><td></td><td>LAI</td><td>03C NA48</td><td>K<sub>L</sub><sup>0</sup> &rarr; &pi;<sup>+</sup>&pi;<sup>-</sup>e<sup>+</sup>e<sup>-</sup></td></tr><tr><td>-0.054&plusmn;0.026</td><td></td><td>MOLZON</td><td>78</td><td>K<sub>S</sub> regen. by electrons</td></tr><tr><td colspan="5">&bull; &bull; &bull; We do not use the following data for averages, fits, limits, etc. &bull; &bull; &bull;</td></tr><tr><td>-0.087&plusmn;0.046</td><td></td><td>BLATNIK</td><td>79</td><td>VMD + dispersion relations</td></tr><tr><td>-0.050&plusmn;0.130</td><td></td><td>FOETH</td><td>69B</td><td>K<sub>S</sub> regen. by electrons</td></tr></tbody></table>

### Re(ε)

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>1.596&plusmn;0.013</td><td>1 AMBROSINO 06H</td><td>KLOE</td></tr></tbody></table>

&bull; &bull; &bull; We do not use the following data for averages, fits, limits, etc. &bull; &bull; &bull;

1.664&plusmn;0.010 2 LAI 05A NA48

1 AMBROSINO 06H uses Bell-Steinberger relations with the following measurements: $B(K^0_L \to \pi^+\pi^-)$ in AMBROSINO 06F, $B(K^0_S \to \pi^0\pi^0)$ in AMBROSINO 05B, the $K^0_S$-semileptonic charge asymmetry in AMBROSINO 06E, and $K^0$-semileptonic results in ANGELOPOULOS 98F.

2 LAI 05A values are obtained through unitarity (Bell-Steinberger relations), improving determination of $\eta_{000}$ and combining other data from PDG 04 and APOSTOLAKIS 99B.

### CPT-VIOLATION PARAMETERS

In $K^0$-$\bar{K}^0$ mixing, if CP-violating interactions include a T conserving part then

$$ \begin{aligned} |K_S| &= |[K_1] + (\epsilon + \delta)|K_2|/\sqrt{1 + |\epsilon + \delta|^2} \\ |K_L| &= |[K_2] + (\epsilon - \delta)|K_1|/\sqrt{1 + |\epsilon - \delta|^2} \end{aligned} $$

where

$$ \begin{aligned} |K_1| &= |[K^0] + [\bar{K}^0]|/\sqrt{2} \\ |K_2| &= |[K^0] - [\bar{K}^0]|/\sqrt{2} \end{aligned} $$

and

$$ |\bar{K}^0| = CP|K^0| $$

The parameter $\delta$ specifies the CPT-violating part.

Estimates of $\delta$ are given below assuming the validity of the $\Delta S=\Delta Q$ rule. See also THOMSON 95 for a test of CPT-symmetry conservation in $K^0$ decays using the Bell-Steinberger relation.

### REAL PART OF $\delta$

A nonzero value violates CPT invariance.

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2.51 &plusmn; 2.25</td><td>1 ABOUZAID</td><td>11 KTEV</td><td></td><td></td></tr><tr><td colspan="5">&bull; &bull; &bull; We do not use the following data for averages, fits, limits, etc. &bull; &bull; &bull;</td></tr><tr><td>2.3 &plusmn; 2.7</td><td></td><td>2 AMBROSINO 06H</td><td>KLOE</td><td></td></tr><tr><td>2.4 &plusmn; 2.8</td><td></td><td>3 APOSTOLA...</td><td>RVUE</td><td></td></tr><tr><td>2.9 &plusmn; 2.6 &plusmn; 0.6</td><td>1.3M</td><td>4 ANGELOPO...</td><td>98F CPLR</td><td></td></tr><tr><td>180 &plusmn; 200</td><td>6481</td><td>5 DEMIDOV</td><td>95</td><td>K<sub>L3</sub> reanalysis</td></tr></tbody></table>

1 ABOUZAID 11 uses Bell-Steinberger relations.

2 AMBROSINO 06H uses Bell-Steinberger relations with the following measurements: $B(K^0_L \to \pi^+\pi^-)$ in AMBROSINO 06F, $B(K^0_S \to \pi^0\pi^0)$ in AMBROSINO 05B, the $K^0_S$-semileptonic charge asymmetry in AMBROSINO 06E, and $K^0$-semileptonic results in ANGELOPOULOS 98F.

3 APOSTOLAKIS 99B assumes only unitarity and combines CPCLEAR and other results.

4 ANGELOPOULOS 98F use $\Delta S=\Delta Q$. If $\Delta S=\Delta Q$ is not assumed, they find $\Re\delta=(3.0 \pm 3.3 \pm 0.6) \times 10^{-4}$.

5 DEMIDOV 95 reanalyzes data from HART 73 and NIEBERGALL 74.

### IMAGINARY PART OF $\delta$

A nonzero value violates CPT invariance.

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>-1.5 &plusmn; 1.6</td><td>1 ABOUZAID</td><td>11 KTEV</td><td></td><td></td></tr><tr><td colspan="5">&bull; &bull; &bull; We do not use the following data for averages, fits, limits, etc. &bull; &bull; &bull;</td></tr><tr><td>0.4 &plusmn; 2.1</td><td></td><td>2 AMBROSINO 06H</td><td>KLOE</td><td></td></tr><tr><td>0.2 &plusmn; 2.0</td><td></td><td>3 LAI</td><td>05A NA48</td><td></td></tr><tr><td>2.4 &plusmn; 5.0</td><td></td><td>4 APOSTOLA...</td><td>99B RVUE</td><td></td></tr><tr><td>90 &plusmn; 290 &plusmn; 100</td><td>1.3M</td><td>5 ANGELOPO...</td><td>CPLR</td><td></td></tr><tr><td>2100 &plusmn; 3700</td><td>6481</td><td>6 DEMIDOV</td><td>95</td><td>K<sub>L3</sub> reanalysis</td></tr></tbody></table>

1 ABOUZAID 11 uses Bell-Steinberger relations.
² AMBROSINO 06H uses Bell-Steinberger relations with the following measurements: $B(K_L^0 \to \pi^+\pi^-)$ in AMBROSINO 06r, $B(K_S^0 \to \pi^0\pi^0)$ in AMBROSINO 05b, the $K_S^0$-semileptonic charge asymmetry in AMBROSINO 06e, and $K^0$-semileptonic results in ANGELOPOULOS 98f.

³ LAI 05A values are obtained through unitarity (Bell-Steinberger relations), improving determination of $\eta_{000}$ and combining other data from PDG 04 and APOSTOLAKIS 99b.

⁴ APOSTOLAKIS 99B assumes only unitarity and combines CPLEAR and other results.

⁵ If $\Delta S = \Delta Q$ is not assumed, ANGELOPOULOS 98f finds $\text{Im}\delta = (-15 \pm 23 \pm 3) \times 10^{-3}$.

⁶ DEMIDOV 95 reanalyzes data from HART 73 and NIEBERGALL 74.

## Re(y)

A non-zero value would violate CPT invariance in $\Delta S = \Delta Q$ amplitude. Re(y) is the following combination of $K_{e3}$ decay amplitudes:

$$ \text{Re}(y) = \text{Re} \left( \frac{\Lambda(K_L^0 \to e^- \pi^+ \nu_e)^* - \Lambda(K^0 \to e^+ \pi^- \nu_e)}{\Lambda(K_L^0 \to e^- \pi^+ \nu_e)^* + \Lambda(K^0 \to e^+ \pi^- \nu_e)} \right) $$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.4±2.5</strong></td><td>13k</td><td>1 AMBROSINO 06E</td><td>KLOE</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

0.3±3.1

² APOSTOLAO... 99B CPLR

¹ They use the PDG 04 for the $K_L^0$ semileptonic charge asymmetry and PDG 04 (CP review, CPT NOT ASSUMED) for Re(e).

² Constrained by Bell-Steinberger (or unitarity) relation.

## Re(x_−)

A non-zero value would violate CPT invariance in decay amplitudes with $\Delta S \neq \Delta Q$. $x_−$, used here to define Re(x_−), and $x_+$, used below in the $\Delta S = \Delta Q$ section are the following combinations of $K_{e3}$ decay amplitudes:

$$ x_{\pm} = \frac{1}{2} \left( \frac{\Lambda(K_L^0 \to \pi^- e^+ \nu_e)^*}{\Lambda(K_L^0 \to \pi^- e^+ \nu_e)^*} \pm \frac{\Lambda(K^0 \to \pi^+ e^- \bar{\nu}_e)^*}{\Lambda(K^0 \to \pi^+ e^- \bar{\nu}_e)^*} \right). $$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>-2.9±2.0</strong></td><td></td><td>1 AMBROSINO 06H</td><td>KLOE</td><td></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

-0.8±2.5

13k

-0.5±3.0

² APOSTOLAO... 99B CPLR Strangeness tagged

2 ±13 ±3

650k ANGELOPO... 98F Strangeness tagged

¹ AMBROSINO 06H uses Bell-Steinberger relations with the following measurements: $B(K_L^0 \to \pi^+\pi^-)$ in AMBROSINO 06r, $B(K_S^0 \to \pi^0\pi^0)$ in AMBROSINO 05b, the $K_S^0$-semileptonic charge asymmetry in AMBROSINO 06e, and $K^0$-semileptonic results in ANGELOPOULOS 98f.

² Uses PDG 04 for the $K_L^0$ semileptonic charge asymmetry and Re(δ) from CPLEAR, ANGELOPOULOS 98f.

³ Constrained by Bell-Steinberger (or unitarity) relation.

$$ |m_{K^0} - m_{\bar{K}^0}| / m_{\text{average}} $$

A test of CPT invariance. "Our Evaluation" is described in the "Tests of Conservation Laws" section. It assumes CPT invariance in the decay and neglects some contributions from decay channels other than $\pi\pi$.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>&lt;6 x 10<sup>-19</sup></strong></td><td>90</td><td>PDG</td><td>12</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

(-3 ± 4) x 10<sup>-18</sup>

¹ ANGELOPO... 99B RVUE

¹ ANGELOPOULOS 99B assumes only unitarity and combines CPLEAR and other results.

$$ (\Gamma_{K^0} - \Gamma_{\bar{K}^0}) / m_{\text{average}} $$

A test of CPT invariance.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>(7.8±8.4) x 10<sup>-18</sup></strong></td><td>1 ANGELOPO... 99B RVUE</td><td></td></tr></tbody></table>

¹ ANGELOPOULOS 99B assumes only unitarity and combines CPLEAR with other results. Correlated with $(m_{K^0} - m_{\bar{K}^0}) / m_{\text{average}}$ with a correlation coefficient of -0.95.

## TESTS OF $\Delta S = \Delta Q$ RULE

### Re(x_+)

A non-zero value would violate the $\Delta S = \Delta Q$ rule in CPT conserving transitions. $x_+$ is defined above in the Re(x_−) section.

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>-0.9± 3.0 OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>-2 ±10</td><td>1 BATLEY</td><td>07D NA48</td><td></td></tr><tr><td>-0.5± 3.6</td><td>13k</td><td>2 AMBROSINO 06E KLOE</td><td></td></tr><tr><td>-1.8± 6.1</td><td></td><td>3 ANGELOPO... 98D CPLR</td><td></td></tr></tbody></table>

¹ Result obtained from the measurement $\Gamma(K_S^0 \to \pi e\nu) / \Gamma(K_L^0 \to \pi e\nu) = 0.993 \pm 0.34$, neglecting possible CPT non-invariance and using PDG 06 values of $B(K_L^0 \to \pi e\nu) = 0.4053 \pm 0.0015$, $\tau_L = (5.114 \pm 0.021) \times 10^{-8}$ s and $\tau_S = (0.8958 \pm 0.0005) \times 10^{-10}$ s.

² Re(x_+) can be shown to be equal to the following combination of rates:

$$ \text{Re}(x_+) = \frac{\Gamma(K_S^0 \to \pi e \nu) - \Gamma(K_L^0 \to \pi e \nu)}{\Gamma(K_S^0 \to \pi e \nu) + \Gamma(K_L^0 \to \pi e \nu)} $$

which is valid up to first order in terms violating CPT and/or the $\Delta S = \Delta Q$ rule.

³ Obtained neglecting CPT violating amplitudes.

## $K^0$ REFERENCES

<table><tr><td>TOMARADZE</td><td>14</td><td>PR D89 031501</td><td>A. Tomaradze et al.</td><td>(NWES, WAYIN)</td></tr><tr><td>PDG</td><td>12</td><td>PR D86 001000</td><td>J. Beringer et al.</td><td>(PDG Collab.)</td></tr><tr><td>ABOUZAID</td><td>11</td><td>PR D83 092001</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>AMBROSINO</td><td>07B</td><td>JHEP 0712 073</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>BATLEY</td><td>07D</td><td>PL B653 145</td><td>J.R. Batley et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>ABOUZAID</td><td>06</td><td>PL B61 01801</td><td>E. Abouzaid et al.</td><td>(KTeV Collab.)</td></tr><tr><td>AMBROSINO</td><td>06E</td><td>PL B636 173</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>AMBROSINO</td><td>06F</td><td>PL B638 140</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>AMBROSINO</td><td>06H</td><td>JHEP 0612 011</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>PDG</td><td>06</td><td>JP G33 1</td><td>W.-M. Yao et al.</td><td>(PDG Collab.)</td></tr><tr><td>AMBROSINO</td><td>05A</td><td>PL B619 61</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>LAI</td><td>05A</td><td>PL B610 165</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>PDG</td><td>04</td><td>PL B592 1</td><td>S. Eildeman et al.</td><td>(PDG Collab.)</td></tr><tr><td>LAI</td><td>03C</td><td>EPJ C30 33</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>LAI</td><td>02</td><td>PL B533 196</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>ANGELOPO...</td><td>01B</td><td>EPJ C22 55</td><td>A. Angelopoulos et al.</td><td>(CPLEAR Collab.)</td></tr><tr><td>ANGELOPO...</td><td>99B</td><td>PL B471 332</td><td>A. Angelopoulos et al.</td><td>(CPLEAR Collab.)</td></tr><tr><td>APOSTOLAO...</td><td>99B</td><td>PL B456 297</td><td>A. Apostolakis et al.</td><td>(CPLEAR Collab.)</td></tr><tr><td>ANGELOPO...</td><td>98D</td><td>PL B444 38</td><td>A. Angelopoulos et al.</td><td>(CPLEAR Collab.)</td></tr><tr><td>Also</td><td></td><td>EPJ C22 55</td><td>A. Angelopoulos et al.</td><td>(CPLEAR Collab.)</td></tr><tr><td>ANGELOPO...</td><td>98E</td><td>PL B444 43</td><td>A. Angelopoulos et al.</td><td>(CPLEAR Collab.)</td></tr><tr><td>ANGELOPO...</td><td>98F</td><td>PL B444 52</td><td>A. Angelopoulos et al.</td><td>(CPLEAR Collab.)</td></tr><tr><td>Also</td><td></td><td>EPJ C22 55</td><td>A. Angelopoulos et al.</td><td>(CPLEAR Collab.)</td></tr><tr><td>DEMIDOV</td><td>95</td><td>PAN 58 968</td><td>V. Demidov, K. Gusev, E. Shabalin</td><td>(ITEP)</td></tr><tr><td>From YAF</td><td>58 1041</td><td></td><td></td><td></td></tr><tr><td>THOMSON</td><td>95</td><td>PR D51 1412</td><td>G.B. Thomson, Y. Zou</td><td>(RUTG)</td></tr><tr><td>BARKOV</td><td>87B</td><td>SJNP 46 630</td><td>L.M. Barkov et al.</td><td>(NOVO)</td></tr><tr><td></td><td></td><td>Translated from YAF 46 1088.</td><td></td><td></td></tr><tr><td>BARKOV</td><td>85B</td><td>JETPL 42 138</td><td>L.M. Barkov et al.</td><td>(NOVO)</td></tr><tr><td>BLATNIK</td><td>79</td><td>Translated from ZETFP 42 113.</td><td></td><td></td></tr><tr><td>MOLZON</td><td>78</td><td>PL 49B 103</td><td>5. Blatnik, J. Stahov, C.B. Lang</td><td>(TUZL, GRAZ)</td></tr><tr><td>NEIBERGALL</td><td>74</td><td>PL 41 1213</td><td>W.R. Molzon et al.</td><td>(EFI+)</td></tr><tr><td>HART</td><td>73</td><td>NP B66 317</td><td>F. Niebergall et al.</td><td>(CERN, ORSAY, VIEN)</td></tr><tr><td>FOETH</td><td>69B</td><td>PL 30B 276</td><td>J.C. Hart et al.</td><td>(CAVE, RHEL)</td></tr><tr><td>HILL</td><td>68B</td><td>PL 165 1534</td><td>H. Foeth et al.</td><td>(AACH, CERN, TORI)</td></tr><tr><td>FITCH</td><td>67</td><td>PR 164 1711</td><td>D.G. Hill et al.</td><td>(BNL, CMU)</td></tr><tr><td>BALTAY</td><td>66</td><td>PR 142 932</td><td>V.L. Fitch et al.</td><td>(PRIN)</td></tr><tr><td>BURNSTEIN</td><td>65</td><td>PR 138 B895</td><td>C. Baltay et al.</td><td>(YALE, BNL)</td></tr><tr><td>Kim</td><td>65B</td><td>PR 140 B1334</td><td>R.A. Burnstein, H.A. Rubin</td><td>(UMD)</td></tr><tr><td>CHRISTENS...</td><td>64</td><td>PLR 13 138</td><td>J.K. Kim, L. Kirsch, D. Miller</td><td>(COLU)</td></tr><tr><td>ROSWARD...</td><td>59</td><td>PLR 2 110</td><td>J.H. Christenson et al.</td><td>(PRIN)</td></tr><tr><td>ROSWARD...</td><td>59</td><td>PLR 2 110</td><td>F.S. Crawford et al.</td><td>(LRL)</td></tr><tr><td>ROSWARD...</td><td>59</td><td>PLR 2 110</td><td>A.H. Rosenfeld, F.T. Solmitz, R.D. Tripp</td><td>(LRL)</td></tr></table>



$$ K_S^0 $$

$$ I(J^P) = \frac{1}{2}(0^{-}) $$

## $K_S^0$ MEAN LIFE

For earlier measurements, beginning with BOLDT 58B, see our 1986 edition, Physics Letters 170B 130 (1986).

OUR FIT is described in the note on "CP violation in $K_L$ decays" in the $K_S^0$ Particle Listings. The result labeled "OUR FIT Assuming CPT" ["OUR FIT Not Assuming CPT"] includes all measurements except those with the comment "Not assuming CPT" ["Assuming CPT"). Measurements with neither comment do not assume CPT and enter both fits.

