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

<table><tr><td>&lt; 5.1</td><td>90</td><td><sup>3</sup> AHN</td><td>17</td><td>KOTO</td></tr><tr><td>&lt; 2.6</td><td>90</td><td><sup>4</sup> AHN</td><td>10</td><td>K391</td></tr><tr><td>&lt; 6.7</td><td>90</td><td><sup>5</sup> AHN</td><td>08</td><td>K391</td></tr><tr><td>&lt;21</td><td>90</td><td><sup>6</sup> AHN</td><td>06</td><td>K391</td></tr><tr><td>&lt;59</td><td>90</td><td>ALAVI-HARATI100</td><td>00</td><td>KTEV</td></tr></table>

¹ AHN 21 result is based on data collected in 2016, 2017 and 2018, which corresponds to 3.05×10¹⁹ protons on target. A single event sensitivity of (7.20 ± 0.05 ± 0.66)×10⁻¹⁰ was achieved with 3 candidate events observed and total 1.22 ± 0.26 background events.

² AHN 19 result is based on data collected in 2015, which corresponds to 2.2×10¹⁹ protons on target. A single event sensitivity of (1.30 ± 0.01 ± 0.14) × 10⁻⁹ was achieved with no candidate events observed. An upper limit of < 2.4 × 10⁻⁹ at the 90% C.L. for the $K_L → π^0X^0$ decay was also set, where $X^0$ is an invisible particle with a mass of 135 MeV/c².

³ AHN 17 result is based on the first 100 hours of physics running in 2013. One candidate event was observed with an expected background of 0.34 ± 0.16 events. An upper limit of < 3.7 × 10⁻⁸ at the 90% C.L. for the $K_L → π^0X^0$ decay was also set, where $X^0$ is an invisible particle with a mass of 135 MeV/c².

⁴ Obtained combining Run-2 (AHN 08) and Run-3 data.

⁵ Value obtained using data from February to April 2005.

⁶ Value obtained analyzing 10% of data of RUN 1 (performed in 2004).

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

<table><thead><tr><th>VALUE</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><4.1 × 10<sup>-7</sup></td><td>90</td><td>1</td><td>OGATA</td><td>11</td><td>K391</td></tr></tbody></table>

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

<table><tr><td>&lt;4.7 × 10<sup>-5</sup></td><td>90</td><td>2</td><td>NIX</td><td>07</td><td>K391</td></tr></table>

¹ Using 2005 Run-1 data. OGATA 11 also sets a limit on the $K_L^0 → π^0π^0X →$ invisible particles process: the limit on the branching fraction varied from 7.0×10⁻⁷ to 4.0×10⁻⁵ for the mass of X ranging from 50 to 200 MeV/c².

² Observed 1 event with expected background of 0.43 ± 0.35 events. NIX 07 also measured $B(K_L^0 → π^0π^0P) < 1.2 × 10⁻⁶$ at 90% CL, where P is the pseudoscalar particle and $m_P < 100$ MeV.

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

Test of lepton family number conservation.

<table><thead><tr><th>VALUE (units 10<sup>-11</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><4.7</td><td>90</td><td></td><td>AMBROSE</td><td>98B B871</td></tr></tbody></table>

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

<table><tr><td>&lt;9.4</td><td>90</td><td>0</td><td>AKAGI</td><td>95</td><td>SPEC</td></tr><tr><td>&lt;3.9</td><td>90</td><td>0</td><td>ARISAKA</td><td>93</td><td>B791</td></tr><tr><td>&lt;3.3</td><td>90</td><td>0</td><td>1 ARISAKA</td><td>93</td><td>B791</td></tr></table>

¹ This is the combined result of ARISAKA 93 and MATHIAZHAGAN 89.

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

Test of lepton family number conservation.

<table><thead><tr><th>VALUE (units 10<sup>-11</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><4.12</td><td>90</td><td>0</td><td>ALAVI-HARATI03B</td><td>KTEV</td><td></td></tr></tbody></table>

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

<table><tr><td>&lt; 12.3</td><td>90</td><td>0</td><td>1 ALAVI-HARATI01H</td><td>KTEV</td><td>Sup. by ALAVI-HARATI 03B</td></tr><tr><td>&lt;610</td><td>90</td><td>0</td><td>1 GU</td><td>96</td><td>E799</td></tr></table>

¹ Assuming uniform phase space distribution.

$$ \Gamma(\pi^0 \mu^{\pm} e^{\mp}) / \Gamma_{\text{total}} $$

Test of lepton family number conservation.

<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><tbody><tr><td><4.76</td><td>90</td><td></td><td>ABOUZAID</td><td>08C KTEV</td></tr></tbody></table>

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

<table><tr><td>&lt;62</td><td>90</td><td></td><td>ARISAKA</td><td>98</td><td>E799</td></tr></table>

$$ \Gamma(\pi^0 \pi^0 \mu^{\pm} e^{\mp}) / \Gamma_{\text{total}} $$

Test of lepton family number conservation.

<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><tbody><tr><td><1.7</td><td>90</td><td></td><td>ABOUZAID</td><td>20</td><td>KOTO</td></tr></tbody></table>

### Lorentz invariance violating modes

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

<table><thead><tr><th>VALUE</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><1.7 × 10<sup>-7</sup></td><td>90</td><td></td><td>1 SHIMIZU</td><td>20</td><td>KOTO</td></tr></tbody></table>

¹ SHIMIZU 20 uses data collected from 2016 to 2018 at the J-PARC KOTO experiment.

The single event sensitivity is (7.1 ± 0.3 ± 1.6)×10⁻⁸. No candidate event was observed.

See the related review(s):

$V_{ud}$, $V_{us}$ the Cabibbo Angle, and CKM Unitarity

## ENERGY DEPENDENCE OF $K_L^0$ DALITZ PLOT

For discussion, see note on Dalitz plot parameters in the $K^±$ section of the Particle Listings above. For definitions of $a_ν$, $a_t$, $a_u$, and $a_ν$, see the earlier version of the same note in the 1982 edition of this Review published in Physics Letters **111B** 70 (1982).

$$ |\text{matrix element}|^2 = 1 + g\nu + h\nu^2 + j\nu + k\nu^2 + f\nu \\ \text{where } u = (s_3 - s_0) / m_{\pi}^2 \text{ and } v = (s_2 - s_1) / m_{\pi}^2 $$

### LINEAR COEFFICIENT g FOR $K_L^0 → π^+π^-π^0$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.678 ±0.008</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td><td>Error includes scale factor of 1.5. See the ideogram below.</td></tr><tr><td>0.6823 ±0.0044</td><td>±0.0044</td><td>500k</td><td>ANGELOPO...</td><td>98c CPLR</td></tr><tr><td>0.681 ±0.024</td><td></td><td>6499</td><td>CHO</td><td>77 HBC</td></tr><tr><td>0.620 ±0.023</td><td></td><td>4709</td><td>PEACH</td><td>77 HBC</td></tr><tr><td>0.677 ±0.010</td><td></td><td>509k</td><td>MESSNER</td><td>74 ASPK a<sub>ν</sub> = -0.917 ± 0.013</td></tr></tbody></table>

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

<table><tr><td>0.69 ±0.07</td><td>192</td><td><sup>1</sup> BALDO...</td><td>75</td><td>HLBC</td></tr><tr><td>0.590 ±0.022</td><td>56k</td><td><sup>1</sup> BUCHANAN</td><td>75</td><td>SPEC a<sub>u</sub> = -0.277 ± 0.010</td></tr><tr><td>0.619 ±0.027</td><td>20k</td><td><sup>1,2</sup> BISI</td><td>74</td><td>ASPK a<sub>t</sub> = -0.282 ± 0.011</td></tr><tr><td>0.612 ±0.032</td><td></td><td><sup>1</sup> ALEXANDER</td><td>73b</td><td>HBC</td></tr><tr><td>0.73 ±0.04</td><td>3200</td><td><sup>1</sup> BRANDENB...</td><td>73</td><td>HBC</td></tr><tr><td>0.608 ±0.043</td><td>1486</td><td><sup>1</sup> KRENZ</td><td>72</td><td>HLBC a<sub>t</sub> = -0.277 ± 0.018</td></tr><tr><td>0.650 ±0.012</td><td>29k</td><td><sup>1</sup> ALBROW</td><td>70</td><td>ASPK a<sub>ν</sub> = -0.858 ± 0.015</td></tr><tr><td>0.593 ±0.022</td><td>36k</td><td><sup>1,3</sup> BUCHANAN</td><td>70</td><td>SPEC a<sub>u</sub> = -0.278 ± 0.010</td></tr><tr><td>0.664 ±0.056</td><td>4400</td><td><sup>1</sup> SMITH</td><td>70</td><td>OSPK a<sub>t</sub> = -0.306 ± 0.024</td></tr><tr><td>0.400 ±0.045</td><td>2446</td><td><sup>1</sup> BASILE</td><td>68b</td><td>OSPK a<sub>t</sub> = -0.188 ± 0.020</td></tr><tr><td>0.649 ±0.044</td><td>1350</td><td><sup>1</sup> HOPKINS</td><td>67</td><td>HBC a<sub>t</sub> = -0.294 ± 0.018</td></tr><tr><td>0.428 ±0.055</td><td>1198</td><td><sup>1</sup> NEFKENS</td><td>67</td><td>OSPK a<sub>u</sub> = -0.204 ± 0.025</td></tr></table>

¹ Quadratic dependence required by some experiments. (See sections on “QUADRATIC COEFFICIENT h” and “QUADRATIC COEFFICIENT k” below.) Correlations prevent us from averaging results of fits not including g, h, and k terms.

² BISI 74 value comes from quadratic fit with quad. term consistent with zero. g error is thus larger than if linear fit were used.

³ BUCHANAN 70 result revised by BUCHANAN 75 to include radiative correlations and to use more reliable $K_L^0$ momentum spectrum of second experiment (had same beam).

WEIGHTED AVERAGE 0.678±0.008 (Error scaled by 1.5)

<figure><img src="image_514.png" /></figure>

(Confidence Level = 0.076)

Linear coeff. g for $K_L^0 → π^+π^-π^0$ matrix element squared

### QUADRATIC COEFFICIENT h FOR $K_L^0 → π^+π^-π^0$

See notes in section “LINEAR COEFFICIENT g FOR $K_L^0 → π^+π^-π^0$ | MATRIX ELEMENT|^2” above.

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.076 ±0.006</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td></tr><tr><td>0.061 ±0.004</td><td>±0.015</td><td>500k</td><td>ANGELOPO...</td><td>98c CPLR</td></tr><tr><td>0.095 ±0.032</td><td></td><td>6499</td><td>CHO</td><td>77 HBC</td></tr><tr><td>0.048 ±0.036</td><td></td><td>4709</td><td>PEACH</td><td>77 HBC</td></tr><tr><td>0.079 ±0.007</td><td></td><td>509k</td><td>MESSNER</td><td>74 ASPK</td></tr></tbody></table>

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

<table><tr><td>-0.011 ±0.018</td><td>29k</td><td><sup>1</sup> ALBROW</td><td>70</td><td>ASPK</td></tr><tr><td>0.043 ±0.052</td><td>4400</td><td><sup>1</sup> SMITH</td><td>70</td><td>OSPK</td></tr></table>

¹ Quadratic coefficients h and k required by some experiments. (See section on “QUADRATIC COEFFICIENT k” below.) Correlations prevent us from averaging results of fits not including g, h, and k terms.

### QUADRATIC COEFFICIENT k FOR $K_L^0 → π^+π^-π^0$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.0099 ±0.0015</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td></tr><tr><td>0.0104 ±0.0017</td><td>±0.0024</td><td>500k</td><td>ANGELOPO...</td><td>98c CPLR</td></tr><tr><td>0.024 ±0.010</td><td></td><td>6499</td><td>CHO</td><td>77 HBC</td></tr><tr><td>-0.008 ±0.012</td><td></td><td>4709</td><td>PEACH</td><td>77 HBC</td></tr><tr><td>0.0097 ±0.0018</td><td></td><td>509k</td><td>MESSNER</td><td>74 ASPK</td></tr></tbody></table>
**LINEAR COEFFICIENT j FOR K<sup>0</sup><sub>L</sub> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup> (CP-VIOLATING TERM)**
Listed in CP-violation section below.

**QUADRATIC COEFFICIENT f FOR K<sup>0</sup><sub>L</sub> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup> (CP-VIOLATING TERM)**
Listed in CP-violation section below.

**QUADRATIC COEFFICIENT h FOR K<sup>0</sup><sub>L</sub> → π<sup>0</sup>π<sup>0</sup>π<sup>0</sup>**
We do not average measurements that do not account for the effect of final state rescattering.

<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>+0.59 ±0.20 ±1.16</td><td>68M</td><td>1 ABOUZAID</td><td>08A KTEV</td></tr></tbody></table>

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

<table><tbody><tr><td>-6.1 ±0.9 ±0.5</td><td>14.7M</td><td>2 LAI</td><td>01B NA48</td></tr><tr><td>-3.3 ±1.1 ±0.7</td><td>5M</td><td>2,3 SOMALWAR</td><td>92 E731</td></tr></tbody></table>

¹Result obtained using C13pl model of CABIBBO 05 to include ππ rescattering effects. The systematic error includes an external error of 1.06 × 10⁻³ from the parametrization input of (a₀-a₂) m<sub>π⁺</sub> = 0.268 ± 0.017 from BATLEY 06b.

²LAI 01B and SOMALWAR 92 results do not include ππ final state rescattering effects.

³SOMALWAR 92 chose m<sub>π⁺</sub> as normalization to make it compatible with the Particle Data Group K<sup>0</sup><sub>L</sub> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup> definitions.

## K<sup>0</sup><sub>L</sub> FORM FACTORS

For discussion, see note on form factors in the K<sup>±</sup> section of the Particle Listings above.

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

f<sub>+</sub> and f<sub>-</sub> are form factors for the vector matrix element.

f<sub>S</sub> and f<sub>T</sub> refer to the scalar and tensor term.

$$f_0(t) = f_+(t) + f_-(t) t / (m^2 K_0^0 - m_{\pi^+}^2).$$

t = momentum transfer to the π.

λ<sub>+</sub> and λ<sub>0</sub> are the linear expansion coefficients of f<sub>+</sub> and f<sub>0</sub>:

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

For quadratic expansion

$$f_{+}(t) = f_{+}(0) (1 + \lambda_{+}^{\prime} t / m_{\pi^{+}}^{2} + \frac{\lambda_{+}^{\prime\prime}}{2} t^{2} / m_{\pi^{+}}^{4})$$

as used by KTeV. If there is a non-vanishing quadratic term, then λ<sub>+</sub>.

represents an average slope, which is then different from λ'<sub>+</sub>.

NA48 (K<sub>e3</sub>) and ISTRA quadratic expansion coefficients are converted with

$$\lambda'_{+} PDG = \lambda_{+} \frac{m_{\pi^{+}}}{m_{\pi^{0}}} NA48 \text{ and } \lambda''_{+} PDG = 2 \lambda'_{+} NA48$$

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

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

ISTRA linear expansion coefficients are converted with

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

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<sub>V</sub> and M<sub>S</sub> are the vector and scalar pole masses.

The dispersive parametrization is

$$f_{+}(t) = f_{+}(0) \exp\left[\frac{t}{m_{\pi}^{2}}(\Lambda_{+} + H(t))\right];$$

$$f_{0}(t) = f_{+}(0) \exp\left[\frac{t}{m_{K}^{2} - m_{\pi}^{2}}(\ln[C] - G(t))\right],$$

where Λ<sub>+</sub> is the slope parameter and ln[C] = ln[ f<sub>0</sub> (m<sub>K</sub><sup>2</sup> - m<sub>π</sub><sup>2</sup> ) ]

is the logarithm of the scalar form factor at the Callan-Treiman point.

H(t) and G(t) are dispersive integrals.

The following abbreviations are used:

DP = Dalitz plot analysis.

PI = π spectrum analysis.

MU = μ spectrum analysis.

POL = μ polarization analysis.

BR = K<sup>0</sup><sub>μ3</sub>/K<sup>0</sup><sub>e3</sub> branching ratio analysis.

E = positron or electron spectrum analysis.

RC = radiative corrections.

**λ<sub>+</sub> (LINEAR ENERGY DEPENDENCE OF f<sub>+</sub> IN K<sup>0</sup><sub>e3</sub> DECAY)**

For radiative correction of K<sup>0</sup><sub>e3</sub> DP, see GINSBERG 67, BECHERRAWY 70, CIRIGLIANO 02, CIRIGLIANO 04, and ANDRE 07. Results labeled OUR FIT are discussed in the review “K<sup>±</sup><sub>μ3</sub> and K<sup>0</sup><sub>μ3</sub> Form Factors” in the K<sup>±</sup> Listings. For earlier, lower statistics results, see the 2004 edition of this review, Physics Letters B592 1 (2004).

<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></table>

².82 ±0.04 OUR FIT Error includes scale factor of 1.1. Assuming μ-e universality

².85 ±0.14 OUR AVERAGE Error includes scale factor of 1.1. Assuming μ-e universality

2.86 ±0.05 ±0.04 2M AMBROSINO 06D KLOE

2.832±0.037±0.043 1.9M ALEXOPOU... 04A KTEV PI, no μ = e

2.88 ±0.04 ±0.11 5.6M 1 LAI 04C NA48 DP

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

<table><tbody><tr><td>2.84 ±0.07 ±0.13</td><td>5.6M</td><td>2 LAI</td><td>04C NA48 DP</td></tr><tr><td>2.45 ±0.12 ±0.22</td><td>366k</td><td>APOSTOLA...</td><td>00 CPLR DP</td></tr><tr><td>3.06 ±0.34</td><td>74k</td><td>BIRULEV</td><td>81 SPEC DP</td></tr><tr><td>3.12 ±0.25</td><td>500k</td><td>GJESDAL</td><td>76 SPEC DP</td></tr><tr><td>2.70 ±0.28</td><td>25k</td><td>BLUMENTHAL75</td><td>SPEC DP</td></tr></tbody></table>

¹Results from linear fit and assuming only vector and axial couplings.

²Results from linear fit with |f<sub>S</sub>/f<sub>+</sub>| and |f<sub>T</sub>/f<sub>+</sub>| free.

**λ<sub>+</sub> (LINEAR ENERGY DEPENDENCE OF f<sub>+</sub> IN K<sup>0</sup><sub>μ3</sub> DECAY)**

Results labeled OUR FIT are discussed in the review “K<sup>±</sup><sub>μ3</sub> and K<sup>0</sup><sub>μ3</sub> Form Factors” in the K<sup>±</sup> Listings. For earlier, lower statistics results, see the 2004 edition of this review, Physics Letters B592 1 (2004).

<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>2.82 ±0.04 OUR FIT</td><td>Error includes scale factor of 1.1. Assuming μ-e universality</td><td></td><td></td><td></td></tr><tr><td>2.71 ±0.10 OUR FIT</td><td>Error includes scale factor of 1.4. Not assuming μ-e universality</td><td></td><td></td><td></td></tr><tr><td>2.67 ±0.06 ±0.08</td><td>2.3M</td><td>1 LAI</td><td>07A NA48 DP</td><td></td></tr><tr><td>2.745 ±0.088 ±0.063</td><td>1.5M</td><td>ALEXOPOU...</td><td>04A KTEV DP, no μ = e</td><td></td></tr><tr><td>2.813 ±0.051</td><td>3.4M</td><td>ALEXOPOU...</td><td>04A KTEV PI, DP, μ = e</td><td></td></tr><tr><td>3.0 ±0.3</td><td>1.6M</td><td>DONALDSON</td><td>74B SPEC DP</td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>4.27 ±0.44</td><td>150k</td><td>BIRULEV</td><td>81 SPEC DP</td></tr></tbody></table>

¹LAI 07A gives a correlation -0.40 between their λ<sub>0</sub> and λ<sub>+</sub> measurements.

**λ<sub>0</sub> (LINEAR ENERGY DEPENDENCE OF f<sub>0</sub> IN K<sup>0</sup><sub>μ3</sub> DECAY)**

Wherever possible, we have converted the above values of ξ(0) into values of λ<sub>0</sub> using the associated λ'<sub>+</sub> and dξ(0)/dλ<sub>+</sub>. Results labeled OUR FIT are discussed in the review “K<sup>±</sup><sub>μ3</sub> and K<sup>0</sup><sub>μ3</sub> Form Factors” in the K<sup>±</sup> Listings. For earlier, lower statistics results, see the 2004 edition of this review, Physics Letters B592 1 (2004).

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>dfλ<sub>0</sub>/dλ<sub>+</sub></th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.38 ±0.10 OUR FIT</td><td>Error includes scale factor of 2.2. Assuming μ-e universality</td><td></td><td></td><td></td><td></td></tr><tr><td>1.42 ±0.23 OUR FIT</td><td>Error includes scale factor of 2.8. Not assuming μ-e universality</td><td></td><td></td><td></td><td></td></tr><tr><td>1.17 ±0.07 ±0.10</td><td>2.3M</td><td>1 LAI</td><td>07A NA48 DP</td><td></td><td></td></tr><tr><td>1.657 ±0.125</td><td>-0.44</td><td>1.5M</td><td>2 ALEXOPOU...</td><td>04A KTEV DP, no μ = e</td><td></td></tr><tr><td>1.635 ±0.121</td><td>-0.85</td><td>3.4M</td><td>3 ALEXOPOU...</td><td>04A KTEV PI, DP, μ = e</td><td></td></tr><tr><td>+1.9 ±0.4</td><td>-0.47</td><td>1.6M</td><td>4 DONALDSON</td><td>74B SPEC DP</td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>3.41 ±0.67</td><td>unknown</td><td>150k</td><td>5 BIRULEV</td><td>81 SPEC DP</td></tr></tbody></table>

¹LAI 07A gives a correlation -0.40 between their λ<sub>0</sub> and λ<sub>+</sub> measurements.

²ALEXOPOULOS 04A gives a correlation -0.36 between their λ<sub>0</sub> and λ<sub>+</sub> measurements.

³ALEXOPOULOS 04A gives a correlation -0.36 between their λ<sub>0</sub> and λ<sub>+</sub> measurements.

⁴DONALDSON 74B dλ<sub>0</sub>/dλ<sub>+</sub> obtained from figure 18.

⁵BIRULEV 81 gives dλ<sub>0</sub>/dλ<sub>+</sub> = -1.5, giving an unreasonably narrow error ellipse which dominates all other results. We use dλ<sub>0</sub>/dλ<sub>+</sub> = 0.

**λ'<sub>+</sub> (LINEAR K<sup>0</sup><sub>e3</sub> FORM FACTOR FROM QUADRATIC FIT)**

<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></table>

².40 ±0.12 OUR FIT Error includes scale factor of 1.1. Assuming μ-e universality

².49 ±0.13 OUR FIT Error includes scale factor of 1.1. Not assuming μ-e universality

².48 ±0.17 OUR AVERAGE Error includes scale factor of 1.5. See the ideogram below.

<table><tbody><tr><td>2.55 ±0.15 ±0.10</td><td>2M</td><td>1 AMBROSINO</td><td>06D KLOE</td></tr></tbody></table>

<table><tbody><tr><td>2.167±0.137±0.143</td><td>1.9M</td><td>2 ALEXOPOU...</td><td>04A KTEV PI, no μ = e</td></tr></tbody></table>

<table><tbody><tr><td>2.80 ±0.19 ±0.15</td><td>5.6M</td><td>3 LAI</td><td>04C NA48 DP</td></tr></tbody></table>

¹We use AMBROSINO 06D result in the fit not assuming μ-e universality. This result enters the fit assuming μ-e universality via AMBROSINO 07C measurement of λ'<sub>+</sub> in K<sub>μ3</sub> decays. AMBROSINO 06D gives a correlation -0.95 between their λ'<sub>+</sub> and λ''<sub>+</sub>.

²ALEXOPOULOS 04A gives a correlation -0.97 between their λ'<sub>+</sub> and λ''<sub>+</sub>.

³For LAI 04C we calculate a correlation -0.88 between their λ'<sub>+</sub> and λ''<sub>+</sub>.

WEIGHTED AVERAGE
2.48±0.17 (Error scaled by 1.5)

<figure><img src="image_515.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.

**λ'<sub>+</sub> (LINEAR K<sup>0</sup><sub>e3</sub> FORM FACTOR FROM QUADRATIC FIT) (units 10<sup>-2</sup>)**
$\lambda''_+(\text{QUADRATIC } K_{e3}^0 \text{ FORM FACTOR})$

<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><b>0.20</b> ±0.05</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 1.2. Assuming μ-e universality</td><td></td><td></td></tr><tr><td><b>0.16</b> ±0.05</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 1.1. Not assuming μ-e universality</td><td></td><td></td></tr><tr><td><b>0.17</b> ±0.07</td><td><b>OUR AVERAGE</b></td><td>Error includes scale factor of 1.5. See the ideogram below.</td><td></td><td></td></tr><tr><td>0.14 ±0.07</td><td>±0.04</td><td>2M</td><td>1 AMBROSINO</td><td>06D KLOE</td></tr><tr><td>0.287 ±0.057</td><td>±0.053</td><td>1.9M</td><td>2 ALEXOPOU...</td><td>04A KTEV PI, no μ = e</td></tr><tr><td>0.04 ±0.08</td><td>±0.04</td><td>5.6M</td><td>3,4 LAI</td><td>04C NA48 DP</td></tr></tbody></table>

WEIGHTED AVERAGE
0.17±0.07 (Error scaled by 1.5)

<figure><img src="image_516.png" /><figcaption>$\lambda''_+(\text{QUADRATIC } K_{e3}^0 \text{ FORM FACTOR})$ (units $10^{-2}$)</figcaption></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.