<table><thead><tr><th>VALUE (10<sup>-10</sup> s)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.8954 ±0.0004</strong></td><td><strong>OUR FIT</strong></td><td>Error includes scale factor of 1.1.</td><td>Assuming CPT</td><td></td></tr><tr><td><strong>0.89564 ±0.00033</strong></td><td><strong>OUR FIT</strong></td><td>Not assuming CPT</td><td></td><td></td></tr><tr><td>0.89589 ±0.00070</td><td></td><td>1,2 ABOUZAID</td><td>11 KTEV</td><td>Not assuming CPT</td></tr><tr><td>0.89623 ±0.00047</td><td></td><td>1,3 ABOUZAID</td><td>11 KTEV</td><td>Assuming CPT</td></tr><tr><td>0.89562 ±0.00029 ±0.00043</td><td>20M</td><td>4 AMBROSINO</td><td>11 KLOE</td><td>Not assuming CPT</td></tr><tr><td>0.89598 ±0.00048 ±0.00051</td><td>16M</td><td>LAI</td><td>02c NA48</td><td></td></tr><tr><td>0.8971 ±0.0021</td><td></td><td>BERTANZA</td><td>97 NA31</td><td></td></tr><tr><td>0.8941 ±0.0014 ±0.0009</td><td></td><td>SCHWINGEN...</td><td>95 E773</td><td>Assuming CPT</td></tr><tr><td>0.8929 ±0.0016</td><td></td><td>GIBBONS</td><td>93 E731</td><td>Assuming CPT</td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.8965 ±0.0007</td><td></td><td>5 ALAVI-HARATI 03</td><td>KTEV</td><td>Assuming CPT</td></tr><tr><td>0.8958 ±0.0013</td><td></td><td>6 ALAVI-HARATI 03</td><td>KTEV</td><td>Not assuming CPT</td></tr><tr><td>0.8920 ±0.0044</td><td>214k</td><td>GROSSMAN</td><td>87 SPEC</td><td></td></tr><tr><td>0.905 ±0.007</td><td></td><td>7 ARONSON</td><td>82b SPEC</td><td></td></tr><tr><td>0.881 ±0.009</td><td>26k</td><td>ARONSON</td><td>76 SPEC</td><td></td></tr><tr><td>0.8926 ±0.0032 ±0.0002</td><td></td><td>8 CARITHERS</td><td>75 SPEC</td><td></td></tr><tr><td>0.8937 ±0.0048</td><td>6M</td><td>GEWENIGER</td><td>74B ASPK</td><td></td></tr><tr><td>0.8958 ±0.0045</td><td>50k</td><td>9 SKJEGGEST...</td><td>72 HBC</td><td></td></tr><tr><td>0.856 ±0.008</td><td>19994</td><td>10 DONALD</td><td>68B HBC</td><td></td></tr><tr><td>0.872 ±0.009</td><td>20000</td><td>9,10 HILL</td><td>68 DBC</td><td></td></tr></tbody></table>

¹ The two ABOUZAID 11 values use the same full KTeV dataset from 1996, 1997, and 1999. The first enters the "assuming CPT" fit and the second enters the "not assuming CPT" fit.

² ABOUZAID 11 fit has $\Delta m, \tau_S, \phi_e, \text{Re}(e'/e)$, and $\text{Im}(e'/e)$ as free parameters. See $\text{Im}(e'/e)$ in the "$K_L^0$ CP violation" section for correlation information.

³ ABOUZAID 11 fit has $\Delta m$ and $\tau_S$ free but constrains $\phi_e$ to the Superweak value, i.e. assumes CPT. This $\tau_S$ value is correlated with their $\Delta m = m_{K_L^0} - m_{K_S^0}$ measurement in the $K_L^0$ listings. The correlation coefficient $\rho(\tau_S, \Delta m) = -0.670$.

⁴ Fit to the proper time distribution.

⁵ This ALAVI-HARATI 03 fit has $\Delta m$ and $\tau_S$ free but constrains $\phi_{-+}$ to the Superweak value, i.e. assumes CPT. This $\tau_S$ value is correlated with their $\Delta m = m_{K_L^0} - m_{K_S^0}$ measurement in the $K_L^0$ listings. The correlation coefficient $\rho(\tau_S, \Delta m) = -0.396$.

⁶ This ALAVI-HARATI 03 fit has $\Delta m, \phi_{-+}$, and $\tau_{K_S}$ free. See $\phi_{-+}$ in the "$K_L$ CP violation" section for correlation information. Superseded by ABOUZAID 11.

⁷ This ALAVI-HARATI 03 fit has $\Delta m, \phi_{-+}$, and $\tau_{K_S}$ free. See $\phi_{-+}$ in the "$K_L$ CP violation" section for correlation information. Superseded by ABOUZAID 11.
⁷ ARONSON 82 find that $K_S^0$ mean life may depend on the kaon energy.

⁸ CARITHERS 75 measures the $\Delta m$ dependence of the total decay rate (inverse mean life) to be $\Gamma(K_S^0) = [(1.122 \pm 0.004) + 0.16(\Delta m - 0.5348)]/\Delta m|10^{10}/\text{s}$, or, in terms of mean life, CARITHERS 75 measures $\tau_S = (0.8913 \pm 0.0032) - 0.238 [\Delta m - 0.5348] (10^{-10} \text{ s})$. We have adjusted the measurement to use our best values of $(\Delta m = 0.5293 \pm 0.0009) (10^{10} \hbar s^{-1})$. Our first error is their experiment's error and our second error is the systematic error from using our best values.

⁹ HILL 68 has been changed by the authors from the published value (0.865 ± 0.009) because of a correction in the shift due to $\eta_+$. SKJEGGESTAD 72 and HILL 68 give detailed discussions of systematics encountered in this type of experiment.

¹⁰ Pre-1971 experiments are excluded from the average because of disagreement with later more precise experiments.

## K_S⁰ DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction (Γ<sub>i</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th></tr></thead><tbody><tr><td colspan="3"><strong>Hadronic modes</strong></td></tr><tr><td>Γ<sub>1</sub></td><td>π<sup>0</sup>π<sup>0</sup></td><td>(30.69 ± 0.05) %</td></tr><tr><td>Γ<sub>2</sub></td><td>π<sup>+</sup>π<sup>-</sup></td><td>(69.20 ± 0.05) %</td></tr><tr><td>Γ<sub>3</sub></td><td>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>(3.5<sup>+1.1</sup><sub>-0.9</sub>) × 10<sup>-7</sup></td></tr><tr><td colspan="3"><strong>Modes with photons or ℓℓ' pairs</strong></td></tr><tr><td>Γ<sub>4</sub></td><td>π<sup>+</sup>π<sup>-</sup>γ</td><td>[a,b] (1.79 ± 0.05) × 10<sup>-3</sup></td></tr><tr><td>Γ<sub>5</sub></td><td>π<sup>+</sup>π<sup>-</sup>e<sup>+</sup>e<sup>-</sup></td><td>(4.79 ± 0.15) × 10<sup>-5</sup></td></tr><tr><td>Γ<sub>6</sub></td><td>π<sup>0</sup>γγ</td><td>[a] (4.9 ± 1.8) × 10<sup>-8</sup></td></tr><tr><td>Γ<sub>7</sub></td><td>γγ</td><td>(2.63 ± 0.17) × 10<sup>-6</sup></td></tr><tr><td>Γ<sub>8</sub></td><td>μ<sup>+</sup>μ<sup>-</sup>μ<sup>+</sup>μ<sup>-</sup></td><td>&lt; 5.1 × 10<sup>-12</sup></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3"><strong>Semileptonic modes</strong></td></tr><tr><td>Γ<sub>9</sub></td><td>π<sup>±</sup>e<sup>∓</sup>ν<sub>e</sub></td><td>[c] (7.14 ± 0.06) × 10<sup>-4</sup></td></tr><tr><td>Γ<sub>10</sub></td><td>π<sup>±</sup>μ<sup>∓</sup>ν<sub>μ</sub></td><td>[c,d] (4.56 ± 0.20) × 10<sup>-4</sup></td></tr></tbody></table>

### CP violating (CP) and $\Delta S = 1$ weak neutral current (S1) modes

<table><tbody><tr><td>Γ<sub>11</sub></td><td>3π<sup>0</sup></td><td>CP</td><td>&lt; 2.6 × 10<sup>-8</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>12</sub></td><td>μ<sup>+</sup>μ<sup>-</sup></td><td>S1</td><td>&lt; 2.1 × 10<sup>-10</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>13</sub></td><td>e<sup>+</sup>e<sup>-</sup></td><td>S1</td><td>&lt; 9 × 10<sup>-9</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>14</sub></td><td>π<sup>0</sup>e<sup>+</sup>e<sup>-</sup></td><td>S1</td><td>[a] (3.0<sup>+1.5</sup><sub>-1.2</sub>) × 10<sup>-9</sup></td><td></td></tr><tr><td>Γ<sub>15</sub></td><td>π<sup>0</sup>μ<sup>+</sup>μ<sup>-</sup></td><td>S1</td><td>(2.9<sup>+1.5</sup><sub>-1.2</sub>) × 10<sup>-9</sup></td><td></td></tr></tbody></table>

[a] See the Particle Listings below for the energy limits used in this measurement.

[b] Most of this radiative mode, the low-momentum $\gamma$ part, is also included in the parent mode listed without $\gamma$'s.

[c] The value is for the sum of the charge states or particle/antiparticle states indicated.

[d] Not a measurement. Calculated as $0.666 \cdot B(\pi^{\pm} e^{\mp} \nu_{e})$.

## CONSTRAINED FIT INFORMATION

An overall fit to 4 branching ratios uses 5 measurements and one constraint to determine 4 parameters. The overall fit has a $\chi^2 = 0.6$ for 2 degrees of freedom.

The following off-diagonal array elements are the correlation coefficients $\langle\delta x_i \delta x_j\rangle/(\delta x_i - \delta x_j)$, in percent, from the fit to the branching fractions, $\chi_i \equiv \Gamma_i/\Gamma_{\text{total}}$. The fit constrains the $x_i$ whose labels appear in this array to sum to one.

<figure><img src="image_510.png" /></figure>

## K_S⁰ DECAY RATES

<table><thead><tr><th>Γ(π<sup>±</sup>e<sup>∓</sup>ν<sub>e</sub>)</th><th>VALUE (10<sup>6</sup> s<sup>-1</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>• • •</td><td>We do not use the following data for averages, fits, limits, etc. • • •</td><td></td><td></td><td></td><td></td></tr><tr><td>8.1 ± 1.6</td><td>75</td><td>1 AKHMETSHIN 99</td><td>CMD2</td><td>Tagged K<sub>S</sub><sup>0</sup> using φ → K<sub>L</sub><sup>0</sup>K<sub>S</sub><sup>0</sup></td><td></td></tr><tr><td>7.50 ± 0.08</td><td></td><td>2 PDG</td><td>98</td><td></td><td></td></tr><tr><td>seen</td><td></td><td>BURGUN</td><td>72</td><td>HBC</td><td>K<sup>+</sup> p → K<sup>0</sup> pπ<sup>+</sup></td></tr><tr><td>9.3 ± 2.5</td><td></td><td>AUBERT</td><td>65</td><td>HLBC</td><td>ΔS = ΔQ, CP cons. not assumed</td></tr></tbody></table>

¹ AKHMETSHIN 99 is from a measured branching ratio $B(K_S^0 \to \pi e \nu_e) = (7.2 \pm 1.4) \times 10^{-4}$ and $\tau_{K_S^0} = (0.8934 \pm 0.0008) \times 10^{-10}$ s. Not independent of measured branching ratio.

² PDG 98 from $K_S^0$ measurements, assuming that $\Delta S = \Delta Q$ in $K^0$ decay so that $\Gamma(K_S^0 \to \pi^\pm e^\mp \nu_e) = \Gamma(K_L^0 \to \pi^\pm e^\mp \nu_e)$.

## Γ(π±μ∓νμ) / Γ<sub>1</sub>

<table><thead><tr><th>VALUE (10<sup>6</sup> s<sup>-1</sup>)</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>• • •</td><td></td><td></td></tr><tr><td>5.25 ± 0.07</td><td>1 PDG</td><td>98</td></tr></tbody></table>

¹ PDG 98 from $K_L^0$ measurements, assuming that $\Delta S = \Delta Q$ in $K^0$ decay so that $\Gamma(K_S^0 \to \pi^\pm \mu^\mp \nu_\mu) = \Gamma(K_L^0 \to \pi^\pm \mu^\mp \nu_\mu)$.

## K_S⁰ BRANCHING RATIOS

### Hadronic modes

## Γ(π⁰π⁰)/Γ<sub>total</sub> / Γ<sub>1</sub>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>0.335 ± 0.014</td><td>1066</td><td>BROWN</td><td>63 HLBC</td></tr><tr><td>0.288 ± 0.021</td><td>198</td><td>CHRETIEN</td><td>63 HLBC</td></tr><tr><td>0.30 ± 0.035</td><td></td><td>BROWN</td><td>61 HLBC</td></tr></tbody></table>

## Γ(π<sup>+</sup>π<sup>-</sup>)/Γ<sub>total</sub> / Γ<sub>2</sub>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.670 ± 0.010</td><td>3447</td><td>DOYLE</td><td>69 HBC</td><td>π<sup>-</sup> p → ΛK<sup>0</sup></td></tr></tbody></table>

## Γ(π<sup>+</sup>π<sup>-</sup>)/Γ(π⁰π⁰) / Γ<sub>2</sub>/Γ<sub>1</sub>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2.255 ± 0.005</td><td>OUR FIT</td><td>1 AMBROSINO</td><td>06C</td><td>KLOE</td></tr><tr><td>2.2549 ± 0.0054</td><td>2 AMBROSINO</td><td>06C</td><td>KLOE</td><td></td></tr><tr><td>2.236 ± 0.003</td><td>02b</td><td>ALOISIO</td><td>02b</td><td>KLOE</td></tr><tr><td>2.11 ± 0.09</td><td>1315</td><td>EVERHART</td><td>76 WIRE</td><td>π<sup>-</sup> p → ΛK<sup>0</sup></td></tr><tr><td>2.169 ± 0.094</td><td>16k</td><td>COWELL</td><td>74 OSPK</td><td>π<sup>-</sup> p → ΛK<sup>0</sup></td></tr><tr><td>2.16 ± 0.08</td><td>4799</td><td>HILL</td><td>73 DBC</td><td>K<sup>+</sup> d → K<sup>0</sup> p p</td></tr><tr><td>2.22 ± 0.10</td><td>3068</td><td>ALITTI</td><td>72 HBC</td><td>K<sup>+</sup> p → π<sup>+</sup> p K<sup>0</sup></td></tr><tr><td>2.22 ± 0.08</td><td>6380</td><td>MORSE</td><td>72b DBC</td><td>K<sup>+</sup> n → K<sup>0</sup> p</td></tr><tr><td>2.10 ± 0.11</td><td>701</td><td>NAGY</td><td>72 HLBC</td><td>K<sup>+</sup> n → K<sup>0</sup> p</td></tr><tr><td>2.22 ± 0.095</td><td>6150</td><td>BALTAY</td><td>71 HBC</td><td>K p → K<sup>0</sup> neutrals</td></tr><tr><td>2.282 ± 0.043</td><td>7944</td><td>MOFFETT</td><td>70 OSPK</td><td>K<sup>+</sup> n → K<sup>0</sup> p</td></tr><tr><td>2.12 ± 0.17</td><td>267</td><td>BOZOKI</td><td>69 HLBC</td><td>K<sup>+</sup> n → K<sup>0</sup> p</td></tr><tr><td>2.285 ± 0.055</td><td>3016</td><td>GOBBI</td><td>69 OSPK</td><td>K<sup>+</sup> n → K<sup>0</sup> p</td></tr><tr><td>2.10 ± 0.06</td><td>3700</td><td>MORFIN</td><td>69 HLBC</td><td>K<sup>+</sup> n → K<sup>0</sup> p</td></tr></tbody></table>

¹ This result combines AMBROSINO 06C KLOE 2001-02 data with ALOISIO 02b KLOE 2000 data. $K_S^0 \to \pi^+\pi^- \text{ fully inclusive.}$

² Includes radiative decays $\pi^+\pi^-\gamma$.

³ The directly measured quantity is $K_S^0 \to \pi^+\pi^- / \text{all } K^0 = 0.345 \pm 0.005$.

⁴ NAGY 72 is a final result which includes BOZOKI 69.

⁵ The directly measured quantity is $K_S^0 \to \pi^+\pi^- / \text{all } K^0 = 0.345 \pm 0.005$.

⁶ MOFFETT 70 is a final result which includes GOBBI 69.

## Γ(π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>)/Γ<sub>total</sub> / Γ<sub>3</sub>

<table><thead><tr><th>VALUE (units 10<sup>-7</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>3.5<sup>+1.1</sup><sub>-0.9</sub> OUR AVERAGE</td><td></td><td></td><td></td><td></td></tr><tr><td>4.7<sup>+2.2</sup><sub>-1.7</sub></td><td>1 BATLEY</td><td>05</td><td>NA48</td><td></td></tr><tr><td>2.5<sup>+1.3</sup><sub>-1.0</sub></td><td>500k</td><td>2 ADLER</td><td>97B</td><td>CPLR</td></tr><tr><td>4.8<sup>+2.2</sup><sub>-1.6</sub></td><td>3 ZOU</td><td></td><td>96</td><td>E621</td></tr><tr><td>• • •</td><td>We do not use the following data for averages, fits, limits, etc. • • •</td><td></td><td></td><td></td></tr><tr><td>4.1<sup>+2.5</sup><sub>-1.9</sub></td><td>4 ADLER</td><td>96E</td><td>CPLR</td><td>Sup. by ADLER 97B</td></tr><tr><td>3.9<sup>+5.4</sup><sub>-1.8</sub></td><td>5 THOMSON</td><td>94</td><td>E621</td><td>Sup. by ZOU 96</td></tr></tbody></table>

¹ BATLEY 05 is obtained by measuring the interference parameters in $K_S$, $K_L \to \pi^+\pi^-\pi^0$: Re($\lambda$) = 0.038 ± 0.008 ± 0.006 and Im($\lambda$) = -0.013 ± 0.005 ± 0.004; the correlation coeff. between Re($\lambda$) and Im($\lambda$) is 0.66 (statistical only).

² ADLER 97B find the CP-conserving parameters Re($\lambda$) = (28 ± 7 ± 3) × 10<sup>-3</sup>, Im($\lambda$) = (-10 ± 8 ± 2) × 10<sup>-3</sup>. They estimate $B(K_S^0 \to \pi^+\pi^-\pi^0)$ from Re($\lambda$) and the $K_L^0$ decay parameters. See also ANGELOPOULOS 98c.

³ ZOU 96 is from the the measured quantities $|\rho_{+-}| = 0.039^{+0.009}_{-0.006}$ ± 0.005 and $\phi_{\rho} = (-9 \pm 18)^\circ$.

⁴ ADLER 96E is from the measured quantities Re($\lambda$) = 0.036 ± 0.010<sup>+0.002</sup><sub>-0.003</sub> and Im($\lambda$) consistent with zero. Note that the quantity $\lambda$ is the same as $\rho_{+-}$ used in other footnotes.

⁵ THOMSON 94 calculates this branching ratio from their measurements $|\rho_{+-}| = 0.035^{+0.019}_{-0.011}$ ± 0.004 and $\phi_{\rho} = (-59 \pm 48)^\circ$ where $|\rho_{+-}|e^{i\phi_{\rho}} = A(K_S^0 \to \pi^+\pi^-\pi^0, I = 2)/A(K_L^0 \to \pi^+\pi^-\pi^0)$.
## Modes with photons or $ℓℓ$ pairs

$\Gamma(\pi^+\pi^-\gamma)/\Gamma(\pi^+\pi^-)$

$\Gamma_4/\Gamma_2$

VALUE (units 10⁻³)

EVT$^S$

2.59±0.08 OUR AVERAGE

2.56±0.09 1286

2.68±0.15 76

DOCUMENT ID

TECN

COMMENT

• • • We do not use the following data for averages, fits, limits, etc. • • •

7.10±0.22 3723

RAMBERG

93

E731

p$_{γ}$ >20 MeV/c

3.0 ±0.6 29

2 BOBISUT

74

HLBC

p$_{γ}$ >40 MeV/c

2.8 ±0.6 73

3 BURGUN

73

HBC

p$_{γ}$ >50 MeV/c

¹TAUREG 76 find direct emission contribution <0.06, CL = 90%.

²BOBISUT 74 not included in average because p$_{γ}$ cut differs. Estimates direct emission contribution to be 0.5 or less, CL = 95%.

³BURGUN 73 estimates that direct emission contribution is 0.3 ± 0.6.