$\lambda'_+(\text{LINEAR } K_{\mu 3}^0 \text{ FORM FACTOR FROM QUADRATIC FIT})$

<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><b>2.40</b> ±0.12</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 1.2. Assuming μ-e universality</td><td></td><td></td></tr><tr><td><b>1.89</b> ±0.24</td><td><b>OUR FIT</b></td><td>Not assuming μ-e universality</td><td></td><td></td></tr><tr><td>2.23 ±0.98</td><td>±0.37</td><td>1.8M</td><td>1 AMBROSINO</td><td>07C KLOE no μ = e</td></tr><tr><td>2.56 ±0.15</td><td>±0.09</td><td>3.8M</td><td>1 AMBROSINO</td><td>07C KLOE μ = e</td></tr><tr><td>2.05 ±0.22</td><td>±0.24</td><td>2.3M</td><td>1 LAI</td><td>07A NA48 DP</td></tr><tr><td>1.703 ±0.319</td><td>±0.177</td><td>1.5M</td><td>1 ALEXOPOU...</td><td>04A KTEV DP, no μ = e</td></tr><tr><td>2.064 ±0.175</td><td></td><td>3.4M</td><td>1 ALEXOPOU...</td><td>04A KTEV PI, DP, μ = e</td></tr></tbody></table>

$\lambda''_+(\text{QUADRATIC } K_{\mu 3}^0 \text{ FORM FACTOR})$

<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><b>0.20</b> ±0.05</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 1.2. Assuming μ-e universality</td><td></td><td></td></tr><tr><td><b>0.37</b> ±0.12</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 1.3. Not assuming μ-e universality</td><td></td><td></td></tr><tr><td>0.48 ±0.49</td><td>±0.16</td><td>1.8M</td><td>1 AMBROSINO</td><td>07C KLOE no μ = e</td></tr><tr><td>0.15 ±0.07</td><td>±0.04</td><td>3.8M</td><td>1 AMBROSINO</td><td>07C KLOE μ = e</td></tr><tr><td>0.26 ±0.09</td><td>±0.10</td><td>2.3M</td><td>1 LAI</td><td>07A NA48 DP</td></tr><tr><td>0.443 ±0.131</td><td>±0.072</td><td>1.5M</td><td>1 ALEXOPOU...</td><td>04A KTEV DP, no μ = e</td></tr><tr><td>0.320 ±0.069</td><td></td><td>3.4M</td><td>1 ALEXOPOU...</td><td>04A KTEV PI, DP, μ = e</td></tr></tbody></table>

$\lambda_0(\text{LINEAR } \ell_0 K_{\mu 3}^0 \text{ FORM FACTOR FROM QUADRATIC FIT})$

<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><b>1.16</b> ±0.09</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 1.2. Assuming μ-e universality</td><td></td><td></td></tr><tr><td><b>1.07</b> ±0.14</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 1.3. Not assuming μ-e universality</td><td></td><td></td></tr><tr><td>0.91 ±0.59</td><td>±0.26</td><td>1.8M</td><td>1 AMBROSINO</td><td>07C KLOE no μ = e</td></tr><tr><td>1.54 ±0.18</td><td>±0.13</td><td>3.8M</td><td>2 AMBROSINO</td><td>07C KLOE μ = e</td></tr><tr><td>0.95 ±0.11</td><td>±0.08</td><td>2.3M</td><td>3 LAI</td><td>07A NA48 DP</td></tr><tr><td>1.281 ±0.136</td><td>±0.122</td><td>1.5M</td><td>4 ALEXOPOU...</td><td>04A KTEV DP, no μ = e</td></tr><tr><td>1.372 ±0.131</td><td></td><td>3.4M</td><td>5 ALEXOPOU...</td><td>04A KTEV PI, DP, μ = e</td></tr></tbody></table>

$$ \begin{array}{c} \lambda'_+ \\ \lambda''_+ \\ \lambda_0 \end{array} \begin{array}{c} \lambda''_+ \\ -0.97 \\ 0.81 \end{array} \begin{array}{c} 1 \\ -0.91 \end{array} $$

$$ \begin{array}{c} \lambda'_+ \\ \lambda''_+ \\ \lambda_0 \end{array} \begin{array}{c} \lambda''_+ \\ -0.95 \\ 0.29 \end{array} \begin{array}{c} 1 \\ -0.38 \end{array} $$

$$ \begin{array}{c} \lambda'_+ \\ \lambda''_+ \\ \lambda_0 \end{array} \begin{array}{c} \lambda''_+ \\ -0.96 \\ 0.63 \end{array} \begin{array}{c} 1 \\ -0.73 \end{array} $$

$$ \begin{array}{ccc} \lambda'_+ & \lambda''_+ & \lambda_0 \\ \lambda'_+ & 1 & \\ \lambda''_+ & -0.96 & 1 \\ \lambda_0 & 0.65 & -0.75 & 1 \end{array} $$

$$ \begin{array}{ccc} \lambda'_+ & \lambda''_+ & \lambda_0 \\ \lambda'_+ & 1 & \\ \lambda''_+ & -0.97 & 1 \\ \lambda_0 & 0.34 & -0.44 & 1 \end{array} $$

$M_V^\mu (\text{POLE MASS FOR } K_{e3}^0 \text{ DECAY})$

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>878</b> ±6</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 1.1. Assuming μ-e universality</td><td></td><td></td></tr><tr><td><b>875</b> ±5</td><td><b>OUR AVERAGE</b></td><td></td><td></td><td></td></tr><tr><td>870 ±6</td><td>±7</td><td>2M</td><td>AMBROSINO</td><td>06D KLOE</td></tr><tr><td>881.03 ±5.12</td><td>±4.94</td><td>1.9M</td><td>ALEXOPOU...</td><td>04A KTEV PI, no μ = e</td></tr><tr><td>859 ±18</td><td></td><td>5.6M</td><td>LAI</td><td>04C NA48</td></tr></tbody></table>

$M_V^\mu (\text{POLE MASS FOR } K_{\mu 3}^0 \text{ DECAY})$

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>878</b> ±6</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 1.1. Assuming μ-e universality</td><td></td><td></td></tr><tr><td><b>900</b> ±21</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 1.7. Not assuming μ-e universality</td><td></td><td></td></tr><tr><td>905 ±9</td><td>±17</td><td>2.3M</td><td>1 LAI</td><td>07A NA48 DP</td></tr><tr><td>889.19 ±12.81</td><td>±9.92</td><td>1.5M</td><td>1 ALEXOPOU...</td><td>04A KTEV PI, no μ = e</td></tr><tr><td>882.32 ±6.54</td><td></td><td>3.4M</td><td>1 ALEXOPOU...</td><td>04A KTEV PI, DP, μ = e</td></tr></tbody></table>

$M_S^\mu (\text{POLE MASS FOR } K_{\mu 3}^0 \text{ DECAY})$

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>1250</b> ±90</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 2.6. Assuming μ-e universality</td><td></td><td></td></tr><tr><td><b>1220</b> ±80</td><td><b>OUR FIT</b></td><td>Error includes scale factor of 2.3. Not assuming μ-e universality</td><td></td><td></td></tr><tr><td>1400 ±46</td><td>±53</td><td>2.3M</td><td>1 LAI</td><td>07A NA48 DP</td></tr><tr><td>1167.14 ±28.30</td><td>±31.04</td><td>1.5M</td><td>2 ALEXOPOU...</td><td>04A KTEV PI, no μ = e</td></tr><tr><td>1173.80 ±39.47</td><td></td><td>3.4M</td><td>3 ALEXOPOU...</td><td>04A KTEV PI, DP, μ = e</td></tr></tbody></table>

$\Lambda_+(\text{DISPERSIVE VECTOR FORM FACTOR FOR } K_{\mu 3}^0 \text{ DECAY})$

See the review on "$K_{\ell 3}^\pm$ and $K_{\mu 3}^0$ Form Factors" for details of the dispersive parametrization.

<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><b>2.51</b> ±0.06</td><td><b>OUR AVERAGE</b></td><td>Error includes scale factor of 1.5. See the ideogram below.</td><td></td><td></td></tr><tr><td>2.509 ±0.035</td><td>±0.043</td><td>3.4M</td><td>1 ABOUZAID</td><td>10 KTEV μ = e</td></tr><tr><td>2.57 ±0.04</td><td>±0.04</td><td>3.8M</td><td>2 AMBROSINO</td><td>07C KLOE μ = e</td></tr><tr><td>2.33 ±0.05</td><td>±0.08</td><td>2.3M</td><td>3 LAI</td><td>07A NA48 DP</td></tr></tbody></table>

WEIGHTED AVERAGE
2.51±0.06 (Error scaled by 1.5)

<figure><img src="image_517.png" /><figcaption>$\Lambda_+$ (DISPERSIVE VECTOR FORM FACTOR FOR $K_{\mu 3}^0$ DECAY) (units</figcaption></figure>

<footnote n="1">¹ We use AMBROSINO 06d result in the fit not assuming $\mu-e$ universality. This result enters the fit assuming $\mu-e$ universality via AMBROSINO 07c measurement of $\lambda''_+$ in $K_{\mu 3}$ decays. AMBROSINO 06d gives a correlation -0.95 between their $\lambda'_+$ and $\lambda''_+$.</footnote>

<footnote n="2">² ALEXOPOULOS 04A gives a correlation -0.97 between their $\lambda'_+$ and $\lambda''_+$.</footnote>

<footnote n="3">³ Values doubled to agree with PDG conventions described above.</footnote>

<footnote n="4">⁴ LAI 04C gives a correlation -0.88 between their $\lambda'_+$ and $\lambda''_+$.</footnote>

<footnote n="1">¹ See section $\lambda_0$ below for correlations.</footnote>

<footnote n="1">¹ See section $\lambda_0$ below for correlations.</footnote>

<footnote n="1">¹ AMBROSINO 07c, not assuming $\mu-e$ universality, gives a correlation matrix</footnote>

<footnote n="2">² AMBROSINO 07c, assuming $\mu-e$ universality, gives a correlation matrix</footnote>

<footnote n="3">³ LAI 07a gives a correlation matrix</footnote>

<footnote n="4">⁴ ALEXOPOULOS 04A, not assuming $\mu-e$ universality, gives a correlation matrix</footnote>

<footnote n="5">⁵ ALEXOPOULOS 04A, assuming $\mu-e$ universality, gives a correlation matrix</footnote>

<footnote n="1">¹ See section $M_S^\mu$ below for correlations.</footnote>

<footnote n="1">¹ LAI 07a gives a correlation -0.47 between their $M_S^\mu$ and $M_V^\mu$ measurements, not assuming $\mu-e$ universality.</footnote>

<footnote n="2">² ALEXOPOULOS 04A gives a correlation -0.46 between their $M_S^\mu$ and $M_V^\mu$ and measurements, not assuming $\mu-e$ universality.</footnote>

<footnote n="3">³ ALEXOPOULOS 04A gives a correlation -0.40 between their $M_S^\mu$ and $M_V^\mu$ and measurements, assuming $\mu-e$ universality.</footnote>

<footnote n="1">¹ Obtained from a sample of 1.9 M $K_{e3}$ and 1.5 M $K_{\mu 3}$. The correlation between $\Lambda_+$ and $\ln(C)$ is -0.269.</footnote>

<footnote n="2">² AMBROSINO 07c results include 2M $K_{e3}$ events from AMBROSINO 06d. The correlation between $\Lambda_+$ and $\ln(C)$ is -0.26.</footnote>

<footnote n="3">³ LAI 07a gives a correlation -0.44 between their $\Lambda_+$ and $\ln(C)$ measurements.</footnote>

<footnote>$10^{-2}$)</footnote>
In(C) (DISPERSIVE SCALAR FORM FACTOR FOR K<sup>0</sup><sub>μ3</sub> DECAY)

See the review on "K<sup>±</sup><sub>3</sub> and K<sup>0</sup><sub>3</sub> Form Factors" for details of the dispersive parametrization.

<table><thead><tr><th>VALUE (units 10<sup>-1</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>1.75 ±0.18</b></td><td><b>OUR AVERAGE</b></td><td colspan="3">Error includes scale factor of 2.0. See the ideogram below.</td></tr><tr><td>1.915 ±0.078 ±0.094</td><td>3.4M</td><td>1 ABOUZAID</td><td>10 KTEV</td><td>μ = e</td></tr><tr><td>2.04 ±0.19 ±0.15</td><td>3.8M</td><td>2 AMBROSINO</td><td>07C KLOE</td><td>μ = e</td></tr><tr><td>1.438 ±0.080 ±0.112</td><td>2.3M</td><td>3 LAI</td><td>07A NA48</td><td>DP</td></tr></tbody></table>

¹Obtained from a sample of 1.9 M K<sub>e3</sub> and 1.5 M K<sub>μ3</sub>. The correlation between Λ<sub>+</sub> and ln(C) is -0.269.

²AMBROSINO 07c results include 2M K<sub>e3</sub> events from AMBROSINO 06d. We convert (Λ<sub>+</sub>, Λ<sub>0</sub>) to (Λ<sub>+</sub>, ln(C)) parametrization using ln(C) = (Λ<sub>0</sub> · 11.713 + 0.0398) ± 0.0041, where the error is due to theory parametrization of the form factor. The correlation between Λ<sub>+</sub> and ln(C) is -0.26.

³LAI 07A gives a correlation -0.44 between their Λ<sub>+</sub> and ln(C) measurements.

<figure><img src="image_518.png" /></figure>

In(C) (DISPERSIVE SCALAR FORM FACTOR FOR K<sup>0</sup><sub>μ3</sub> DECAY) (units 10<sup>-1</sup>)

a₁(t₀, Q²) FORM FACTOR PARAMETER

See HILL 06 for a definition of this parameter.

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>1.023 ± 0.028 ± 0.029</td><td>2M</td><td>1 ABOUZAID</td><td>06C KTEV</td></tr></tbody></table>

¹Q² = 2 GeV², t₀ = 0.49 (mK - mπ)². Correlation between a₁ and a₂: ρ₁₂ = -0.064.

a₂(t₀, Q²) FORM FACTOR PARAMETER

See HILL 06 for a definition of this parameter.

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>0.75 ± 1.58 ± 1.47</td><td>2M</td><td>1 ABOUZAID</td><td>06C KTEV</td></tr></tbody></table>

¹Q² = 2 GeV², t₀ = 0.49 (mK - mπ)². Correlation between a₁ and a₂: ρ₁₂ = -0.064.

|f<sub>S</sub>/f<sub>+</sub>| FOR K<sup>0</sup><sub>e3</sub> DECAY

Ratio of scalar to f<sub>+</sub> 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>COMMENT</th></tr></thead><tbody><tr><td>1.5<sup>+0.7</sup><sub>-1.0</sub> ± 1.2</td><td>5.6M</td><td>1 LAI</td><td>04C NA48</td><td></td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;9.5</td><td>95</td><td>18k</td><td>HILL</td><td>78</td><td>STRC</td></tr><tr><td>&lt;7.</td><td>68</td><td>48k</td><td>BIRULEV</td><td>76</td><td>SPEC</td><td>See also BIRULEV 81</td></tr><tr><td>&lt;4.</td><td>68</td><td>25k</td><td>BLUMENTHAL75</td><td>SPEC</td><td></td></tr></tbody></table>

¹Results from linear fit with |f<sub>S</sub>/f<sub>+</sub>| and |f<sub>T</sub>/f<sub>+</sub>| free.

|f<sub>T</sub>/f<sub>+</sub>| FOR K<sup>0</sup><sub>e3</sub> DECAY

Ratio of tensor to f<sub>+</sub> 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>COMMENT</th></tr></thead><tbody><tr><td>5<sup>+3</sup><sub>-4</sub> ± 3</td><td>5.6M</td><td>1 LAI</td><td>04C NA48</td><td></td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;40.</td><td>95</td><td>18k</td><td>HILL</td><td>78</td><td>STRC</td></tr><tr><td>&lt;34.</td><td>68</td><td>48k</td><td>BIRULEV</td><td>76</td><td>SPEC</td><td>See also BIRULEV 81</td></tr><tr><td>&lt;23.</td><td>68</td><td>25k</td><td>BLUMENTHAL75</td><td>SPEC</td><td></td></tr></tbody></table>

¹Results from linear fit with |f<sub>S</sub>/f<sub>+</sub>| and |f<sub>T</sub>/f<sub>+</sub>| free.

|f<sub>T</sub>/f<sub>+</sub>| FOR K<sup>0</sup><sub>μ3</sub> DECAY

Ratio of tensor to f<sub>+</sub> couplings.

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>12. ± 12.</td><td>BIRULEV</td><td>81 SPEC</td></tr></tbody></table>

α<sub>K*</sub> DECAY FORM FACTOR FOR K<sub>L</sub> → ℓ<sup>+</sup>ℓ<sup>-</sup>γ, K<sup>0</sup><sub>L</sub> → ℓ<sup>+</sup>ℓ<sup>-</sup>ℓ<sup>+</sup>ℓ<sup>-</sup>γ
Average of all α<sub>K*</sub> measurements (from each of three datablocks following this one)
assuming lepton universality.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th></tr></thead><tbody><tr><td>-0.205 ± 0.022</td><td>OUR AVERAGE</td></tr></tbody></table>

<figure><img src="image_519.png" /></figure>

α<sub>K*</sub> DECAY FORM FACTOR FOR K<sub>L</sub> → ℓ<sup>+</sup>ℓ<sup>-</sup>γ, K<sup>0</sup><sub>L</sub> → ℓ<sup>+</sup>ℓ<sup>-</sup>ℓ<sup>+</sup>ℓ<sup>-</sup>γ

α<sub>K*</sub> DECAY FORM FACTOR FOR K<sub>L</sub> → e<sup>+</sup>e<sup>-</sup>γ

α<sub>K*</sub> is the constant in the model of BERGSTROM 83 which measures the relative strength of the vector-vector transition K<sub>L</sub> → K<sup>*</sup>γ with K<sup>*</sup> → ρ, ω, φ → γ* and the pseudoscalar-pseudoscalar transition K<sub>L</sub> → π, η, η', η'' → γγ*.

The data in this block is included in the average printed for a previous datablock.

-0.217 ± 0.034 OUR AVERAGE Error includes scale factor of 2.4.

<table><tbody><tr><td>-0.207 ± 0.012 ± 0.009</td><td>83k</td><td>1 ABOUZAID</td><td>07B KTEV</td></tr><tr><td>-0.36 ± 0.06 ± 0.02</td><td>6864</td><td>FANTI</td><td>99B NA48</td></tr><tr><td>-0.28 ± 0.13</td><td></td><td>BARR</td><td>90B NA31</td></tr><tr><td>-0.280 ± 0.099</td><td></td><td>OHL</td><td>90B B845</td></tr></tbody></table>

¹ABOUZAID 07B measures C·α<sub>K*</sub> = -0.517 ± 0.030 ± 0.022. We assume C = 2.5, as in all other measurements.

α<sub>K*</sub> DECAY FORM FACTOR FOR K<sub>L</sub> → μ<sup>+</sup>μ<sup>-</sup>γ

α<sub>K*</sub> is the constant in the model of BERGSTROM 83 described in the previous section.

The data in this block is included in the average printed for a previous datablock.

-0.158 ± 0.027 OUR AVERAGE

<table><tbody><tr><td>-0.160 ± 0.026</td><td>9100</td><td>ALAVI-HARATI01G</td><td>KTEV</td></tr><tr><td>-0.04 ± 0.24</td><td></td><td>FANTI</td><td>97 NA48</td></tr></tbody></table>

α<sub>K*</sub> eff DECAY FORM FACTOR FOR K<sub>L</sub> → e<sup>+</sup>e<sup>-</sup>e<sup>+</sup>e<sup>-</sup>

α<sub>K*</sub> eff is the parameter describing the relative strength of an intermediate pseudoscalar decay amplitude and a vector meson decay amplitude in the model of BERGSTROM 83. It takes into account both the radiative effects and the form factor. Since there are two e<sup>+</sup>e<sup>-</sup> pairs here compared with one in e<sup>+</sup>e<sup>-</sup>γ decays, a factorized expression is used for the e<sup>+</sup>e<sup>-</sup>e<sup>+</sup>e<sup>-</sup> decay form factor.

The data in this block is included in the average printed for a previous datablock.

-0.14 ± 0.16 ± 0.15 441 ALAVI-HARATI01D KTEV

α<sub>DIP</sub> DECAY FORM FACTOR FOR K<sup>0</sup><sub>L</sub> → ℓ<sup>+</sup>ℓ<sup>-</sup>γ, K<sup>0</sup><sub>L</sub> → ℓ<sup>+</sup>ℓ<sup>-</sup>ℓ<sup>+</sup>ℓ<sup>-</sup>γ

Average of all α<sub>DIP</sub> measurements (from each of three datablocks following this one)
assuming lepton universality.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th></tr></thead><tbody><tr><td>-1.69 ± 0.08 OUR AVERAGE</td><td>Includes data from the 3 datablocks that follow this one.</td></tr><tr><td></td><td>Error includes scale factor of 1.7.</td></tr></tbody></table>

α<sub>DIP</sub> DECAY FORM FACTOR FOR K<sup>0</sup><sub>L</sub> → e<sup>+</sup>e<sup>-</sup>γ

α<sub>DIP</sub> parameter in K<sup>0</sup><sub>L</sub> → γ<sup>*</sup>γ* form factor by DAMBROSIO 98, motivated by vector meson dominance and a proper short distance behavior.

The data in this block is included in the average printed for a previous datablock.

-1.729 ± 0.043 ± 0.028 83k ABOUZAID 07B KTEV

α<sub>DIP</sub> DECAY FORM FACTOR FOR K<sup>0</sup><sub>L</sub> → μ<sup>+</sup>μ<sup>-</sup>γ

α<sub>DIP</sub> is a constant in the model of DAMBROSIO 98 described in the previous section.

The data in this block is included in the average printed for a previous datablock.

-1.54 ± 0.10 9100 ALAVI-HARATI01G KTEV
### $\alpha_{DIP}$ DECAY FORM FACTOR FOR $K_L^0 \to e^+e^-\mu^+\mu^-$

$\alpha_{DIP}$ is a constant in the model of CAMBROSIO 98 described in the previous section.

**VALUE**
**EVTS**
**DOCUMENT ID**
**TECN**
The data in this block is included in the average printed for a previous datablock.

-1.59±0.37 131 ALAVI-HARATI03B KTEV

### $a_1/a_2$ FORM FACTOR FOR M1 DIRECT EMISSION AMPLITUDE

Form factor = $\tilde{g}_{M1}[1 + \frac{a_1/a_2}{(M_p^2 - M_K^2) + 2M_K E_\gamma}]$ as described in ALAVI-HARATI 00B.

<table><thead><tr><th>VALUE (GeV<sup>2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>-0.737±0.014</strong> OUR AVERAGE</td><td></td><td></td><td></td><td></td></tr><tr><td>-0.744±0.027±0.032</td><td>5241</td><td>1 ABOUZAID</td><td>06 KTEV</td><td>π<sup>+</sup>π<sup>-</sup>e<sup>+</sup>e<sup>-</sup></td></tr><tr><td>-0.738±0.007±0.018</td><td>111k</td><td>2 ABOUZAID</td><td>06A KTEV</td><td>π<sup>+</sup>π<sup>+</sup>γ</td></tr><tr><td>-0.81 <sup>+0.07</sup><sub>-0.13</sub></td><td>±0.02</td><td>3 LAI</td><td>03C NA48</td><td>π<sup>+</sup>π<sup>-</sup>e<sup>+</sup>e<sup>-</sup></td></tr><tr><td>-0.737±0.026±0.022</td><td></td><td>4 ALAVI-HARATI01B</td><td></td><td>π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>-0.720±0.028±0.009</td><td>1766</td><td>5 ALAVI-HARATI00B</td><td>KTEV</td><td>π<sup>+</sup>π<sup>-</sup>e<sup>+</sup>e<sup>-</sup></td></tr></tbody></table>

1 ABOUZAID 06 also measured $|\tilde{g}_{M1}| = 1.11 \pm 0.14$.

2 ABOUZAID 06A also measured $|\tilde{g}_{M1}| = 1.198 \pm 0.035 \pm 0.086$.

3 LAI 03C also measured $\tilde{g}_{M1} = 0.99^{+0.28}_{-0.27} \pm 0.07$.

4 ALAVI-HARATI 01b fit gives $\chi^2$/DOF = 38.8/27. Linear and quadratic fits give $\chi^2$/DOF = 43.2/27 and 37.6/26 respectively.

5 ALAVI-HARATI 00B also measured $|\tilde{g}_{M1}| = 1.35^{+0.20}_{-0.17} \pm 0.04$.

### $\tilde{\gamma}_S$ DECAY FORM FACTOR FOR $K_L^0 \to \pi^+\pi^0 e^+\nu_e$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.049±0.011</strong> OUR AVERAGE</td><td></td><td>Error includes scale factor of 1.7.</td></tr><tr><td>0.052±0.006±0.002</td><td>BATLEY</td><td>04 NA48</td></tr><tr><td>0.010±0.016±0.017</td><td>MAKOFF</td><td>93 E731</td></tr></tbody></table>

### $\tilde{\gamma}_P$ DECAY FORM FACTOR FOR $K_L^0 \to \pi^+\pi^0 e^+\nu_e$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>-0.052±0.012</strong> OUR AVERAGE</td><td></td><td></td></tr><tr><td>-0.051±0.011±0.005</td><td>BATLEY</td><td>04 NA48</td></tr><tr><td>-0.079±0.049±0.022</td><td>MAKOFF</td><td>93 E731</td></tr></tbody></table>

### $\lambda_g$ DECAY FORM FACTOR FOR $K_L^0 \to \pi^\pm\pi^0 e^+\nu_e$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.085±0.020</strong> OUR AVERAGE</td><td></td><td></td></tr><tr><td>0.087±0.019±0.006</td><td>BATLEY</td><td>04 NA48</td></tr><tr><td>0.014±0.087±0.070</td><td>MAKOFF</td><td>93 E731</td></tr></tbody></table>

### $\tilde{\hbar}$ DECAY FORM FACTOR FOR $K_L^0 \to \pi^\pm\pi^0 e^+\nu_e$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>-0.30±0.13</strong> OUR AVERAGE</td><td></td><td></td></tr><tr><td>-0.32±0.12±0.07</td><td>BATLEY</td><td>04 NA48</td></tr><tr><td>-0.07±0.31±0.31</td><td>MAKOFF</td><td>93 E731</td></tr></tbody></table>

### $L_3$ CHIRAL PERT. THEO. PARAM. FOR $K_L^0 \to \pi^\pm\pi^0 e^+\nu_e$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>-3.96±0.28</strong> OUR AVERAGE</td><td></td><td>Error includes scale factor of 1.6.</td></tr><tr><td>-4.1 ±0.2</td><td>BATLEY</td><td>04 NA48</td></tr><tr><td>-3.4 ±0.4</td><td>1 MAKOFF</td><td>93 E731</td></tr></tbody></table>

1 MAKOFF 93 sign has been changed to negative to agree with the sign convention used in BATLEY 04.

### $a_\gamma$, VECTOR MESON EXCHANGE CONTRIBUTION

<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>-0.43±0.06</strong> OUR AVERAGE</td><td></td><td>Error includes scale factor of 1.5.</td><td></td><td></td></tr><tr><td>-0.31±0.05±0.07</td><td>1.4k</td><td>1 ABOUZAID</td><td>08 KTEV</td><td></td></tr><tr><td>-0.46±0.03±0.04</td><td></td><td>LAI</td><td>02B NA48</td><td>$K_L^0 \to \pi^0 2\gamma$</td></tr><tr><td>-0.67±0.21±0.12</td><td></td><td>ALAVI-HARATI01E</td><td>KTEV</td><td>$K_L^0 \to \pi^0 e^+ e^- \gamma$</td></tr></tbody></table>

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

-0.72±0.05±0.06 2 ALAVI-HARATI09B KTEV $K_L^0 \to \pi^0 2\gamma$

1 Using KTeV dataset collected in 1996, 1997, and 1999.

2 Superseded by ABOUZAID 08.

### See the related review(s):

#### CP Violation in $K_L^0$ Decays

### CP-VIOLATION PARAMETERS IN $K_L^0$ DECAYS

#### CHARGE ASYMMETRY IN $K_{\beta3}^0$ DECAYS

Such asymmetry violates CP. It is related to Re($\epsilon$).

### $A_L$ = weighted average of $A_L(\mu)$ and $A_L(e)$

In previous editions and in the literature the symbol used for this asymmetry was $\delta_L$ or $\delta$. We use $A_L$ for consistency with $B^0$ asymmetry notation and with recent $K_S^0$ notation.

<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>0.332±0.006</strong> OUR AVERAGE</td><td></td><td></td><td></td><td>Includes data from the 2 datablocks that follow this one.</td></tr><tr><td>0.333±0.050</td><td>33M</td><td>WILLIAMS</td><td>73 ASPK</td><td>$K_{\mu3} + K_{e3}$</td></tr></tbody></table>

### $A_L(\mu) = [\Gamma(\pi^-\mu^+\nu_\mu) - \Gamma(\pi^+\mu^-\nu_\mu)]/\text{SUM}$

Only the combined value below is put into the Meson Summary Table.

**VALUE (%)**
**EVTS**
**DOCUMENT ID**
**TECN**
The data in this block is included in the average printed for a previous datablock.

### $0.304±0.025$ OUR AVERAGE

<table><tr><td>0.313±0.029</td><td>15M</td><td>GEWENIGER</td><td>74 ASPK</td></tr><tr><td>0.278±0.051</td><td>7,7M</td><td>PICCIONI</td><td>72 ASPK</td></tr></table>

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

<table><tr><td>0.60 ±0.14</td><td>4.1M</td><td>MCCARTHY</td><td>73 CNTR</td></tr><tr><td>0.57 ±0.17</td><td>1M</td><td>1 PACIOTTI</td><td>69 OSPK</td></tr><tr><td>0.403±0.134</td><td>1M</td><td>1 DORFAN</td><td>67 OSPK</td></tr></table>

1 PACIOTTI 69 is a reanalysis of DORFAN 67 and is corrected for $\mu^+\mu^-$ range difference in MCCARTHY 72.

### $A_L(e) = [\Gamma(\pi^-e^+\nu_e) - \Gamma(\pi^+e^-\nu_e)]/\text{SUM}$

Only the combined value below is put into the Meson Summary Table.

**VALUE (%)**
**EVTS**
**DOCUMENT ID**
**TECN**
The data in this block is included in the average printed for a previous datablock.

### $0.334±0.007$ OUR AVERAGE

<table><tr><td>0.3322±0.0058±0.0047</td><td>298M</td><td>ALAVI-HARATI02</td><td></td></tr><tr><td>0.341 ±0.018</td><td>34M</td><td>GEWENIGER</td><td>74 ASPK</td></tr><tr><td>0.318 ±0.038</td><td>40M</td><td>FITCH</td><td>73 ASPK</td></tr><tr><td>0.346 ±0.033</td><td>10M</td><td>MARX</td><td>70 CNTR</td></tr></table>

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

<table><tr><td>0.36 ±0.18</td><td>600k</td><td>ASHFORD</td><td>72 ASPK</td></tr><tr><td>0.246 ±0.059</td><td>10M</td><td>1 SAAL</td><td>69 CNTR</td></tr><tr><td>0.224 ±0.036</td><td>10M</td><td>1 BENNETT</td><td>67 CNTR</td></tr></table>

1 SAAL 69 is a reanalysis of BENNETT 67.

### PARAMETERS FOR $K_L^0 \to 2\pi$ DECAY

$$\eta_{+-} = A(K_L^0 \to \pi^+\pi^-) / A(K_S^0 \to \pi^+\pi^-)$$

$$\eta_{00} = A(K_L^0 \to \pi^0\pi^0) / A(K_S^0 \to \pi^0\pi^0)$$

The fitted values of $|\eta_{+-}|$ and $|\eta_{00}|$ given below are the results of a fit to $|\eta_{+-}|$, $|\eta_{00}|$, $|\eta_{+-}|$, and Re($\epsilon^\prime/\epsilon$). Independent information on $|\eta_{+-}|$ and $|\eta_{00}|$ can be obtained from the fitted values of the $K_L^0 \to \pi\pi$ and $K_S^0 \to \pi\pi$ branching ratios and the $K_L^0$ and $K_S^0$ lifetimes. This information is included as data in the $|\eta_{+-}|$ and $|\eta_{00}|$ sections with a Document ID "BRFIT." See the note "CP violation in $K_L$ decays" above for details.

### $|\eta_{00}| = |A(K_L^0 \to 2\pi^0) / A(K_S^0 \to 2\pi^0)|$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>2.220±0.011</strong> OUR FIT</td><td></td><td></td><td>Error includes scale factor of 1.8.</td></tr><tr><td><strong>2.243±0.014</strong></td><td></td><td></td><td>BRFIT 16</td></tr></tbody></table>

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

<table><tr><td>2.47 ±0.31 ±0.24</td><td>ANGELOPO... 98</td><td>CPLR</td><td></td></tr><tr><td>2.49 ±0.40</td><td>1 ADLER 96b</td><td>CPLR</td><td>Sup. by ANGELOPOULOS 98</td></tr><tr><td>2.33 ±0.18</td><td>CHRISTENS... 79</td><td>ASPK</td><td></td></tr><tr><td>2.71 ±0.37</td><td>2 WOLFF 71</td><td>OSPK</td><td>Cu reg., 4y's</td></tr><tr><td>2.95 ±0.63</td><td>2 CHOLLET 70</td><td>OSPK</td><td>Cu reg., 4y's</td></tr></table>

1 Error is statistical only.

2 CHOLLET 70 gives $|\eta_{00}| = (1.23 \pm 0.24) \times (\text{regeneration amplitude}, 2 \text{ GeV/c})/10000 \text{mb}$. WOLFF 71 gives $|\eta_{00}| = (1.13 \pm 0.12) \times (\text{regeneration amplitude}, 2 \text{ GeV/c})/10000 \text{mb}$. We compute both $|\eta_{00}|$ values for (regeneration amplitude, 2 GeV/c) and 2 GeV/c) = 24 ± 2mb. This regeneration amplitude results from averaging over FAISSNER 69, extrapolated using optical-model calculations of Bohm et al., Physics Letters 27B 594 (1968) and the data of BALATS 71. (From H. Faissner, private communication).

### $|\eta_{+-}| = |A(K_L^0 \to \pi^+\pi^-) / A(K_S^0 \to \pi^+\pi^-)|$

<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>2.232±0.011</strong> OUR FIT</td><td></td><td></td><td></td><td>Error includes scale factor of 1.8.</td></tr><tr><td><strong>2.226±0.007</strong></td><td></td><td></td><td></td><td>BRFIT 16</td></tr></tbody></table>

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

<table><tr><td>2.223±0.012</td><td>1 LAI</td><td>07 NA48</td><td></td></tr><tr><td>2.219±0.013</td><td>2 AMBROSINO</td><td>06F KLOE</td><td></td></tr><tr><td>2.228±0.010</td><td>3 ALEXOPOU... 04</td><td>KTEV</td><td></td></tr><tr><td>2.286±0.023±0.026</td><td>70M APOSTOLA... 99C</td><td>CPLR</td><td>$K_L^0 \to K_S^0$ asymmetry</td></tr><tr><td>2.310±0.043±0.031</td><td>5 ADLER 95b</td><td>CPLR</td><td>$K_L^0 \to K_S^0$ asymmetry</td></tr><tr><td>2.32 ±0.14 ±0.03</td><td>10<sup>5</sup> ADLER 92b</td><td>CPLR</td><td>$K_L^0 \to K_S^0$ asymmetry</td></tr><tr><td>2.30 ±0.035</td><td>GEWENIGER 74B</td><td>ASPK</td><td></td></tr></table>

1 Value obtained from the NA48 measurements of $\Gamma(K_L^0 \to \pi^+\pi^-) / \Gamma(K_L^0 \to \pi e^+e^-)$ and $\tau_{K_S^0}^0$ and KLOE measurements of $B(K_S^0 \to \pi^+\pi^-)$ and $\tau_{K_L^0}^0$. $\Gamma(K_L^0 \to \pi^+\pi^- \text{IB})$) but exclude the direct emission component $B(K_S^0 \to \pi^+\pi^- \text{(DE)})$. Their $|\eta_{+-}|$ value is not directly used in our fit, but enters the fit via their branching ratio and lifetime measurements.

2 AMBROSINO 06F uses KLOE branching ratios and $\tau_L$ together with $\tau_S$ from PDG 04. Their $|\eta_{+-}|$ value is not directly used in our fit, but enters the fit via their branching ratio and lifetime measurements.
³ ALEXOPOULOS 04 $|η_{+-}|$ uses their $K_L^0$ to $ππ$ branching fractions, $τ_S = (0.8963 ± 0.0005) × 10^{-10}$ s from the average of KTeV and NA48 $τ_S$ measurements, and assumes that $Γ(K_S^0 → πℓν_ℓ) = Γ(K_0^0 → πℓν_ℓ)$ giving $B(K_0^0 → πℓν_ℓ) = 0.118$. Their $η_{+-}$ is not directly used in our fit, but enters our fit via their branching ratio measurements.

⁴ APOSTOLAKIS 99c report $(2.264 ± 0.023 ± 0.026 + 9.1[τ_S - 0.8934]) × 10^{-3}$. We evaluate for our 2006 best value $τ_S = (0.8958 ± 0.0005) × 10^{-10}$ s.

⁵ ADLER 95b report $(2.312 ± 0.043 ± 0.030 - 1[Δm - 0.5274] + 9.1[τ_S - 0.8926]) × 10^{-3}$. We evaluate for our 1996 best values $Δm = (0.5304 ± 0.0014) × 10^{-10}$ $ħs^{-1}$ and $τ_S = (0.8927 ± 0.0009) × 10^{-10}$ s. Superseded by APOSTOLAKIS 99c.

$$|\epsilon| = (2|η_{+-}| + |η_{00}|)/3$$

This expression is a very good approximation, good to about one part in $10^{-4}$ because of the small measured value of $φ_{00} - φ_{+-}$ and small theoretical ambiguities.

VALUE (units $10^{-3}$)

DOCUMENT ID

2.228 ±0.011 OUR FIT

Error includes scale factor of 1.8.

$$|η_{00}/η_{+-}|$$

VALUE

EVTS

DOCUMENT ID

TECN

0.9950 ±0.0007 OUR FIT

Error includes scale factor of 1.6.

0.9930 ±0.0020 OUR AVERAGE

$$0.9931 ± 0.0020$$

1,2 BARR

93D NA31

$$0.9904 ± 0.0084 ± 0.0036$$

3 WOODS

88 E731

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

0.9939 ±0.0013 ±0.0015

1M BARR

93D NA31

0.9899 ±0.0020 ±0.0025

1 BURKHARDT

88 NA31

¹ This is the square root of the ratio *R* given by BURKHARDT 88 and BARR 93D.

² This is the combined results from BARR 93D and BURKHARDT 88, taking into account a common systematic uncertainty of 0.0014.

³ We calculate $|η_{00}/η_{+-}| = 1-3(ε'/ε)$ from WOODS 88 ($ε'/ε$) value.

$$\mathrm{Re}(\epsilon'/\epsilon) = (1 - |η_{00}/η_{+-}|)/3$$

We have neglected terms of order $ω·Re(ε'/ε)$, where $ω = Re(A_2)/Re(A_0) \simeq 1/22$. If included, this correction would lower Re($ε'/ε$) by about $0.04 × 10^{-3}$. See SOZZI 04.

VALUE (units $10^{-3}$)

DOCUMENT ID

TECN

COMMENT

1.66 ±0.23 OUR FIT

Error includes scale factor of 1.6.

1.68 ±0.20 OUR AVERAGE

Error includes scale factor of 1.4. See the diagram

below.

$$1.92 ± 0.21$$

1 ABOUZAID

11 KTEV

Assuming

CPT

$$1.47 ± 0.22$$

BATLEY

02 NA48

$$0.74 ± 0.52 ± 0.29$$

GIBBONS

93B E731

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

$$2.3 ± 0.65$$

2,3 BARR

93D NA31

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

$$2.110 ± 0.343$$

1,4 ABOUZAID

11 KTEV

Not assuming

CPT

$$2.07 ± 0.28$$

ALAVI-HARATI03

KTEV

In ABOUZAID 11

$$1.53 ± 0.26$$

LAI

01C NA48

Incl. in

BATLEY 02

$$2.80 ± 0.30 ± 0.28$$

ALAVI-HARATI99D

KTEV

In ALAVI-HARATI 03

$$1.85 ± 0.45 ± 0.58$$

FANTI

99C NA48

In LAI 01C

$$2.0 ± 0.7$$

5 BARR

93D NA31

$$-0.4 ± 1.4 ± 0.6$$

PATTERSON

90 E731

In GIBBONS 93B

$$3.3 ± 1.1$$

5 BURKHARDT

88 NA31

$$3.2 ± 2.8 ± 1.2$$

2 WOODS

88 E731

¹ The two ABOUZAID 11 values use the same data. The fits are performed with and without CPT invariance requirement.

² These values are derived from $|η_{00}/η_{+-}|$ measurements. They enter the average in this section but enter the fit via the $|η_{00}/η_{+-}|$ only.

³ This is the combined results from BARR 93D and BURKHARDT 88, taking into account their common systematic uncertainty.

⁴ We use ABOUZAID 11 Re($ε'/ε$) value with CPT assumption in our fits for $|η_{+-}|$, $|η_{00}|$, and Re($ε'/ε$).

⁵ These values are derived from $|η_{00}/η_{+-}|$ measurements.

WEIGHTED AVERAGE
1.68±0.20 (Error scaled by 1.4)

<figure><img src="image_520.png" /></figure>

$$\mathrm{Re}(\epsilon'/\epsilon) = (1 - |\eta_{00}/\eta_{+-}|)/3$$

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.

(Confidence Level = 0.132)

## $\phi_{+-}$, PHASE of $η_{+-}$

The dependence of the phase on $Δm$ and $τ_S$ is given for each experiment in the comments below, where $Δm$ is the $K_L^0 - K_S^0$ mass difference in units $10^{10}$ $ħs^{-1}$ and $τ_S$ is the $K_S$ mean life in units $10^{-10}$ s. We also give the regeneration phase $φ_f$ in the comments below.

OUR FIT is described in the note on "CP violation in $K_L$ decays" in the $K_L^0$ Particle Listings. Most experiments in this section are included in both the "Not Assuming CPT" and "Assuming CPT" fits. In the latter fit, they have little direct influence on $φ_{+-}$ because their errors are large compared to that assuming CPT, but they influence $Δm$ and $τ_S$ through their dependencies on these parameters, which are given in the footnotes.

<table><thead><tr><th>VALUE (°)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>43.51 ±0.05 OUR FIT</td><td colspan="4">Error includes scale factor of 1.2. Assuming CPT</td></tr><tr><td>43.4 ±0.5 OUR FIT</td><td colspan="4">Error includes scale factor of 1.2. Not assuming CPT</td></tr><tr><td>42.9 ±0.6 ±0.3</td><td>70M</td><td>1 APOSTOLA...</td><td>99c CPLR</td><td>K<sup>0</sup>·K<sup>0</sup> asymmetry</td></tr><tr><td>42.9 ±0.8 ±0.2</td><td></td><td>2,3 SCHWINGEN...</td><td>95 E77</td><td>CH<sub>1,1</sub> regenerator</td></tr><tr><td>41.4 ±0.9 ±0.2</td><td></td><td>3,4 GIBBONS</td><td>93 E731</td><td>B<sub>4</sub>C regenerator</td></tr><tr><td>44.5 ±1.6 ±0.5</td><td></td><td>5 CAROSI</td><td>90 NA31</td><td>Vacuum regen.</td></tr><tr><td>43.3 ±1.0 ±0.5</td><td></td><td>6 GEWENIGER</td><td>74b ASPK</td><td></td></tr></tbody></table>

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

$$43.76 ± 0.64$$

7 ABOUZAID

11 KTEV

Not assuming

$$44.12 ± 0.72 ± 1.20$$

8 ALAVI-HARATI03

KTEV

Not assuming

$$42.5 ± 0.4 ± 0.3$$

9,10 ADLER

96C RVUE

$$43.4 ± 1.1 ± 0.3$$

11 ADLER

95B CPLR

K<sup>0</sup>·K<sup>0</sup>

$$42.3 ± 4.4 ± 1.4$$

12 ADLER

92B CPLR

K<sup>0</sup>·K<sup>0</sup>

$$47.7 ± 2.0 ± 0.9$$

3,13 KARLSSON

90 E731

$$44.3 ± 2.8 ± 0.2$$

14 CARITHERS

75 SPEC

C

regenerator

¹ APOSTOLAKIS 99c measures $φ_{+-} = (43.19 ± 0.53 ± 0.28) + 300 [Δm - 0.5301] (°)$. We have adjusted the measurement to use our best values of ($Δm = 0.5293 ± 0.0009$) ($10^{10}$ $ħs^{-1}$). Our first error is their experiment's error and our second error is the systematic error from using our best values.

² SCHWINGENHEUER 95 measures $φ_{+-} = (43.53 ± 0.76) + 173 [Δm - 0.5282] - 275 [τ_S - 0.8926] (°)$. We have adjusted the measurement to use our best values of ($Δm = 0.5293 ± 0.0009$) ($10^{10}$ $ħs^{-1}$), ($τ_S = 0.8954 ± 0.0004$) ($10^{-10}$ s). Our first error is their experiment's error and our second error is the systematic error from using our best values.

³ These experiments measure $φ_{+-} - φ_f$ and calculate the regeneration phase from the power law momentum dependence of the regeneration amplitude using analyticity and dispersion relations. SCHWINGENHEUER 95 [GIBBONS 93] includes a systematic error of $0.35°$ [$0.5°$] for uncertainties in their modeling of the regeneration amplitude.

⁴ GIBBONS 93 measures $φ_{+-} = (42.21 ± 0.9) + 189 [Δm - 0.5257] - 460 [τ_S - 0.8922] (°)$. We have adjusted the measurement to use our best values of ($Δm = 0.5293 ± 0.0009$) ($10^{10}$ $ħs^{-1}$), ($τ_S = 0.8954 ± 0.0004$) ($10^{-10}$ s). Our first error is their experiment's error and our second error is the systematic error from using our best values. This is actually reported in SCHWINGENHEUER 95, footnote 8. GIBBONS 93 reports $φ_{+-}$ ($42.2 ± 1.4$)⁵. They measure $φ_{+-} - φ_f$ and calculate the regeneration phase $φ_f$ from the power law momentum dependence of the regeneration amplitude using analyticity. An error of $0.6°$ is included for possible uncertainties in the regeneration phase.

⁵ CAROSI 90 measures $φ_{+-} = (46.9 ± 1.4 ± 0.7) + 579 [Δm - 0.5351] + 303 [τ_S - 0.8922] (°)$. We have adjusted the measurement to use our best values of ($Δm = 0.5293 ± 0.0009$) ($10^{10}$ $ħs^{-1}$), ($τ_S = 0.8954 ± 0.0004$) ($10^{-10}$ s). Our first error is their experiment's error and our second error is the systematic error from using our best values.

⁶ GEWENIGER 74b measures $φ_{+-} = (49.4 ± 1.0) + 565 [Δm - 0.540] (°)$. We have adjusted the measurement to use our best values of ($Δm = 0.5293 ± 0.0009$) ($10^{10}$ $ħs^{-1}$). Our first error is their experiment's error and our second error is the systematic error from using our best values.

⁷ Not independent of other phase parameters reported in ABOUZAID 11.

⁸ ALAVI-HARATI 03 $φ_{+-}$ is correlated with their $Δm = m_{K_L^0} - m_{K_S^0}$ and $τ_{KS}$ measurements in the $K_L^0$ and $K_S^0$ sections respectively. The correlation coefficients are $ρ(φ_{+-}, Δm) = 0.955$, $ρ(φ_{+-}, τ_S) = -0.871$, and $ρ(τ_S, Δm) = -0.840$. CPT is not assumed. Uses scintillator Pb regenerator. Superseded by ABOUZAID 11.

⁹ ADLER 96c measures $φ_{+-} = (43.82 ± 0.41) + 339 [Δm - 0.5307] - 252 [τ_S - 0.8922] (°)$. We have adjusted the measurement to use our best values of ($Δm = 0.5293 ± 0.0009$) ($10^{10}$ $ħs^{-1}$), ($τ_S = 0.8954 ± 0.0004$) ($10^{-10}$ s). Our first error is their experiment's error and our second error is the systematic error from using our best values.

¹⁰ ADLER 96c is the result of a fit which includes nearly the same data as entered into the "OUR FIT" value in the 1996 edition of this Review (Physical Review **D54** 1 (1996)).

¹¹ ADLER 95b measures $φ_{+-} = (42.7 ± 0.9 ± 0.6) + 316 [Δm - 0.5274] + 30 [τ_S - 0.8926] (°)$. We have adjusted the measurement to use our best values of ($Δm = 0.5293 ± 0.0009$) ($10^{10}$ $ħs^{-1}$), ($τ_S = 0.8954 ± 0.0004$) ($10^{-10}$ s). Our first error is their experiment's error and our second error is the systematic error from using our best values.

¹² ADLER 92b quote separately two systematic errors: ±0.4 from their experiment and ±1.0 degrees due to the uncertainty in the value of $Δm$.

¹³ KARLSSON 90 systematic error does not include regeneration phase uncertainty.

¹⁴ CARITHERS 75 measures $φ_{+-} = (45.5 ± 2.8) + 224 [Δm - 0.5348] (°)$. We have adjusted the measurement to use our best values of ($Δm = 0.5293 ± 0.0009$) ($10^{10}$ $ħs^{-1}$). Our first error is their experiment's error and our second error is the systematic error from using our best values. $φ_f = -40.9 ± 2.6°$.
## $\phi_{00}$, PHASE OF $\eta_{00}$

See comment in $\phi_{+\pm}$ header above for treatment of $\Delta m$ and $\tau_S$ dependence, as well as for the inclusion of data in both the “Assuming CPT” and “Not Assuming CPT” fits.

OUR FIT is described in the note on “CP violation in $K_L$ decays” in the $K_L^0$ Particle Listings.

<table><thead><tr><th>VALUE (°)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>43.52 ±0.05</td><td>OUR FIT</td><td>Error includes scale factor of 1.2. Assuming CPT</td><td></td></tr><tr><td>43.7 ±0.6</td><td>OUR FIT</td><td>Error includes scale factor of 1.2. Not assuming CPT</td><td></td></tr><tr><td>44.5 ±2.3 ±0.5</td><td></td><td>1 CAROSI</td><td>90 NA31</td></tr><tr><td>44.06 ±0.68</td><td></td><td>2 ABOUZAID</td><td>11 KTEV Not assuming CPT</td></tr><tr><td>41.7 ±5.9 ±0.2</td><td></td><td>3 ANGELOPOU... 98</td><td>CPLR</td></tr><tr><td>50.8 ±7.1 ±1.7</td><td></td><td>4 ADLER</td><td>96B CPLR Sup. by ANGELOPOULOS 98</td></tr><tr><td>47.4 ±1.4 ±0.9</td><td></td><td>5 KARLSSON</td><td>90 E731</td></tr></tbody></table>

1 CAROSI 90 measures $\phi_{00} = (47.1 \pm 2.1 \pm 1.0) + 579 [\Delta m - 0.5351] + 252 [\tau_S - 0.8922] (°)$. We have adjusted the measurement to use our best values of $(\Delta m = 0.5293 \pm 0.0009) (10^{10} \hbar s^{-1})$, $(\tau_S = 0.8954 \pm 0.0004) (10^{-10} s)$. Our first error is their experiment's error and our second error is the systematic error from using our best values.

2 Not independent of other phase parameters reported in ABOUZAID 11.

3 ANGELOPOULOS 98 measures $\phi_{00} = (42.0 \pm 5.6 \pm 1.9) + 240 [\Delta m - 0.5307] (°)$. 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. The $\tau_S$ dependence is negligible.

4 ADLER 96b identified initial neutral kaon individually as being a $K^0$ or a $\bar{K}^0$. The systematic uncertainty is $\pm 1.5°$ combined in quadrature with $\pm 0.8°$ due to $\Delta m$.

5 KARLSSON 90 systematic error does not include regeneration phase uncertainty.

$$ \phi_e = (2\phi_{+\pm} + \phi_{00})/3 $$

This expression is a very good approximation, good to about $10^{-3}$ degrees because of the small measured values of $\phi_{00} - \phi_{+\pm}$ and Re $\epsilon'/\epsilon$, and small theoretical ambiguities.

<table><thead><tr><th>VALUE (°)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>43.52 ±0.04</td><td>OUR FIT</td><td>Error includes scale factor of 1.2. Assuming CPT</td><td></td></tr><tr><td>43.5 ±0.5</td><td>OUR FIT</td><td>Error includes scale factor of 1.3. Not assuming CPT</td><td></td></tr><tr><td>43.5164 ±0.0002 ±0.0509</td><td></td><td>1 SUPERWEAK 16</td><td>Assuming CPT</td></tr><tr><td>43.86 ±0.63</td><td></td><td>2 ABOUZAID 11</td><td>KTEV Not assuming CPT</td></tr></tbody></table>

1 SUPERWEAK 16 is a fake measurement used to impose the CPT or Superweak constraint $\phi_{+\pm} = \phi_{SW} = \tan^{-1}[2 \frac{\Delta m}{\hbar} (\frac{\tau_S \tau_T}{\tau_L - \tau_S})]$. This “measurement” is linearized using values near the PDG 04 edition values of $\Delta m$, $\tau_S$ and $\tau_L$, and then adjusted to our current values as described in the following “measurement”. SUPERWEAK 16 measures $\phi_e = (43.50258 \pm 0.00021) + 54.1 [\Delta m - 0.5289] + 32.0 [\tau_S - 0.89564] (°)$. We have adjusted the measurement to use our best values of $(\Delta m = 0.5293 \pm 0.0009) (10^{10} \hbar s^{-1})$, $(\tau_S = 0.8954 \pm 0.0004) (10^{-10} s)$. Our first error is their experiment's error and our second error is the systematic error from using our best values.