$\Gamma(\pi^+\pi^-e^+e^-)/\Gamma_{\text{total}}$

$\Gamma_5/\Gamma$

VALUE (units 10⁻⁵)

EVT$^S$

4.79±0.15 OUR AVERAGE

4.83±0.11±0.14 23k

4.69±0.30 676

DOCUMENT ID

TECN

COMMENT

• • • We do not use the following data for averages, fits, limits, etc. • • •

4.71±0.23±0.22 620

2,3 LAI

03c

NA48

4.5 ±0.7 ±0.4 56

LAI

00b

NA48

¹BATLEY 11 reports $[\Gamma(K_S^0 \to \pi^+\pi^- e^+e^-)/\Gamma_{\text{total}}] / [B(K_L^0 \to \pi^+\pi^-\pi^0)] / [B(\pi^0 \to e^+e^-\gamma)] = (3.28 \pm 0.06 \pm 0.04) \times 10^{-2}$ which we multiply by our best values $B(K_S^0 \to \pi^+\pi^-\pi^0) = (12.54 \pm 0.05) \times 10^{-2}$, $B(\pi^0 \to e^+e^-\gamma) = (1.174 \pm 0.035) \times 10^{-2}$. Our first error is their experiment's error and our second error is the systematic error from using our best values. Also a limit on the absolute value of the interference between bremsstrahlung and E1 transition is given: $< 4 \times 10^{-7}$ at 90% CL.

²Uses normalization BR($K_L \to \pi^+\pi^-\pi^0$)*BR($\pi^0 \to e^+e^-$) = (1.505±0.047)×10⁻³ from our 2000 Edition.

³Second error is 0.16(syst)±0.15(normal) combined in quadrature.

$\Gamma(\pi^0\gamma\gamma)/\Gamma_{\text{total}}$

$\Gamma_6/\Gamma$

VALUE (units 10⁻⁶)

CL$^S$

EVT$^S$

4.9±1.6±0.9 17

1

LAI

04

NA48

$m^2_{\gamma\gamma}/m^2_K > 0.2$

• • • We do not use the following data for averages, fits, limits, etc. • • •

<33 90

LAI

03b

NA48

$m^2_{\gamma\gamma}/m^2_K > 0.2$

¹Spectrum also measured and found consistent with the one generated by a constant matrix element.

$\Gamma(\gamma\gamma)/\Gamma_{\text{total}}$

$\Gamma_7/\Gamma$

VALUE (units 10⁻⁵)

CL$^S$

EVT$^S$

2.63 ±0.17 OUR AVERAGE

2.26 ±0.12 ±0.06 711

2.713±0.063±0.005 7.5k

Error includes scale factor of 3.1.

¹AMBROSINO

08c

KLOE

$\phi \to K_S^0 K_L^0$

• • • We do not use the following data for averages, fits, limits, etc. • • •

2.58 ±0.36 ±0.22 149

LAI

00

NA48

2.2 ±1.1 16

3 BARR

95b

NA31

2.4 ±0.9 35

4 BARR

95b

NA31

< 13 90

BALATS

89

SPEC

2.4 ±1.2 19

BURKHARDT

87

NA31

<133 90

BARMIN

86b

XEBE

¹AMBROSINO 08c reports $(2.26 \pm 0.12 \pm 0.06) \times 10^{-6}$ from a measurement of $[\Gamma(K_S^0 \to \gamma\gamma)/\Gamma_{\text{total}}] \times [B(K_S^0 \to \pi^0\pi^0)]$ assuming $B(K_S^0 \to \pi^0\pi^0) = (30.69 \pm 0.05) \times 10^{-2}$.

²LAI 03 reports $[\Gamma(K_S^0 \to \gamma\gamma)/\Gamma_{\text{total}}] / [B(K_S^0 \to \pi^0\pi^0)] = (8.84 \pm 0.18 \pm 0.10) \times 10^{-6}$ which we multiply by our best value $B(K_S^0 \to \pi^0\pi^0) = (30.69 \pm 0.05) \times 10^{-2}$. Our first error is their experiment's error and our second error is the systematic error from using our best value.

³BARR 95b result is calculated using $B(K_L \to \gamma\gamma) = (5.86 \pm 0.17) \times 10^{-4}$.

⁴BARR 95b quotes this as the combined BARR 95b + BURKHARDT 87 result after rescaling BURKHARDT 87 to use same branching ratios and lifetimes as BARR 95b.

$\Gamma(\mu^+\mu^-\mu^+\mu^-)/\Gamma_{\text{total}}$

$\Gamma_8/\Gamma$

VALUE (units 10⁻⁵)

CL$^S$

DOCUMENT ID

TECN

<5.1 × 10⁻¹² 90

1

AAIJ

23AE

LHCB

¹AAIJ 23AE uses 5.1 fb⁻¹ of LHCb data recorded from 2016 to 2018.

## Semileptonic modes

$\Gamma(\mu^\pm e^\mp\nu_e)/\Gamma_{\text{total}}$

$\Gamma_9/\Gamma$

VALUE (units 10⁻⁴)

EVT$^S$

DOCUMENT ID

TECN

COMMENT

7.14 ±0.06 OUR FIT

7.04 ±0.08 OUR AVERAGE

7.046±0.18±0.16 1

1 BATLEY

07D

NA48

6.91 ±0.34±0.15 624

2 ALOISIO

02

KLOE

Tagged $K_S^0$ using $\phi \to K_L^0 K_S^0$

• • • We use the following data for averages but not for fits. • • •

7.05 ±0.09

13k ³ AMBROSINO 06E KLOE Not fitted

• • • We do not use the following data for averages, fits, limits, etc. • • •

7.2 ±1.4

75 AKHMETSHIN 99 CMD2 Tagged $K_S^0$ using $\phi \to K_L^0 K_S^0$

¹Reconstructed from $K_S^0(\bar{K}^0)(t) \to \pi e \nu$ distributions using PDG values of $B(K_L^0 \to \pi e \nu) = 0.4053 \pm 0.0015$, $\tau_L = (5.114 \pm 0.021) \times 10^{-8}$ s and $\tau_S = (0.8958 \pm 0.0005) \times 10^{-10}$ s.

²Uses the PDG 00 value for $B(K_S^0 \to \pi^+\pi^-)$.

³Obtained by imposing $\Sigma_i B(K_S^0 \to i) = 1$, where $i$ runs over all the four branching ratios $\pi^+\pi^-, \pi^0\pi^0, \pi e \nu$, and $\pi\mu\nu$. Input value of $B(K_S^0 \to \pi^+\pi^-) / B(K_S^0 \to \pi^0\pi^0)$ from AMBROSINO 06c is used. To derive $\Gamma(K_S^0 \to \pi^+\mu\nu) / \Gamma(K_S^0 \to \pi^+\nu e)$, lepton universality is assumed, radiative corrections from ANDRE 07 are used, and phase space integrals are taken from KTeV, ALEXOPOULOS 04A. This branching fraction enters our fit via their $\Gamma(\pi^\pm e^\mp\nu_e) / \Gamma(\pi^+\pi^-)$ branching ratio measurement.

$\Gamma(\pi^\pm\mu^\mp\nu_\mu)/\Gamma_{\text{total}}$

$\Gamma_{10}/\Gamma$

VALUE (units 10⁻⁴)

EVT$^S$

4.56±0.20 OUR FIT

4.56±0.11±0.17 7223

1 BABUSCI

20

KLOE

direct measurement

¹Value obtained by normalizing to the KLOE measurement $B(K_S^0 \to \pi^+\pi^-) = (69.196 \pm 0.051)\%$. Also comparison with the PDG 18 based derived value leads to a lepton flavor universality test $|V_{us} f_+(0)|^2 K_S^0 \to \pi\mu\nu / |V_{us} f_+(0)|^2 K_S^0 \to \pi e \nu = 0.975 \pm 0.044$.

$\Gamma(\pi^\pm e^\mp\nu_e)/\Gamma(\pi^+\pi^-)$

$\Gamma_9/\Gamma_2$

VALUE (units 10⁻³)

EVT$^S$

1.032 ±0.008 OUR FIT

1.0338±0.0054±0.0064

1 BABUSCI

23

KLOE

• • • We do not use the following data for averages, fits, limits, etc. • • •

1.019 ±0.011 ±0.007

13k

²AMBROSINO 06E KLOE

¹BABUSCI 23 measured $\Gamma(K_S^0 \to \pi e \nu) / \Gamma(K_S^0 \to \pi^+\pi^-) = (1.0421 \pm 0.0066 \pm 0.0075) \times 10^{-3}$ based on data collected from 2004 to 2005. About 50k signal events were reconstructed from the dataset corresponding to an integrated luminosity of 1.63 fb⁻¹. The quoted value is their combination of this result with the previous measurement of AMBROSINO 06e. The correlation coefficient between the two measurements is 12%.

²AMBROSINO 06E result is included in BABUSCI 23.

## CP violating (CP) and $\Delta S = 1$ weak neutral current (S1) modes

$\Gamma(3\pi^0)/\Gamma_{\text{total}}$

$\Gamma_{11}/\Gamma$

Violates CP conservation.

VALUE (units 10⁻⁷)

CL$^S$

EVT$^S$

< 0.26 90

590M

1

BABUSCI

13c

KLOE

$\phi \to K_L^0 K_S^0$

• • • We do not use the following data for averages, fits, limits, etc. • • •

< 1.2 90

37.8M

AMBROSINO

05b

KLOE

< 7.4 90

4.9M

2

LAI

05a

NA48

<140 90

7M

ACHASOV

99d

SND

<190 90

17300

3

ANGELOPO...

98b

CPLR

<370 90

BARMIN

83

HLBC

¹BABUSCI 13c uses $1.7 \text{ fb}^{-1}$ of data of $\phi \to K_S^0 K_S^0$ decays with $K_S^0$ interaction in the calorimeter, collected from 2004 to 2005. No candidate events were found in the data with an expected background of $0.04^{+0.15}_{-0.03}$ events. Upper limit is obtained by normalizing to $K_S^0 \to 2\pi^0$ decays.

²LAI 05a value is obtained from their bound on $|\eta_{000}|$ (not assuming CPT) and $B(K_S^0 \to 3\pi^0) = 0.211 \pm 0.003$, and PDG 04 values for $K_S^0$ and $K_S^0$ lifetimes. If CPT is assumed then $B(K_S^0 \to 3\pi^0)_{CPT} < 2.3 \times 10^{-7}$ at 90% CL.

³ANGELOPOULOS 98b is from Im($\eta_{000}$) = -0.05 ± 0.12 ± 0.05, assuming Re($\eta_{000}$) = Re($\epsilon$) = 1.635 × 10⁻³ and using the value $B(K_L^0 \to \pi^0\pi^0\pi^0) = 0.2112 \pm 0.0027$.

$\Gamma(\mu^+\mu^-)/\Gamma_{\text{total}}$

$\Gamma_{12}/\Gamma$

Test for $\Delta S = 1$ weak neutral current. Allowed by first-order weak interaction combined with electromagnetic interaction.

VALUE (units 10⁻⁵)

CL$^S$

90

1

AAIJ

20AE

LHCB

<2.1 × 10⁻¹⁰ 90

1

AAIJ

17BQ

LHCB

• • • We do not use the following data for averages, fits, limits, etc. • • •

<8 × 10⁻¹⁰ 90

2

AAIJ

13G

LHCB

<9 × 10⁻⁹ 90

3

AAIJ

13G

LHCB

<3.2 × 10⁻⁷ 90

GJESDAL

73

ASPK

<7 × 10⁻⁶ 90

HYAMS

69b

OSPK

¹AAIJ 20AE uses 8.6 fb⁻¹ of LHCb data from 2011 to 2012 and 2016 to 2018. The result utilizes the normalization mode branching fraction $B(K_S^0 \to \pi^+\pi^-) = (69.20 \pm 0.05) \times 10^{-2}$ from PDG 18. Supersedes AAIJ 17BQ.

²AAIJ 17BQ uses 3.0 fb⁻¹ of $pp$ collisions at $\sqrt{s} = 7$ and 8 TeV. The result utilizes the normalization mode branching fraction $B(K_S^0 \to \pi^+\pi^-) = (69.20 \pm 0.05) \times 10^{-2}$ from PDG 16. Supersedes AAIJ 13G.

³AAIJ 13G uses 1.0 fb⁻¹ of $pp$ collisions at $\sqrt{s} = 7$ TeV. They obtained $B(K_S^0 \to \mu^+\mu^-) < 11 \times 10^{-9}$ at 95% C.L.
**Γ(e⁺e⁻)/Γ<sub>total</sub>**
Test for ΔS = 1 weak neutral current. Allowed by first-order weak interaction combined with electromagnetic interaction.

<table><thead><tr><th>VALUE (units 10<sup>-7</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt; 0.09</td><td>90</td><td>1 AMBROSINO</td><td>09A</td><td>KLOE e<sup>+</sup>e<sup>-</sup> → φ → K<sub>S</sub><sup>0</sup> κ<sub>L</sub><sup>0</sup></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>&lt; 1.4</td><td>90</td><td>ANGELOPO...</td><td>97</td><td>CPLR</td></tr><tr><td>&lt; 28</td><td>90</td><td>BLICK</td><td>94</td><td>CNTR Hyperon facility</td></tr><tr><td>&lt;100</td><td>90</td><td>BARMIN</td><td>86</td><td>XEBC</td></tr></table>

¹ AMBROSINO 09A reports < 0.09 × 10⁻⁷ from a measurement of [Γ(K⁰₅ → e⁺e⁻)/Γ<sub>total</sub> / [B(K⁰₅ → π⁺π⁻)] assuming B(K⁰₅ → π⁺π⁻) = (69.20 ± 0.05) × 10⁻².

**Γ(π⁰e⁺e⁻)/Γ<sub>total</sub>**
Test for ΔS = 1 weak neutral current. Allowed by first-order weak interaction combined with electromagnetic interaction.

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>3.0<sup>+1.5</sup><sub>-1.2</sub>±0.2</td><td>7</td><td>1 BATLEY</td><td>03</td><td>NA48</td><td>m<sub>ee</sub> > 0.165 GeV</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>&lt; 140</td><td>90</td><td>LAI</td><td>01</td><td>NA48</td></tr><tr><td>&lt; 1100</td><td>90</td><td>BARR</td><td>93B</td><td>NA31</td></tr><tr><td>&lt;45000</td><td>90</td><td>GIBBONS</td><td>88</td><td>E731</td></tr></table>

¹ BATLEY 03 extrapolate also to the full kinematical region using a constant form factor and a vector matrix element. The resulting branching ratio is (5.8<sup>+2.9</sup><sub>-2.4</sub>) × 10⁻⁹.

**Γ(π⁰μ⁺μ⁻)/Γ<sub>total</sub>**
Test for ΔS = 1 weak neutral current. Allowed by first-order weak interaction combined with electromagnetic interaction.

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2.9<sup>+1.5</sup><sub>-1.2</sub>±0.2</td><td>6</td><td>1 BATLEY</td><td>04A</td><td>NA48/1 K⁰₅ beam</td></tr></tbody></table>

¹ Background estimate is 0.22<sup>+0.18</sup><sub>-0.11</sub> events. Branching ratio assumes a vector matrix element and unit form factor.

### K⁰₅ FORM FACTORS

For discussion, see note on K<sub>e3</sub> form factors in the K<sup>+</sup> section of the Particle Listings above. Because the semileptonic branching fraction is smaller in K⁰₅ than K⁰<sub>S</sub> by the ratio of the mean lives, the K⁰₅ semileptonic form factor has so far been measured only in the K<sub>e3</sub> mode using the linear expansion $f_+(t) = f_+(0) (1 + \lambda_+ t / m_\pi^2)$, which gives the vector form factor $f_+(t)$ relative to its value at $t = 0$.

### λ<sub>+</sub> (LINEAR ENERGY DEPENDENCE OF f<sub>+</sub> IN K⁰₃<sub>e3</sub> DECAY)

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>3.39±0.41</td><td>15k</td><td>AMBROSINO</td><td>06E KLOE</td></tr></tbody></table>

### CP VIOLATION IN K<sub>S</sub> → 3π

Written 1996 by T. Nakada (Paul Scherrer Institute) and L. Wolfenstein (Carnegie-Mellon University).

The possible final states for the decay K⁰ → π⁺π⁻π⁰ have isospin *I* = 0, 1, 2, and 3. The *I* = 0 and *I* = 2 states have CP = +1 and K_S can decay into them without violating CP symmetry, but they are expected to be strongly suppressed by centrifugal barrier effects. The *I* = 1 and *I* = 3 states, which have no centrifugal barrier, have CP = -1 so that the K_S decay to these requires CP violation.

In order to see CP violation in K_S → π⁺π⁻π⁰, it is necessary to observe the interference between K_S and K_L decay, which determines the amplitude ratio

$$ \eta_{+-0} = \frac{A(K_S \rightarrow \pi^+ \pi^- \pi^0)}{A(K_L \rightarrow \pi^+ \pi^- \pi^0)}. \quad (1) $$

If η<sub>+-0</sub> is obtained from an integration over the whole Dalitz plot, there is no contribution from the *I* = 0 and *I* = 2 final states and a nonzero value of η<sub>+-0</sub> is entirely due to CP violation.

Only *I* = 1 and *I* = 3 states, which are CP = -1, are allowed for K⁰ → π⁰π⁰π⁰ decays and the decay of K_S into 3π⁰

is an unambiguous sign of CP violation. Similarly to η<sub>+-0</sub>, η<sub>000</sub> is defined as

$$ \eta_{000} = \frac{A(K_S \rightarrow \pi^0 \pi^0 \pi^0)}{A(K_L \rightarrow \pi^0 \pi^0 \pi^0)}. \quad (2) $$

If one assumes that CPT invariance holds and that there are no transitions to *I* = 3 (or to nonsymmetric *I* = 1 states), it can be shown that

$$ \begin{aligned} \eta_{+-0} &= \eta_{000} \\ &= \epsilon + i \frac{\operatorname{Im} a_1}{\operatorname{Re} a_1}. \end{aligned} \quad (3) $$

With the Wu-Yang phase convention, $a_1$ is the weak decay amplitude for K⁰ into *I* = 1 final states; $\epsilon$ is determined from CP violation in $K_L \rightarrow 2\pi$ decays. The real parts of η<sub>+-0</sub> and η<sub>000</sub> are equal to Re(ε). Since currently-known upper limits on |η<sub>+-0</sub>| and |η<sub>000</sub>| are much larger than |ε|, they can be interpreted as upper limits on Im(η<sub>+-0</sub>) and Im(η<sub>000</sub>) and so as limits on the CP-violating phase of the decay amplitude $a_1$.

### CP-VIOLATION PARAMETERS IN K⁰₅ DECAY

$$ A_S = [\Gamma(K_S^0 \rightarrow \pi^- e^+ \nu_e) - \Gamma(K_S^0 \rightarrow \pi^+ e^- \bar{\nu}_e)] / \text{SUM} $$
Such asymmetry violates CP. If CPT is assumed then $A_S = 2$ Re(ε).

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>-3.8±5.0±2.6</td><td>83k</td><td>1 ANASTASI</td><td>18A KLOE</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$ 1.5±9.6±2.9 \quad 13k \quad \text{AMBROSINO} \quad \text{06E KLOE} $$

¹ ANASTASI 18A result is a combination of the new measurement and AMBROSINO 06E. The new ANASTASI 18A measurement using data collected from 2004-2005, which corresponds to an integrated luminosity of 1.63 fb⁻¹ is $A_S = (-4.9 \pm 5.7 \pm 2.6) \times 10^{-3}$.