2 ABOUZAID 11 uses the full KTeV dataset collected in 1996, 1997, and 1999. See Im($\epsilon'/\epsilon$) section for correlation information.

$$ \mathrm{Im}(\epsilon'/\epsilon) = -(\phi_{00} - \phi_{+\pm})/3 $$

For small $|\epsilon'/\epsilon|$, Im($\epsilon'/\epsilon$) is related to the phases of $\eta_{00}$ and $\eta_{+\pm}$ by the above expression.

<table><thead><tr><th>VALUE (°)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>-0.002 ±0.005</td><td>OUR FIT</td><td>Error includes scale factor of 1.7. Assuming CPT</td><td></td></tr><tr><td>-0.11 ±0.11</td><td>OUR FIT</td><td>Not assuming CPT</td><td></td></tr><tr><td>-0.0985 ±0.1157</td><td></td><td>1 ABOUZAID 11</td><td>KTEV Not assuming CPT</td></tr></tbody></table>

1 ABOUZAID 11 uses the full KTeV dataset collected in 1996, 1997, and 1999. The fit has $\Delta m$, $\tau_S$, $\phi_e$, Re($\epsilon'/\epsilon$), and Im($\epsilon'/\epsilon$) as free parameters. The reported value of Im($\epsilon'/\epsilon$) = $(-17.20 \pm 20.20) \times 10^{-4}$ rad. The correlation coefficients are $\rho(\phi_e, \Delta m) = 0.828$, $\rho(\phi_e, \tau_S) = -0.765$, $\rho(\Delta m, \tau_S) = -0.858$, $\rho(\mathrm{Im}(\epsilon'/\epsilon), \phi_e) = -0.041$, $\rho(\mathrm{Im}(\epsilon'/\epsilon), \Delta m) = 0.026$, $\rho(\mathrm{Im}(\epsilon'/\epsilon), \tau_S) = -0.010$.

## 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 $K_L^0$ rest frame.

### CP ASYMMETRY A in $K_L^0 \to \pi^+\pi^- e^+e^-$

<table><thead><tr><th>VALUE (%)</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>13.7 ±1.5</td><td>OUR AVERAGE</td><td></td></tr><tr><td>13.6 ±1.4 ±1.5</td><td></td><td>ABOUZAID 06 KTEV</td></tr><tr><td>14.2 ±3.0 ±1.9</td><td></td><td>LAI 03C NA48</td></tr><tr><td>13.6 ±2.5 ±1.2</td><td></td><td>ALAVI-HARATI00B KTEV</td></tr></tbody></table>

## PARAMETERS FOR $e^+e^-$ ASYMMETRY DECAYS

These are the CP-violating parameters in the $\phi$ distribution, where $\phi$ is the angle between the planes of the two $e^+e^-$ pairs in the kaon rest frame:

$$ d\tau/d\phi \propto 1 + \beta_{CP} \cos(2\phi) + \gamma_{CP} \sin(2\phi) $$

where $\beta_{CP} = -0.20$ and $\gamma_{CP} = 0$ values correspond to no CP violation.

### $\beta_{CP}$ from $K_L^0 \to e^+e^+e^+e^-$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>-0.19 ±0.07</td><td>OUR AVERAGE</td><td></td><td></td><td></td></tr><tr><td>-0.13 ±0.10 ±0.03</td><td>200</td><td>1 LAI</td><td>05B NA48</td><td></td></tr><tr><td>-0.23 ±0.09 ±0.02</td><td>441</td><td>ALAVI-HARATI01D KTEV Mee &gt; 8 MeV/c<sup>2</sup></td><td></td><td></td></tr></tbody></table>

1 LAI 05B obtains $\beta_{CP} = -0.13 \pm 0.10 (\text{stat})$ if $\gamma_{CP} = 0$ is assumed.

### $\gamma_{CP}$ from $K_L^0 \to e^+e^+e^-$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.01 ±0.11</td><td>OUR AVERAGE</td><td>Error includes scale factor of 1.6.</td><td></td><td></td></tr><tr><td>+0.13 ±0.10 ±0.03</td><td></td><td>LAI</td><td>05B NA48</td><td></td></tr><tr><td>-0.09 ±0.09 ±0.02</td><td></td><td>ALAVI-HARATI01D KTEV Mee &gt; 8 MeV/c<sup>2</sup></td><td></td><td></td></tr></tbody></table>

## CHARGE ASYMMETRY IN $\pi^+\pi^-\pi^0$ DECAYS

These are CP-violating charge-asymmetry parameters, defined at beginning of section “LINEAR COEFFICIENT g FOR $K_L^0 \to \pi^+\pi^-\pi^0$ above.

See also note on Dalitz plot parameters in $K^\pm$ section and note on “CP violation in $K_L$ decays” above.

### LINEAR COEFFICIENT j FOR $K_L^0 \to \pi^+\pi^-\pi^0$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>0.0012 ±0.0008</td><td>OUR AVERAGE</td><td></td><td></td></tr><tr><td>0.0010 ±0.0024 ±0.0030</td><td></td><td>500k ANGELOPO... 98C CPLR</td><td></td></tr><tr><td>-0.001 ±0.011</td><td></td><td>6499 CHO 77</td><td></td></tr><tr><td>0.001 ±0.003</td><td></td><td>4709 PEACH 77</td><td></td></tr><tr><td>0.0013 ±0.0009</td><td></td><td>3M SCRIBANO 70</td><td></td></tr><tr><td>0 ± 0.017</td><td></td><td>4400 SMITH 70 OSPK</td><td></td></tr><tr><td>0.001 ±0.004</td><td></td><td>238k BLANPIED 68</td><td></td></tr></tbody></table>

### QUADRATIC COEFFICIENT f FOR $K_L^0 \to \pi^+\pi^-\pi^0$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>0.0045 ±0.0024 ±0.0059</td><td></td><td>500k ANGELOPO... 98C CPLR</td><td></td></tr></tbody></table>

## PARAMETERS for $K_L^0 \to \pi^+\pi^-\gamma$ DECAY

$$ |\eta_{+-\gamma}| = |A(K_L^0 \to \pi^+\pi^-\gamma, \mathrm{CP \ violating})/A(K_S^0 \to \pi^+\pi^-\gamma)| $$

<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>2.35 ±0.07</td><td>OUR AVERAGE</td><td></td><td></td></tr><tr><td>2.359 ±0.062 ±0.040</td><td></td><td>MATTHEWS 95 E773</td><td></td></tr><tr><td>2.15 ±0.26 ±0.20</td><td></td><td>RAMBERG 93B E731</td><td></td></tr></tbody></table>

### $\phi_{+\gamma} = \text{phase of } \eta_{+-\gamma}$

<table><thead><tr><th>VALUE (°)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>44 ± 4</td><td>OUR AVERAGE</td><td></td><td></td></tr><tr><td>43.8 ± 3.5 ± 1.9</td><td></td><td>MATTHEWS 95 E773</td><td></td></tr><tr><td>72 ± 23 ± 17</td><td></td><td>RAMBERG 93B E731</td><td></td></tr></tbody></table>

### $|\epsilon'_{+-\gamma}|/\epsilon$ for $K_L^0 \to \pi^+\pi^-\gamma$

<table><thead><tr><th>VALUE</th><th>CL% EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>&lt;0.3</td><td>90 3671</td><td>1 RAMBERG 93B E731</td><td></td></tr></tbody></table>

1 RAMBERG 93b limit on $|\epsilon'_{+-\gamma}|/\epsilon$ assumes than any difference between $\eta_{+-\gamma}$ and $\eta_{+-\gamma}$ is due to direct CP violation.

### $|\beta_{E1}|$ for $K_L^0 \to \pi^+\pi^-\gamma$

This parameter is the amplitude of the direct emission of a CP violating E1 electric dipole photon.

<table><thead><tr><th>VALUE</th><th>CL% EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;0.21</td><td>90 111k</td><td>ABOUZAID 06A KTEV E*<sub>γ</sub> &gt; 20 MeV</td><td></td><td></td></tr></tbody></table>

## T VIOLATION TESTS IN $K_L^0$ DECAYS

### Im($\epsilon$) in $K_{\mu 3}^0$ DECAY (from transverse $\mu$ pol.)

Test of T reversal invariance.

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>-0.007 ±0.026</td><td>OUR AVERAGE</td><td></td><td></td><td></td></tr><tr><td>0.009 ±0.030</td><td>12M MORSE 80 CNTR Polarization</td><td></td><td></td><td></td></tr><tr><td>0.35 ±0.30</td><td>207k 1 CLARK 77 SPEC POL, t=0</td><td></td><td></td><td></td></tr><tr><td>-0.085 ±0.064</td><td>2.2M 2 SANDWEISS 73 CNTR POL, t=0</td><td></td><td></td><td></td></tr><tr><td>-0.02 ±0.08</td><td>LONGO 69 CNTR POL, t=3.3</td><td></td><td></td><td></td></tr><tr><td>-0.2 ±0.6</td><td>ABRAMS 68B OSPK Polarization</td><td></td><td></td><td></td></tr></tbody></table>

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

0.012 ±0.026 SCHMIDT 79 CNTR Repl. by MORSE 80

1 CLARK 77 value has additional $\xi(0)$ dependence +0.21Re[$\xi(0)$].

2 SANDWEISS 73 value corrected from value quoted in their paper due to new value of Re($\xi$). See footnote 4 of SCHMIDT 79.

## CPT-INVARIANCE TESTS IN $K_L^0$ DECAYS

### PHASE DIFFERENCE $\phi_{00} - \phi_{+\pm}$

Test of CPT.

OUR FIT is described in the note on “CP violation in $K_L$ decays” in the $K_L^0$ Particle Listings.

<table><thead><tr><th>VALUE (°)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.006 ±0.014</td><td>OUR FIT</td><td>Error includes scale factor of 1.7. Assuming CPT</td><td></td></tr><tr><td>0.34 ±0.32</td><td>OUR FIT</td><td>Not assuming CPT</td><td></td></tr><tr><td>0.006 ±0.008</td><td></td><td>1 SUPERWEAK 16</td><td>Assuming CPT</td></tr><tr><td>-0.30 ±0.88</td><td></td><td>2 SCHWINGEN...95</td><td>Combined E731, E773</td></tr></tbody></table>
• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>0.30</td><td>±0.35</td></tr><tr><td>0.39</td><td>±0.22</td><td>±0.45</td></tr><tr><td>0.62</td><td>±0.71</td><td>±0.75</td></tr><tr><td>-1.6</td><td>±1.2</td></tr><tr><td>0.2</td><td>±2.6</td><td>±1.2</td></tr><tr><td>-0.3</td><td>±2.4</td><td>±1.2</td></tr></table>

<table><tr><td>3 ABOUZAID</td><td>11</td><td>KTEV</td><td>Not assuming CPT</td></tr><tr><td>4 ALAVI-HARATI03</td><td>10</td><td>KTEV</td><td></td></tr><tr><td></td><td></td><td>SCHWINGEN...</td><td>95 E773</td></tr><tr><td>5 GIBBONS</td><td>93</td><td>E731</td><td></td></tr><tr><td>6 CAROSI</td><td>90</td><td>NA31</td><td></td></tr><tr><td>KARLSSON</td><td>90</td><td>E731</td><td></td></tr></table>









1 SUPERWEAK 16 is a fake experiment to constrain $\phi_{00} - \phi_{+-}$ to a small value as described in the note "CP violation in $K_L$ decays."

2 This SCHWINGENHEUER 95 values is the combined result of SCHWINGENHEUER 95 and GIBBONS 93, accounting for correlated systematic errors.

3 Not independent of other phase parameters reported in ABOUZAID 11.

4 ALAVI-HARATI 03 fit Re($\ell^t/\ell$), Im($\ell^t/\ell$), $\Delta m$, $\tau_S$, and $\phi_{+-}$ simultaneously, not assuming CPT. Phase difference is obtained from $\phi_{00} - \phi_{+-} \approx -3\,\text{Im}(\ell^t/\ell)$ for small $|\ell^t/\ell|$. Superseded by ABOUZAID 11.

5 GIBBONS 93 give detailed dependence of systematic error on lifetime (see the section on the $K_S^0$ mean life) and mass difference (see the section on $m_{K_L^0} - m_{K_S^0}$).

6 CAROSI 90 is excluded from the fit because it is not independent of $\phi_{+-}$ and $\phi_{00}$ values.

## PHASE DIFFERENCE $\phi_{+-} - \phi_{SW}$

Test of CPT. The Superweak phase $\phi_{SW} \equiv \tan^{-1}(2\Delta m/\Delta\Gamma)$ where $\Delta m = m_{K_L^0} - m_{K_S^0}$ and $\Delta\Gamma = \bar{\hbar}(\tau_L - \tau_S)/(\tau_L \tau_S)$.

<table><tr><td>VALUE (°)</td></tr><tr><td>0.61 ±0.62 ±1.01</td></tr></table>

<table><tr><td>DOCUMENT ID</td><td>TECN</td></tr><tr><td>1 ALAVI-HARATI03</td><td>KTEV</td></tr></table>

1 ALAVI-HARATI 03 fit is the same as their $\phi_{+-}$, $\tau_{K_S}$, $\Delta m$ fit, except that the parameter $\phi_{+-} - \phi_{SW}$ is used in place of $\phi$.

$$ \text{Re}(\frac{2\eta_{+-} + \frac{3}{2}\eta_{00}) - \frac{A}{2}) $$
Test of CPT

<table><tr><td>VALUE (units 10<sup>-6</sup>)</td></tr><tr><td>-3 ± 35</td></tr></table>

<table><tr><td>DOCUMENT ID</td><td>TECN</td></tr><tr><td>1 ALAVI-HARATI02</td><td>E799</td></tr></table>

Uses $A_L$ from $K_{e3}$ decays

1 ALAVI-HARATI 02 uses PDG 00 values of $\eta_{+-}$ and $\eta_{00}$.

## $\Delta S = \Delta Q$ IN $K^0$ DECAYS

The relative amount of $\Delta S \neq \Delta Q$ component present is measured by the parameter $x$, defined as

$$ x = A(\bar{K}^0 \to \pi^- \ell^+ \nu)/A(K^0 \to \pi^- \ell^+ \nu). $$

We list Re{$x$} and Im{$x$} for $K_{e3}$ and $K_{\mu 3}$ combined.

$$ x = A(\bar{K}^0 \to \pi^- \ell^+ \nu)/A(K^0 \to \pi^- \ell^+ \nu) = A(\Delta S = -\Delta Q)/A(\Delta S = \Delta Q) $$

## REAL PART OF $x$

<table><tr><td>VALUE</td></tr><tr><td>-0.0018 ±0.0041 ±0.0045</td></tr></table>

<table><tr><td>EVTS</td></tr><tr><td>DOCUMENT ID</td><td>TECN</td></tr><tr><td>23AE</td><td>ANGELOPO...</td><td>98D</td><td>CPLR</td><td>$K_{e3}$ from $K^0$</td></tr></table>

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

<table><tr><td>0.10</td><td>+0.18</td><td>79</td></tr><tr><td>-0.19</td><td></td><td></td></tr></table>

<table><tr><td>SMITH</td><td>75B</td><td>WIRE</td></tr></table>

<table><tr><td>0.04</td><td>±0.03</td></tr></table>

<table><tr><td>NIEBERGALL</td><td>74</td><td>ASPK</td></tr></table>

<table><tr><td>-0.008</td><td>±0.044</td></tr></table>

<table><tr><td>FACKLER</td><td>73</td><td>OSPK</td></tr></table>

<table><tr><td>-0.03</td><td>±0.07</td></tr></table>

<table><tr><td>HART</td><td>73</td><td>OSPK</td></tr></table>

<table><tr><td>-0.070</td><td>±0.036</td></tr></table>

<table><tr><td>MALLARY</td><td>73</td><td>OSPK</td></tr></table>

<table><tr><td>0.03</td><td>±0.06</td></tr></table>

<table><tr><td>1 BURGUN</td><td>72</td><td>HBC</td></tr></table>

<table><tr><td>0.04</td><td>+0.10</td><td>100</td></tr></table>

<table><tr><td>2 GRAHAM</td><td>72</td><td>OSPK</td></tr></table>

<table><tr><td>-0.07</td><td>±0.13</td></tr></table>

<table><tr><td>2 GRAHAM</td><td>72</td><td>OSPK</td></tr></table>

<table><tr><td>-0.05</td><td>±0.09</td></tr></table>

<table><tr><td>1 BURGUN</td><td>71</td><td>HBC</td></tr></table>

<table><tr><td>0.26</td><td>+0.10</td><td>126</td></tr></table>

<table><tr><td>MANN</td><td>72</td><td>HBC</td></tr></table>

<table><tr><td>-0.13</td><td>±0.11</td></tr></table>

<table><tr><td>2 MANTSCH</td><td>72</td><td>OSPK</td></tr></table>

<table><tr><td>0.04</td><td>±0.07</td></tr></table>

<table><tr><td>1 BURGUN</td><td>71</td><td>HBC</td></tr></table>

<table><tr><td>0.07</td><td>+0.08</td></tr></table>

<table><tr><td>2 BURGUN</td><td>71</td><td>HBC</td></tr></table>

<table><tr><td>0.25</td><td>+0.07</td><td>252</td></tr></table>

<table><tr><td>WEBBER</td><td>71</td><td>HBC</td></tr></table>

<table><tr><td>0.12</td><td>+0.09</td></tr></table>

<table><tr><td>3 CHO</td><td>70</td><td>DBC</td></tr></table>

<table><tr><td>-0.020</td><td>±0.025</td></tr></table>

<table><tr><td>4 BENNETT</td><td>69</td><td>CNTR</td></tr></table>

<table><tr><td>LITTENBERG</td><td>69</td><td>OSPK</td></tr></table>

<table><tr><td>0.09</td><td>+0.14</td><td>686</td></tr><tr><td>-0.16</td><td></td><td></td></tr></table>

<table><tr><td>4 BENNETT</td><td>68</td><td>CNTR</td></tr></table>

<table><tr><td>0.03</td><td>±0.03</td></tr></table>

<table><tr><td>JAMES</td><td>68</td><td>HBC</td></tr></table>

<table><tr><td>0.09</td><td>+0.07</td><td>121</td></tr></table>

<table><tr><td></td><td></td><td>121</td></tr></table>

<table><tr><td>0.17</td><td>+0.16</td><td>116</td></tr></table>

<table><tr><td>1 FELDMAN</td><td>67B</td><td>OSPK</td></tr></table>

<table><tr><td>0.17</td><td>+0.10</td></tr></table>

<table><tr><td>3 HILL</td><td>67</td><td>DBC</td></tr></table>

<table><tr><td>0.035</td><td>+0.11</td><td>196</td></tr></table>

<table><tr><td>AUBERT</td><td>65</td><td>HLBC</td></tr></table>

<table><tr><td>0.06</td><td>+0.18</td><td>152</td></tr></table>

<table><tr><td>5 BALDO...</td><td>65</td><td>HLBC</td></tr></table>

<table><tr><td>-0.04</td><td>±0.44</td></tr></table>

<table><tr><td>5 BALDO...</td><td>65</td><td>HLBC</td></tr></table>

<table><tr><td>-0.08</td><td>+0.16</td><td>109</td></tr></table>

<table><tr><td>6 FRANZINI</td><td>65</td><td>HBC</td></tr></table>

<table><tr><td>6 FRANZINI</td><td>65</td><td>HBC</td></tr></table>

1 BURGUN 72 is a final result which includes BURGUN 71.

2 First GRAHAM 72 value is second GRAHAM 72 value combined with MANTSCH 72.

3 CHO 70 is analysis of unambiguous events in new data and HILL 67.

4 BENNETT 69 is a reanalysis of BENNETT 68.

5 BALDO-CEOLIN 65 gives $x$ and $\theta$ converted by us to Re($x$) and Im($x$).

6 FRANZINI 65 gives $x$ and $\theta$ for Re($x$) and Im($x$). See SCHMIDT 67.

## IMAGINARY PART OF $x$

Assumes $m_{K_L^0} - m_{K_S^0}$ positive. See Listings above.

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.0012 ±0.0019</td><td>640k</td><td>1 ANGELOPO...</td><td>98E</td><td>CPLR $K_{e3}$ from $K^0$</td></tr><tr><td>-0.10</td><td>+0.16</td><td>79</td><td>SMITH</td><td>75B WIRE $\pi^- p \to K^0 \Lambda$</td></tr><tr><td>-0.06</td><td>±0.05</td><td>4724</td><td>NIEBERGALL</td><td>74 ASPK $K^+ p \to K^0 p \pi^+$</td></tr><tr><td>-0.017</td><td>±0.060</td><td>1757</td><td>FACKLER</td><td>73 OSPK $K_{e3}$ from $K^0$</td></tr><tr><td>0.09</td><td>±0.07</td><td>1367</td><td>HART</td><td>73 OSPK $K_{e3}$ from $K^0 \Lambda$</td></tr><tr><td>0.107</td><td>+0.092</td><td>1079</td><td>MALLARY</td><td>73 OSPK $K_{e3}$ from $K^0 \Lambda X$</td></tr><tr><td>0.07</td><td>+0.06</td><td>410</td><td>2 BURGUN</td><td>72 HBC $K^+ p \to K^0 p \pi^+$</td></tr><tr><td>0.12</td><td>+0.17</td><td>100</td><td>3 GRAHAM</td><td>72 OSPK $K_{\mu 3}$ from $K^0 \Lambda$</td></tr><tr><td>0.05</td><td>±0.13</td><td>442</td><td>3 GRAHAM</td><td>72 OSPK $\pi^- p \to K^0 \Lambda$</td></tr><tr><td>0.21</td><td>+0.15</td><td>126</td><td>MANN</td><td>72 HBC $K^- p \to n \bar{K}^0$</td></tr><tr><td>-0.04</td><td>±0.16</td><td>342</td><td>3 MANTSCH</td><td>72 OSPK $K_{e3}$ from $K^0 \Lambda$</td></tr><tr><td>0.12</td><td>+0.08</td><td>222</td><td>2 BURGUN</td><td>71 HBC $K^+ p \to K^0 p \pi^+$</td></tr><tr><td>-0.09</td><td></td><td></td><td>WEBBER</td><td>71 HBC $K^- p \to n \bar{K}^0$</td></tr><tr><td>0.0</td><td>±0.08</td><td>252</td><td>4 CHO</td><td>70 DBC $K^+ d \to K^0 p p$</td></tr><tr><td>-0.08</td><td>±0.07</td><td>215</td><td>LITTENBERG</td><td>69 OSPK $K^+ n \to K^0 p$</td></tr><tr><td>-0.11</td><td>+0.10</td><td>686</td><td></td><td></td></tr><tr><td>+0.22</td><td>+0.37</td><td>121</td><td>JAMES</td><td>68 HBC $\bar{p} p$</td></tr><tr><td>-0.29</td><td></td><td></td><td>FELDMAN</td><td>67B OSPK $\pi^- p \to K^0 \Lambda$</td></tr><tr><td>0.0</td><td>±0.25</td><td>116</td><td>4 HILL</td><td>67 DBC $K^+ d \to K^0 p p$</td></tr><tr><td>-0.20</td><td>±0.10</td><td>335</td><td></td><td></td></tr><tr><td>-0.21</td><td>+0.11</td><td>196</td><td>AUBERT</td><td>65 HLBC $K^+$ charge exch.</td></tr><tr><td>-0.44</td><td>+0.32</td><td>152</td><td>5 BALDO...</td><td>65 HLBC $K^+$ charge exch.</td></tr><tr><td>-0.30</td><td>+0.40</td><td>109</td><td>6 FRANZINI</td><td>65 HBC $\bar{p} p$</td></tr></tbody></table>

1 Superseded by ANGELOPOULOS 01B.

2 BURGUN 72 is a final result which includes BURGUN 71.

3 First GRAHAM 72 value is second GRAHAM 72 value combined with MANTSCH 72.

4 Footnote 10 of HILL 67 should read +0.58, not -0.58 (private communication) CHO 70 is analysis of unambiguous events in new data and HILL 67.