### PARAMETERS FOR K⁰₅ → 3π DECAY

$$ \text{Im}(\eta_{+0})^2 = \frac{\Gamma(K_S^0 \rightarrow \pi^+ \pi^- \pi^0, \text{CP-violating})}{\Gamma(K_L^0 \rightarrow \pi^+ \pi^- \pi^0)} \quad \text{CPT assumed valid (i.e. Re}(\eta_{+0}) \approx 0). $$

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$ \begin{array}{l} <0.23 \quad 90 \quad 601 \quad 1 \text{ BARMIN} \quad 85 \quad \text{HLBC} \\ <0.12 \quad 90 \quad 384 \quad 1 \text{ METCALF} \quad 72 \quad \text{ASPK} \end{array} $$

¹ BARMIN 85 find Re(η<sub>+0</sub>) = (0.05 ± 0.17) and Im(η<sub>+0</sub>) = (0.15 ± 0.33). Includes events of BALDO-CEOLIN 75.

$$ \text{Im}(\eta_{+0}) = \frac{\text{Im}(A(K_S^0 \rightarrow \pi^+ \pi^- \pi^0, \text{CP-violating}) / A(K_L^0 \rightarrow \pi^+ \pi^- \pi^0))}{\text{Im}(K_S^0 \rightarrow \pi^+ \pi^- \pi^0)} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>-0.002±0.009<sup>+0.002</sup><sub>-0.001</sub></td><td>500k</td><td>1 ADLER</td><td>97B CPLR</td><td></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$ \begin{array}{l} -0.002±0.018±0.003 \quad 137k \quad 2 \text{ ADLER} \quad 96D CPLR \quad \text{Sup. by ADLER 97B} \\ -0.015±0.017±0.025 \quad 272k \quad 3 \text{ ZOU} \quad 94 \quad \text{SPEC} \end{array} $$

¹ ADLER 97B also find Re(η<sub>+0</sub>) = -0.002 ± 0.007<sup>+0.004</sup><sub>-0.001</sub>. See also ANGELOPO-LOS 98C.

² The ADLER 96D fit also yields Re(η<sub>+0</sub>) = 0.006 ± 0.013 ± 0.001 with a correlation +0.66 between real and imaginary parts. Their results correspond to |η<sub>+0</sub>| < 0.037 with 90% CL.

³ ZOU 94 use theoretical constraint Re(η<sub>+0</sub>) = Re(ε) = 0.0016. Without this constraint they find Im(η<sub>+0</sub>) = 0.019 ± 0.061 and Re(η<sub>+0</sub>) = 0.019 ± 0.027.

$$ \text{Im}(\eta_{000})^2 = \frac{\Gamma(K_S^0 \rightarrow 3\pi^0)}{\Gamma(K_L^0 \rightarrow 3\pi^0)} \quad \text{CPT assumed valid (i.e. Re}(\eta_{000}) \approx 0). $$

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$ \begin{array}{l} <0.1 \quad 90 \quad 632 \quad 1 \text{ BARMIN} \quad 83 \quad \text{HLBC} \\ <0.28 \quad 90 \quad 2 \text{ GJESDAL} \quad 74B \quad \text{SPEC} \quad \text{Indirect meas.} \end{array} $$

¹ BARMIN 83 find Re(η<sub>000</sub>) = (-0.08 ± 0.18) and Im(η<sub>000</sub>) = (-0.05 ± 0.27). Assuming CPT invariance they obtain the limit quoted above.

² GJESDAL 74B uses K<sub>2π</sub>, K<sub>μ3</sub>, and K<sub>e3</sub> decay results, unitarity, and CPT. Calculates |(η<sub>000</sub>)| = 0.26 ± 0.20. We convert to upper limit.
$$ \mathrm{Im}(\eta_000) = \mathrm{Im}(A(K_S^0 \to \pi^0 \pi^0 \pi^0)/A(K_L^0 \to \pi^0 \pi^0 \pi^0)) $$

$K_S^0 \to \pi^0 \pi^0 \pi^0$ violates CP conservation, in contrast to $K_S^0 \to \pi^+ \pi^- \pi^0$ which has a CP-conserving part.

<table><thead><tr><th>VALUE</th><th>EVT'S</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>-0.001 ± 0.016 OUR AVERAGE</strong></td></tr><tr><td>0.000 ± 0.009 ± 0.013</td><td>4.9M</td><td>1 LAI</td><td>05A</td><td>NA48</td><td>Assumes CPT</td></tr><tr><td>-0.05 ± 0.12 ± 0.05</td><td>17300</td><td>2 ANGELOPO...</td><td>98B</td><td>CPLR</td><td>Assumes CPT</td></tr></tbody></table>

1 LAI 05A assumes Re($\eta_{000}$)=Re(c)=1.66 × 10⁻³. The equivalent limit is $|\eta_{000}|CPT < 0.025$ at 90% CL Without assuming CPT invariance, they obtain Re($\eta_{000}$)=-0.002 ± 0.011 ± 0.015 and Im($\eta_{000}$)=-0.003 ± 0.013 ± 0.017 with a statistical correlation coefficient of 0.77 and an overall correlation coefficient of 0.57 between imaginary and real part. The equivalent limit is $|\eta_{000}| < 0.045$ at 90% CL

2 ANGELOPOULOS 98b assumes Re($\eta_{000}$) = Re(c) = 1.635 × 10⁻³. Without assuming CPT invariance, they obtain Re($\eta_{000}$) = 0.18 ± 0.14 ± 0.06 and Im($\eta_{000}$) = 0.15 ± 0.20 ± 0.03.

$$ |\eta_{000}| = |A(K_S^0 \to 3\pi^0)/A(K_L^0 \to 3\pi^0)| $$

A non-zero value violates CP invariance.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>EVT'S</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;0.0088</strong></td><td>90</td><td>590M</td><td>BABUSCI</td><td>13c</td><td>KLOE</td></tr><tr><td colspan="6">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>&lt;0.018</td><td>90</td><td>37.8M</td><td>AMBROSINO</td><td>05B</td><td>KLOE</td></tr><tr><td>&lt;0.045</td><td>90</td><td>4.9M</td><td>LAI</td><td>05A</td><td>NA48</td></tr></tbody></table>

## DECAY-PLANE ASYMMETRY IN $\pi^+\pi^- e^+ e^-$ DECAYS

This is the CP-violating asymmetry

$$ A = \frac{N_{\sin\phi\cos\phi > 0.0} - N_{\sin\phi\cos\phi < 0.0}}{N_{\sin\phi\cos\phi > 0.0} + N_{\sin\phi\cos\phi < 0.0}} $$

where $\phi$ is the angle between the $e^+ e^-$ and $\pi^+ \pi^-$ planes in the $K_S^0$ rest frame.

$$ CP \text{ asymmetry } A \text{ in } K_S^0 \to \pi^+\pi^- e^+ e^- $$

<table><thead><tr><th>VALUE (%)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>-0.4 ± 0.8 OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>-0.4 ± 0.8</td><td>1 BATLEY</td><td>11</td><td>NA48 2002 data</td></tr><tr><td>-1.1 ± 4.1</td><td>LAI</td><td>03c</td><td>NA48 1998+1999 data</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>0.5 ± 4.0 ± 1.6</td><td>LAI</td><td>03c</td><td>NA48 1999 data</td></tr><tr><td colspan="4">1 The result is used to set the limit A &lt; 1.5% at 90% C.L.</td></tr></tbody></table>

## $K_S^0$ REFERENCES

<table><tbody><tr><td>AAJ</td><td>23AE PR D108 1031102</td><td>R. Aaij et al.</td><td>(LHCb Collab.)</td></tr><tr><td>BABUSCI</td><td>23 JHEP 2302 098</td><td>D. Babusci et al.</td><td>(KLOE-2 Collab.)</td></tr><tr><td>AAJ</td><td>20AE PR L125 231801</td><td>R. Aaij et al.</td><td>(LHCb Collab.)</td></tr><tr><td>BABUSCI</td><td>20 PL B804 135378</td><td>D. Babusci et al.</td><td>(KLOE-2 Collab.)</td></tr><tr><td>ANASTASI</td><td>18A JHEP 1809 021</td><td>A. Anastasi et al.</td><td>(KLOE-2 Collab.)</td></tr><tr><td>PDG</td><td>18 PR D98 030001</td><td>M. Tanabashi et al.</td><td>(PDG Collab.)</td></tr><tr><td>AAJ</td><td>17BQ EPJ C77 678</td><td>R. Aaij et al.</td><td>(LHCb Collab.)</td></tr><tr><td>PDG</td><td>16 CP C40 100001</td><td>C. Patrignani et al.</td><td>(PDG Collab.)</td></tr><tr><td>AAJ</td><td>13C JHEP 1301 090</td><td>R. Aaij et al.</td><td>(LHCb Collab.)</td></tr><tr><td>BABUSCI</td><td>13C PL B723 54</td><td>D. Babusci et al.</td><td>(KLOE-2 Collab.)</td></tr><tr><td>ABOUZAID</td><td>11 PR D83 092001</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>AMBROSINO</td><td>11 EPJ C71 1604</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>BATLEY</td><td>11 B694 301</td><td>J.R. Batley et al.</td><td>(CERN NA48/1 Collab.)</td></tr><tr><td>AMBROSINO</td><td>09A PL B672 203</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>AMBROSINO</td><td>08C JHEP 0805 051</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>ANDRE</td><td>07 ANP 322 2518</td><td>T. Andre</td><td>(EFI)</td></tr><tr><td>BATLEY</td><td>07B B653 145</td><td>J.R. Batley et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>AMBROSINO</td><td>06C EPJ C48 767</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>AMBROSINO</td><td>06E PL B636 173</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>AMBROSINO</td><td>05B PL B619 61</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>BATLEY</td><td>05 PL B630 31</td><td>J.R. Batley et al.</td><td>(NA48 Collab.)</td></tr><tr><td>LAI</td><td>05A PL B610 165</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>ALEXPOU...</td><td>04A EPJ D70 092007</td><td>T. Alexopoulos et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>BATLEY</td><td>04A PL B599 197</td><td>J.R. Batley et al.</td><td>(NA48 Collab.)</td></tr><tr><td>LAI</td><td>04 PL B578 276</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>PDG</td><td>04 PL B592 1</td><td>S. Eildeman et al.</td><td>(PDG Collab.)</td></tr><tr><td>ALAVI-HARATI</td><td>03 PR D67 012005</td><td>A. Alavi-Harati et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>Also</td><td>03 PR D70 079904 (errat.)</td><td>A. Alavi-Harati et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>BATLEY</td><td>03 PL B576 43</td><td>J.R. Batley et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>LAI</td><td>03 PL B551 7</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>LAI</td><td>03B PL B556 105</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>LAI</td><td>03C EPJ C30 33</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>ALOISIO</td><td>02 PL B535 37</td><td>A. Aloisio et al.</td><td>(KLOE Collab.)</td></tr><tr><td>ALOISIO</td><td>02B PL B537 21</td><td>A. Aloisio et al.</td><td>(KLOE Collab.)</td></tr><tr><td>LAI</td><td>02C PL B537 28</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>LAI</td><td>01 PL B514 253</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>LAI</td><td>00 PL B493 29</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>LAI</td><td>00B PL B496 137</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>PDG</td><td>00 EPJ C15 1</td><td>D. E. Groom et al.</td><td>(PDG Collab.)</td></tr><tr><td>ACHASOV</td><td>99D PL B459 674</td><td>M.N. Achasov et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>AKHMETSHIN</td><td>99 PL B456 90</td><td>R.R. Akhmetshin et al.</td><td>(Novosibirsk CMD-2 Collab.)</td></tr><tr><td>ANGELOPO...</td><td>98B PL B425 391</td><td>A. Angelopoulos et al.</td><td>(CPLAR Collab.)</td></tr><tr><td>ANGELOPO...</td><td>98C EPJ C5 389</td><td>A. Angelopoulos et al.</td><td>(CPLAR Collab.)</td></tr><tr><td>PDG</td><td>98 PL B31 1</td><td>C. Caso et al.</td><td>(PDG Collab.)</td></tr><tr><td>ADLER</td><td>97B PL A407 193</td><td>R. Adler et al.</td><td>(CPLAR Collab.)</td></tr><tr><td>ANGELOPO...</td><td>97 PL B413 232</td><td>A. Angelopoulos et al.</td><td>(CPLAR Collab.)</td></tr><tr><td>BERTANZA</td><td>97 ZPHY C37 629</td><td>L. Bertanza (PISA, CERN, EDIN, MAINZ, ORSAY+)</td><td></td></tr><tr><td>ADLER</td><td>96D PL B370 167</td><td>R. Adler et al.</td><td>(CPLAR Collab.)</td></tr><tr><td>ADLER</td><td>96E PL B374 313</td><td>R. Adler et al.</td><td>(CPLAR Collab.)</td></tr><tr><td>ZOU</td><td>96 PL B369 362</td><td>Y. Zou et al.</td><td>(RUTG, MINN, MICH)</td></tr><tr><td>BARR</td><td>95B PL B351 579</td><td>G.D. Barr et al.</td><td>(CERN, EDIN, MAINZ, LALO+)</td></tr><tr><td>SWINGEN...</td><td>95 PRL 74 4376</td><td>A. Schwingenheuer et al.</td><td>(EFI, CHIC+)</td></tr><tr><td>BLICK</td><td>94 PL B334 231</td><td>A.M. Blick et al.</td><td>(SERP, JINR)</td></tr><tr><td>THOMSON</td><td>94 PL B337 414</td><td>G.B. Thomson et al.</td><td>(RUTG, MINN, MICH)</td></tr><tr><td>ZOU</td><td>94 PL B329 519</td><td>Y. Zou et al.</td><td>(RUTG, MINN, MICH)</td></tr><tr><td>BARR</td><td>93B PL B304 381</td><td>G.D. Barr et al.</td><td>(CERN, EDIN, MAINZ, LALO+)</td></tr><tr><td>GIBBONS</td><td>93 PL B70 1199</td><td>L.K. Gibbons et al.</td><td>(FNAL E731 Collab.)</td></tr><tr><td>Also</td><td>93 PL R50 5225</td><td>L.K. Gibbons et al.</td><td>(FNAL E731 Collab.)</td></tr><tr><td>RAMBERG</td><td>93 PL R55 625</td><td>E. Ramberg et al.</td><td>(FNAL E731 Collab.)</td></tr><tr><td>BALATS</td><td>89 SJNP 43 828</td><td>M.Y. Balats et al.</td><td>(ITEP)</td></tr></tbody></table>

<table><tbody><tr><td>GIBBONS</td><td>88 PRL 61 2661</td><td>L.K. Gibbons et al.</td><td>(FNAL E731 Collab.)</td></tr><tr><td>BURKHARDT</td><td>87 PL B139 139</td><td>H. Burkhardt et al.</td><td>(CERN, EDIN, MAINZ+)</td></tr><tr><td>GROSSMAN</td><td>87 PL 59 18</td><td>N. Grossman et al.</td><td>(MINN, MICH, RUTG)</td></tr><tr><td>BARMIN</td><td>86 SJNP 44 622</td><td>V.V. Barmin et al.</td><td>(ITEP)</td></tr><tr><td>BARMIN</td><td>86B NC 96A 159</td><td>Translated from YAF 44 965.</td><td></td></tr><tr><td>BARMIN</td><td>86B PL 170B 130</td><td>V.V. Barmin et al.</td><td>(ITEP, PADO)</td></tr><tr><td>BARMIN</td><td>85 NC 85A 67</td><td>V.V. Barmin et al.</td><td>(ITEP, PADO)</td></tr><tr><td>BARMIN</td><td>86 PL 41 759</td><td>V.V. Barmin et al.</td><td>(ITEP)</td></tr><tr><td>BARMIN</td><td>83 PL 128B 129</td><td>V.V. Barmin et al.</td><td>(ITEP, PADO)</td></tr><tr><td>BARMIN</td><td>83 PL 39 269</td><td>V.V. Barmin et al.</td><td>(ITEP, PADO)</td></tr><tr><td>ARONSON</td><td>82 PRL 48 1078</td><td>S.H. Aronson et al.</td><td>(BNL, CHIC, STAN+)</td></tr><tr><td>ARONSON</td><td>82B PRL 48 1306</td><td>S.H. Aronson et al.</td><td>(BNL, CHIC, PURD)</td></tr><tr><td>Also</td><td>PL 116B 73</td><td>E. Fischbach et al.</td><td>(PURD, BNL, CHIC)</td></tr><tr><td>Also</td><td>PR D28 476</td><td>S.H. Aronson et al.</td><td>(BNL, CHIC, PURD)</td></tr><tr><td>Also</td><td>PR D28 495</td><td>S.H. Aronson et al.</td><td>(BNL, CHIC, PURD)</td></tr><tr><td>ARONSON</td><td>76 PL 32A 236</td><td>S.H. Aronson et al.</td><td>(WISC, EFI, UCSD+)</td></tr><tr><td>EVERHART</td><td>76 PR D14 661</td><td>G.C. Everhart et al.</td><td>(PENN)</td></tr><tr><td>TAUREG</td><td>76 PL 65B 92</td><td>H. Taureg et al.</td><td>(HEIDH, CERN, DORT)</td></tr><tr><td>BALDO-</td><td>75 NC 25A 688</td><td>M. Baldo-Coein et al.</td><td>(PADO, WISC)</td></tr><tr><td>CARITHERS</td><td>75 PRL 34 1244</td><td>W.C.J. Carithers et al.</td><td>(COLU, NYU)</td></tr><tr><td>BOBISUT</td><td>74 LNC 11 646</td><td>F. Bobisut et al.</td><td>(PADO)</td></tr><tr><td>COWELL</td><td>74 PR D10 2083</td><td>P.L. Cowell et al.</td><td>(STON, COLU)</td></tr><tr><td>GEWENIGER</td><td>74B PL 48B 487</td><td>C. Geweniger et al.</td><td>(CERN, HEIDH)</td></tr><tr><td>GJESDAL</td><td>74B PL 52B 119</td><td>S. Gjedsal et al.</td><td>(CERN, HEIDH)</td></tr><tr><td>BURGUN</td><td>73 PL 46B 481</td><td>G. Burgun et al.</td><td>(CERN, HEIDH)</td></tr><tr><td>GJESDAL</td><td>73 PL 44B 217</td><td>S. Gjedsal et al.</td><td>(CERN, HEIDH)</td></tr><tr><td>HILL</td><td>73 PL 290</td><td>D.G. Hill et al.</td><td>(BNL, CMU)</td></tr><tr><td>ALLITTI</td><td>72 PL 39B 568</td><td>J. Allitti, E. Lesquoy, A. Muller</td><td>(SACL)</td></tr><tr><td>BURGUN</td><td>72 NP B50 194</td><td>G. Burgun et al.</td><td>(SACL, CERN, OSLO)</td></tr><tr><td>METCALF</td><td>72 PL 40B 703</td><td>M. Metcalf et al.</td><td>(CERN, IPN, WIEN)</td></tr><tr><td>MORSE</td><td>72B PRL 28 388</td><td>R. Morse et al.</td><td>(COLO, PRIN, UMD)</td></tr><tr><td>NAGY</td><td>72 PL 47 94</td><td>E. Nagy, F. Tebisz, G. Vesztorgombi</td><td>(BUDA)</td></tr><tr><td>NAGY</td><td>72 PL 30B 498</td><td>G. Bozoki et al.</td><td>(BUDA)</td></tr><tr><td>NAGY</td><td>72 NP B48 343</td><td>O. Skjeggestad et al.</td><td>(OSLO, CERN, SACL)</td></tr><tr><td>BALTAY</td><td>71 PL 27 1678</td><td>C. Baltay et al.</td><td>(COLU)</td></tr><tr><td>Also</td><td>70 Thesis Nevis 187</td><td>W.A. Cooper</td><td>(COLU)</td></tr><tr><td>MOFFETT</td><td>70 BAPS 15 512</td><td>R. Moffett et al.</td><td>(ROCH)</td></tr><tr><td>BOZOKI</td><td>69 B08 498</td><td>G. Bozoki et al.</td><td>(BUDA)</td></tr><tr><td>DOYLE</td><td>69 Thesis UCLR 18139</td><td>J.C. Doyle</td><td>(LRL)</td></tr><tr><td>GOBBI</td><td>69 PL 22 682</td><td>B. Gobbi et al.</td><td>(ROCH)</td></tr><tr><td>HYAMS</td><td>69B PL 29B 521</td><td>B.D. Hyams et al.</td><td>(CERN, MPIM)</td></tr><tr><td>MORFING</td><td>69B PL 23 660</td><td>J.G. Morfin, D. Sinclair</td><td>(MICH)</td></tr><tr><td>DONALD</td><td>68B PL 27B 58</td><td>R.A. Donald et al.</td><td>(LIVP, CERN, IPNP+)</td></tr><tr><td>HILL</td><td>68 PR 171 1418</td><td>D.G. Hill et al.</td><td>(BNL, CMU)</td></tr><tr><td>AUBERT</td><td>65 PL 17 59</td><td>B. Aubert et al.</td><td>(EPOL, ORSAY)</td></tr><tr><td>BROWN</td><td>63 PR 130 769</td><td>J.L. Brown et al.</td><td>(LRL, MICH)</td></tr><tr><td>CHRETIEN</td><td>63 PR 131 2208</td><td>M. Chretien et al.</td><td>(BRAN, BROW, HARV+)</td></tr><tr><td>BROWN</td><td>61 NC 19 1155</td><td>J.L. Brown et al.</td><td>(MICH)</td></tr><tr><td>BOLDT</td><td>58B PL 1 150</td><td>E. Boldt, D.O. Caldwell, W. Pal</td><td>(MIT)</td></tr></tbody></table>

## OTHER RELATED PAPERS

LITTENBERG 93 ARNPS 43 729 L.S. Littenberg, G. Valencia (BNL, FNAL)

BATTISTON 92 PRPL 214 293 R. Battiston et al. (PGIA, CERN, TRSTT)

Status and Perspectives of K Decay Physics
TRILLING 65B. UCRL 16473 G.N. Trilling (LRL)

Updated from 1965 Argonne Conference, page 115. CERN Conf. 827 (LRL)

FITCH 61 NC 22 1160 V.L. Fitch, P.A. Piroue, R.B. Perkins (PRIN+)

GOOD 61 PR 124 1223 R.H. Good et al. (LRL)

BIRGE 60 Rochester Conf. 601 R.W. Birge et al. (LRL, WISC)

<figure><img src="image_511.png" /></figure>

$$ I(J^P) = \frac{1}{2}(0^{-}) $$

$$ m_{K_L^0} - m_{K_S^0} $$

For earlier measurements, beginning with GOOD 61 and FITCH 61, see our 1986 edition, Physics Letters 170B 132 (1986).