5 BALDO-CEOLIN 65 gives $x$ and $\theta$ converted by us to Re($x$) and Im($x$).

6 FRANZINI 65 gives $x$ and $\theta$ for Re($x$) and Im($x$). See SCHMIDT 67.

## $K_L^0$ REFERENCES

<table><tr><td>AAJI</td><td>23AE</td><td>PR D108 L031102</td><td>R. Aaij et al.</td><td>(LHCb Collab.)</td></tr><tr><td>AHN</td><td>21</td><td>PRL 126 121801</td><td>J.K. Ahn et al.</td><td>(KOTO Collab.)</td></tr><tr><td>SHIMIZU</td><td>20</td><td>PR D102 051103</td><td>N. Shimizu et al.</td><td>(KOTO Collab.)</td></tr><tr><td>AHN</td><td>19</td><td>PRL 122 021802</td><td>J.K. Ahn et al.</td><td>(KOTO Collab.)</td></tr><tr><td>AHN</td><td>17</td><td>PTEP 2017 021C01</td><td>J.K. Ahn et al.</td><td>(KOTO Collab.)</td></tr><tr><td>BRFIT</td><td>16</td><td>RPP 2016 edition</td><td>C.-J. Lin</td><td>(PDG Collab.)</td></tr><tr><td>ETAFIT</td><td>16</td><td>RPP 2016 edition</td><td>C.-J. Lin</td><td>(PDG Collab.)</td></tr><tr><td>SUPERWEAK</td><td>16</td><td>RPP 2016 edition</td><td>C.-J. Lin</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>ABOUZAID</td><td>11A</td><td>PRL 107 201803</td><td>E. Abouzaid et al.</td><td>(KTeV Collab.)</td></tr><tr><td>OGATA</td><td>11</td><td>PR D84 052009</td><td>R. Ogata et al.</td><td>(KEK E391a Collab.)</td></tr><tr><td>TUNG</td><td>11</td><td>PR D83 031101</td><td>Y.C. Tung et al.</td><td>(KEK E391a Collab.)</td></tr><tr><td>ABOUZAID</td><td>10</td><td>PR D81 052001</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>AHN</td><td>10</td><td>PR D81 072004</td><td>J.K. Ahn et al.</td><td>(KEK E391a Collab.)</td></tr><tr><td>ABOUZAID</td><td>08</td><td>PR D77 112004</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>ABOUZAID</td><td>08A</td><td>PR D78 032009</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>ABOUZAID</td><td>08B</td><td>PR D78 032014</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>ABOUZAID</td><td>08C</td><td>PR 100 131803</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>AHN</td><td>08</td><td>PR 100 201802</td><td>J.K. Ahn et al.</td><td>(KEK E391a Collab.)</td></tr><tr><td>AMBROINO</td><td>08F</td><td>EPJ C55 539</td><td>F. Ambroino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>ABOUZAID</td><td>07B</td><td>PRL 99 051804</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>ABOUZAID</td><td>07C</td><td>PRL 99 081803</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>ABOUZAID</td><td>07D</td><td>PRL 100 052001</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>AMBROINO</td><td>07C</td><td>JHEP 0712 105</td><td>F. Ambroino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>ANDRE</td><td>07</td><td>ANP 322 2518</td><td>T. Andre</td><td>(EFI)</td></tr><tr><td>LAI</td><td>07</td><td>PL B645 26</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>LAI</td><td>07A</td><td>PL B647 341</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>NIX</td><td>07</td><td>PR D76 011101</td><td>J. Nix et al.</td><td>(KEK E391a Collab.)</td></tr><tr><td>ABOUZAID</td><td>06</td><td>PRL 96 101801</td><td>E. Abouzaid et al.</td><td>(KTeV Collab.)</td></tr><tr><td>ABOUZAID</td><td>06A</td><td>PR D74 032004</td><td>E. Abouzaid et al.</td><td>(KTeV Collab.)</td></tr><tr><td>Also</td><td>06C</td><td>PR D74 039905 (errat.)</td><td>E. Abouzaid et al.</td><td>(KTeV Collab.)</td></tr><tr><td>ABOUZAID</td><td>06C</td><td>PR D74 097101</td><td>E. Abouzaid et al.</td><td>(KEK E391a Collab.)</td></tr><tr><td>AHN</td><td>06</td><td>PR D74 051105</td><td>J.K. Ahn et al.</td><td>(KEK E391a Collab.)</td></tr><tr><td>Also</td><td>06</td><td>PR D74 079901 (errat.)</td><td>J.K. Ahn et al.</td><td>(KEK E391a Collab.)</td></tr><tr><td>AMBROINO</td><td>06</td><td>PL B632 43</td><td>F. Ambroino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>AMBROINO</td><td>06D</td><td>PL B636 166</td><td>F. Ambroino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>AMBROINO</td><td>06F</td><td>PL B638 140</td><td>F. Ambroino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>BATLEY</td><td>06B</td><td>PL B633 173</td><td>J.R. Batley et al.</td><td>(CERN NA48/2 Collab.)</td></tr><tr><td>HILL</td><td>06</td><td>PR D74 096006</td><td>(FNAL)</td><td></td></tr><tr><td>PDG</td><td>JP</td><td>JP G33 1</td><td>W.-M. Yao et al.</td><td>(PDG Collab.)</td></tr><tr><td>ALEXOPOUL...</td><td>05</td><td>PR D71 012001</td><td>T. Alexopoulos et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>AMBROINO</td><td>05C</td><td>PL B626 15</td><td>F. Ambroino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>CABIBBO</td><td>05</td><td>JHEP 0503 021</td><td>N. Cabibbo, G. Isidori</td><td>(CERN, ROMAI, FRAS)</td></tr><tr><td>LAI</td><td>05</td><td>PL B605 247</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>LAI</td><td>05B</td><td>PL B615 31</td><td>A. Lai et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>PARK</td><td>05</td><td>PRL 94 021801</td><td>H.K. Park et al.</td><td>(FNAL HyperCP Collab.)</td></tr><tr><td>ALAVI-HARATI 04A</td><td>04</td><td>PR D93 021805</td><td>A. Alavi-Harati et al.</td><td>(FNAL KTeV/E799 Collab.)</td></tr><tr><td>ALEXOPOUL...</td><td>04</td><td>PR D70 092006</td><td>T. Alexopoulos et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>ALEXOPOUL...</td><td>04A</td><td>PR D70 092007</td><td>T. Alexopoulos et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>BATLEY</td><td>04</td><td>PL B959 75</td><td>J.R. Batley et al.</td><td>(CERN NA48 Collab.)</td></tr><tr><td>CIRIGLIANO</td><td>04</td><td>EPJ C35 53</td><td>V. Cirigliano, H. Neufeld, H. Pich</td><td>(CIT, VALUE+)</td></tr></table>
<table>
  <tbody>
    <tr>
      <td>SAAL</td>
      <td>69</td>
      <td>Thesis</td>
      <td>H.J. Saal</td>
      <td>(COLU)</td>
    </tr>
    <tr>
      <td>ABRAMS</td>
      <td>68B</td>
      <td>PR 176 1603</td>
      <td>R.J. Abrams et al.</td>
      <td>(ILL)</td>
    </tr>
    <tr>
      <td>ARNOLD</td>
      <td>68B</td>
      <td>PL 28 56</td>
      <td>R.G. Arnold et al.</td>
      <td>(CERN, ORSAY)</td>
    </tr>
    <tr>
      <td>BASELE</td>
      <td>68B</td>
      <td>PL 28 58</td>
      <td>P. Basile et al.</td>
      <td>(SACL)</td>
    </tr>
    <tr>
      <td>BENNETT</td>
      <td>68B</td>
      <td>PL 27B 244</td>
      <td>S. Bennett et al.</td>
      <td>(COLU, CERN)</td>
    </tr>
    <tr>
      <td>BLANPIED</td>
      <td>68B</td>
      <td>PRL 21 1650</td>
      <td>W.A. Blanpied et al.</td>
      <td>(CASE, HARV, MCGI)</td>
    </tr>
    <tr>
      <td>BOHM</td>
      <td>68B</td>
      <td>PL 27B 594</td>
      <td>A. Bohm et al.</td>
      <td></td>
    </tr>
    <tr>
      <td>BUDAGOV</td>
      <td>68</td>
      <td>NC 57A 182</td>
      <td>L.A. Budagov et al.</td>
      <td>(CERN, ORSAY, IPNP)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td>68</td>
      <td>PL 28B 215</td>
      <td>I.A. Budagov et al.</td>
      <td>(CERN, ORSAY, EPOL)</td>
    </tr>
    <tr>
      <td>JAMES</td>
      <td>68</td>
      <td>NP B8 365</td>
      <td>F. James, H. Briand</td>
      <td>(IPNP, CERN)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td>68</td>
      <td>PRL 21 257</td>
      <td>J.A. Helland, M.J. Longo, K.K. Young</td>
      <td>(UCLA, MICH)</td>
    </tr>
    <tr>
      <td>KULYUKINA</td>
      <td>68</td>
      <td>JETP 26 20</td>
      <td>L.A. Kulyukina et al.</td>
      <td>(JINR)</td>
    </tr>
    <tr>
      <td colspan="4">Translated from ZETF 52 29.</td>
    </tr>
    <tr>
      <td>KUNZ</td>
      <td>68</td>
      <td>Thesis PU-68-46</td>
      <td>P.F. Kunz</td>
      <td>(PRIN)</td>
    </tr>
    <tr>
      <td>BENNETT</td>
      <td>68</td>
      <td>PRL 19 993</td>
      <td>S. Bennett et al.</td>
      <td>(COLU)</td>
    </tr>
    <tr>
      <td>DEBOUARD</td>
      <td>67</td>
      <td>NC 52A 662</td>
      <td>X. de Bouard et al.</td>
      <td>(CERN)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td>67</td>
      <td>PL 15 58</td>
      <td>X. de Bouard et al.</td>
      <td>(CERN, ORSAY, PMIM)</td>
    </tr>
    <tr>
      <td>DEVLIN</td>
      <td>67</td>
      <td>PRL 18 54</td>
      <td>T.J. Devlin et al.</td>
      <td>(PRIN, UMD)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td>67</td>
      <td>PR 169 1045</td>
      <td>G.A. Sayer et al.</td>
      <td>(UMD, PPA, PRIN)</td>
    </tr>
    <tr>
      <td>DORFAN</td>
      <td>67</td>
      <td>PRL 19 987</td>
      <td>D.E. Dorfan et al.</td>
      <td>(SLAC, LRL)</td>
    </tr>
    <tr>
      <td>FELDMAN</td>
      <td>67B</td>
      <td>PR 155 1611</td>
      <td>L. Feldman et al.</td>
      <td>(PENN)</td>
    </tr>
    <tr>
      <td>FITCH</td>
      <td>67</td>
      <td>PR 164 1711</td>
      <td>V.L. Fitch 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>HILL</td>
      <td>67</td>
      <td>PRL 19 668</td>
      <td>D.G. Hill et al.</td>
      <td>(BNL, CMU)</td>
    </tr>
    <tr>
      <td>HOPKINS</td>
      <td>67</td>
      <td>PRL 19 185</td>
      <td>H.W.K. Hopkins, T.C. Bacon, F.R. Eisler</td>
      <td>(BNL)</td>
    </tr>
    <tr>
      <td>NEFKENS</td>
      <td>67</td>
      <td>PR 157 1233</td>
      <td>B.M.K. Nefkens et al.</td>
      <td>(ILL)</td>
    </tr>
    <tr>
      <td>SCHMIDT</td>
      <td>67</td>
      <td>Thesis Nevis 160</td>
      <td>P. Schmidt</td>
      <td>(COLU)</td>
    </tr>
    <tr>
      <td>BEHR</td>
      <td>66</td>
      <td>PL 22 540</td>
      <td>L. Behr et al.</td>
      <td>(EPOL, MILA, PADO, ORSAY)</td>
    </tr>
    <tr>
      <td>HAWKINS</td>
      <td>66</td>
      <td>PL 21 238</td>
      <td>C.J.B. Hawkins</td>
      <td>(YALE)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td>66</td>
      <td>PL 156 1444</td>
      <td>C.J.B. Hawkins</td>
      <td>(YALE)</td>
    </tr>
    <tr>
      <td>ANDERSON</td>
      <td>65</td>
      <td>PRL 14 475</td>
      <td>J.A. Anderson et al.</td>
      <td>(LRL, WISC)</td>
    </tr>
    <tr>
      <td>ASTBURY</td>
      <td>65B</td>
      <td>PL 18 175</td>
      <td>P. Astbury et al.</td>
      <td>(CERN, ZURI)</td>
    </tr>
    <tr>
      <td>AUBERT</td>
      <td>65</td>
      <td>PL 17 59</td>
      <td>B. Aubert et al.</td>
      <td>(EPOL, ORSAY)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td>65</td>
      <td>PL 24B 75</td>
      <td>J.P. Lowys et al.</td>
      <td>(EPOL, ORSAY)</td>
    </tr>
    <tr>
      <td>BALDO...</td>
      <td>65</td>
      <td>NC 38 684</td>
      <td>M. Baldo-Coeлин et al.</td>
      <td>(PADO)</td>
    </tr>
    <tr>
      <td>FRANZINI</td>
      <td>65</td>
      <td>PR 140 B127</td>
      <td>P. Franzini et al.</td>
      <td>(COLU, RUTG)</td>
    </tr>
    <tr>
      <td>GUIDONI</td>
      <td>65</td>
      <td>Argonne Conf. 49</td>
      <td>P. Guidoni et al.</td>
      <td>(BNL, YALE)</td>
    </tr>
    <tr>
      <td>HOPKINS</td>
      <td>65</td>
      <td>Argonne Conf. 67</td>
      <td>H.W.K. Hopkins, T.C. Bacon, F. Eisler</td>
      <td>(VAND+)</td>
    </tr>
    <tr>
      <td>BENKANYAN</td>
      <td>64B</td>
      <td>Argonne Conf. 2 102</td>
      <td>A.S. Aleksanyan et al.</td>
      <td>(YERE)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td>64B</td>
      <td>JETP 19 1019</td>
      <td>A.S. Aleksanyan et al.</td>
      <td>(LEBD, MPEI, YERE)</td>
    </tr>
    <tr>
      <td>ANIKINA</td>
      <td>64</td>
      <td>Translated from ZETF 46 1504.</td>
      <td>M.K. Anikina et al.</td>
      <td>(GEOR, JINR)</td>
    </tr>
    <tr>
      <td>FITCH</td>
      <td>61</td>
      <td>NC 22 1160</td>
      <td>V.L. Fitch, P.A. Piroue, R.B. Perkins</td>
      <td>(PRIN+)</td>
    </tr>
    <tr>
      <td>GOOD</td>
      <td>61</td>
      <td>PR 124 1223</td>
      <td>R.H. Good et al.</td>
      <td>(LRL)</td>
    </tr>
  </tbody>
</table>

OTHER RELATED PAPERS

<table>
  <tbody>
    <tr>
      <td>HAYAKAWA</td>
      <td>93</td>
      <td>PR D48 1150</td>
      <td>M. Hayakawa, A.I. Sanda</td>
      <td>(NAGO)</td>
    </tr>
    <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>WINSTEIN</td>
      <td>93</td>
      <td>RMP 65 1149</td>
      <td>B. Weinstein, L. Wolfenstein</td>
      <td></td>
    </tr>
    <tr>
      <td>BATTISTON</td>
      <td>92</td>
      <td>"The Search for Direct CP Violation"</td>
      <td>R. Battistoni</td>
      <td>(PGIA, CERN, TRSTT)</td>
    </tr>
    <tr>
      <td>BEIR</td>
      <td>92</td>
      <td>PR D46 2265</td>
      <td>C.O. Dib, R.D. Peccei</td>
      <td>(UCLA)</td>
    </tr>
    <tr>
      <td>KLEINKNECHT</td>
      <td>92</td>
      <td>CNPQ 20 281</td>
      <td>K. Kleinknecht</td>
      <td>(MAINZ)</td>
    </tr>
    <tr>
      <td>NEW Results on CP Violation in Decays of</td>
      <td></td>
      <td>Neutral K Mesons.</td>
      <td>K. Kleinknecht</td>
      <td>(MAINZ)</td>
    </tr>
    <tr>
      <td>KLEINKNECHT</td>
      <td>90</td>
      <td>ZPHY C46 557</td>
      <td></td>
      <td>(EDIN)</td>
    </tr>
    <tr>
      <td>PEACH</td>
      <td>90</td>
      <td>JP G16 131</td>
      <td>K.J. Peach</td>
      <td>(TRIU)</td>
    </tr>
    <tr>
      <td>PRYMAN</td>
      <td>89</td>
      <td>IJMP A4 79</td>
      <td>D.A. Bryman</td>
      <td></td>
    </tr>
    <tr>
      <td>"Rare Kaon Decays"</td>
      <td></td>
      <td></td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <td>KLEINKNECHT</td>
      <td>76</td>
      <td>ARNPS 26 1</td>
      <td>K. Kleinknecht</td>
      <td>(DORT)</td>
    </tr>
    <tr>
      <td>GINSBERG</td>
      <td>73</td>
      <td>PR D8 3887</td>
      <td>E.S. Ginsberg, J. Smith</td>
      <td>(MIT, STON)</td>
    </tr>
    <tr>
      <td>GINSBERG</td>
      <td>70</td>
      <td>PR D1 229</td>
      <td>E.S. Ginsberg</td>
      <td>(HAIF)</td>
    </tr>
    <tr>
      <td>HEUSSE</td>
      <td>70</td>
      <td>LNC 3 449</td>
      <td>P. Heusse et al.</td>
      <td>(ORSAY)</td>
    </tr>
    <tr>
      <td>CRONIN</td>
      <td>68C</td>
      <td>Vienna Conf. 281</td>
      <td>J.W. Cronin</td>
      <td>(PRIN)</td>
    </tr>
    <tr>
      <td>RUBBIA</td>
      <td>67</td>
      <td>PL 24B 531</td>
      <td>C. Rubbia, J. Steinberger</td>
      <td>(CERN, COLU)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td></td>
      <td>PL 23 167</td>
      <td>C. Rubbia, J. Steinberger</td>
      <td>(CERN, COLU)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td></td>
      <td>PL 20 207</td>
      <td>Affl-Steinberger et al.</td>
      <td>(CERN)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td></td>
      <td>PL 21 595</td>
      <td>Affl-Steinberger et al.</td>
      <td>(CERN)</td>
    </tr>
    <tr>
      <td>AUERBACH</td>
      <td>66</td>
      <td>PR 149 1052</td>
      <td>L.B. Auerbach et al.</td>
      <td>(PENN)</td>
    </tr>
    <tr>
      <td>Also</td>
      <td></td>
      <td>PR 112 192</td>
      <td>L.B. Auerbach et al.</td>
      <td>(PENN)</td>
    </tr>
    <tr>
      <td>STONE</td>
      <td>66B</td>
      <td>PRL 17 116</td>
      <td>A. Firestone et al.</td>
      <td>(YALE, BNL)</td>
    </tr>
    <tr>
      <td>BEHR</td>
      <td>65</td>
      <td>Argonne Conf. 59</td>
      <td>L. Behr et al.</td>
      <td>(EPOL, MILA, PADO)</td>
    </tr>
    <tr>
      <td>MESTVIRISH...</td>
      <td>65</td>
      <td>JINR P 2449</td>
      <td>A.N. Mestvirshilli et al.</td>
      <td>(JINR)</td>
    </tr>
    <tr>
      <td>TRILLING</td>
      <td>65B</td>
      <td>UCRL 16473</td>
      <td>G.N. Trilling</td>
      <td>(LRL)</td>
    </tr>
    <tr>
      <td colspan="4">Updated from 1965 Argonne Conference, page 115.</td>
    </tr>
    <tr>
      <td>JOVANOV...</td>
      <td>63</td>
      <td>BNL Conf. 42</td>
      <td>J.V. Jovanovich et al.</td>
      <td>(BNL, UMD)</td>
    </tr>
  </tbody>
</table>

$K_0^*(700)$

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

also known as $\kappa$; was $K_0^*(800)$

See the related review(s):

Scalar Mesons below 1 GeV

$K_0^*(700) \text{ T-Matrix Pole } \sqrt{s}$

<table>
  <thead>
    <tr>
      <th>VALUE (MeV)</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>(630-730) - i (260-340) OUR ESTIMATE</td>
      <td>(see Fig. 64.1 in the review)</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <td>(702 ± 12<sup>+4</sup><sub>-5</sub>) - i (285 ± 16<sup>+8</sup><sub>-13</sub>)</td>
      <td>1 DANILKIN</td>
      <td>21 RVUE</td>
      <td>Compilation</td>
    </tr>
    <tr>
      <td>(648 ± 7) - i (280 ± 16)</td>
      <td>2 PELAEZ</td>
      <td>20 RVUE</td>
      <td>πK → πK</td>
    </tr>
    <tr>
      <td>(670 ± 18) - i (295 ± 28)</td>
      <td>3 PELAEZ</td>
      <td>17 RVUE</td>
      <td>πK → πK</td>
    </tr>
    <tr>
      <td>(764 ± 63<sup>+71</sup><sub>-54</sub>) - i (306 ± 149<sup>+143</sup><sub>-85</sub>)</td>
      <td>4 ABLIKIM</td>
      <td>11B BES2</td>
      <td>1.3k J/ψ → K<sup>0</sup><sub>S</sub> K<sup>0</sup><sub>S</sub> π<sup>+</sup> π<sup>-</sup></td>
    </tr>
    <tr>
      <td>(665 ± 9) - i (268<sup>+21</sup><sub>-6</sub>)</td>
      <td>5 GUO</td>
      <td>11B RVUE</td>
      <td></td>
    </tr>
    <tr>
      <td>(849 ± 77<sup>+18</sup><sub>-14</sub>) - i (256 ± 40<sup>+46</sup><sub>-22</sub>)</td>
      <td>4 ABLIKIM</td>
      <td>10E BES2</td>
      <td>1.4k J/ψ → K<sup>±</sup> K<sup>0</sup><sub>S</sub> π<sup>±</sup> π<sup>0</sup></td>
    </tr>
    <tr>
      <td>(663 ± 8 ± 34) - i (329 ± 5 ± 22)</td>
      <td>6 BUGG</td>
      <td>10 RVUE</td>
      <td>S-matrix pole</td>
    </tr>
    <tr>
      <td>(706.0 ± 1.8 ± 22.8) - i (319.4 ± 2.2 ± 20.2)</td>
      <td>7 BONVICINI</td>
      <td>08A CLEO</td>
      <td>141k D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> π<sup>+</sup></td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>(841 ± 30<sup>+81</sup><sub>-73</sub>) - i (309 ± 45<sup>+48</sup><sub>-72</sub>)</td>
      <td>4 ABLIKIM</td>
      <td>06C BES2</td>
      <td>25k J/ψ → <span style="text-decoration: overline;">K</span><sup>*(892)</sup>0 K<sup>+</sup> π<sup>-</sup></td>
    </tr>
    <tr>
      <td>(750<sup>+30</sup><sub>-55</sub>) - i (342 ± 60)</td>
      <td>8 BUGG</td>
      <td>06 RVUE</td>
      <td>πK → πK</td>
    </tr>
    <tr>
      <td>(658 ± 13) - i (279 ± 12)</td>
      <td>9 DESCOTES-G..06</td>
      <td>06 RVUE</td>
      <td>Kp → K<sup>-</sup> π<sup>+</sup> n</td>
    </tr>
    <tr>
      <td>757 ± 33) - i (279 ± 41)</td>
      <td>10 GUO</td>
      <td>06 RVUE</td>
      <td>K<sup>-</sup> p → K<sup>-</sup> π<sup>+</sup> n</td>
    </tr>
    <tr>
      <td>(694 ± 53) - i (303 ± 30)</td>
      <td>11 ZHOU</td>
      <td>06 RVUE</td>
      <td>Kp → K<sup>-</sup> π<sup>+</sup> n</td>
    </tr>
    <tr>
      <td>(594 ± 79) - i (362 ± 166)</td>
      <td>11 ZHENG</td>
      <td>04 RVUE</td>
      <td>K<sup>-</sup> p → K<sup>-</sup> π<sup>+</sup> n</td>
    </tr>
    <tr>
      <td>(722 ± 60) - i (386 ± 50)</td>
      <td>11 BUGG</td>
      <td>03 RVUE</td>
      <td>11 K<sup>-</sup> p → K<sup>-</sup> π<sup>+</sup> n</td>
    </tr>
    <tr>
      <td>(875 ± 75) - i (335 ± 110)</td>
      <td>12 ISHIDA</td>
      <td>97B RVUE</td>
      <td>11 K<sup>-</sup> p → K<sup>-</sup> π<sup>+</sup> n</td>
    </tr>
    <tr>
      <td>727 - i 263</td>
      <td>13 VANBEVEREN 86</td>
      <td>RVUE</td>
      <td></td>
    </tr>
  </tbody>
</table>

1 Data driven analysis using partial-wave dispersion relations.

2 Extracted employing $\pi K$ partial wave analysis from ESTABROOKS 78 and ASTON 88, Roy-Steiner equations and once subtracted forward dispersion relations.

3 Reanalysis of ESTABROOKS 78 and ASTON 88 satisfying Forward Dispersion Relations and using sequences of Pade approximants.

4 Extracted from Breit-Wigner parameters.

5 Fit to scattering phase shifts using UchPT amplitudes with explicit resonances.

6 Supersedes BUGG 06. Combined analysis of ASTON 88, ABLIKIM 06C, AITALA 06, and LINK 09 using an s-dependent width with couplings to $K \pi$ and $K \eta'$, and the Adler zero near thresholds.

7 From a complex pole included in the fit. Using parameters from the model that fits data best.

8 Reanalysis of ASTON 88, AITALA 02, and ABLIKIM 06c using for the $\kappa$ an s-dependent width with an Adler zero near threshold.

9 Using Roy-Steiner equations (ROY 71) consistent with unitarity, analyticity and crossing symmetry constraints.

10 From UchPT fitted to MERCER 71, BINGHAM 72 and ESTABROOKS 78. Amplitude shown to be consistent with data of ABLIKIM 06C.

11 Reanalysis of ASTON 88 data.

12 Reanalysis of ASTON 88 using interfering Breit-Wigner amplitudes. Extracted from Breit-Wigner parameters.

13 Unitarized Quark Model.

$K_0^*(700) \text{ Breit-Wigner Mass}$

<table>
  <thead>
    <tr>
      <th>VALUE (MeV)</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>845 ±17</td>
      <td>OUR AVERAGE</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <td>826 ±49</td>
      <td>13k</td>
      <td>1 ABLIKIM</td>
      <td>J/ψ → K<sup>0</sup><sub>S</sub> K<sup>0</sup><sub>S</sub> π<sup>+</sup> π<sup>-</sup></td>
    </tr>
    <tr>
      <td>810 ±68</td>
      <td>14k</td>
      <td>2 ABLIKIM</td>
      <td>J/ψ → K<sup>±</sup> K<sup>0</sup><sub>S</sub> π<sup>+</sup> π<sup>0</sup></td>
    </tr>
    <tr>
      <td>856 ±17</td>
      <td>54k</td>
      <td>LINK</td>
      <td>07B FOCs D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> π<sup>+</sup></td>
    </tr>
    <tr>
      <td>878 ±23</td>
      <td>25k</td>
      <td>3 ABLIKIM</td>
      <td>06C BES2 J/ψ → <span style="text-decoration: overline;">K</span><sup>*(892)</sup>0 K<sup>+</sup> π<sup>-</sup></td>
    </tr>
    <tr>
      <td>797 ±19</td>
      <td>15k</td>
      <td>4,5 AITALA</td>
      <td>02 E791 D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> π<sup>+</sup></td>
    </tr>
  </tbody>
</table>

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

<table>
  <tbody>
    <tr>
      <td>888.0 ± 1.9</td>
      <td>141k</td>
      <td>6 BONVICINI</td>
      <td>08A CLEO D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> π<sup>+</sup></td>
    </tr>
    <tr>
      <td>855 ± 15</td>
      <td>0.6k</td>
      <td>7 CAWLFIELD</td>
      <td>06A CLEO D<sup>0</sup> → K<sup>+</sup> K<sup>-</sup> π<sup>0</sup></td>
    </tr>
    <tr>
      <td>905 ±65</td>
      <td>30</td>
      <td>8 ISHIDA</td>
      <td>97B RVUE 11 K<sup>-</sup> p → K<sup>-</sup> π<sup>+</sup> n</td>
    </tr>
  </tbody>
</table>

1 The Breit-Wigner parameters from a fit with seven intermediate resonances. The S-matrix pole position is $(764 \pm 63^{+71}_{-54}) - i (306 \pm 149^{+143}_{-85})$ MeV.

2 From a fit including ten additional resonances and energy-independent Breit-Wigner width.

3 A fit in the $K_0^*(700) + K^*(892) + K^*(1410)$ model with mass and width of the $K_0^*(700)$ from ABLIKIM 06c well describes the left slope of the $K_0^0$ $\pi^-$ invariant mass spectrum in $\tau^- \to K_0^0 \pi^- \nu_T$ decay studied by EPIFANOV 07. Averaged value from different parameterizations.

4 Not seen by KOPP 01 using 7070 events of $D^0 \to K^- \pi^+ \pi^0$. LINK 02E and LINK 05I show clear evidence for a constant non-resonant scalar amplitude rather than $K_0^*(700)$ in their high statistics analysis of $D^+ \to K^- \pi^+ \mu^+ \nu_T$.

5 AUBERT 07T does not find evidence for the charged $K_0^*(700)$ using 11k events of $D^0 \to K^- K^+ \pi^0$.

6 Using parameters from the model that fits data best.

7 Breit-Wigner parameters. A significant S-wave can be also modeled as a non-resonant contribution.

8 Reanalysis of ASTON 88 using interfering Breit-Wigner amplitudes.

$K_0^*(700) \text{ Breit-Wigner Width}$

<table>
  <thead>
    <tr>
      <th>VALUE (MeV)</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>468 ± 30</td>
      <td>OUR AVERAGE</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <td>449 ±156</td>
      <td>144k</td>
      <td>1.3k</td>
      <td>1 ABLIKIM J/ψ → K<sup>0</sup><sub>S</sub> K<sup>0</sup><sub>S</sub> π<sup>+</sup> π<sup>-</sup></td>
    </tr>
    <tr>
      <td>536 ± 87</td>
      <td>14k</td>
      <td>2 ABLIKIM</td>
      <td>10E BES2 J/ψ → K<sup>±</sup> K<sup>0</sup><sub>S</sub> π<sup>+</sup> π<sup>0</sup></td>
    </tr>
    <tr>
      <td>464 ± 28</td>
      <td>54k</td>
      <td>LINK</td>
      <td>07B FOCs D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> π<sup>+</sup></td>
    </tr>
    <tr>
      <td>499 ± 52</td>
      <td>25k</td>
      <td>3 ABLIKIM</td>
      <td>06C BES2 J/ψ → <span style="text-decoration: overline;">K</span><sup>*(892)</sup>0 K<sup>+</sup> π<sup>-</sup></td>
    </tr>
    <tr>
      <td>410 ± 43</td>
      <td>15k</td>
      <td>4,5 AITALA</td>
      <td>02 E791 D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> π<sup>+</sup></td>
    </tr>
  </tbody>
</table>

1 The Breit-Wigner parameters from a fit with seven intermediate resonances. The S-matrix pole position is $(764 \pm 63^{+71}_{-54}) - i (306 \pm 149^{+143}_{-85})$ MeV.
# Meson Particle Listings

$K_0^*(700), K^*(892)$

² From a fit including ten additional resonances and energy-independent Breit-Wigner width.

³ A fit in the $K_0^*(700) + K^*(892) + K^{*(1410)}$ model with mass and width of the $K_0^*(700)$ from ABLIKIM 06c well describes the left slope of the $K_0^0\pi^-$ invariant mass spectrum in $\tau^- \to K_0^0\pi^-\nu_\tau$ decay studied by EPIFANOV 07. Averaged value from different parameterizations.

⁴ Not seen by KOPP 01 using 7070 events of $D^0 \to K^-\pi^+\pi^0$. LINK 02e and LINK 05i show clear evidence for a constant non-resonant scalar amplitude rather than $K_0^*(700)$ in their high statistics analysis of $D^+ \to K^-\pi^+\mu^+\nu_\mu$.

⁵ AUBERT 07T does not find evidence for the charged $K_0^*(700)$ using 11k events of $D^0 \to K^-\pi^+\pi^0$.

⁶ Using parameters from the model that fits data best.

⁷ Statistical error only. A fit to the Dalitz plot including the $K_0^*(700)\pm, K^*(892)\pm$, and $\phi$ resonances modeled as Breit-Wigners. A significant S-wave can be also modeled as a non-resonant contribution.

⁸ Reanalysis of ASTON 88 using interfering Breit-Wigner amplitudes.

## $K_0^*(700)$ DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction (Γ<sub>i</sub>/Γ)</th></tr></thead><tbody><tr><td>Γ<sub>1</sub> Kπ</td><td>100 %</td></tr></tbody></table>

## $K_0^*(700)$ REFERENCES

<table><tbody><tr><td>DANILKIN</td><td>21</td><td>PR D103 114023</td><td>I. Danilkin, O. Deineka, M. Vanderhaegen (MAINZ)</td></tr><tr><td>PELAEZ</td><td>20</td><td>PRL 124 172001</td><td>J.R. Pelaez et al.</td></tr><tr><td>PELAEZ</td><td>17</td><td>EPJ C77 91</td><td>J.R. Pelaez, A.Rodas, J.R. de Elvira</td></tr><tr><td>PELAEZ</td><td>11B</td><td>PL B698 183</td><td>M. Ablikim et al.</td></tr><tr><td>ABLIKIM</td><td>11B</td><td>PR D84 034005</td><td>Z.-H. Guo, J.A. Oller</td></tr><tr><td>ABLIKIM</td><td>10E</td><td>PL B693 88</td><td>M. Ablikim et al.</td></tr><tr><td>BUGG</td><td>10</td><td>PR D81 014002</td><td>D.V. Bugg</td></tr><tr><td>LINK</td><td>09</td><td>PL B681 14</td><td>J.M. Link et al.</td></tr><tr><td>BONVICINI</td><td>08A</td><td>PR D78 052001</td><td>G. Bonvicini et al.</td></tr><tr><td>AUBERT</td><td>07T</td><td>PR D76 011102</td><td>B. Aubert et al.</td></tr><tr><td>EPIFANOV</td><td>07T</td><td>PL B654 65</td><td>D. Epifanov et al.</td></tr><tr><td>LINK</td><td>07B</td><td>PL B653 1</td><td>J.M. Link et al.</td></tr><tr><td>ABLIKIM</td><td>06C</td><td>PL B633 681</td><td>M. Ablikim et al.</td></tr><tr><td>AITALA</td><td>06</td><td>PR D73 032004</td><td>E.M. Aitala et al.</td></tr><tr><td>Also</td><td>06</td><td>PR D74 059901 (errat.)</td><td>E.M. Aitala et al.</td></tr><tr><td>BUGG</td><td>06</td><td>PL B632 471</td><td>D.V. Bugg</td></tr><tr><td>CAWLFIELD</td><td>06A</td><td>PR D74 031108</td><td>C. Cawfield et al.</td></tr><tr><td>DESCOTES-G...</td><td>06</td><td>EPJ C48 553</td><td>S. Descotes-Genon, B. Moussallam</td></tr><tr><td>GUO</td><td>06</td><td>NP A773 78</td><td>F.K. Guo et al.</td></tr><tr><td>ZHOU</td><td>06</td><td>NP A775 212</td><td>Z.Y. Zhou, H.Q. Zheng</td></tr><tr><td>LINK</td><td>05I</td><td>PL B621 72</td><td>J.M. Link et al.</td></tr><tr><td>ZHENG</td><td>04</td><td>NP A733 235</td><td>H.Q. Zheng et al.</td></tr><tr><td>BUGG</td><td>03</td><td>PL B572 1</td><td>D.V. Bugg</td></tr><tr><td>AITALA</td><td>02E</td><td>PRL 89 121801</td><td>E.M. Aitala et al.</td></tr><tr><td>LINK</td><td>02E</td><td>PL B535 43</td><td>J.M. Link et al.</td></tr><tr><td>KOPP</td><td>01</td><td>PR D63 092001</td><td>S. Kopp et al.</td></tr><tr><td>ISHIDA</td><td>97B</td><td>PTP 98 621</td><td>S. Ishida et al.</td></tr><tr><td>ASTON</td><td>88</td><td>NP B296 493</td><td>D. Aston et al.</td></tr><tr><td>VANBEVEREN</td><td>86</td><td>ZPHY C30 615</td><td>E. van Beveren et al.</td></tr><tr><td>ESTABROOKS</td><td>78</td><td>NP B133 490</td><td>P.G. Estabrooks et al.</td></tr><tr><td>BINGHAM</td><td>72</td><td>NP B41 1</td><td>H.H. Bingham et al.</td></tr><tr><td>MERCER</td><td>71</td><td>NP B32 381</td><td>R. Mercer et al.</td></tr><tr><td>ROY</td><td>71</td><td>PL B63 353</td><td>S.M. Roy</td></tr></tbody></table>

$K^*(892)$

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

## $K^*(892)$ T-Matrix Pole $\sqrt{s}$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4">(890 ± 14) - i (26 ± 6) OUR ESTIMATE</td></tr><tr><td>(890 ± 2) - i (25.6 ± 1.2)</td><td>1 PELAEZ</td><td>20</td><td>RVUE πK → πK</td></tr><tr><td>(892 ± 1) - i (29 ± 1)</td><td>2 PELAEZ</td><td>17</td><td>RVUE πK → πK</td></tr><tr><td>(889 ± 13) - i (24 ± 4)</td><td>3 PELAEZ</td><td>04A</td><td>RVUE πK → πK</td></tr></tbody></table>

¹ Extracted employing $\pi K$ partial wave analysis from ESTABROOKS 78 and ASTON 88, Roy-Steiner equations and once subtracted forward dispersion relations.

² Reanalysis of ESTABROOKS 78 and ASTON 88 satisfying Forward Dispersion Relations and using sequences of Pade approximants.

³ Reanalysis of data from ESTABROOKS 78 and ASTON 88 in the unitarized ChPT model.

## $K^*(892)$ MASS

### CHARGED ONLY, HADROPRODUCED

<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>891.67 ± 0.26</td><td>OUR AVERAGE</td><td></td><td></td><td></td><td></td></tr><tr><td>892.2 ± 0.5</td><td>± 1.7</td><td>ALBRECHT</td><td>20</td><td>CBAR</td><td>0.9 p̄p → K<sup>+</sup>K<sup>-</sup>π<sup>0</sup></td></tr><tr><td>892.6 ± 0.5</td><td>± 0.5</td><td>BAUBILLIER</td><td>84B</td><td>HBC</td><td>8.25 K<sup>-</sup>p → K̄Oπ<sup>-</sup>p</td></tr><tr><td>888 ± 3</td><td>± 5840</td><td>NAPIER</td><td>84</td><td>SPEC +</td><td>200 π<sup>-</sup>p → 2K<sup>0</sup>S<sup>-</sup>X</td></tr><tr><td>891 ± 1</td><td>± 1</td><td>NAPIER</td><td>84</td><td>SPEC +</td><td>200 π<sup>-</sup>p → 2K<sup>0</sup>S<sup>-</sup>X</td></tr><tr><td>891.7 ± 2.1</td><td>± 3700</td><td>BARTH</td><td>83</td><td>HBC</td><td>70 K<sup>+</sup>p → K<sup>0</sup>π<sup>+</sup>X</td></tr><tr><td>891 ± 1</td><td>± 4100</td><td>TOAFF</td><td>81</td><td>HBC</td><td>6.5 K<sup>-</sup>p → K̄Oπ<sup>-</sup>p</td></tr><tr><td>892.8 ± 1.6</td><td>± 1800</td><td>AJINENKO</td><td>80</td><td>HBC +</td><td>32 K<sup>+</sup>p → K<sup>0</sup>π<sup>+</sup>X</td></tr><tr><td>890.7 ± 0.9</td><td>± 1800</td><td>AGUILAR...</td><td>78B</td><td>HBC</td><td>0.76 p̄p → K<sup>+</sup>K<sup>0</sup>π<sup>±</sup></td></tr><tr><td>886.6 ± 2.4</td><td>± 1225</td><td>BALAND</td><td>78</td><td>HBC ±</td><td>12 p̄p → (Kπ)<sup>±</sup>X</td></tr></tbody></table>

<table><tbody><tr><td>891.7 ± 0.6</td><td>6706</td><td>COOPER</td><td>78</td><td>HBC ±</td><td>0.76 p̄p → (Kπ)<sup>±</sup>X</td></tr><tr><td>891.9 ± 0.7</td><td>9000</td><td>1 PALER</td><td>75</td><td>HBC</td><td>14.3 K<sup>-</sup>p → (Kπ)<sup>-</sup>X</td></tr><tr><td>892.2 ± 1.5</td><td>4404</td><td>AGUILAR...</td><td>71B</td><td>HBC</td><td>3.9, 4.6 K<sup>-</sup>p → (Kπ)<sup>-</sup>p</td></tr><tr><td>891 ± 2</td><td>1000</td><td>CRENNELL</td><td>69D</td><td>DBC</td><td>3.9 K<sup>+</sup>N → K<sup>0</sup>π<sup>-</sup>X</td></tr><tr><td>890 ± 3.0</td><td>720</td><td>BARLOW</td><td>67</td><td>HBC ±</td><td>1.2 p̄p → (K<sup>0</sup>π<sup>+</sup>)K<sup>+</sup></td></tr><tr><td>889 ± 3.0</td><td>600</td><td>BARLOW</td><td>67</td><td>HBC ±</td><td>1.2 p̄p → (K<sup>0</sup>π<sup>+</sup>)K<sup>+</sup></td></tr><tr><td>891 ± 2.3</td><td>620</td><td>2 DEBAERE</td><td>67B</td><td>HBC +</td><td>3.5 K<sup>+</sup>p → K<sup>0</sup>π<sup>+</sup>p</td></tr><tr><td>891.0 ± 1.2</td><td>1700</td><td>3 WOJCICKI</td><td>64</td><td>HBC</td><td>1.7 K<sup>-</sup>p → K̄Oπ<sup>-</sup>p</td></tr></tbody></table>

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

<table><tbody><tr><td>893.6 ± 0.1</td><td>+0.2<br>-0.3</td><td>183k</td><td>ABLIKIM</td><td>19AQ BES</td><td>±</td><td>J/ψ → K<sup>+</sup>K<sup>-</sup>π<sup>0</sup></td></tr><tr><td>895.6 ± 0.8</td><td>4k</td><td>4 LEES</td><td>17C</td><td>BABR</td><td>±</td><td>J/ψ → K<sup>0</sup>π<sup>±</sup>π<sup>+</sup></td></tr><tr><td>893.2 ± 0.1</td><td>± 1.0</td><td>190k</td><td>5 AAIJ</td><td>16N</td><td>LHCB</td><td>D<sup>0</sup> → K<sup>0</sup>S K<sup>0</sup>π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>893.5 ± 1.1</td><td>27k</td><td>6 ABELE</td><td>99D</td><td>CBAR</td><td>±</td><td>0.0 p̄p → K<sup>+</sup>K<sup>-</sup>π<sup>0</sup></td></tr><tr><td>890.4 ± 0.2</td><td>± 0.5</td><td>80k</td><td>7 BIRD</td><td>89</td><td>LASS</td><td>11 K<sup>-</sup>p → K̄Oπ<sup>-</sup>p</td></tr><tr><td>890.0 ± 2.3</td><td>800</td><td>2,3 CLELAND</td><td>82</td><td>SPEC +</td><td>±</td><td>30 K<sup>+</sup>p → K<sup>0</sup>π<sup>+</sup>p</td></tr><tr><td>896.0 ± 1.1</td><td>3200</td><td>2,3 CLELAND</td><td>82</td><td>SPEC +</td><td>±</td><td>50 K<sup>+</sup>p → K<sup>0</sup>Sπ<sup>+</sup>p</td></tr><tr><td>893 ± 1</td><td>3600</td><td>2,3 CLELAND</td><td>82</td><td>SPEC +</td><td>±</td><td>50 K<sup>+</sup>p → K<sup>0</sup>Sπ<sup>-</sup>p</td></tr><tr><td>896.0 ± 1.9</td><td>380</td><td>DELFOSSE</td><td>81</td><td>SPEC +</td><td>±</td><td>50 K<sup>±</sup>p → K<sup>±</sup>π<sup>0</sup>p</td></tr><tr><td>886.0 ± 2.3</td><td>187</td><td>DELFOSSE</td><td>81</td><td>SPEC -</td><td>±</td><td>50 K<sup>±</sup>p → K<sup>±</sup>π<sup>0</sup>p</td></tr><tr><td>894.2 ± 2.0</td><td>765</td><td>2 CLARK</td><td>73</td><td>HBC</td><td>±</td><td>3.13 K<sup>-</sup>p → K̄Oπ<sup>-</sup>p</td></tr><tr><td>894.3 ± 1.5</td><td>1150</td><td>2,3 CLARK</td><td>73</td><td>HBC</td><td>±</td><td>3.3 K<sup>+</sup>p → K̄Oπ<sup>-</sup>p</td></tr><tr><td>892.0 ± 2.6</td><td>341</td><td>2 SCHWEING...</td><td>68</td><td>HBC</td><td>±</td><td>5.5 K<sup>-</sup>p → K̄Oπ<sup>-</sup>p</td></tr></tbody></table>

¹ Inclusive reaction. Complicated background and phase-space effects.

² Mass errors enlarged by us to $Γ/\sqrt{N}$. See note.

³ Number of events in peak reevaluated by us.

⁴ From a Dalitz plot analysis in an isobar model with charged and neutral $K^*(892)$ masses and widths floating.

⁵ Average of fit results with different parametrizations for the $Kπ$ S-wave.

⁶ K-matrix pole.

⁷ From a partial wave amplitude analysis.

### CHARGED ONLY, PRODUCED IN $\tau$ LEPTON DECAYS

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>895.47 ± 0.20</td><td>± 0.74</td><td>53k</td><td>1 EPIFANOV</td><td>07 BELL</td><td>τ<sup>-</sup> → K<sup>0</sup>S π<sup>-</sup>ν<sub>T</sub></td></tr><tr><td colspan="6">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>892.0 ± 0.5</td><td>± 0.5</td><td>2 BOITO</td><td>10</td><td>RVUE</td><td>τ<sup>-</sup> → K<sup>0</sup>S π<sup>-</sup>ν<sub>T</sub></td></tr><tr><td>892.0 ± 0.9</td><td>± 0.9</td><td>3,4 BOITO</td><td>09</td><td>RVUE</td><td>τ<sup>-</sup> → K<sup>0</sup>S π<sup>-</sup>ν<sub>T</sub></td></tr><tr><td>895.3 ± 0.2</td><td>± 0.2</td><td>4,5 JAMIN</td><td>08</td><td>RVUE</td><td>τ<sup>-</sup> → K<sup>0</sup>S π<sup>-</sup>ν<sub>T</sub></td></tr><tr><td>896.4 ± 0.9</td><td>± 0.9</td><td>12k</td><td>6 BONVICINI</td><td>02 CLEO</td><td>τ<sup>-</sup> → K<sup>π</sup>0ν<sub>T</sub></td></tr><tr><td>895 ± 2</td><td>± 2</td><td>7 BARATE</td><td>99R</td><td>ALEC</td><td>τ<sup>-</sup> → K<sup>π</sup>0ν<sub>T</sub></td></tr></tbody></table>

¹ From a fit in the $K_0^*(700) + K^*(892) + K^*(1410)$ model.

² From the pole position of the $Kπ$ vector form factor using EPIFANOV 07 and constraints from $K_{1/3}$ decays in ANTONELLI 10.

³ From the pole position of the $Kπ$ vector form factor in the complex s-plane and using EPIFANOV 07 data.

⁴ Systematic uncertainties not estimated.

⁵ Reanalysis of EPIFANOV 07 using resonance chiral theory.

⁶ Calculated by us from the shift by 4.7 ± 0.9 MeV (statistical uncertainty only) reported in BONVICINI 02 with respect to the world average value from PDG 00.

⁷ With mass and width of the $K^*(1410)$ fixed at 1412 MeV and 227 MeV, respectively.

### NEUTRAL ONLY

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5">895.55 ± 0.20</td><td>OUR AVERAGE</td></tr><tr><td>894.68 ± 0.25</td><td>± 0.05</td><td>1 ABLIKIM</td><td>16F</td><td>BES3</td><td>D<sup>+</sup> → K<sup>-</sup>π<sup>+</sup>e<sup>+</sup>ν<sub>e</sub></td></tr><tr><td>895.4 ± 0.2</td><td>± 0.2</td><td>2 DEL-AMO-SA...</td><td>11H</td><td>BABR</td><td>D<sup>+</sup> → K<sup>-</sup>π<sup>+</sup>e<sup>+</sup>ν<sub>e</sub></td></tr><tr><td>895.7 ± 0.2</td><td>± 0.3</td><td>3 BONVICINI</td><td>08A</td><td>CLEO</td><td>D<sup>+</sup> → K<sup>-</sup>π<sup>+</sup>π<sup>+</sup></td></tr><tr><td>895.41 ± 0.32</td><td>+0.35<br>-0.43</td><td>18k</td><td>4 LINK</td><td>05I</td><td>FOCS D<sup>+</sup> → K<sup>-</sup>π<sup>+</sup>μ<sup>+</sup>ν<sub>μ</sub></td></tr><tr><td>896 ± 2</td><td>± 2</td><td>BARBERIS</td><td>98E</td><td>OMEG</td><td>450 p̄p → p̄pS<sup>+</sup>K<sup>+</sup>*R*</td></tr><tr><td>895.9 ± 0.5</td><td>± 0.2</td><td>ASTON</td><td>88</td><td>OMEG</td><td>20-70 γp</td></tr><tr><td>895.42 ± 0.63</td><td>± 0.63</td><td>25k</td><td>5 ATKINSON</td><td>86</td><td>OMEG 20-70 γp</td></tr><tr><td>894.63 ± 0.76</td><td>± 0.76</td><td>20k</td><td>5 ATKINSON</td><td>86</td><td>OMEG 20-70 γp</td></tr><tr><td>897 ± 1</td><td>± 1</td><td>28k</td><td>EVANGELIS...</td><td>80</td><td>OMEG 10 π<sup>-</sup>p → K<sup>+</sup>K<sup>-</sup> (A, Σ)</td></tr><tr><td>898.4 ± 1.4</td><td>± 1.4</td><td>1180</td><td>AGUILAR...</td><td>78B</td><td>HBC 0.76 p̄p → K<sup>+</sup>F<sup>0</sup>π<sup>±</sup></td></tr><tr><td>894.9 ± 1.6</td><td>± 1.6</td><td>78</td><td>WICKLUND</td><td>78</td><td>ASPK 3, 4, 6 K<sup>±</sup>N → (Kπ)<sup>0</sup>N</td></tr><tr><td>897.6 ± 0.9</td><td>± 0.9</td><td>78</td><td>BOWLER</td><td>78</td><td>DBC 5.4 K<sup>+</sup>d → K<sup>+</sup>π<sup>-</sup>p̄p</td></tr><tr><td>895.5 ± 1.0</td><td>± 1.0</td><td>3600</td><td>MCCUBBIN</td><td>75</td><td>HBC 3.6 K<sup>-</sup>p → K<sup>-</sup>π<sup>+</sup>n</td></tr><tr><td>897.1 ± 0.7</td><td>± 0.7</td><td>22k</td><td>5 PALER</td><td>75</td><td>HBC 14.3 K<sup>-</sup>p → (Kπ)<sup>0</sup>X</td></tr><tr><td>896.0 ± 0.6</td><td>± 0.6</td><td>10k</td><td>FOX</td><td>74</td><td>RVUE 2 K<sup>-</sup>p → K<sup>+</sup>π<sup>+</sup>n</td></tr><tr><td>896.0 ± 0.6</td><td>± 0.6</td><td>10k</td><td>FOX</td><td>74</td><td>RVUE 2 K<sup>+</sup>n → K<sup>+</sup>π<sup>-</sup>p</td></tr><tr><td>896 ± 2</td><td>± 2</td><td>3186</td><td>6 MATISON</td><td>74</td><td>HBC 12 K<sup>+</sup>p → K<sup>+</sup>π<sup>-</sup>Δ</td></tr><tr><td>896 ± 1</td><td>± 1</td><td>3186</td><td>LEWIS</td><td>73</td><td>HBC 2.1-2.7 K<sup>+</sup>p → Kππp</td></tr><tr><td>894.0 ± 1.3</td><td>± 1.3</td><td>73</td><td>6 LINGLIN</td><td>73</td><td>HBC 2-13 K<sup>+</sup>p → K<sup>+</sup>π<sup>-</sup>π<sup>+</sup>p</td></tr><tr><td>898.4 ± 1.3</td><td>± 1.3</td><td>1700</td><td>7 BUCHNER</td><td>72</td><td>DBC 4.6 K<sup>+</sup>n → K<sup>+</sup>π<sup>-</sup>p</td></tr><tr><td>897.9 ± 1.1</td><td>± 1.1</td><td>2934</td><td>7 AGUILAR...</td><td>71B</td><td>HBC 3.9, 4.6 K<sup>-</sup>p → K<sup>-</sup>π<sup>+</sup>n</td></tr><tr><td>898.0 ± 0.7</td><td>± 0.7</td><td>5362</td><td>7 AGUILAR...</td><td>71B</td><td>HBC 3.9, 4.6 K<sup>-</sup>p → K<sup>-</sup>π<sup>+</sup>p</td></tr><tr><td>895 ± 1</td><td>± 1</td><td>4300</td><td>8 HABER</td><td>70</td><td>DBC 3 K<sup>-</sup>N → K<sup>-</sup>π<sup>+</sup>X</td></tr><tr><td>893.7 ± 2.0</td><td>± 2.0</td><td>10k</td><td>DAVIS</td><td>69</td><td>HBC 12 K<sup>+</sup>p → K<sup>+</sup>π<sup>-</sup>π<sup>+</sup>p</td></tr><tr><td>894.7 ± 1.4</td><td>± 1.4</td><td>1040</td><td>7 DAUBER</td><td>67B</td><td>HBC 2.0 K<sup>-</sup>p → K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>p</td></tr></tbody></table>
• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>895.50 ± 0.92 ± 2.6</td><td></td><td><sup>9</sup>ADUSZKIEW...20A</td><td>NA61</td><td>158 p p</td></tr><tr><td>898.1 ± 1.0</td><td>4k</td><td><sup>10</sup>LEES</td><td>17c</td><td>BABR</td><td>J/ψ → K<sup>0</sup> S K<sup>±</sup> π<sup>∓</sup></td></tr><tr><td>895.53 ± 0.17</td><td></td><td>LEES</td><td></td><td></td><td></td></tr><tr><td>894.9 ± 0.5 ± 0.7</td><td>14.4k</td><td><sup>11</sup>MITCHELL</td><td>13f</td><td>BABR</td><td>D<sup>+</sup> → K<sup>+</sup> K<sup>−</sup> π<sup>+</sup></td></tr><tr><td>896.2 ± 0.3</td><td>20k</td><td><sup>12</sup>AUBERT</td><td>09a</td><td>CLEO</td><td>D<sup>+</sup> S<sup>−</sup> → K<sup>+</sup> K<sup>−</sup> π<sup>+</sup></td></tr><tr><td>900.7 ± 1.1</td><td>5900</td><td>BARTH</td><td>83</td><td>HBC</td><td>10.6 e<sup>+</sup> e<sup>−</sup> → K<sup>0</sup> K<sup>±</sup> π<sup>∓</sup>γ</td></tr></table>

1 Taking also into account the $K_0^*(1430)^0$ and $K_2^*(1430)^0$.

2 Taking into account the $K^*(892)^0$, S-wave and P-wave ($K^*(1410)^0$).

3 From the isobar model with a complex pole for the $κ$.

4 Fit to $Kπ$ mass spectrum includes a non-resonant scalar component.

5 Inclusive reaction. Complicated background and phase-space effects.

6 From pole extrapolation.

7 Mass errors enlarged by us to $Γ/\sqrt{N}$. See note.

8 Number of events in peak reevaluated by us.

9 For transverse momenta between 0.6 and 0.8 GeV/c and rapidity $0 < y < 0.5$.

10 From a Dalitz plot analysis in an isobar model with charged and neutral $K^*(892)$ masses and widths floating.

11 This value comes from a fit with $χ^2$ of 178/117.

12 Systematic uncertainties not estimated.

WEIGHTED AVERAGE
895.55±0.20 (Error scaled by 1.7)

<figure><img src="image_521.png" /></figure>

## K*(892) MASSES AND MASS DIFFERENCES

Unrealistically small errors have been reported by some experiments. We use simple “realistic” tests for the minimum errors on the determination of a mass and width from a sample of $N$ events:

$$ \delta_{\min}(m) = \frac{\Gamma}{\sqrt{N}}, \quad \delta_{\min}(\Gamma) = 4 \frac{\Gamma}{\sqrt{N}}. \qquad (1) $$

We consistently increase unrealistic errors before averaging. For a detailed discussion, see the 1971 edition of this Note.