OUR FIT is described in the note on "CP violation in $K_L$ decays" in the $K_L^0$ Particle Listings. The result labeled "OUR FIT Assuming CPT" ["OUR FIT Not Assuming CPT"] includes all measurements except those with the comment "Not assuming CPT" ["Assuming CPT"). Measurements with neither comment do not assume CPT and enter both fits.

<table><thead><tr><th>VALUE (10<sup>10</sup> h<sup>-1</sup> s<sup>-1</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.5293 ± 0.0009</td><td>OUR FIT</td><td>Error includes scale factor of 1.3. Assuming CPT</td><td></td></tr><tr><td>0.5289 ± 0.0100</td><td>OUR FIT</td><td>Not assuming CPT</td><td></td></tr><tr><td>0.52797 ± 0.00195</td><td></td><td>1,2 ABOUZAID 11 KTEV</td><td>Not assuming CPT</td></tr><tr><td>0.52699 ± 0.00123</td><td></td><td>1,3 ABOUZAID 11 KTEV</td><td>Assuming CPT</td></tr><tr><td>0.5240 ± 0.0044 ± 0.0033</td><td></td><td>APOSTOLA... 99c CPLR</td><td>$K_0^0 \cdot \pi^+ \pi^-$ to $\pi^+ \pi^-$</td></tr><tr><td>0.5297 ± 0.0030 ± 0.0022</td><td></td><td>4 SCHWINGEN... 95 E773</td><td>20-160 GeV K beams</td></tr><tr><td>0.5286 ± 0.0028</td><td></td><td>5 GIBBONS 93 E731</td><td>Assuming CPT</td></tr><tr><td>0.5257 ± 0.0049 ± 0.0021</td><td></td><td>4 GIBBONS 93c E731</td><td>Not assuming CPT</td></tr><tr><td>0.5340 ± 0.00255 ± 0.0015</td><td></td><td>6 GEWENIGER 74c SPEC</td><td>Gap method</td></tr><tr><td>0.5334 ± 0.0040 ± 0.0015</td><td></td><td>6,7 GJESDAL 74 SPEC</td><td>Gap method</td></tr><tr><td colspan="4">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.5261 ± 0.0015</td><td>8 ALAVI-HARATI03</td><td>KTEV</td><td>Assuming CPT</td></tr><tr><td>0.5288 ± 0.0043</td><td>9 ALAVI-HARATI03</td><td>KTEV</td><td>Not assuming CPT</td></tr><tr><td>0.5343 ± 0.0063 ± 0.0025</td><td>10 ANGELOPO... 01 CPLR</td><td></td><td></td></tr><tr><td>0.5295 ± 0.0020 ± 0.0003</td><td>11 ANGELOPO... 98d CPLR</td><td></td><td>Assuming CPT</td></tr><tr><td>0.5307 ± 0.0013</td><td>12 ADLER 96c RVUE</td><td></td><td></td></tr><tr><td>0.5274 ± 0.0029 ± 0.0005</td><td>11 ADLER 95 CPLR</td><td>Sup. by ANGELOPOU-LOS 98b</td><td></td></tr><tr><td>0.482 ± 0.014</td><td>13 ARONSON 82b SPEC</td><td>E=30-110 GeV</td><td></td></tr><tr><td>0.534 ± 0.007</td><td>14 CARNEGIE 71 ASPK</td><td>Gap method</td><td></td></tr><tr><td>0.542 ± 0.006</td><td>14 ARONSON 70 ASPK</td><td>Gap method</td><td></td></tr><tr><td>0.542 ± 0.006</td><td>CULLEN 70 CNTR</td><td></td><td></td></tr></tbody></table>

1 The two ABOUZAID 11 values use the same data. The first enters the "assuming CPT" fit and the second enters the "not assuming CPT" fit.
²ABOUZAID 11 fit has $\Delta m$, $\tau_S$, $\phi_\epsilon$, Re($\epsilon'/\epsilon$), and Im($\epsilon'/\epsilon$) as free parameters. See Im($\epsilon'/\epsilon$) in the "K<sup>0</sup><sub>L</sub> CP violation" section for correlation information.

³ABOUZAID 11 fit has $\Delta m$ and $\tau_S$ free but constrains $\phi_\epsilon$ to the Superweak value, i.e. assumes CPT. See "K<sup>0</sup><sub>S</sub> Mean Life" section for correlation information.

⁴Fits $\Delta m$ and $\phi_{+-}$ simultaneously. GIBBONS 93c systematic error is from B. Winstein via private communication. 20-160 GeV K beams.

⁵GIBBONS 93 value assume $\phi_{+-} = \phi_{00} = \phi_{SW} = (43.7 \pm 0.2)^\circ$, i.e. assumes CPT. 20-160 GeV K beams.

⁶These two experiments have a common systematic error due to the uncertainty in the momentum scale, as pointed out in WAHL 89.

⁷GJESDAL 74 uses charge asymmetry in K<sup>0</sup><sub>3</sub> decays.

⁸ALAVI-HARATI 03 fit $\Delta m$ and $\tau_{K_S^0}$ simultaneously. $\phi_{+-}$ is constrained to the Super-weak value, i.e. CPT is assumed. See "K<sup>0</sup><sub>S</sub> Mean Life" section for correlation information. Superseded by ABOUZAID 11.

⁹ALAVI-HARATI 03 fit $\Delta m$, $\phi_{+-}$, and $\tau_{K_S}$ simultaneously. See $\phi_{+-}$ in the "K<sub>L</sub> CP violation" section for correlation information. Superseded by ABOUZAID 11.

¹⁰ANGELOPOULOS 01 uses strong interactions strangeness tagging at two different times.

¹¹Uses K<sup>0</sup><sub>e3</sub> and K<sup>0</sup><sub>e3</sub> strangeness tagging at production and decay. Assumes CPT conservation on $\Delta S = -\Delta Q$ transitions.

¹²ADLER 96c is the result of a fit which includes nearly the same data as entered into the "OUR FIT" value above.

¹³ARONSON 82 find that $\Delta m$ may depend on the kaon energy.

¹⁴ARONSON 70 and CARNEGIE 71 use $K_S^0$ mean life = (0.862 ± 0.006) × 10<sup>-10</sup> s. We have not attempted to adjust these values for the subsequent change in the $K_S^0$ mean life or in $\eta_{+-}$.

## K<sup>0</sup><sub>L</sub> MEAN LIFE

<table><thead><tr><th>VALUE (10<sup>-8</sup> s)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

5.116 ± 0.021 OUR FIT Error includes scale factor of 1.1.

5.099 ± 0.021 OUR AVERAGE

<table><tr><td>5.072 ± 0.011 ± 0.035</td><td>13M</td><td>1 AMBROSINO 06</td><td>KLOE</td><td>Σ<sub>i</sub> B<sub>i</sub> = 1</td></tr><tr><td>5.092 ± 0.017 ± 0.025</td><td>15M</td><td>AMBROSINO 05C</td><td>KLOE</td><td></td></tr><tr><td>5.154 ± 0.044</td><td>0.4M</td><td>VOSBURGH</td><td>72</td><td>CNTR</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

5.15 ± 0.14 DEVLIN 67 CNTR

¹AMBROSINO 06 uses $\phi \to K_L K_S$ with $K_L$ tagged by $K_S \to \pi^+ \pi^-$. The four major $K_L$ BR's are measured, the small remainder ($\pi^+ \pi^-$, $\pi^0 \pi^0$, $\gamma \gamma$) is taken from PDG 04. This KLOE $K_L$ lifetime is obtained by imposing $\Sigma_{i} B_{i} = 1$. The correlation matrix among the four measured $K_L$ BR's and this $K_L$ lifetime is

<table><thead><tr><th></th><th>K<sub>e3</sub></th><th>K<sub>μ3</sub></th><th>3π<sup>0</sup></th><th>π<sup>+</sup> π<sup>-</sup> π<sup>0</sup></th><th>τ<sub>K<sub>L</sub></sub></th></tr></thead><tbody><tr><th>K<sub>e3</sub></th><td>1</td><td>-0.25</td><td>-0.56</td><td>-0.07</td><td>0.25</td></tr><tr><th>K<sub>μ3</sub></th><td></td><td>1</td><td>-0.43</td><td>-0.20</td><td>0.33</td></tr><tr><th>3π<sup>0</sup></th><td></td><td></td><td>1</td><td>-0.39</td><td>-0.21</td></tr><tr><th>π<sup>+</sup> π<sup>-</sup> π<sup>0</sup></th><td></td><td></td><td></td><td>1</td><td>-0.39</td></tr><tr><th>τ<sub>K<sub>L</sub></sub></th><td></td><td></td><td></td><td></td><td>1</td></tr></tbody></table>

These correlations are taken into account in our fit. The average of this KLOE mean life measurement and the independent KLOE measurement in AMBROSINO 05C is (5.084 ± 0.023) × 10<sup>-8</sup> s.

## K<sup>0</sup><sub>L</sub> DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction (Γ<sub>i</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th></tr></thead></table>

### Semileptonic modes

Γ<sub>1</sub> $\pi^{\pm} e^{\mp} \nu_e$ [a] (40.55 ± 0.11) % S=1.7
Called K<sup>0</sup><sub>e3</sub>.

Γ<sub>2</sub> $\pi^{\pm} \mu^{\mp} \nu_{\mu}$ [a] (27.04 ± 0.07) % S=1.1
Called K<sup>0</sup><sub>μ3</sub>.

Γ<sub>3</sub> ($\pi \mu$ atom) $\nu$ (1.05 ± 0.11) × 10<sup>-7</sup>

Γ<sub>4</sub> $\pi^0 \pi^\pm e^\mp \nu$ [a] (5.20 ± 0.11) × 10<sup>-5</sup>

Γ<sub>5</sub> $\pi^\pm e^\mp \nu e^+ e^-$ [a] (1.26 ± 0.04) × 10<sup>-5</sup>

### Hadronic modes, including Charge conjugation × Parity Violating (CPV) modes

Γ<sub>6</sub> 3π<sup>0</sup> (19.52 ± 0.12) % S=1.6

Γ<sub>7</sub> $\pi^+ \pi^- \pi^0$ (12.54 ± 0.05) % S=1.6

Γ<sub>8</sub> $\pi^+ \pi^-$ CPV [b] (1.967 ± 0.010) × 10<sup>-3</sup> S=1.5

Γ<sub>9</sub> $\pi^0 \pi^0$ CPV (8.64 ± 0.06) × 10<sup>-4</sup> S=1.8

### Semileptonic modes with photons

Γ<sub>10</sub> $\pi^{\pm} e^{\mp} \nu_e \gamma$ [a,c,d] (3.79 ± 0.06) × 10<sup>-3</sup>

Γ<sub>11</sub> $\pi^{\pm} \mu^{\mp} \nu_{\mu} \gamma$ [a] (5.65 ± 0.23) × 10<sup>-4</sup>

### Hadronic modes with photons or $\ell \ell \ell$ pairs

Γ<sub>12</sub> $\pi^0 \pi^0 \gamma$ < 2.43 × 10<sup>-7</sup> CL=90%

Γ<sub>13</sub> $\pi^+ \pi^- \gamma$ [c,d] (4.15 ± 0.15) × 10<sup>-5</sup> S=2.8

Γ<sub>14</sub> $\pi^+ \pi^- \gamma$ (DE) (2.84 ± 0.11) × 10<sup>-5</sup> S=2.0

Γ<sub>15</sub> $\pi^0 2 \gamma$ [c] (1.273 ± 0.033) × 10<sup>-6</sup>

Γ<sub>16</sub> $\pi^0 \gamma e^+ e^-$ (1.62 ± 0.17) × 10<sup>-8</sup>

### Other modes with photons or $\ell \ell \ell$ pairs

Γ<sub>17</sub> 2γ (5.47 ± 0.04) × 10<sup>-4</sup> S=1.1

Γ<sub>18</sub> 3γ < 7.4 × 10<sup>-8</sup> CL=90%

Γ<sub>19</sub> $e^+ e^-$ γ (9.4 ± 0.4) × 10<sup>-6</sup> S=2.0

Γ<sub>20</sub> $\mu^+ \mu^-$ γ (3.59 ± 0.11) × 10<sup>-7</sup> S=1.3

Γ<sub>21</sub> $\mu^+ \mu^-$ $\mu^+ \mu^-$ < 2.3 × 10<sup>-9</sup> CL=90%

Γ<sub>22</sub> $e^+ e^-$ $\gamma \gamma$ [c] (5.95 ± 0.33) × 10<sup>-7</sup>

Γ<sub>23</sub> $\mu^+ \mu^-$ $\gamma \gamma$ [c] (1.0 ± 0.8) × 10<sup>-8</sup>

### Charge conjugation × Parity (CP) or Lepton Family number (LF) violating modes, or $\Delta S = 1$ weak neutral current (S1) modes

Γ<sub>24</sub> $\mu^+ \mu^-$ S1 (6.84 ± 0.11) × 10<sup>-9</sup>

Γ<sub>25</sub> $e^+ e^-$ S1 (9 ± 6) × 10<sup>-12</sup>

Γ<sub>26</sub> $\pi^+ \pi^-$ $e^+ e^-$ S1 [c] (3.11 ± 0.19) × 10<sup>-7</sup>

Γ<sub>27</sub> $\pi^0 \pi^0$ $e^+ e^-$ S1 < 6.6 × 10<sup>-9</sup> CL=90%

Γ<sub>28</sub> $\pi^0 \pi^0 \mu^+ \mu^-$ S1 < 9.2 × 10<sup>-11</sup> CL=90%

Γ<sub>29</sub> $\mu^+ \mu^-$ $e^+ e^-$ S1 (2.69 ± 0.27) × 10<sup>-9</sup>

Γ<sub>30</sub> $e^+ e^-$ $e^+ e^-$ S1 (3.56 ± 0.21) × 10<sup>-8</sup>

Γ<sub>31</sub> $\pi^0 \mu^+ \mu^-$ CP, S1 [e] < 3.8 × 10<sup>-10</sup> CL=90%

Γ<sub>32</sub> $\pi^0 \pi^+ \pi^-$ CP, S1 [e] < 2.8 × 10<sup>-10</sup> CL=90%

Γ<sub>33</sub> $\pi^0 \nu \bar{\nu}$ CP, S1 [f] < 3.0 × 10<sup>-9</sup> CL=90%

Γ<sub>34</sub> $\pi^0 \nu \nu$ S1 < 8.1 × 10<sup>-7</sup> CL=90%

Γ<sub>35</sub> $e^+ \mu^\mp$ LF [a] < 4.7 × 10<sup>-12</sup> CL=90%

Γ<sub>36</sub> $e^+ e^+ \mu^\mp \mu^\mp$ LF [a] < 4.12 × 10<sup>-11</sup> CL=90%

Γ<sub>37</sub> $\pi^0 \mu^+ \mu^-$ LF [a] < 7.6 × 10<sup>-11</sup> CL=90%

Γ<sub>38</sub> $\pi^0 \pi^0 \mu^+ \mu^+ e^+ e^-$ LF < 1.7 × 10<sup>-10</sup> CL=90%

### Lorentz invariance violating modes

Γ<sub>39</sub> $\pi^0 \gamma$ < 1.7 × 10<sup>-7</sup> CL=90%

[a] The value is for the sum of the charge states or particle/antiparticle states indicated.

[b] This mode includes gammas from inner bremsstrahlung but not the direct emission mode $K_L^0 \to \pi^+ \pi^- \gamma$ (DE).

[c] See the Particle Listings below for the energy limits used in this measurement.

[d] Most of this radiative mode, the low-momentum $\gamma$ part, is also included in the parent mode listed without $\gamma$'s.

[e] Allowed by higher-order electroweak interactions.

[f] Violates CP in leading order. Test of direct CP violation since the indirect CP-violating and CP-conserving contributions are expected to be suppressed.

## CONSTRAINED FIT INFORMATION

An overall fit to the mean life and 15 branching ratios uses 27 measurements and one constraint to determine 11 parameters. The overall fit has a $\chi^2 = 37.4$ for 17 degrees of freedom.

The following off-diagonal array elements are the correlation coefficients $\langle \delta p_i \delta p_j \rangle / (\delta p_i \delta p_j)$, in percent, from the fit to parameters $p_i$, including the branching fractions, $x_i \equiv \Gamma_i / \Gamma_{\text{total}}$. The fit constrains the $x_i$ whose labels appear in this array to sum to one.

<table><tr><td>x<sub>2</sub></td><td>-21</td></tr><tr><td>x<sub>6</sub></td><td>-77 -29</td></tr><tr><td>x<sub>7</sub></td><td>-15 -20 -18</td></tr><tr><td>x<sub>8</sub></td><td>53 -11 -47 4</td></tr><tr><td>x<sub>9</sub></td><td>30 -23 -11 -12 64</td></tr><tr><td>x<sub>13</sub></td><td>6 -1 -6 0 12 8</td></tr><tr><td>x<sub>14</sub></td><td>6 -1 -6 0 11 7 93</td></tr><tr><td>x<sub>17</sub></td><td>-46 -22 64 -14 -21 8 -3 -3</td></tr><tr><td>x<sub>19</sub></td><td>-5 -2 7 -1 -3 -1 0 0 4</td></tr><tr><td>Γ</td><td>-27 -9 24 15 -13 -6 -2 -2 15 2</td></tr></table>

<table><thead><tr><th>Mode</th><th>Rate (10<sup>8</sup> s<sup>-1</sup>)</th><th>Scale factor</th></tr></thead></table>

Γ<sub>1</sub> $\pi^{\pm} e^{\mp} \nu_e$ [a] 0.07927 ± 0.00034 1.1

Called K<sup>0</sup><sub>e3</sub>.