### $mK^*(892)^0 - mK^*(892)^\pm$

<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><strong>6.7±1.2 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>7.7±1.7</td><td>2980</td><td>AGUILAR-...</td><td>78B</td><td>HBC</td><td>±0 0.76 p p → K∓K<sup>0</sup> S π<sup>±</sup></td></tr><tr><td>5.7±1.7</td><td>7338</td><td>AGUILAR-...</td><td>71B</td><td>HBC</td><td>-0 3.9,4.6 K<sup>-</sup> p</td></tr><tr><td>6.3±4.1</td><td>283</td><td><sup>1</sup>BARASH</td><td>67B</td><td>HBC</td><td>0.0 p p</td></tr></tbody></table>

## K*(892) RANGE PARAMETER

All from partial wave amplitude analyses.

<table><thead><tr><th>VALUE (GeV<sup>-1</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>2.1 ± 0.5 ± 0.5</td><td>243k</td><td>1 DEL-AMO-SA.111</td><td>BABR</td><td>0</td><td>D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> e<sup>+</sup> ν<sub>e</sub></td></tr><tr><td>3.96 ± 0.54<sup>+1.31</sup><sub>-0.90</sub></td><td>18k</td><td>2 LINK</td><td>05I</td><td>FOCS</td><td>D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> μ<sup>+</sup> ν<sub>μ</sub></td></tr><tr><td>3.4 ± 0.7</td><td></td><td>ASTON</td><td>88</td><td>LASS</td><td>0 11 K<sup>-</sup> p → K<sup>-</sup> π<sup>+</sup> n</td></tr></tbody></table>

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

$$ 12.1 ± 3.2 ± 3.0 \qquad \text{BIRD} \qquad 89 \text{ LASS} \quad - \quad 11 K^{-} p \rightarrow \bar{K}^{0} \pi^{-} p $$

1 Taking into account the $K^*(892)^0$, S-wave and P-wave ($K^*(1410)^0$).

2 Fit to $Kπ$ mass spectrum includes a non-resonant scalar component.

## K*(892) WIDTH

### CHARGED ONLY, HADROPRODUCED

<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><strong>51.4±0.8 OUR FIT</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><strong>51.4±0.8 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>54.4±0.9±1.7</td><td></td><td>ALBRECHT</td><td>20</td><td>CBAR</td><td>0.9 p p → K<sup>+</sup> K<sup>-</sup> π<sup>0</sup></td></tr><tr><td>49 ± 2</td><td>5840</td><td>BAUBILLIER</td><td>84B</td><td>HBC</td><td>8.25 K<sup>-</sup> p → K<sup>0</sup> π<sup>-</sup> p</td></tr><tr><td>56 ± 4</td><td></td><td>NAPIER</td><td>84</td><td>SPEC</td><td>200 π<sup>-</sup> p → 2K<sup>0</sup> S X</td></tr><tr><td>51 ± 2</td><td>4100</td><td>TOAFF</td><td>81</td><td>HBC</td><td>6.5 K<sup>-</sup> p → K<sup>0</sup> π<sup>-</sup> p</td></tr><tr><td>50.5±5.6</td><td></td><td>AJINENKO</td><td>80</td><td>HBC</td><td>32 K<sup>+</sup> p → K<sup>0</sup> π<sup>+</sup> X</td></tr><tr><td>45.8±3.6</td><td>1800</td><td>AGUILAR-...</td><td>78B</td><td>HBC</td><td>0.76 p p → K<sup>+</sup> K<sup>0</sup> S π<sup>±</sup></td></tr><tr><td>52.0±2.5</td><td>6706</td><td><sup>1</sup>COOPER</td><td>78</td><td>HBC</td><td>0.76 p p → (Kπ)<sup>±</sup> X</td></tr><tr><td>52.1±2.2</td><td>9000</td><td><sup>2</sup>PALER</td><td>75</td><td>HBC</td><td>14.3 K<sup>-</sup> p → (Kπ)<sup>-</sup> X</td></tr><tr><td>46.3±6.7</td><td>765</td><td><sup>1</sup>CLARK</td><td>73</td><td>HBC</td><td>3.13 K<sup>-</sup> p → K<sup>0</sup> π<sup>-</sup> p</td></tr><tr><td>48.2±5.7</td><td>1150</td><td><sup>1,3</sup>CLARK</td><td>73</td><td>HBC</td><td>3.3 K<sup>-</sup> p → K<sup>0</sup> π<sup>-</sup> p</td></tr><tr><td>54.3±3.3</td><td>4404</td><td><sup>1</sup>AGUILAR-...</td><td>71B</td><td>HBC</td><td>3.9,4.6 K<sup>-</sup> p → (Kπ)<sup>-</sup> p</td></tr><tr><td>46 ± 5</td><td>1700</td><td><sup>1,3</sup>WOJCICKI</td><td>64</td><td>HBC</td><td>1.7 K<sup>-</sup> p → K<sup>0</sup> π<sup>-</sup> p</td></tr></tbody></table>

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

<table><tr><td>46.7±0.2<sup>+0.1</sup><sub>-0.2</sub></td><td>183k</td><td>ABLIKIM</td><td>19AQ BES</td><td>±</td><td>J/ψ → K<sup>+</sup> K<sup>-</sup> π<sup>0</sup></td></tr><tr><td>43.6±1.3</td><td>4k</td><td><sup>4</sup>LEES</td><td>17c</td><td>BABR</td><td>J/ψ → K<sup>0</sup> S K<sup>±</sup> π<sup>+</sup></td></tr><tr><td>47.2±0.3±2.3</td><td>190k</td><td><sup>5</sup>AAIJ</td><td>16N</td><td>LHCB</td><td>D<sup>0</sup> → K<sup>0</sup> S K<sup>±</sup> π<sup>+</sup></td></tr><tr><td>54.8±1.7</td><td>27k</td><td><sup>6</sup>ABELE</td><td>99D</td><td>CBAR</td><td>0.0 p p → K<sup>+</sup> K<sup>-</sup> π<sup>0</sup></td></tr><tr><td>45.2±1 ± 2</td><td>80k</td><td><sup>7</sup>BIRD</td><td>89</td><td>LASS</td><td>11 K<sup>-</sup> p → K<sup>0</sup> π<sup>-</sup> p</td></tr><tr><td>42.8±7.1</td><td>3700</td><td>BARTH</td><td>83</td><td>HBC</td><td>70 K<sup>+</sup> p → K<sup>0</sup> π<sup>+</sup> X</td></tr><tr><td>64.0±9.2</td><td>800</td><td><sup>1,3</sup>CLELAND</td><td>82</td><td>SPEC</td><td>30 K<sup>+</sup> p → K<sup>0</sup> S π<sup>+</sup> p</td></tr><tr><td>62.0±4.4</td><td>3200</td><td><sup>1,3</sup>CLELAND</td><td>82</td><td>SPEC</td><td>50 K<sup>+</sup> p → K<sup>0</sup> S π<sup>+</sup> p</td></tr><tr><td>55 ± 4</td><td>3600</td><td><sup>1,3</sup>CLELAND</td><td>82</td><td>SPEC</td><td>50 K<sup>+</sup> p → K<sup>0</sup> S π<sup>-</sup> p</td></tr><tr><td>62.6±3.8</td><td>380</td><td>DELFOSSE</td><td>81</td><td>SPEC</td><td>50 K<sup>±</sup> p → K<sup>±</sup> π<sup>0</sup> p</td></tr><tr><td>50.5±3.9</td><td>187</td><td>DELFOSSE</td><td>81</td><td>SPEC</td><td>50 K<sup>±</sup> p → K<sup>±</sup> π<sup>0</sup> p</td></tr></table>

### CHARGED ONLY, PRODUCED IN $τ$ LEPTON DECAYS

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>46.2±0.6±1.2</strong></td><td>53k</td><td><sup>1</sup>EPIFANOV</td><td>07</td><td>BELL</td><td>τ<sup>-</sup> → K<sup>0</sup> S π<sup>-</sup> ν<sub>T</sub></td></tr><tr><td>46.5±1.1</td><td></td><td><sup>2</sup>BOITO</td><td>10</td><td>RVUE</td><td>τ<sup>-</sup> → K<sup>0</sup> S π<sup>-</sup> ν<sub>T</sub></td></tr><tr><td>46.2±0.4</td><td></td><td><sup>3,4</sup>BOITO</td><td>09</td><td>RVUE</td><td>τ<sup>-</sup> → K<sup>0</sup> S π<sup>-</sup> ν<sub>T</sub></td></tr><tr><td>47.5±0.4</td><td></td><td><sup>4,5</sup>JAMIN</td><td>08</td><td>RVUE</td><td>τ<sup>-</sup> → K<sup>0</sup> S π<sup>-</sup> ν<sub>T</sub></td></tr><tr><td>55 ± 8</td><td></td><td><sup>6</sup>BARATE</td><td>99R</td><td>ALEP</td><td>τ<sup>-</sup> → K<sup>0</sup> π<sup>0</sup> ν<sub>T</sub></td></tr></tbody></table>

### NEUTRAL ONLY

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>47.3 ± 0.5 OUR FIT</strong></td><td>30k</td><td>Error includes scale factor of 2.0.</td><td></td><td></td></tr><tr><td><strong>47.3 ± 0.5 OUR AVERAGE</strong></td><td></td><td>Error includes scale factor of 2.0. See the ideogram below.</td><td></td><td></td></tr><tr><td>46.53±0.56±0.31</td><td></td><td><sup>1</sup>ABLIKIM</td><td>16F</td><td>BES3</td><td>D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> e<sup>+</sup> ν<sub>e</sub></td></tr><tr><td>46.5 ± 0.3 ± 0.2</td><td>243k</td><td><sup>2</sup>DEL-AMO-SA..11I</td><td>BABR</td><td>D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> e<sup>+</sup> ν<sub>e</sub></td></tr><tr><td>45.3 ± 0.6 ± 0.6</td><td>141k</td><td><sup>3</sup>BONVICINI</td><td>08A</td><td>CLEO</td><td>D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> π<sup>+</sup></td></tr><tr><td>47.79±0.86<sup>+1.32</sup><sub>-1.06</sub></td><td>18k</td><td><sup>4</sup>LINK</td><td>05I</td><td>FOCS</td><td>D<sup>+</sup> → K<sup>-</sup> π<sup>+</sup> μ<sup>+</sup> ν<sub>μ</sub></td></tr></tbody></table>

<footnote n="1">1 Number of events in peak reevaluated by us.</footnote>

<footnote n="1">1 Width errors enlarged by us to $4 \times \Gamma/\sqrt{N}$; see note.</footnote>

<footnote n="2">2 Inclusive reaction. Complicated background and phase-space effects.</footnote>

<footnote n="3">3 Number of events in peak reevaluated by us.</footnote>

<footnote n="4">4 From a Dalitz plot analysis in an isobar model with charged and neutral $K^*(892)$ masses and widths floating.</footnote>

<footnote n="5">5 Average of fit results with different parametrizations for the $Kπ$ S-wave.</footnote>

<footnote n="6">6 K-matrix pole.</footnote>

<footnote n="7">7 From a partial wave amplitude analysis.</footnote>

<footnote n="1">1 From a fit in the $K_0^*(700) + K^*(892) + K^*(1410)$ model.</footnote>

<footnote n="2">2 From the pole position of the $Kπ$ vector form factor using EPIFANOV 07 and constraints from $K_{1/3}$ decays in ANTONELLI 10.</footnote>

<footnote n="3">3 From the pole position of the $Kπ$ vector form factor in the complex s-plane and using EPIFANOV 07 data.</footnote>

<footnote n="4">4 Systematic uncertainties not estimated.</footnote>

<footnote n="5">5 Reanalysis of EPIFANOV 07 using resonance chiral theory.</footnote>

<footnote n="6">6 With mass and width of the $K^*(1410)$ fixed at 1412 MeV and 227 MeV, respectively.</footnote>
# Meson Particle Listings

## K*(892)

<table><tbody><tr><td>54</td><td>±3</td><td>BARBERIS</td><td>98E</td><td>OMEG</td><td>450 pp → p<sub>f</sub> p<sub>S</sub> K<sup>*</sup> R<sup>*</sup></td></tr><tr><td>50.8</td><td>±0.8</td><td>±0.9</td><td>ASTON</td><td>88</td><td>LASS</td><td>11 K<sup>-</sup> p → K<sup>-</sup>π<sup>+</sup> n</td></tr><tr><td>46.5</td><td>±4.3</td><td>5900</td><td>BARTH</td><td>83</td><td>HBC</td><td>70 K<sup>+</sup> p → K<sup>+</sup>π<sup>-</sup> X</td></tr><tr><td>54</td><td>±2</td><td>28k</td><td>EVANGELIS...</td><td>80</td><td>OMEG</td><td>10 π<sup>-</sup> p → K<sup>+</sup>π<sup>-</sup> (Λ, Σ)</td></tr><tr><td>45.9</td><td>±4.8</td><td>1180</td><td>AGUILAR...</td><td>78B</td><td>HBC</td><td>0.76 p → K<sup>-</sup> K<sup>0</sup> π<sup>±</sup></td></tr><tr><td>51.2</td><td>±1.7</td><td></td><td>WICKLUND</td><td>78</td><td>ASPK</td><td>3,4,6 K<sup>±</sup> N → (Kπ)<sup>0</sup> N</td></tr><tr><td>48.9</td><td>±2.5</td><td></td><td>BOWLER</td><td>77</td><td>DBC</td><td>5.4 K<sup>+</sup> d → K<sup>+</sup>π<sup>-</sup> pp</td></tr><tr><td>48</td><td><sup>+3</sup><sub>-2</sub></td><td>3600</td><td>MCCUBBIN</td><td>75</td><td>HBC</td><td>3.6 K<sup>-</sup> p → K<sup>-</sup>π<sup>+</sup> n</td></tr><tr><td>50.6</td><td>±2.5</td><td>22k</td><td><sup>5</sup> PALER</td><td>75</td><td>HBC</td><td>14.3 K<sup>-</sup> p → (Kπ)<sup>0</sup> X</td></tr><tr><td>47</td><td>±2</td><td>10k</td><td>FOX</td><td>74</td><td>RVUE</td><td>2 K<sup>-</sup> p → K<sup>-</sup>π<sup>+</sup> n</td></tr><tr><td>51</td><td>±2</td><td></td><td>FOX</td><td>74</td><td>RVUE</td><td>2 K<sup>+</sup> n → K<sup>+</sup>π<sup>-</sup> p</td></tr><tr><td>46.0</td><td>±3.3</td><td>3186</td><td><sup>6</sup> LEWIS</td><td>73</td><td>HBC</td><td>2.1-2.7 K<sup>+</sup> p → Kππp</td></tr><tr><td>51.4</td><td>±5.0</td><td>1700</td><td><sup>6</sup> BUCHNER</td><td>72</td><td>DBC</td><td>4.6 K<sup>+</sup> n → K<sup>+</sup>π<sup>-</sup> p</td></tr><tr><td>55.8</td><td><sup>+4.2</sup><sub>-3.4</sub></td><td>2934</td><td><sup>6</sup> AGUILAR...</td><td>71B</td><td>HBC</td><td>3.9,4.6 K<sup>-</sup> p → K<sup>-</sup>π<sup>+</sup> n</td></tr><tr><td>48.5</td><td>±2.7</td><td>5362</td><td>AGUILAR...</td><td>71B</td><td>HBC</td><td>3.9,4.6 K<sup>-</sup> p → K<sup>-</sup>π<sup>+</sup> π<sup>-</sup> p</td></tr><tr><td>54.0</td><td>±3.3</td><td>4300</td><td><sup>6,7</sup> HABER</td><td>70</td><td>DBC</td><td>3 K<sup>-</sup> N → K<sup>-</sup>π<sup>+</sup> X</td></tr><tr><td>53.2</td><td>±2.1</td><td>10k</td><td><sup>6</sup> DAVIS</td><td>69</td><td>HBC</td><td>12 K<sup>+</sup> p → K<sup>+</sup>π<sup>-</sup> π<sup>+</sup> p</td></tr><tr><td>44</td><td>±5.5</td><td>1040</td><td><sup>6</sup> DAUBER</td><td>67B</td><td>HBC</td><td>2.0 K<sup>-</sup> p → K<sup>-</sup>π<sup>+</sup> π<sup>-</sup> p</td></tr></tbody></table>

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

<table><tbody><tr><td>48.8</td><td>±1.8</td><td>±2.0</td><td><sup>8</sup> ADUSZKIEW...</td><td>20A</td><td>NA61</td><td>158 pp</td></tr><tr><td>52.6</td><td>±1.7</td><td>4k</td><td><sup>9</sup> LEES</td><td>17c</td><td>BABR</td><td>J/ψ → K<sup>0</sup> S K<sup>±</sup> π<sup>∓</sup></td></tr><tr><td>44.90 ± 0.30</td><td></td><td></td><td>LEES</td><td>13f</td><td>BABR</td><td>D<sup>+</sup> → K<sup>+</sup> K<sup>π</sup> +</td></tr><tr><td>45.7</td><td>±1.1</td><td>±0.5</td><td><sup>10</sup> MITCHELL</td><td>09A</td><td>CLEO</td><td>D<sup>+</sup> → K<sup>+</sup> K<sup>π</sup> +</td></tr><tr><td>50.6</td><td>±0.9</td><td>20k</td><td><sup>11</sup> AUBERT</td><td>07AK</td><td>BABR</td><td>10.6 e<sup>+</sup> e<sup>-</sup> → K<sup>0</sup> K<sup>±</sup> π<sup>∓</sup> γ</td></tr></tbody></table>

1 Taking also into account the $K_0^*(1430)^0$ and $K_2^*(1430)^0$.

2 Taking into account the $K^*(892)^0$, S-wave and P-wave ($K^*(1410)^0$).

3 From the isobar model with a complex pole for the $\kappa$.

4 Fit to $K\pi$ mass spectrum includes a non-resonant scalar component.

5 Inclusive reaction. Complicated background and phase-space effects.

6 Width errors enlarged by us to $4 \times \Gamma/\sqrt{N}$; see note.

7 Number of events in peak reevaluated by us.

8 For transverse momenta between 0.6 and 0.8 GeV/c and rapidity $0 < y < 0.5$.

9 From a Dalitz plot analysis in an isobar model with charged and neutral $K^*(892)$ masses and widths floating.

10 This value comes from a fit with $\chi^2$ of 178/117.

11 Systematic uncertainties not estimated.

WEIGHTED AVERAGE
47.3±0.5 (Error scaled by 2.0)

<figure><img src="image_522.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.

(Confidence Level < 0.0001)

NEUTRAL ONLY (MeV)

## K*(892) DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>Confidence level</th></tr></thead><tbody><tr><td>Γ<sub>1</sub> Kπ</td><td>~ 100</td><td>%</td></tr><tr><td>Γ<sub>2</sub> (Kπ)<sup>±</sup></td><td>( 99.902 ± 0.009 ) %</td><td></td></tr><tr><td>Γ<sub>3</sub> (Kπ)<sup>0</sup></td><td>( 99.754 ± 0.021 ) %</td><td></td></tr><tr><td>Γ<sub>4</sub> K<sup>0</sup>γ</td><td>( 2.46 ± 0.21 ) × 10<sup>-3</sup></td><td></td></tr><tr><td>Γ<sub>5</sub> K<sup>±</sup>γ</td><td>( 9.8 ± 0.9 ) × 10<sup>-4</sup></td><td></td></tr><tr><td>Γ<sub>6</sub> Kππ</td><td>&lt; 7</td><td>× 10<sup>-4</sup></td><td>95%</td></tr></tbody></table>

## CONSTRAINED FIT INFORMATION

An overall fit to the total width and a partial width uses 14 measurements and one constraint to determine 3 parameters. The overall fit has a $\chi^2 = 10.7$ for 12 degrees of freedom.

The following off-diagonal array elements are the correlation coefficients $\langle \delta\rho_i \delta\rho_j \rangle / (\delta\rho_i \cdot \delta\rho_j)$, 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.

$$ \begin{array}{c} x_5 \\ \Gamma \end{array} \begin{array}{c} -100 \\ 17 \\ \hline -17 \\ x_2 \end{array} \quad \begin{array}{c} x_5 \end{array} $$

<table><thead><tr><th>Mode</th><th>Rate (MeV)</th></tr></thead><tbody><tr><td>Γ<sub>2</sub> (Kπ)<sup>±</sup></td><td>51.4 ± 0.8</td></tr><tr><td>Γ<sub>5</sub> K<sup>±</sup>γ</td><td>0.050 ± 0.005</td></tr></tbody></table>

## CONSTRAINED FIT INFORMATION

An overall fit to the total width and a partial width uses 23 measurements and one constraint to determine 3 parameters. The overall fit has a $\chi^2 = 68.4$ for 21 degrees of freedom.

The following off-diagonal array elements are the correlation coefficients $\langle \delta\rho_i \delta\rho_j \rangle / (\delta\rho_i \cdot \delta\rho_j)$, 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.

$$ \begin{array}{c} x_4 \\ \Gamma \end{array} \begin{array}{c} -100 \\ 13 \\ \hline -13 \\ x_3 \end{array} \quad \begin{array}{c} x_4 \end{array} $$

<table><thead><tr><th>Mode</th><th>Rate (MeV)</th><th>Scale factor</th></tr></thead><tbody><tr><td>Γ<sub>3</sub> (Kπ)<sup>0</sup></td><td>47.2 ± 0.5</td><td>2.0</td></tr><tr><td>Γ<sub>4</sub> K<sup>0</sup>γ</td><td>0.117 ± 0.010</td><td></td></tr></tbody></table>

## K*(892) PARTIAL WIDTHS

<table><thead><tr><th>Γ(K<sup>0</sup>γ)</th><th>VALUE (keV)</th><th>ΔEVT</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>116 ± 10</td><td>OUR FIT</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>116.5 ± 9.9</td><td></td><td>584</td><td>CARLSMITH</td><td>86</td><td>SPEC</td><td>0</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>±</sup>γ)</th><th>VALUE (keV)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>50 ± 5 OUR FIT</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>50 ± 5 OUR AVERAGE</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>48 ± 11</td><td></td><td>BERG</td><td>83</td><td>SPEC</td><td>—</td><td>156 K<sup>-</sup> A → K<sup>-</sup>πA</td></tr><tr><td>51 ± 5</td><td></td><td>CHANDLEE</td><td>83</td><td>SPEC</td><td>+</td><td>200 K<sup>+</sup> A → K<sup>+</sup>πA</td></tr></tbody></table>

## K*(892) BRANCHING RATIOS

<table><thead><tr><th>Γ(K<sup>0</sup>γ)/Γ<sub>total</sub></th><th>VALUE (units 10<sup>-3</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>2.46 ± 0.21 OUR FIT</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1.5 ± 0.7</td><td></td><td>CARITHERS</td><td>75B</td><td>CNTR</td><td>0</td><td>8-16 K<sup>0</sup> A</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>±</sup>γ)/Γ<sub>total</sub></th><th>VALUE (units 10<sup>-3</sup>)</th><th>ΔCL</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.98 ± 0.09 OUR FIT</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>&lt; 1.6</td><td>95</td><td>BEMPORAD</td><td>73</td><td>CNTR</td><td>+</td><td>10-16 K<sup>+</sup> A</td></tr></tbody></table>

<table><thead><tr><th>Γ(Kππ)/Γ((Kπ)<sup>±</sup>)</th><th>VALUE</th><th>ΔCL</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt; 7 × 10<sup>-4</sup></td><td>95</td><td></td><td>JONGEJANS</td><td>78</td><td>HBC</td><td>4 K<sup>-</sup> p → pK<sup>0</sup>2π</td></tr></tbody></table>

<table><thead><tr><th>• • • We do not use the following data for averages, fits, limits, etc. • • •</th></tr></thead><tbody><tr><td>&lt;20 × 10<sup>-4</sup></td><td>WOJCICKI</td><td>64</td><td>HBC</td><td>—</td><td>1.7 K<sup>-</sup> p → K<sup>0</sup>π<sup>-</sup> p</td></tr></tbody></table>

## K*(892) REFERENCES

ADUSZKIEW... 20A EPJ C80 460

ALBRECHT 20 EPJ C80 453

A. Aduszkiewicz et al. (CERN NA61 Collab.)

M. Albrecht et al. (Crystal Barrel Collab.)

PELAEZ 20 PRL 124 172001

J.R. Pelaez et al. (BESIII Collab.)