Γ<sub>2</sub> $\pi^{\pm} \mu^{\mp} \nu_{\mu}$ [a] 0.05286 ± 0.00025 1.1

Called K<sup>0</sup><sub>μ3</sub>.
# Meson Particle Listings

## $K_L^0$

<table><tr><td>$\Gamma_6$</td><td>$3\pi^0$</td><td>0.03815 ± 0.00030</td><td>1.5</td></tr><tr><td>$\Gamma_7$</td><td>$\pi^+\pi^-\pi^0$</td><td>0.02451 ± 0.00015</td><td></td></tr><tr><td>$\Gamma_8$</td><td>$\pi^+\pi^-$</td><td>[b] (3.844 ± 0.023) × 10<sup>-4</sup></td><td>1.2</td></tr><tr><td>$\Gamma_9$</td><td>$\pi^0\pi^0$</td><td>(1.690 ± 0.013) × 10<sup>-4</sup></td><td>1.4</td></tr><tr><td>$\Gamma_{13}$</td><td>$\pi^+\pi^-\gamma$</td><td>[c,d] (8.11 ± 0.29) × 10<sup>-6</sup></td><td>2.7</td></tr><tr><td>$\Gamma_{14}$</td><td>$\pi^+\pi^-\gamma(\text{DE})$</td><td>(5.55 ± 0.21) × 10<sup>-6</sup></td><td>2.0</td></tr><tr><td>$\Gamma_{17}$</td><td>$2\gamma$</td><td>(1.069 ± 0.010) × 10<sup>-4</sup></td><td>1.2</td></tr><tr><td>$\Gamma_{19}$</td><td>$e^+e^-\gamma$</td><td>(1.84 ± 0.08) × 10<sup>-6</sup></td><td>1.9</td></tr></table>

## $K_L^0$ DECAY RATES

<table><caption>Γ(π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>)</caption><thead><tr><th>VALUE (10<sup>6</sup> s<sup>-1</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>2.451 ± 0.015 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>2.32</td><td>+0.13</td><td>192</td><td>BALDO...</td><td>75</td><td>HLBC</td><td>Assumes CP</td></tr><tr><td>2.35</td><td>±0.20</td><td>180</td><td>1 JAMES</td><td>72</td><td>IBC</td><td>Assumes CP</td></tr><tr><td>2.71</td><td>±0.28</td><td>99</td><td>CHO</td><td>71</td><td>DBC</td><td>Assumes CP</td></tr><tr><td>2.5</td><td>±0.3</td><td>98</td><td>1 JAMES</td><td>71</td><td>IBC</td><td>Assumes CP</td></tr><tr><td>2.12</td><td>±0.33</td><td>50</td><td>MEISNER</td><td>71</td><td>IBC</td><td>Assumes CP</td></tr><tr><td>2.20</td><td>±0.35</td><td>53</td><td>WEBBER</td><td>70</td><td>IBC</td><td>Assumes CP</td></tr><tr><td>2.62</td><td>+0.28</td><td>136</td><td>BEHR</td><td>66</td><td>HLBC</td><td>Assumes CP</td></tr><tr><td>3.26</td><td>±0.77</td><td>18</td><td>ANDERSON</td><td>65</td><td>IBC</td><td></td></tr><tr><td>1.4</td><td>±0.4</td><td>14</td><td>FRANZINI</td><td>65</td><td>IBC</td><td></td></tr></table>

¹ JAMES 72 is a final measurement and includes JAMES 71.

<table><caption>Γ(π<sup>+</sup>e<sup>+</sup>ν<sub>e</sub>)</caption><thead><tr><th>VALUE (10<sup>6</sup> s<sup>-1</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>7.927 ± 0.034 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>7.81 ± 0.56</td><td>620</td><td>CHAN</td><td>71</td><td>IBC</td><td></td></tr><tr><td>7.52</td><td>+0.85</td><td></td><td></td><td></td><td>ΔS = ΔQ, CP assumed</td></tr></table>

<table><caption>Γ(π<sup>+</sup>e<sup>+</sup>ν<sub>e</sub>) + Γ(π<sup>+</sup>μ<sup>+</sup>ν<sub>μ</sub>) (Γ<sub>1</sub>+Γ<sub>2</sub>)</caption><thead><tr><th>VALUE (10<sup>6</sup> s<sup>-1</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>13.21 ± 0.05 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>12.4 ± 0.7</td><td>410</td><td>1 BURGUN</td><td>72</td><td>IBC</td><td>K<sup>+</sup>p → K<sup>0</sup>pπ<sup>+</sup></td></tr><tr><td>8.47 ± 1.69</td><td>126</td><td>1 MANN</td><td>72</td><td>IBC</td><td>K<sup>-</sup>p → nK<sup>0</sup></td></tr><tr><td>13.1 ± 1.3</td><td>252</td><td>1 WEBBER</td><td>71</td><td>IBC</td><td>K<sup>-</sup>p → nK<sup>0</sup></td></tr><tr><td>11.6 ± 0.9</td><td>393</td><td>1,2 CHO</td><td>70</td><td>DBC</td><td>K<sup>+</sup>n → K<sup>0</sup>p</td></tr><tr><td>10.3 ± 0.8</td><td>335</td><td>2 HILL</td><td>67</td><td>DBC</td><td>K<sup>+</sup>n → K<sup>0</sup>p</td></tr><tr><td>9.85</td><td>+1.15</td><td>109</td><td>1 FRANZINI</td><td>65</td><td>IBC</td><td></td></tr></table>

¹ Assumes ΔS = ΔQ rule.

² CHO 70 includes events of HILL 67.

## $K_L^0$ BRANCHING RATIOS

### Semileptonic modes

<table><caption>Γ(π<sup>+</sup>e<sup>+</sup>ν<sub>e</sub>)/Γ<sub>total</sub></caption><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.4055 ± 0.0011 OUR FIT</strong></td><td></td><td></td><td></td></tr><tr><td><strong>0.4047 ± 0.0028 OUR AVERAGE</strong></td><td></td><td></td><td></td></tr></tbody></table>

<table><tr><td>0.4055 ± 0.0011</td><td>EVTS</td><td>DOCUMENT ID</td><td>TECN</td></tr><tr><td>0.4047 ± 0.0028</td><td>EVTS</td><td>DOCUMENT ID</td><td>TECN</td></tr></table>

¹ There are correlations between these five KLOE measurements: B(K<sub>L</sub> → πeν), B(K<sub>L</sub> → πμν), B(K<sub>L</sub> → 3π<sup>0</sup>), B(K<sub>L</sub> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>), and τK<sub>L</sub> measured in AMBROSINO 06. See the footnote for the τK<sub>L</sub> measurement for the correlation matrix.

² ALEXOPOULOS 04 constrains $\sum_i B_i = 0.9993$ for the six major K<sub>L</sub> branching fractions. The correlations among these branching fractions are taken into account in our fit. The correlation matrix is

<table><tr><td>K<sub>e3</sub></td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>K<sub>μ3</sub></td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3π<sup>0</sup></td><td>-0.77</td><td>-0.62</td><td>1</td><td></td><td></td><td></td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>0.18</td><td>0.08</td><td>-0.54</td><td>1</td><td></td><td></td></tr><tr><td>π<sup>+</sup>π<sup>-</sup></td><td>0.28</td><td>0.22</td><td>-0.48</td><td>0.49</td><td>1</td><td></td></tr><tr><td>π<sup>0</sup>π<sup>0</sup></td><td>-0.72</td><td>-0.54</td><td>0.89</td><td>-0.46</td><td>-0.39</td><td>1</td></tr></table>

<table><caption>Γ(π<sup>+</sup>μ<sup>+</sup>ν<sub>μ</sub>)/Γ<sub>total</sub></caption><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.2704 ± 0.0007 OUR FIT</strong></td><td></td><td></td><td></td></tr><tr><td><strong>0.2700 ± 0.0008 OUR AVERAGE</strong></td><td></td><td></td><td></td></tr></tbody></table>

<table><tr><td>0.2704 ± 0.0007</td><td>EVTS</td><td>DOCUMENT ID</td><td>TECN</td></tr><tr><td>0.2700 ± 0.0008</td><td>EVTS</td><td>DOCUMENT ID</td><td>TECN</td></tr></table>

¹ There are correlations between these five KLOE measurements: B(K<sub>L</sub> → πeν), B(K<sub>L</sub> → πμν), B(K<sub>L</sub> → 3π<sup>0</sup>), B(K<sub>L</sub> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>), and τK<sub>L</sub> measured in AMBROSINO 06. See the footnote for the τK<sub>L</sub> measurement for the correlation matrix.

² For correlations with other ALEXOPOULOS 04 measurements, see the footnote with their B(K<sub>L</sub> → πeν) measurement.

$$ \frac{[\Gamma(\pi^{\pm} e^{\mp} \nu_{e}) + \Gamma(\pi^{\pm} \mu^{\mp} \nu_{\mu})]}{\Gamma_{\text{total}}} \quad (\Gamma_{1} + \Gamma_{2})/\Gamma $$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th></tr></thead><tbody><tr><td><strong>0.6760 ± 0.0012 OUR FIT</strong></td><td>Error includes scale factor of 1.6.</td></tr></tbody></table>

$$ \frac{\Gamma(\pi^{\pm} \mu^{\mp} \nu_{\mu})/\Gamma(\pi^{\pm} e^{\mp} \nu_{e})}{\Gamma_{2}/\Gamma_{1}} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.6669 ± 0.0027 OUR FIT</strong></td><td>Error includes scale factor of 1.2.</td><td></td><td></td><td></td></tr><tr><td><strong>0.666 ± 0.004 OUR AVERAGE</strong></td><td>Error includes scale factor of 1.6.</td><td></td><td></td><td></td></tr></tbody></table>

• • • We use the following data for averages but not for fits. • • •

<table><tr><td>0.6740 ± 0.0059</td><td>13M</td><td>1 AMBROSINO</td><td>06</td><td>KLOE</td><td>Not in fit</td></tr><tr><td>0.6640 ± 0.0014 ± 0.0022</td><td>394M</td><td>2 ALEXOPOULOS...</td><td>04</td><td>KTEV</td><td>Not in fit</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>0.702 ± 0.011</td><td>33k</td><td>CHO</td><td>80</td><td>HBC</td><td></td></tr><tr><td>0.662 ± 0.037</td><td>10k</td><td>WILLIAMS</td><td>74</td><td>ASPK</td><td></td></tr><tr><td>0.741 ± 0.044</td><td>6700</td><td>BRANDENB...</td><td>73</td><td>HBC</td><td></td></tr><tr><td>0.662 ± 0.030</td><td>1309</td><td>EVANS</td><td>73</td><td>HLBC</td><td></td></tr><tr><td>0.68 ± 0.08</td><td>3548</td><td>BASILE</td><td>70</td><td>OSPK</td><td></td></tr><tr><td>0.71 ± 0.05</td><td>770</td><td>BUDAGOV</td><td>68</td><td>HLBC</td><td></td></tr></table>

¹ AMBROSINO 06 enters the fit via their separate measurements of these two modes.

² ALEXOPOULOS 04 enters the fit via their separate measurements of these two modes.

$$ \frac{\Gamma((\pi\mu\text{atom})\nu)/\Gamma(\pi^{\pm}\mu^{\mp}\nu_{\mu})}{\Gamma_{3}/\Gamma_{2}} $$

<table><thead><tr><th>VALUE (units 10<sup>-7</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>SPEC</th></tr></thead><tbody><tr><td><strong>3.90 ± 0.39</strong></td><td>155</td><td>1 ARONSON</td><td>86</td><td></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

¹ ARONSON 86 quote theoretical value of (4.31 ± 0.08) × 10<sup>-7</sup>.

$$ \frac{\Gamma(\pi^{0} \pi^{\pm} e^{\mp} \nu_{e})/\Gamma_{\text{total}}}{\Gamma_{4}/\Gamma_{5}} $$

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>5.20 ± 0.11 OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>5.21 ± 0.07 ± 0.09</td><td>5402</td><td>BATLEY</td><td>04</td><td>NA48</td></tr><tr><td>5.16 ± 0.20 ± 0.22</td><td>729</td><td>MAKOFF</td><td>93</td><td>E731</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>6.2 ± 2.0</td><td>16</td><td>CARROLL</td><td>80C</td><td>SPEC</td></tr><tr><td>&lt; 220</td><td>90</td><td>1 DONALDSON</td><td>74</td><td>SPEC</td></tr></table>

¹ DONALDSON 74 uses $K_L^0 \rightarrow \pi^+\pi^-\pi^0/(\text{all } K_L^0)$ decays = 0.126.

$$ \frac{\Gamma(\pi^{\pm} e^{\mp} \nu e^{\pm} e^{-})/\Gamma(\pi^{+} \pi^{-} \pi^{0})}{\Gamma_{6}/\Gamma_{7}} $$

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>10.02 ± 0.17 ± 0.29</strong></td><td>19k</td><td>1 ABOUZAID</td><td>07C</td><td>KTEV M<sub>ee</sub> > 5 MeV, E<sup>*</sup><sub>ee</sub> > 30 MeV</td></tr></tbody></table>

¹ $E_{ee}^*$ is the energy of the $e^+e^-$ pair in the kaon rest frame. ABOUZAID 07c reports $[\Gamma(K_L^0 \rightarrow \pi^+\pi^-\nu e^+e^-)/\Gamma(K_L^0 \rightarrow \pi^+\pi^-\pi^0)] / [B(\pi^0 \rightarrow e^+e^-)] = (8.54 \pm 0.07 \pm 0.13) \times 10^{-3}$ which we multiply by our best value $B(\pi^0 \rightarrow e^+e^-) = (1.174 \pm 0.035) \times 10^{-2}$. Our first error is their experiment's error and our second error is the systematic error from using our best value.

### Hadronic modes,

### including Charge conjugation × Parity Violating (CPV) modes

$$ \frac{\Gamma(\pi^0)/\Gamma_{\text{total}}}{\Gamma_{6}/\Gamma_{7}} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.1952 ± 0.0012 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

¹969 ± 0.0026 OUR AVERAGE Error includes scale factor of 2.0.

• • • We use the following data for averages but not for fits. • • •

<table><tr><td>0.1997 ± 0.0003 ± 0.0019</td><td>13M</td><td>1 AMBROSINO</td><td>06</td><td>KLOE</td><td>Not fitted</td></tr><tr><td>0.1945 ± 0.0018</td><td>1</td><td>ALEXOPOULOS...</td><td>04</td><td>KTEV</td><td>Not fitted</td></tr></table>

¹ We exclude these B(K<sub>L</sub> → 3π<sup>0</sup>) measurements from our fit because the authors have constrained K<sub>L</sub> branching fractions to sum to one. It enters our fit via the other measurements from the experiment and their correlations, along with our constraint that the fitted branching fractions sum to one.

$$ \frac{\Gamma(\pi^0)/\Gamma(\pi^{\pm} e^{\mp} \nu_{e})}{\Gamma_{6}/\Gamma_{7}} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.481 ± 0.004 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

• • • We use the following data for averages but not for fits. • • •

<table><tr><td>0.4782 ± 0.0014 ± 0.0053</td><td>209k</td><td>1 ALEXOPOULOS...</td><td>04</td><td>KTEV</td><td>Not in fit</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

¹ This measurement enters the fit via their separate measurements of these two modes.

$$ \frac{\Gamma(\pi^0)/[\Gamma(\pi^{\pm} e^{\mp} \nu_{e}) + \Gamma(\pi^{\pm} \mu^{\mp} \nu_{\mu}) + \Gamma(\pi^{+} \pi^{-} \pi^{0})]}{\Gamma_{6}/(\Gamma_{1} + \Gamma_{2})/\Gamma_{7}} $$

• • • We do not use the following data for averages, fits, limits, etc. • • •

• • • We use the following data for averages but not for fits. • • •

<table><tr><td>0.251 ± 0.014</td><td>549</td><td>BUDAGOV</td><td>68</td><td>HLBC</td><td>ORSAY measur.</td></tr><tr><td>0.277 ± 0.021</td><td>444</td><td>BUDAGOV</td><td>68</td><td>HLBC</td><td>Ecole polytec.meas</td></tr><tr><td>0.31 ± 0.07</td><td>29</td><td>KULYUKINA</td><td>68</td><td>CC</td><td></td></tr><tr><td>-0.06</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.24 ± 0.08</td><td>24</td><td>ANIKINA</td><td>64</td><td>CC</td><td></td></tr></table>

$$ \frac{\Gamma(\pi^0)/\Gamma(\pi^+\pi^-\pi^0)}{\Gamma_{6}/\Gamma_{7}} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>1.557 ± 0.012 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

• • • We use the following data for averages but not for fits. • • •
• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>1.611 ± 0.014 ± 0.034</td><td>28k</td><td>KREUTZ</td><td>95</td><td>NA31</td></tr><tr><td>1.65 ± 0.07</td><td>883</td><td>BARMIN</td><td>72b</td><td>HLBC</td></tr><tr><td>1.80 ± 0.13</td><td>1010</td><td>BUDAGOV</td><td>68</td><td>HLBC</td></tr><tr><td>2.0 ± 0.6</td><td>188</td><td>ALEKSANYAN</td><td>64b</td><td>FBC</td></tr></table>

¹ AMBROSINO 06 enters the fit via their separate measurements of these two modes.

$$ \Gamma(\pi^{+} \pi^{-} \pi^{0})/\Gamma_{\text{total}} \quad \Gamma_{7/\Gamma} $$

$$ \text{VALUE} \quad \text{EVTs} $$

$$ \text{DOCUMENT ID} \quad \text{TECN} $$

$$ \text{0.1254} \pm 0.0005 \text{ OUR FIT} $$

$$ \text{0.1255} \pm 0.0006 \text{ OUR AVERAGE} $$

$$ \begin{array}{l} 0.1263 \pm 0.0004 \pm 0.0011 \quad 13M \quad 1 \text{ AMBROSINO} \quad 06 \quad \text{KLOE} \\ 0.1252 \pm 0.0007 \quad 2 \text{ ALEXOPOU} \quad 04 \quad \text{KTEV} \end{array} $$

¹ There are correlations between these five KLOE measurements: $B(K_L \to \pi e \nu)$, $B(K_L \to \pi \mu \nu)$, $B(K_L \to 3\pi^0)$, $B(K_L \to \pi^+ \pi^- \pi^0)$, and $\tau_{K_L}$ measured in AMBROSINO 06. See the footnote for the $\tau_{K_L}$ measurement for the correlation matrix.

² For correlations with other ALEXOPOULOS 04 measurements, see the footnote with their $B(K_L \to \pi e \nu)$ measurement.

$$ \Gamma(\pi^{+} \pi^{-} \pi^{0})/\Gamma(\pi^{\pm} e^{\mp} \nu_{e}) \quad \Gamma_{7/\Gamma_{1}} $$

$$ \text{VALUE} \quad \text{EVTs} $$

$$ \text{DOCUMENT ID} \quad \text{TECN} $$

$$ \text{COMMENT} $$

$$ \text{1.3092} \pm 0.0016 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.1.} $$

• • • We use the following data for averages but not for fits. • • •

$$ \text{0.3078} \pm 0.0005 \pm 0.0017 \quad 799k \quad 1 \text{ ALEXOPOU} \quad 04 \quad \text{KTEV} \quad \text{Not in fit} $$

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$ 0.336 \pm 0.003 \pm 0.007 \quad 28k \quad \text{KREUTZ} \quad 95 \quad \text{NA31} $$

¹ This measurement enters the fit via their separate measurements for the two modes.

$$ \Gamma(\pi^{+} \pi^{-} \pi^{0})/\Gamma(\pi^{\pm} e^{\mp} \nu_{e}) + \Gamma(\pi^{\pm} \mu^{\mp} \nu_{\mu}) + \Gamma(\pi^{+} \pi^{-} \pi^{0}) \quad \Gamma_{7}/(\Gamma_{1}+\Gamma_{2}+\Gamma_{7}) $$

$$ \text{VALUE} \quad \text{EVTs} $$

$$ \text{DOCUMENT ID} \quad \text{TECN} $$

$$ \text{COMMENT} $$

$$ \text{0.1565} \pm 0.0006 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.1.} $$

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>0.163 ± 0.003</td><td>6499</td><td>CHO</td><td>77</td><td>HBC</td></tr><tr><td>0.1605 ± 0.0038</td><td>1590</td><td>ALEXANDER</td><td>73b</td><td>HBC</td></tr><tr><td>0.146 ± 0.004</td><td>3200</td><td>BRANDENB... 73</td><td></td><td>HBC</td></tr><tr><td>0.159 ± 0.010</td><td>558</td><td>EVANS</td><td>73</td><td>HLBC</td></tr><tr><td>0.167 ± 0.016</td><td>1402</td><td>KULYUKINA 68</td><td></td><td>CC</td></tr><tr><td>0.161 ± 0.005</td><td></td><td>HOPKINS</td><td>67</td><td>HBC</td></tr><tr><td>0.162 ± 0.015</td><td>126</td><td>HAWKINS</td><td>66</td><td>HBC</td></tr><tr><td>0.159 ± 0.015</td><td>326</td><td>ASTBURY</td><td>65b</td><td>CC</td></tr><tr><td>0.178 ± 0.017</td><td>566</td><td>GUIDONI</td><td>65</td><td>HBC</td></tr><tr><td>0.144 ± 0.004</td><td>1729</td><td>HOPKINS</td><td>65</td><td>HBC</td></tr></table>

$$ \Gamma(\pi^{+} \pi^{-})/\Gamma_{\text{total}} \quad \Gamma_{8/\Gamma} \quad \text{Violates CP conservation.} $$

$$ \text{VALUE} \quad \text{(units 10}^{-3}) \quad \text{DOCUMENT ID} \quad \text{TECN} $$

$$ \text{1.967} \pm 0.010 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.5.} $$

$$ \text{1.975} \pm 0.012 \quad 1 \text{ ALEXOPOU} \quad 04 \quad \text{KTEV} $$

¹ For correlations with other ALEXOPOULOS 04 measurements, see the footnote with their $B(K_L \to \pi e \nu)$ measurement.

$$ \Gamma(\pi^{+} \pi^{-})/\Gamma(\pi^{\pm} e^{\mp} \nu_{e}) \quad \Gamma_{8/\Gamma_{1}} $$

$$ \text{VALUE} \quad \text{(units 10}^{-3}) \quad \text{EVTs} $$

$$ \text{DOCUMENT ID} \quad \text{TECN} $$

$$ \text{COMMENT} $$

$$ \text{4.849} \pm 0.020 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.1.} $$

$$ \text{4.840} \pm 0.020 \text{ OUR AVERAGE} $$

$$ 4.826 \pm 0.022 \pm 0.016 \quad 47k \quad 1 \text{ LAI} \quad 07 \quad \text{NA48} $$

• • • We use the following data for averages but not for fits. • • •

$$ 4.856 \pm 0.017 \pm 0.023 \quad 84k \quad 2 \text{ ALEXOPOU} \quad 04 \quad \text{KTEV} \quad \text{Not in fit} $$

¹ The LAI 07 central value of 4.835 × 10⁻³ has been reduced by 0.19% to 4.826 × 10⁻³ to subtract the contribution from the direct emission mode $K_L^0 \to \pi^+ \pi^- \gamma(\text{DE})$.

² This measurement enters the fit via their separate measurements for the two modes.

$$ \left[ \Gamma(\pi^{+} \pi^{-}) + \Gamma(\pi^{+} \pi^{-} \gamma(\text{DE})) \right] / \Gamma(\pi^{\pm} \mu^{\mp} \nu_{\mu}) \quad (\Gamma_{8} + \Gamma_{14}) / \Gamma_{2} $$

$$ \text{VALUE} \quad \text{(units 10}^{-3}) \quad \text{EVTs} $$

$$ \text{7.38} \pm 0.04 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.4.} $$

$$ \text{7.275} \pm 0.042 \pm 0.054 \quad 45k \quad 1 \text{ AMBROSINO} \quad 06f \quad \text{KLOE} $$

¹ Fully inclusive. Taking $B(K_L^0 \to \pi \mu \nu)$ from KLOE, AMBROSINO 06, $B(K_L^0 \to \pi^+ \pi^- + \pi^+ \pi^- \gamma(\text{DE})) = (1.963 \pm 0.012 \pm 0.017) \times 10^{-3}$ is obtained.

$$ \Gamma(\pi^{+} \pi^{-})/\Gamma(\pi^{\pm} e^{\mp} \nu_{e}) + \Gamma(\pi^{\pm} \mu^{\mp} \nu_{\mu}) \quad \Gamma_{8}/(\Gamma_{1}+\Gamma_{2}) $$

$$ \text{VALUE} \quad \text{(units 10}^{-3}) \quad \text{EVTs} $$

$$ \text{2.909} \pm 0.013 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.3.} $$

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>3.13 ± 0.14</td><td>1687</td><td>COUPAL</td><td>85</td><td>SPEC</td><td>η<sub>+</sub> = 2.28 ± 0.06</td></tr><tr><td>3.04 ± 0.14</td><td>2703</td><td>DEVOE</td><td>77</td><td>SPEC</td><td>η<sub>-</sub> = 2.25 ± 0.05</td></tr><tr><td>2.51 ± 0.23</td><td>309</td><td>1 DEBOUARD</td><td>67</td><td>OSPK</td><td>η<sub>+</sub> = 2.00 ± 0.09</td></tr><tr><td>2.35 ± 0.19</td><td>525</td><td>1 FITCH</td><td>67</td><td>OSPK</td><td>η<sub>-</sub> = 1.94 ± 0.08</td></tr></table>

¹ Old experiments excluded from fit. See subsection on $\eta_{+-}$ in section on "PARAMETERS FOR $K_L^0 \to 2\pi$ DECAY" below for average $\eta_{+-}$ of these experiments and for note on discrepancy.

$$ \Gamma(\pi^{\pm} e^{\mp} \nu_{e})/\Gamma(2 \text{ tracks}) \quad \Gamma_{1}/(\Gamma_{1}+\Gamma_{2}+0.03508\Gamma_{6}+\Gamma_{7}+\Gamma_{8}) $$

$\Gamma(2 \text{ tracks}) = \Gamma(\pi^{+} e^{\mp} \nu_{e}) + \Gamma(\pi^{\pm} \mu^{\mp} \nu_{\mu}) + 0.03508 \Gamma(3\pi^{0}) + \Gamma(\pi^{+} \pi^{-} \pi^{0}) + \Gamma(\pi^{+} \pi^{-})$ where 0.03508 is the fraction of $3\pi^0$ events with one Dalitz decay ($\pi^0 \to \gamma e^{+} e^{-}$).

$$ \text{VALUE} \quad \text{EVTs} \quad \text{DOCUMENT ID} \quad \text{TECN} $$

$$ \text{0.5006} \pm 0.0009 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.3.} $$

$$ \text{0.4978} \pm 0.0035 \quad 6.8M \quad \text{LAI} \quad 04B \quad \text{NA48} $$

$$ \frac{\Gamma(\pi^{+} \pi^{-})}{\Gamma(\pi^{\pm} e^{\mp} \nu_{e}) + \Gamma(\pi^{\pm} \mu^{\mp} \nu_{\mu}) + \Gamma(\pi^{+} \pi^{-} \pi^{0})} \quad \text{Violates CP conservation.} $$

$$ \text{VALUE} \quad \text{(units 10}^{-3}) \quad \text{EVTs} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} $$

$$ \text{2.454} \pm 0.011 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.3.} $$

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$ 2.60 \pm 0.07 \quad 4200 \quad 1 \text{ MESSNER} \quad 73 \quad \text{ASPK} \quad \eta_{+-} = 2.23 \pm 0.05 $$

¹ From same data as $\Gamma(\pi^+\pi^-)/\Gamma(\pi^+\pi^-\pi^0)$ MESSNER 73, but with different normalization.

$$ \frac{\Gamma(\pi^{+} \pi^{-})}{\Gamma(\pi^{\pm} \pi^{0})} \quad \text{Violates CP conservation.} $$

$$ \text{1.568} \pm 0.010 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.3.} $$

$$ \text{VALUE} \quad \text{(units 10}^{-2}) \quad \text{EVTs} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} $$

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$ 1.64 \pm 0.04 \quad 4200 \quad \text{MESSNER} \quad 73 \quad \text{ASPK} \quad \eta_{+-} = 2.23 $$

$$ \frac{\Gamma(\pi^{0} \pi^{0})}{\Gamma(\pi^{+} \pi^{-})} \quad \text{Violates CP conservation.} $$

$$ \text{VALUE} \quad \text{(units 10}^{-3}) \quad \text{DOCUMENT ID} \quad \text{TECN} $$

$$ \text{0.864} \pm 0.006 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.8.} $$

$$ \text{0.865} \pm 0.012 \quad 1 \text{ ALEXOPOU} \quad 04 \quad \text{KTEV} $$

¹ For correlations with other ALEXOPOULOS 04 measurements, see the footnote with their $B(K_L \to \pi e \nu)$ measurement.

$$ \frac{\Gamma(\pi^{0} \pi^{0})}{\Gamma(\pi^{+} \pi^{-})} \quad \text{Violates CP conservation.} $$

$$ \text{0.4395} \pm 0.0023 \text{ OUR FIT} \quad \text{Error includes scale factor of 2.0.} $$

$$ \text{0.4390} \pm 0.0012 \quad \text{ETAFIT} \quad 16 $$

$$ \frac{\Gamma(\pi^{0} \pi^{0})}{\Gamma(3\pi^{0})} \quad \text{Violates CP conservation.} $$

$$ \text{VALUE} \quad \text{(units 10}^{-2}) \quad \text{EVTs} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} $$

$$ \text{0.443} \pm 0.004 \text{ OUR FIT} \quad \text{Error includes scale factor of 2.1.} $$

• • • We use the following data for averages but not for fits. • • •

$$ \text{0.4446} \pm 0.0016 \pm 0.0019 \quad 100k \quad 1 \text{ ALEXOPOU} \quad 04 \quad \text{KTEV} \quad \text{Not in fit} $$

<table><tr><td>0.37 ± 0.08</td><td>29</td><td>BARMIN</td><td>70</td><td>HLBC</td><td>η<sub>00</sub> = 2.02 ± 0.23</td></tr><tr><td>0.32 ± 0.15</td><td>30</td><td>BUDAGOV</td><td>70</td><td>HLBC</td><td>η<sub>00</sub> = 1.9 ± 0.5</td></tr><tr><td>0.46 ± 0.11</td><td>57</td><td>BANNER</td><td>69</td><td>OSPK</td><td>η<sub>00</sub> = 2.2 ± 0.3</td></tr></table>

¹ This measurement enters the fit via their separate measurements for the two modes.

Semileptonic modes with photons

$$ \frac{\Gamma(\pi^{\pm} e^{\mp} \nu_{e})}{\Gamma(\pi^{\pm} e^{\mp} \nu_{e})} \quad \Gamma_{10/\Gamma_{1}} $$

$$ \text{VALUE} \quad \text{(units 10}^{-2}) \quad \text{EVTs} $$

$$ \text{0.935} \pm 0.015 \text{ OUR AVERAGE} \quad \text{Error includes scale factor of 1.9. See the ideogram below.} $$

<table><tr><td>0.924 ± 0.023 ± 0.016</td><td>9k</td><td>1 AMBROSINO 08f</td><td>KLOE</td><td>E<sup>*</sup><sub>γ</sub> > 30 MeV, θ<sup>*</sup><sub>eγ</sub> > 20°</td></tr><tr><td>0.916 ± 0.017</td><td>4309</td><td>2 ALEXOPOU... 05</td><td>KTEV</td><td>E<sup>*</sup><sub>γ</sub> > 30 MeV, θ<sup>*</sup><sub>eγ</sub> > 20°</td></tr><tr><td>0.964 ± 0.008<sup>+0.011</sup><sub>-0.009</sub></td><td>19k</td><td>LAI</td><td>05</td><td>NA48</td><td>E<sup>*</sup><sub>γ</sub> > 30 MeV, θ<sup>*</sup><sub>eγ</sub> > 20°</td></tr><tr><td>0.908 ± 0.008<sup>+0.013</sup><sub>-0.012</sub></td><td>15k</td><td>ALAVI-HARATI01J</td><td>KTEV</td><td>E<sup>*</sup><sub>γ</sub> ≥ 30 MeV, θ<sup>*</sup><sub>eγ</sub> ≥ 20°</td></tr><tr><td>0.934 ± 0.036<sup>+0.055</sup><sub>-0.039</sub></td><td>1384</td><td>LEBER</td><td>96</td><td>NA31</td><td>E<sup>*</sup><sub>γ</sub> ≥ 30 MeV, θ<sup>*</sup><sub>eγ</sub> ≥ 20°</td></tr></table>

WEIGHTED AVERAGE
0.935±0.015 (Error scaled by 1.9)

<figure><img src="image_512.png" /></figure>

$$ \frac{\Gamma(\pi^{\pm} e^{\mp} \nu_{e})}{\Gamma(\pi^{\pm} e^{\mp} \nu_{e})} \quad (\text{units } 10^{-2}) $$

¹ Direct emission contribution measured $\langle X \rangle = -2.3 \pm 1.3 \pm 1.4$.
²Also measured cut $E_γ^* > 10$ MeV, $θ_e^* > 0°$ 14221 evts: $Γ(π^±e^∓ν_eγ) / Γ(π^±e^∓ν_e) = (4.942 ± 0.062)‰$.

$$Γ(π^±μ^∓ν_μγ)/Γ(π^±μ^∓ν_μ) \qquad Γ_{11}/Γ_2$$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>2.09±0.08 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

$2.09±0.09$

$1$ ALEXOPOU... 05 KTEV $E_γ^* > 30$ MeV

$2.08±0.17^{+0.16}_{-0.21}$

$252$ BENDER 98 NA48 $E_γ^* ≥ 30$ MeV

¹Also measured cut $E_γ^* > 10$ MeV, 1385 evts: $Γ(π^±μ^∓ν_μγ) / Γ(π^±μ^∓ν_μ) = (0.530 ± 0.014 ± 0.012)‰$.

## Hadronic modes with photons or ℓℓ pairs

$$Γ(π^0π^0γ)/Γ_{total} \qquad Γ_{12}/Γ$$

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt; 0.243</strong></td><td>90</td><td>ABOUZAID</td><td>08B</td><td>KTEV $K_L^0 → π^0π_D^0γ, π^0D → eeγ$</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$< 5.6$

$90$ BARR 94 NA31

$<230$

$90$ ROBERTS 94 E799

$$Γ(π^+π^−γ)/Γ(π^+π^−π^0) \qquad Γ_{13}/Γ_7$$

For earlier limits see our 1992 edition Physical Review D45 S1 (1992).

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.23±0.13</td><td>516</td><td>1,2 CARROLL</td><td>80B</td><td>SPEC $E_γ^* > 20$ MeV</td></tr><tr><td>2.33±0.23</td><td>546</td><td>1,3 CARROLL</td><td>80B</td><td>SPEC</td></tr><tr><td>3.56±0.26</td><td>1062</td><td>1,4 CARROLL</td><td>80B</td><td>SPEC $E_γ^* > 20$ MeV</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$1.23±0.13$

$2.33±0.23$

$3.56±0.26$

¹CARROLL 80B quotes $B(π^+π^−γ)$ using normalization $B(π^+π^−π^0) = 0.1239$. We divide by this value to obtain their measured $Γ(π^+π^−γ) / Γ(π^+π^−π^0)$.

²Internal Bremsstrahlung component only.

³Direct $γ$ emission component only.

⁴Both IB and DE components.

$$Γ(π^+π^−γ)/Γ(π^+π^−) \qquad Γ_{13}/Γ_8$$

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>2.11±0.08 OUR FIT</strong></td><td></td><td>Error includes scale factor of 2.9.</td><td></td><td></td></tr></tbody></table>

².11±0.08 OUR AVERAGE Error includes scale factor of 2.9.

$2.08±0.02±0.02$

$2.30±0.07$

¹ALAVI-HARATI 01B includes both Direct Emission (DE) and Inner Bremsstrahlung (IB) processes.

$$Γ(π^+π^−γ(DE))/Γ(π^+π^−γ) \qquad Γ_{14}/Γ_{13}$$

These values assume that $Γ(K_L^0 → π^+π^−γ) = Γ(K_L^0 → π^+π^−γ(DE)) + Γ(K_L^0 → π^+π^−γ(IB))$, the sum of widths for the direct emission (DE) and inner bremsstrahlung (IB) processes, with no IB-DE interference. DE assumes a form factor as described in RAMBERG 93.

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.684±0.009 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td><strong>0.684±0.009 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

$0.689±0.021$

$0.683±0.011$

$0.685±0.041$

$$Γ(π^02γ)/Γ_{total} \qquad Γ_{15}/Γ$$

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>1.273±0.033 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1.28 ± 0.06 ± 0.01</td><td>1.4k</td><td>1 ABOUZAID</td><td>08</td><td>KTEV</td><td></td></tr><tr><td>1.27 ± 0.04 ± 0.01</td><td>2.5k</td><td>2 LAI</td><td>02B</td><td>NA48</td><td></td></tr></tbody></table>

$1.28 ± 0.06 ± 0.01$

• • • We do not use the following data for averages, fits, limits, etc. • • •

$1.68 ± 0.07 ± 0.08$

$1.7 ± 0.2 ± 0.2$

$1.86 ± 0.60 ± 0.60$

$<5.1$

¹ABOUZAID 08 reports $(1.29 ± 0.03 ± 0.05) × 10^{-6}$ from a measurement of $[Γ(K_L^0 → π^02γ)/Γ_{total}] / [B(K_L^0 → π^0π^0)]$ assuming $B(K_L^0 → π^0π^0) = (8.69 ± 0.04) × 10^{-4}$, which we rescale to our best value $B(K_L^0 → π^0π^0) = (8.64 ± 0.06) × 10^{-4}$. Our first error is their experiment's error and our second error is the systematic error from using our best value.

²LAI 02B reports $[Γ(K_L^0 → π^02γ)/Γ_{total}] / [B(K_L^0 → π^0π^0)] = (1.467 ± 0.032 ± 0.032) × 10^{-3}$ which we multiply by our best value $B(K_L^0 → π^0π^0) = (8.64 ± 0.06) × 10^{-4}$. Our first error is their experiment's error and our second error is the systematic error from using our best value. They also find that $B(π^02γ, m_{γγ} < 110$ MeV) < 0.6 × 10^{-8}(90% CL)$.

³ALAVI-HARATI 99B finds that $Γ(π^02γ, m_{γγ} < 240$ MeV) / $Γ(π^02γ) = (17.3 ± 1.3 ± 1.5)‰$. Supersedes by ABOUZAID 08.

⁴BARR 92 find that $Γ(π^02γ, m_{γγ} < 240$ MeV) / $Γ(π^02γ) < 0.09$ (90% CL).

⁵BARR 90C superseded by BARR 92.

$$Γ(π^0γe^+e^-)/Γ_{total} \qquad Γ_{16}/Γ$$

<table><thead><tr><th>VALUE (units 10<sup>-8</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>1.62±0.14±0.09</strong></td><td>125</td><td></td><td></td><td></td><td></td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$2.34±0.35±0.13$

$<71$

¹ABOUZAID 07D includes 1997 (ALAVI-HARATI 01E) and 1999 data. It measures the ratio of $B(K_L^0 → π^0γe^+e^-) / B(K_L^0 → π^0π_D^0)$, where $π_D^0$ is the Dalitz decaying $π^0$, and uses PDG 06 values $B(K_L^0 → π^0π^0) = (8.69 ± 0.04) × 10^{-4}$, and $B(π_D^0 → e^+e^-) = (1.198 ± 0.032) × 10^{-2}$. Supersedes ALAVI-HARATI 01E result.

## Other modes with photons or ℓℓ pairs

$$Γ(2γ)/Γ_{total} \qquad Γ_{17}/Γ$$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

⁵.47±0.04 OUR FIT Error includes scale factor of 1.1.

• • • We do not use the following data for averages, fits, limits, etc. • • •

$4.54±0.84$

$4.5 ± 1.0$

$5.0 ± 1.0$

$5.5 ± 1.1$

¹This value uses $(η_{00}/η_{+-})^2 = 1.05 ± 0.14$. In general, $Γ(2γ)/Γ_{total} = [(4.32 ± 0.55) × 10^{-4}] / [(η_{00}/η_{+-})^2]$.

²Assumes regeneration amplitude in copper at 2 GeV is 22 mb. To evaluate for a given regeneration amplitude and error, multiply by (regeneration amplitude/22mb)$^2$.

$$Γ(2γ)/Γ(3π^0) \qquad Γ_{17}/Γ_6$$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>2.802±0.017 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td><strong>2.802±0.018 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>2.79 ± 0.02 ± 0.02</td><td>27k</td><td>ADINOLFI</td><td>03</td><td>KLOE</td></tr><tr><td>2.81 ± 0.01 ± 0.02</td><td></td><td>LAI</td><td>03</td><td>NA48</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$2.13 ± 0.43$

$2.24 ± 0.28$

• • • We do not use the following data for averages, fits, limits, etc. • • •

$2.5 ± 0.7$

$2.5 ± 0.7$

$1$ TUNG 11 reports the result assuming parity violating interaction and using 2005 data (Run-II and III). Assuming parity conserving or phase space interaction, the 90% upper limits obtained are $7.5 × 10^{-8}$ and $8.6 × 10^{-8}$, respectively.

$$Γ(2γ)/Γ(π^0π^0) \qquad Γ_{17}/Γ_9$$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.633±0.006 OUR FIT</strong></td><td></td><td>Error includes scale factor of 1.4.</td><td></td></tr><tr><td><strong>0.632±0.004±0.008</strong></td><td>110k</td><td>BURKHARDT</td><td>87</td></tr></tbody></table>

².632±0.004±0.008

$$Γ(3γ)/Γ_{total} \qquad Γ_{18}/Γ$$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>&lt;7.4 × 10<sup>-8</sup></strong></td><td>90</td><td>1 TUNG</td><td>11</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$<2.4 × 10^{-7}$

¹TUNG 11 reports the result assuming parity violating interaction and using 2005 data (Run-II and III). Assuming parity conserving or phase space interaction, the 90% upper limits obtained are $7.5 × 10^{-8}$ and $8.6 × 10^{-8}$, respectively.

²Assumes a phase-space decay distribution.

$$Γ(e^+e^-)/Γ_{total} \qquad Γ_{19}/Γ$$

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>9.4±0.4 OUR FIT</strong></td><td></td><td>Error includes scale factor of 2.0.</td><td></td></tr><tr><td><strong>10.0±0.5 OUR AVERAGE</strong></td><td></td><td>Error includes scale factor of 1.5. See the ideogram below.</td><td></td></tr></tbody></table>

².9±0.4 OUR AVERAGE

¹FANTI 99B NA48

².9±0.5 ± 0.5

².9±0.5 ± 0.5

².9±0.4 + 0.6 - 0.5

## WEIGHTED AVERAGE
10.0±0.5 (Error scaled by 1.5)

<figure><img src="image_513.png" /></figure>

Values above of weighted average, error, and scale factor are based upon the data in this ideogram only. They are not necessarily the same as our 'best' values, obtained from a least-squares constrained fit utilizing measurements of other (related) quantities as additional information.

$$Γ(e^+e^-)/Γ_{total} (units 10^{-6})$$

¹For FANTI 99B, the ±0.4 systematic error includes for uncertainties in the calculation, primarily uncertainties in the $π^0 → e^+e^-$ and $K_L^0 → π^0π^0$ branching ratios, evaluated using our 1999 Web edition values.
$$ \Gamma(e^+ e^- \gamma) / \Gamma(3\pi^0) $$

$$ \Gamma_{19}/\Gamma_6 $$

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead></table>

4.82±0.21 OUR FIT Error includes scale factor of 2.0.

<table><thead><tr><th>4.63±0.04±0.13</th><th>83k</th><th>1 ABOUZAID</th><th>07B</th><th>KTEV</th></tr></thead></table>

¹ABOUZAID 07b reports $[\Gamma(K_L^0 \to e^+ e^-)/\Gamma(K_L^0 \to 3\pi^0)] / [3\Gamma(\pi^0 \to 2\gamma)/\Gamma_{total} \times \Gamma(\pi^0 \to e^+ e^-)/\Gamma_{total}] = (1.3302 \pm 0.0046 \pm 0.0103) \times 10^{-3}$ which we multiply by our best value $3\Gamma(\pi^0 \to 2\gamma)/\Gamma_{total} \times \Gamma(\pi^0 \to e^+ e^-)/\Gamma_{total} = 0.0348 \pm 0.0010$. Our first error is their experiment's error and our second error is the systematic error from using our best value.

$$ \Gamma(\mu^+ \mu^- \gamma) / \Gamma_{\text{total}} $$

$$ \Gamma_{20}/\Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-7</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead></table>

3.59±0.11 OUR AVERAGE Error includes scale factor of 1.3.

<table><thead><tr><th>3.62±0.04±0.08</th><th>9100</th><th>ALAVI-HARATI016</th><th>KTEV</th></tr></thead></table>

<table><thead><tr><th>3.4 ± 0.6 ± 0.4</th><th>45</th><th>FANTI</th><th>97</th><th>NA48</th></tr></thead></table>

<table><thead><tr><th>3.23±0.23±0.19</th><th>197</th><th>SPENCER</th><th>95</th><th>E799</th></tr></thead></table>

$$ \Gamma(\mu^+ \mu^- \mu^+ \mu^-) / \Gamma_{\text{total}} $$

$$ \Gamma_{21}/\Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead></table>

<table><thead><tr><th>&lt;2.3 × 10<sup>-9</sup></th><th>90</th><th>1 AAIJ</th><th>23AE</th><th>LHCb</th></tr></thead></table>

¹AAIJ 23AE uses 5.1 fb⁻¹ of LHCb data recorded from 2016 to 2018.

$$ \Gamma(e^+ e^- \gamma\gamma) / \Gamma_{\text{total}} $$

$$ \Gamma_{22}/\Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-7</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

5.95±0.33 OUR AVERAGE ALAVI-HARATI01F KTEV $E_\gamma^* > 5$ MeV

<table><thead><tr><th>5.84±0.15±0.32</th><th>1543</th><th>ALAVI-HARATI01F</th><th>KTEV</th><th>E_\gamma^* > 5 MeV</th></tr></thead></table>

<table><thead><tr><th>8.0 ± 1.5 ± 1.4</th><th>40</th><th>SETZU</th><th>98</th><th>NA31</th><th>E_\gamma^* > 5 MeV</th></tr></thead></table>

<table><thead><tr><th>6.5 ± 1.2 ± 0.6</th><th>58</th><th>NAKAYA</th><th>94</th><th>E799</th><th>E_\gamma^* > 5 MeV</th></tr></thead></table>

<table><thead><tr><th>6.6 ± 3.2</th><th></th><th>MORSE</th><th>92</th><th>B845</th><th>E_\gamma^* > 5 MeV</th></tr></thead></table>

$$ \Gamma(\mu^+ \mu^- \gamma\gamma) / \Gamma_{\text{total}} $$

$$ \Gamma_{23}/\Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

<table><thead><tr><th>10.4<sup>+7.5</sup><sub>-5.9</sub> ± 0.7</th><th>4</th><th>ALAVI-HARATI00E</th><th>KTEV</th><th>m<sub>\gamma\gamma</sub> ≥ 1 MeV/c<sup>2</sup></th></tr></thead></table>

Charge conjugation × Parity (CP) or Lepton Family number (LF) violating modes, or $\Delta S = 1$ weak neutral current (SI) modes

$$ \Gamma(\mu^+ \mu^-) / \Gamma(\pi^+ \pi^-) $$

$$ \Gamma_{24}/\Gamma_8 $$

Test for $\Delta S = 1$ weak neutral current. Allowed by higher-order electroweak interaction.

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

3.48 ± 0.05 OUR AVERAGE AMBROSE 00 B871

<table><thead><tr><th>3.474 ± 0.057</th><th>6210</th><th>AMBROSE</th><th>00</th><th>B871</th></tr></thead></table>

<table><thead><tr><th>3.87 ± 0.30</th><th>179</th><th>1 AKAGI</th><th>95</th><th>SPEC</th></tr></thead></table>

<table><thead><tr><th>3.38 ± 0.17</th><th>707</th><th>HEINSON</th><th>95</th><th>B791</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>3.9 ± 0.3 ± 0.1</th><th>178</th><th>2 AKAGI</th><th>91B</th><th>SPEC</th><th>In AKAGI 95</th></tr></thead></table>

<table><thead><tr><th>3.45 ± 0.18 ± 0.13</th><th>368</th><th>3 HEINSON</th><th>91</th><th>SPEC</th><th>In HEINSON 95</th></tr></thead></table>

<table><thead><tr><th>4.1 ± 0.5</th><th>54</th><th>INAGAKI</th><th>89</th><th>SPEC</th><th>In AKAGI 91B</th></tr></thead></table>

<table><thead><tr><th>2.8 ± 0.3 ± 0.2</th><th>87</th><th>MATHIAZHA...89b</th><th>SPEC</th><th>In HEINSON 91</th></tr></thead></table>

¹AKAGI 95 gives this number multiplied by the PDG 1992 average for $\Gamma(K_L^0 \to \pi^+ \pi^-) / \Gamma(\text{total})$.

²AKAGI 91B give this number multiplied by the 1990 PDG average for $\Gamma(K_L^0 \to \pi^+ \pi^-) / \Gamma(\text{total})$.

³HEINSON 91 give $\Gamma(K_L^0 \to \mu\mu) / \Gamma_{\text{total}}$. We divide out the $\Gamma(K_L^0 \to \pi^+ \pi^-) / \Gamma_{\text{total}}$ PDG average which they used.

$$ \Gamma(e^+ e^-) / \Gamma_{\text{total}} $$

$$ \Gamma_{25}/\Gamma $$

Test for $\Delta S = 1$ weak neutral current. Allowed by higher-order electroweak interaction.

<table><thead><tr><th>VALUE (units 10<sup>-10</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead></table>

<table><thead><tr><th>0.087<sup>+0.057</sup><sub>-0.041</sub></th><th>4</th><th>AMBROSE</th><th>98</th><th>B871</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>&lt;1.6</th><th>90</th><th>1 AKAGI</th><th>95</th><th>SPEC</th></tr></thead></table>

<table><thead><tr><th>&lt;0.41</th><th>90</th><th>0</th><th>1 ARISAKA</th><th>93b</th><th>B791</th></tr></thead></table>

¹ARISAKA 93b includes all events with <6 MeV radiated energy.

$$ \Gamma(\pi^+ \pi^- e^+ e^-) / \Gamma_{\text{total}} $$

$$ \Gamma_{26}/\Gamma $$

Test for $\Delta S = 1$ weak neutral current. Allowed by higher-order electroweak interaction.

<table><thead><tr><th>VALUE (units 10<sup>-7</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

3.11±0.19 OUR AVERAGE 1 LAI 03C NA48

<table><thead><tr><th>3.08±0.09±0.18</th><th>1125</th><th>1 LAI</th><th>03C</th><th>NA48</th></tr></thead></table>

<table><thead><tr><th>3.2 ± 0.6 ± 0.4</th><th>37</th><th>ADAMS</th><th>98</th><th>KTEV</th></tr></thead></table>

<table><thead><tr><th>4.4 ± 1.3 ± 0.5</th><th>13</th><th>TAKEUCHI</th><th>98</th><th>SPEC</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>&lt;4.6</th><th>90</th><th>NOMURA</th><th>97</th><th>SPEC</th><th>m<sub>ee</sub> > 4 MeV</th></tr></thead></table>

¹LAI 03c second error is 0.15(syst)±0.10(normal) combined in quadrature. The normalization uses $BR(K_L^0 \to \pi^+ \pi^- \pi^0) * BR(\pi^0 \to e^+ e^-) = (1.505 \pm 0.047) \times 10^{-3}$ from our 2000 Edition.

$$ \Gamma(\pi^0 \pi^0 e^+ e^-) / \Gamma_{\text{total}} $$

$$ \Gamma_{27}/\Gamma $$

Test for $\Delta S = 1$ weak neutral current. Allowed by higher-order electroweak interaction.

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead></table>

<table><thead><tr><th>&lt;6.6</th><th>90</th><th>1</th><th>ALAVI-HARATI02C</th><th>E799</th></tr></thead></table>

$$ \Gamma(\pi^0 \pi^0 \mu^+ \mu^-) / \Gamma_{\text{total}} $$

$$ \Gamma_{28}/\Gamma $$

Test for $\Delta S = 1$ weak neutral current. Allowed by higher-order electroweak interaction.

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead></table>

¹ABOUZAID 11A also reports $B(K_L^0 \to \pi^0 \pi^0 \chi^0 \to \pi^0 \pi^0 \mu^+ \mu^-) < 1.0 \times 10^{-10}$ at 90% C.L., where the $\chi^0$ is a possible new neutral boson that was reported by PARK 05 with a mass of 214.3 ± 0.5 MeV/c².

$$ \Gamma(\mu^+ \mu^- e^+ e^-) / \Gamma_{\text{total}} $$

$$ \Gamma_{29}/\Gamma $$

Test for $\Delta S = 1$ weak neutral current. Allowed by higher-order electroweak interaction.

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

<table><thead><tr><th>2.69±0.27 OUR AVERAGE</th><th>131</th><th>1 ALAVI-HARATI03B</th><th>KTEV</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>2.62±0.40±0.17</th><th>43</th><th>ALAVI-HARATI01H</th><th>KTEV</th><th>Sup. by ALAVI-HARATI 03B</th></tr></thead></table>

<table><thead><tr><th>&lt;4900</th><th>90</th><th>BALATS</th><th>83</th><th>SPEC</th></tr></thead></table>

¹ALAVI-HARATI 03B also measures the linear slope $\alpha = -1.59 \pm 0.37$.

$$ \Gamma(e^+ e^- e^+ e^-) / \Gamma_{\text{total}} $$

$$ \Gamma_{30}/\Gamma $$

Test for $\Delta S = 1$ weak neutral current. Allowed by higher-order electroweak interaction.

<table><thead><tr><th>VALUE (units 10<sup>-8</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

<table><thead><tr><th>3.56±0.21 OUR AVERAGE</th><th>200</th><th>1 LAI</th><th>05B</th><th>NA48</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>6 ± 2 ± 1</th><th>18</th><th>2 AKAGI</th><th>95</th><th>SPEC</th><th>m<sub>ee</sub> > 470 MeV</th></tr></thead></table>

<table><thead><tr><th>7 ± 3 ± 2</th><th>6</th><th>2 AKAGI</th><th>95</th><th>SPEC</th><th>m<sub>ee</sub> > 470 MeV</th></tr></thead></table>

<table><thead><tr><th>10.4 ± 3.7 ± 1.1</th><th>8</th><th>3 BARR</th><th>95</th><th>NA31</th></tr></thead></table>

<table><thead><tr><th>6 ± 2 ± 1</th><th>18</th><th>AKAGI</th><th>93</th><th>CNTR</th><th>Sup. by AKAGI 95</th></tr></thead></table>

<table><thead><tr><th>4 ± 3</th><th>2</th><th>BARR</th><th>91</th><th>NA31</th><th>Sup. by BARR 95</th></tr></thead></table>

¹LAI 05B uses 1998 and 1999 data. Data are normalized to the observed levels of $K_L^0 \to \pi^+ \pi^- \pi^0$ (π⁰ into Dalitz pair) and PDG 04 values are used for $B(K_L^0 \to \pi^+ \pi^- \pi^0)$ and $B(\pi^0 \to e^+ e^- \gamma)$. The systematic error includes a normalization error of ±0.10.

²Values are for the total branching fraction, acceptance-corrected for the $m_{ee}$ cuts shown.

³Distribution of angles between two $e^+ e^-$ pair planes favors CP = -1 for $K_L^0$.

$$ \Gamma(\pi^0 \mu^+ \mu^-) / \Gamma_{\text{total}} $$

$$ \Gamma_{31}/\Gamma $$

Violates CP in leading order. Test for $\Delta S = 1$ weak neutral current. Allowed by higher-order electroweak interaction.

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead></table>

<table><thead><tr><th>&lt;0.38</th><th>90</th><th>ALAVI-HARATI00D</th><th>KTEV</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>&lt;5.1</th><th>90</th><th>0</th><th>HARRIS</th><th>93</th><th>E799</th></tr></thead></table>

$$ \Gamma(\pi^0 e^+ e^-) / \Gamma_{\text{total}} $$

$$ \Gamma_{32}/\Gamma $$

Violates CP in leading order. Direct and indirect CP-violating contributions are expected to be comparable and to dominate the CP-conserving part. LAI 02B result suggests that CP-violating effects dominate. Test for $\Delta S = 1$ weak neutral current. Allowed by higher-order electroweak interaction.

<table><thead><tr><th>VALUE (units 10<sup>-10</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

<table><thead><tr><th>&lt; 2.8</th><th>90</th><th>1 ALAVI-HARATI04A</th><th>KTEV</th><th>combined result</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>&lt; 3.5</th><th>90</th><th>ALAVI-HARATI04A</th><th>KTEV</th></tr></thead></table>

<table><thead><tr><th>0.047<sup>+0.0022</sup><sub>-0.0018</sub></th><th>90</th><th>2 LAI</th><th>02B</th><th>NA48</th></tr></thead></table>

<table><thead><tr><th>&lt; 5.1</th><th>90</th><th>2</th><th>ALAVI-HARATI01</th><th>KTEV</th></tr></thead></table>

<table><thead><tr><th>0.01 to 0.02</th><th>90</th><th>ALAVI-HARATI09B</th><th>KTEV</th></tr></thead></table>

<table><thead><tr><th>&lt; 43</th><th>90</th><th>0</th><th>HARRIS</th><th>93B</th><th>E799</th></tr></thead></table>

<table><thead><tr><th>&lt; 75</th><th>90</th><th>0</th><th>BARKER</th><th>90</th><th>E731</th></tr></thead></table>

<table><thead><tr><th>&lt; 55</th><th>90</th><th>0</th><th>OHL</th><th>90</th><th>B845</th></tr></thead></table>

<table><thead><tr><th>&lt; 400</th><th>90</th><th>BARR</th><th>88</th><th>NA31</th></tr></thead></table>

<table><thead><tr><th>&lt;3200</th><th>90</th><th>JASTRZEM...</th><th>88</th><th>SPEC</th></tr></thead></table>

¹Combined result of ALAVI-HARATI 04A 1999-2000 data set and ALAVI-HARATI 01 1997 data set.

²LAI 02B uses the absence of a signal in $K_L^0 \to \pi^0 \gamma\gamma$ with $m(\gamma\gamma) < m(\pi^0)$ and their $a_V$ value to predict this value.

$$ \Gamma(\pi^0 \nu\bar{\nu}) / \Gamma_{\text{total}} $$

$$ \Gamma_{33}/\Gamma $$

Violates CP in leading order. Test of direct CP violation since the indirect CP-violating and CP-conserving contributions are expected to be suppressed. Test of $\Delta S = 1$ weak neutral current.

<table><thead><tr><th>VALUE (units 10<sup>-8</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead></table>

<table><thead><tr><th>&lt; 0.49</th><th>90</th><th>1 AHN</th><th>21</th><th>KOTO</th></tr></thead></table>

<table><thead><tr><th>&lt; 0.30</th><th>90</th><th>2 AHN</th><th>19</th><th>KOTO</th></tr></thead></table>