ABLIKIM 19AQ PR D100 032004

M. Ablikim et al. (BABAR Collab.)

LEES 17C PR D95 072007

J.P. Lees et al. (BESIII Collab.)

PELAEZ 17 EPJ C77 91

R. Aalaj et al. (LHCb Collab.)

AAU 16N PR D93 052018

M. Ablikim et al. (BESIII Collab.)

ABLIKIM 15F PR D94 032001

M. Ablikim et al. (BABAR Collab.)
<table><tr><td>DEL-AMO-SA... 111</td><td>PR D83 072001</td><td>P. del Amo Sanchez et al. (BABAR Collab.)</td></tr><tr><td>ANTONELLI... 10</td><td>EPJ D 199 499</td><td>D.R. Antonelli et al. (FlaيراNet Working Group)</td></tr><tr><td>BOITO... 10</td><td>JHEP 1009 031</td><td>D.R. Boito, R. Escrivano, M. Jamin (BARC)</td></tr><tr><td>BOITO... 09</td><td>EPJ C59 821</td><td>D.R. Boito, R. Escrivano, M. Jamin</td></tr><tr><td>MITCHELL... 09A</td><td>PR D79 072008</td><td>R.E. Mitchell et al. (CLEO Collab.)</td></tr><tr><td>BONVICINI... 08A</td><td>PR D78 052001</td><td>G. Bonvicini et al. (CLEO Collab.)</td></tr><tr><td>JAMIN... 08</td><td>PL B664 78</td><td>M. Jamin, A. Pich, J. Portoles</td></tr><tr><td>AUBERT... 07AK</td><td>PR D76 012008</td><td>B. Aubert et al. (BABAR Collab.)</td></tr><tr><td>EPIFANOV... 07</td><td>PL B654 65</td><td>D. Epifanov et al. (BELLE Collab.)</td></tr><tr><td>LINK... 05I</td><td>PL B621 72</td><td>J.R. Pelaez (FNAL FOCUS Collab.)</td></tr><tr><td>PELAEZ... 04A</td><td>MPL A19 2879</td><td>J.R. Pelaez (FNAL FOCUS Collab.) (MADU)</td></tr><tr><td>BONVICINI... 02</td><td>PRL 88 111803</td><td>G. Bonvicini et al. (CLEO Collab.)</td></tr><tr><td>PDG... 00</td><td>EPJ C15 1</td><td>D.E. Groom et al. (PDG Collab.)</td></tr><tr><td>ABELE... 99D</td><td>PL B468 178</td><td>A. Abele et al. (Crystal Barrel Collab.)</td></tr><tr><td>BARATE... 99R</td><td>EPJ C11 599</td><td>R. Barate et al. (ALEPH Collab.)</td></tr><tr><td>BARBERIS... 98E</td><td>PL B436 204</td><td>D. Barberis et al. (Omega Expt.)</td></tr><tr><td>BIRD... 89</td><td>SLAC/332</td><td>P.F. Bird</td></tr><tr><td>ASTON... 88</td><td>NP B296 493</td><td>D. Aston et al. (SLAC, NAGO, CINC, INUS)</td></tr><tr><td>ATKINSON... 86</td><td>ZPHY C30 521</td><td>M. Atkinson et al. (BONN, CERN, GLAS+)</td></tr><tr><td>CARLSMITH... 86</td><td>PRL 56 18</td><td>D. Carlsmith et al. (EFI, SACL)</td></tr><tr><td>BAUBILLIER... 84B</td><td>ZPHY C26 37</td><td>M. Baubillier et al. (BIRM, CERN, GLAS+)</td></tr><tr><td>NAPIER... 84</td><td>NP 149B 514</td><td>A. Napier et al. (TUFTS, ARIZ, FNAL, FLOR+)</td></tr><tr><td>BARTH... 83</td><td>NP B223 296</td><td>(BRUX, CERN, GENO, MONS+)</td></tr><tr><td>BERG... 83</td><td>Thesh UMI 83-21652</td><td>D.M. Berg (ROCH)</td></tr><tr><td>CHANDLER... 83</td><td>PRL 51 168</td><td>C. Chandee et al. (ROCH, FNAL, MINN)</td></tr><tr><td>CLELAND... 82</td><td>NP B206 189</td><td>W.E. Cleland et al. (DURH, GEVA, LAUS+)</td></tr><tr><td>DELFOSSE... 81</td><td>NP B183 349</td><td>A. Delfossé et al. (GEVA, LAUS)</td></tr><tr><td>TOAFF... 81</td><td>PR D23 1500</td><td>S. Toaff et al. (ANL, KANS)</td></tr><tr><td>AVJENKO... 80</td><td>ZPHY C5 177</td><td>I.V. Ajzenenko et al. (SERP, BRUX, MONS+)</td></tr><tr><td>EVANGELIS... 78B</td><td>NP B165 383</td><td>C. Evangelista et al. (BARI, BONN, CERN+)</td></tr><tr><td>AGUILAR... 78B</td><td>NP B141 101</td><td>M. Aguilar-Benitez et al. (MADR, TATA+)</td></tr><tr><td>BALAND... 78</td><td>NP B140 220</td><td>J.F. Baland et al. (MONS, BELG, CERN+)</td></tr><tr><td>COOPER... 78</td><td>NP B136 365</td><td>A.M. Cooper et al. (TATA, CERN, CDEF+)</td></tr><tr><td>ESTABROOKS... 78</td><td>NP B133 490</td><td>P.G. Estabrooks et al. (MCGI, CARL, DURH+)</td></tr><tr><td>Also... 78</td><td>PR D17 658</td><td>P.G. Estabrooks et al. (MCGI, CARL, DURH+)</td></tr><tr><td>JONGEJANS... 78</td><td>NP B139 383</td><td>B. Jongejans et al. (ZEEM, CERN, NIJM+)</td></tr><tr><td>WICKLUND... 78</td><td>PR D17 1197</td><td>A.B. Wicklund et al. (ANL)</td></tr><tr><td>BOWLER... 77</td><td>NP B126 31</td><td>M.G. Bowler et al. (OXF)</td></tr><tr><td>CARITHERS... 75B</td><td>PRL 35 349</td><td>W.C.J. Caritbers et al. (ROCH, MCGI)</td></tr><tr><td>MCCUBBIN... 75</td><td>NP B86 13</td><td>N.A. McCubbin, L. Lyons (OXF)</td></tr><tr><td>PALER... 75</td><td>NP B96 1</td><td>K. Paler et al. (RHEL, SACL, EPOL)</td></tr><tr><td>FOX... 74</td><td>NP B80 403</td><td>G.C. Fox, M.L. Griss (CIT)</td></tr><tr><td>MATISON... 74</td><td>PR D9 1872</td><td>M.J. Matison et al. (LBL)</td></tr><tr><td>BEMPORAD... 73</td><td>NP B51 1</td><td>C. Bemporad et al. (CERN, ETH, LOIC)</td></tr><tr><td>CLARK... 73</td><td>NP B54 432</td><td>A.G. Clark, L. Lyons, D. Radojić (OXF)</td></tr><tr><td>LEWIS... 73</td><td>NP B60 283</td><td>P.H. Lewis et al. (LOWC, LOIC, CDEF)</td></tr><tr><td>LINGLIN... 73</td><td>NP B55 408</td><td>D. Linglin (CERN)</td></tr><tr><td>BUCHNER... 72</td><td>NP B45 333</td><td>K. Buchner et al. (MPIM, CERN, BRUX)</td></tr><tr><td>AGUILAR... 71B</td><td>PR D4 2583</td><td>M. Aguilar-Benitez, R.L. Eisner, J.B. Kinson (BNL)</td></tr><tr><td>HABER... 70</td><td>NP B17 289</td><td>B. Haber et al. (REHO, SACL, BGNA, EPOL)</td></tr><tr><td>CRENNELL... 69D</td><td>PRL 22 487</td><td>D.J. Crennell et al. (BNL)</td></tr><tr><td>DAVIS... 69</td><td>PRL 23 1071</td><td>P.J. Davis et al. (LRL)</td></tr><tr><td>SCHWEING... 68</td><td>PR 166 1317</td><td>F. Schweingruber et al. (ANL, NWES)</td></tr><tr><td>BARASH... 67B</td><td>PR 156 1399</td><td>N. Barash et al. (COLU)</td></tr><tr><td>BARLOW... 67</td><td>NC 50A 701</td><td>J. Barlow et al. (CERN, CDEF, IRAD, LVP)</td></tr><tr><td>DAUBER... 67B</td><td>PR 153 1403</td><td>P.M. Dauber et al. (LCLA)</td></tr><tr><td>DEBAERE... 67B</td><td>NC 51A 401</td><td>W. de Baere et al. (BRUX, CERN)</td></tr><tr><td>WOJCICKI... 64</td><td>PR 135 B484</td><td>S.G. Wojcicki (LRL)</td></tr></table>

$$K_1(1270)$$

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

### $K_1(1270)$ MASS

**VALUE (MeV)**
**DOCUMENT ID**

**1253±7** **OUR AVERAGE** Includes data from the 4 datablocks that follow this one. Error includes scale factor of 2.2. See the ideogram below.

WEIGHTED AVERAGE
1253±7 (Error scaled by 2.2)

<figure><img src="image_523.png" /></figure>

### PRODUCED BY $K^-$, BACKWARD SCATTERING, HYPERON EXCHANGE

**VALUE (MeV)** **EVTS** **DOCUMENT ID** **TECN** **CHG** **COMMENT**

The data in this block is included in the average printed for a previous datablock.

$$1275\pm10 \quad 700 \quad \text{GAVILLET} \quad 78 \quad \text{HBC} \quad + \quad 4.2 K^- p \to \Xi^- (K\pi\pi)^+$$

### PRODUCED BY $K$ BEAMS

**VALUE (MeV)** **DOCUMENT ID** **TECN** **CHG** **COMMENT**

The data in this block is included in the average printed for a previous datablock.

$$1270\pm10 \quad 1 \text{ DAUM} \quad 81 \text{ CNTR} \quad - \quad 63 K^- p \to K^- 2\pi p$$

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

<table><tr><td>~ 1276</td><td><sup>2</sup> TORNQVIST</td><td>82B</td><td>RVUE</td></tr><tr><td>~ 1300</td><td>VERGEEST</td><td>79</td><td>HBC</td><td>-</td><td>4.2 K<sup>-</sup> p → (Kππ)<sup>-</sup> p</td></tr><tr><td>1289±25</td><td><sup>3</sup> CARNEGIE</td><td>77</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr><tr><td>~ 1300</td><td>BRANDENB...</td><td>76</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr><tr><td>~ 1270</td><td>OTTER</td><td>76</td><td>HBC</td><td>-</td><td>10,14,16 K<sup>-</sup> p → (Kππ)<sup>-</sup> p</td></tr><tr><td>1260</td><td>DAVIS</td><td>72</td><td>HBC</td><td>+</td><td>12 K<sup>+</sup> p</td></tr><tr><td>1234±12</td><td>FIRESTONE</td><td>72b</td><td>DBC</td><td>+</td><td>12 K<sup>+</sup> d</td></tr></table>

1 Well described in the chiral unitary approach of GENG 07 with two poles at 1195 and 1284 MeV and widths of 246 and 146 MeV, respectively.

2 From a unitarized quark-model calculation.

3 From a model-dependent fit with Gaussian background to BRANDENBURG 76 data.

### PRODUCED BY BEAMS OTHER THAN $K$ MESONS

**VALUE (MeV)** **EVTS** **DOCUMENT ID** **TECN** **CHG** **COMMENT**

The data in this block is included in the average printed for a previous datablock.

<table><tr><td>1248.1 ± 3.3 ±1.4</td><td>GULER</td><td>11</td><td>BELL</td><td>B<sup>+</sup> → J/ψK<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>• • •</td><td>• • •</td><td></td><td></td><td></td></tr><tr><td>1289.81 ± 0.56±1.66</td><td>894k</td><td>AAIJ</td><td>18AI</td><td>LHCB</td><td>D<sup>0</sup> → K<sup>±</sup>π<sup>±</sup>π<sup>±</sup>π<sup>-</sup></td></tr><tr><td>1279 ±10</td><td>25k</td><td><sup>1</sup> ABLIKIM</td><td>06C</td><td>BES2</td><td>J/ψ → K<sup>+</sup>(892)<sup>0</sup> K<sup>+</sup>π<sup>-</sup></td></tr><tr><td>1294 ±10</td><td>310</td><td>RODEBACK</td><td>81</td><td>HBC</td><td>4 π<sup>-</sup> p → ΛK2π</td></tr><tr><td>1300</td><td>40</td><td>CRENNELL</td><td>72</td><td>HBC</td><td>4.5 π<sup>-</sup> p → ΛK2π</td></tr><tr><td>1242 <sup>+9</sup> <sup>-10</sup></td><td><sup>2</sup> ASTIER</td><td>69</td><td>HBC</td><td>p̄p</td></tr><tr><td>1300</td><td>45</td><td>CRENNELL</td><td>67</td><td>HBC</td><td>6 π<sup>-</sup> p → ΛK2π</td></tr></table>

1 Systematic errors not estimated.

2 This was called the C meson.

### PRODUCED IN $\tau$ LEPTON DECAYS

**VALUE (MeV)** **EVTS** **DOCUMENT ID** **TECN** **CHG** **COMMENT**

The data in this block is included in the average printed for a previous datablock.

$$1254\pm33\pm34 \quad 7k \quad \text{ASNER} \quad 00B \quad \text{CLEO} \quad \pm \quad \tau^- \to K^-\pi^+\pi^-\nu_\tau$$

### $K_1(1270)$ WIDTH

**VALUE (MeV)** **DOCUMENT ID**

**101±12** **OUR AVERAGE** Includes data from the 4 datablocks that follow this one. Error includes scale factor of 2.2. See the ideogram below.

<figure><img src="image_524.png" /></figure>

### PRODUCED BY $K^-$, BACKWARD SCATTERING, HYPERON EXCHANGE

**VALUE (MeV)** **EVTS** **DOCUMENT ID** **TECN** **CHG** **COMMENT**

The data in this block is included in the average printed for a previous datablock.

$$75\pm15 \quad 700 \quad \text{GAVILLET} \quad 78 \quad \text{HBC} \quad + \quad 4.2 K^- p \to \Xi^- K\pi\pi$$

### PRODUCED BY $K$ BEAMS

**VALUE (MeV)** **DOCUMENT ID** **TECN** **CHG** **COMMENT**

The data in this block is included in the average printed for a previous datablock.

<table><tr><td>90±8</td><td><sup>1</sup> DAUM</td><td>81c</td><td>CNTR</td><td>-</td><td>63 K<sup>-</sup> p → K<sup>-</sup> 2πp</td></tr><tr><td>• • •</td><td>• • •</td><td></td><td></td><td></td><td></td></tr><tr><td>~ 150</td><td>VERGEEST</td><td>79</td><td>HBC</td><td>-</td><td>4.2 K<sup>-</sup> p → (Kππ)<sup>-</sup> p</td></tr><tr><td>150±71</td><td><sup>2</sup> CARNEGIE</td><td>77</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr><tr><td>~ 200</td><td>BRANDENB...</td><td>76</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr><tr><td>120</td><td>DAVIS</td><td>72</td><td>HBC</td><td>+</td><td>12 K<sup>+</sup> p</td></tr><tr><td>188±21</td><td>FIRESTONE</td><td>72b</td><td>DBC</td><td>+</td><td>12 K<sup>+</sup> d</td></tr></table>

1 Well described in the chiral unitary approach of GENG 07 with two poles at 1195 and 1284 MeV and widths of 246 and 146 MeV, respectively.

2 From a model-dependent fit with Gaussian background to BRANDENBURG 76 data.
PRODUCED BY BEAMS OTHER THAN K MESONS

The data in this block is included in the average printed for a previous datablock.

<table><tbody><tr><td>119.5</td><td>± 5.2</td><td>±6.7</td><td>GULER</td><td>11</td><td>BELL</td><td>B<sup>+</sup> → J/ψK<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>116.11</td><td>± 1.65</td><td>±2.96</td><td>894k</td><td>AAIJ</td><td>18AI</td><td>LHCB</td><td>D<sup>0</sup> → K<sup>+</sup>π<sup>+</sup>π<sup>-</sup>π<sup>+</sup></td></tr><tr><td>131</td><td>±21</td><td></td><td>25k</td><td><sup>1</sup> ABLIKIM</td><td>06C</td><td>BES2</td><td>J/ψ → K<sup>+</sup>(892)<sup>0</sup> K<sup>+</sup>π<sup>-</sup></td></tr><tr><td>66</td><td>±15</td><td></td><td>310</td><td>RODEBACK</td><td>81</td><td>HBC</td><td>4 π<sup>-</sup> p → ΛK2π</td></tr><tr><td>60</td><td></td><td></td><td>40</td><td>CRENNELL</td><td>72</td><td>HBC</td><td>4.5 π<sup>-</sup> p → ΛK2π</td></tr><tr><td>127</td><td>+7/25</td><td></td><td></td><td>ASTIER</td><td>69</td><td>HBC</td><td>πp</td></tr><tr><td>60</td><td></td><td></td><td>45</td><td>CRENNELL</td><td>67</td><td>HBC</td><td>6 π<sup>-</sup> p → ΛK2π</td></tr></tbody></table>

¹Systematic errors not estimated.

PRODUCED IN τ LEPTON DECAYS

The data in this block is included in the average printed for a previous datablock.

<table><tbody><tr><td>260<sup>+90</sup><sub>-70</sub></td><td>±80</td><td>7k</td><td>ASNER</td><td>00B</td><td>CLEO</td><td>±</td><td>τ<sup>-</sup> → K<sup>-</sup>π<sup>-</sup>π<sup>+</sup>ν<sub>τ</sub></td></tr></tbody></table>

$K_1(1270)$ DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>Scale factor</th></tr></thead><tbody><tr><td>Γ<sub>1</sub> Kρ</td><td>(38 ± 13) %</td><td rowspan="2">2.2</td></tr><tr><td>Γ<sub>2</sub> K<sub>0</sub><sup>*</sup>(1430)π</td><td>(28 ± 4) %</td></tr><tr><td>Γ<sub>3</sub> K<sup>*</sup>(892)π</td><td>(21 ± 10) %</td><td rowspan="3">2.2</td></tr><tr><td>Γ<sub>4</sub> Kω</td><td>(11.0 ± 2.0) %</td></tr><tr><td>Γ<sub>5</sub> Kf<sub>0</sub>(1370)</td><td>(3.0 ± 2.0) %</td></tr><tr><td>Γ<sub>6</sub> γK<sup>0</sup></td><td>seen</td><td></td></tr></tbody></table>

$K_1(1270)$ PARTIAL WIDTHS

<table><thead><tr><th>Γ(Kρ)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>57 ± 5</td><td>MAZZUCATO</td><td>79</td><td>HBC</td><td>+</td></tr><tr><td>75 ± 6</td><td>CARNEGIE</td><td>77B</td><td>ASPK</td><td>±</td></tr></tbody></table>

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

<table><tbody><tr><td>57 ± 5</td><td>MAZZUCATO</td><td>79</td><td>HBC</td><td>+</td><td>4.2 K<sup>-</sup> p → Ξ<sup>-</sup>(Kππ)<sup>+</sup></td></tr><tr><td>75 ± 6</td><td>CARNEGIE</td><td>77B</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sub>0</sub><sup>*</sup>(1430)π)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>26 ± 6</td><td>CARNEGIE</td><td>77B</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

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

<table><tbody><tr><td>26 ± 6</td><td>CARNEGIE</td><td>77B</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>*</sup>(892)π)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>14 ± 11</td><td>MAZZUCATO</td><td>79</td><td>HBC</td><td>+</td></tr><tr><td>2 ± 2</td><td>CARNEGIE</td><td>77B</td><td>ASPK</td><td>±</td></tr></tbody></table>

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

<table><tbody><tr><td>14 ± 11</td><td>MAZZUCATO</td><td>79</td><td>HBC</td><td>+</td><td>4.2 K<sup>-</sup> p → Ξ<sup>-</sup>(Kππ)<sup>+</sup></td></tr><tr><td>2 ± 2</td><td>CARNEGIE</td><td>77B</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

<table><thead><tr><th>Γ(Kω)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>4 ± 4</td><td>MAZZUCATO</td><td>79</td><td>HBC</td><td>+</td></tr><tr><td>24 ± 3</td><td>CARNEGIE</td><td>77B</td><td>ASPK</td><td>±</td></tr></tbody></table>

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

<table><tbody><tr><td>4 ± 4</td><td>MAZZUCATO</td><td>79</td><td>HBC</td><td>+</td><td>4.2 K<sup>-</sup> p → Ξ<sup>-</sup>(Kππ)<sup>+</sup></td></tr><tr><td>24 ± 3</td><td>CARNEGIE</td><td>77B</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

<table><thead><tr><th>Γ(Kf<sub>0</sub>(1370))</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>22 ± 5</td><td>CARNEGIE</td><td>77B</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

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

<table><tbody><tr><td>22 ± 5</td><td>CARNEGIE</td><td>77B</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

<table><thead><tr><th>Γ(γK<sup>0</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>73.2 ± 6.1</td><td>±28.3</td><td>ALAVI-HARATI02B</td><td>KTEV</td><td>K + A → K<sup>*</sup> + A</td></tr></tbody></table>

$K_1(1270)$ BRANCHING RATIOS

<table><thead><tr><th>Γ(Kρ)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.38 ± 0.13</td><td>OUR FIT</td><td></td><td>Error includes scale factor of 2.2.</td></tr></tbody></table>

0.42 ± 0.06 ¹DAUM 81C CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp

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

<table><tbody><tr><td>0.584 ± 0.043</td><td>2 GULER</td><td>11</td><td>BELL</td><td>B<sup>+</sup> → J/ψK<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>dominant</td><td>RODEBACK</td><td>81</td><td>HBC</td><td>4 π<sup>-</sup> p → ΛK2π</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sub>0</sub><sup>*</sup>(1430)π)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.28 ± 0.04</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr></tbody></table>

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

<table><tbody><tr><td>0.0201 ± 0.0064</td><td>2 GULER</td><td>11</td><td>BELL</td><td>B<sup>+</sup> → J/ψK<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>*</sup>(892)π)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.21 ± 0.10</td><td>OUR FIT</td><td></td><td>Error includes scale factor of 2.2.</td></tr><tr><td>0.16 ± 0.05</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr><tr><td>0.171 ± 0.023</td><td>2 GULER</td><td>11</td><td>BELL B<sup>+</sup> → J/ψK<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

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

<table><tbody><tr><td>0.171 ± 0.023</td><td>2 GULER</td><td>11</td><td>BELL B<sup>+</sup> → J/ψK<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>*</sup>(892)π)/Γ(Kρ)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.56 ± 0.29</td><td>OUR FIT</td><td></td><td>Error includes scale factor of 2.2.</td></tr><tr><td>0.99 ± 0.15</td><td>±0.18</td><td>ABLIKIM</td><td>21U BES3</td><td>D<sup>+</sup><sub>S</sub> → K<sub>1</sub>(1270)<sup>0</sup> K<sup>+</sup></td></tr></tbody></table>

<table><tbody><tr><td>0.99 ± 0.15</td><td>±0.18</td><td>ABLIKIM</td><td>21U BES3</td><td>D<sup>+</sup><sub>S</sub> → K<sub>1</sub>(1270)<sup>0</sup> K<sup>+</sup></td></tr></tbody></table>

<table><thead><tr><th>Γ(Kω)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.11 ± 0.02</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr><tr><td>0.225 ± 0.052</td><td>2 GULER</td><td>11</td><td>BELL B<sup>+</sup> → J/ψK<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

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

<table><tbody><tr><td>0.225 ± 0.052</td><td>2 GULER</td><td>11</td><td>BELL B<sup>+</sup> → J/ψK<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

<table><thead><tr><th>Γ(Kω)/Γ(Kρ)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.03 ± 0.02</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;0.30</td><td>95</td><td>RODEBACK</td><td>81</td><td>HBC 4 π<sup>-</sup> p → ΛK2π</td></tr></tbody></table>

<table><thead><tr><th>Γ(Kf<sub>0</sub>(1370))/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.03 ± 0.02</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr></tbody></table>

<table><thead><tr><th>D-wave/S-wave RATIO FOR K<sub>1</sub>(1270) → K<sup>*</sup>(892)π</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.0 ± 0.7</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr></tbody></table>

¹Average from low and high t data.

²Assuming that decays are saturated by the Kρ, K<sub>0</sub><sup>*</sup>(1430)π, K<sup>*</sup>(892)π, Kω decay modes and neglecting interference between them. The values B(ω → π<sup>+</sup>π<sup>-</sup>) = (1.53<sup>+0.11</sup><sub>-0.13</sub>)% and B(K<sub>0</sub><sup>*</sup>(1430) → Kπ) = (93 ± 10)% are used. Systematic uncertainties not estimated.

$K_1(1270)$ REFERENCES

<table><tbody><tr><td>ABLIKIM</td><td>21U PR D104 032011</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>AAIJ</td><td>18AI EPJ C78 443</td><td>R. Aalj et al.</td><td>(LHCb Collab.)</td></tr><tr><td>GULER</td><td>11 PR D83 032005</td><td>H. Guler et al.</td><td>(BELLE Collab.)</td></tr><tr><td>GENG</td><td>07 PR D75 014017</td><td>L.S. Geng et al.</td><td></td></tr><tr><td>ABLIKIM</td><td>06C PL B633 681</td><td>M. Ablikim et al.</td><td>(BES Collab.)</td></tr><tr><td>ALAVI-HARATI</td><td>02B PRL 89 072001</td><td>A. Alavi-Harati et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>ASNER</td><td>00B PR D62 072006</td><td>D.M. Asner et al.</td><td>(CLEO Collab.)</td></tr><tr><td>TORNQVIST</td><td>82B NP B203 268</td><td>N.A. Tornqvist</td><td>(HELS)</td></tr><tr><td>DAUM</td><td>81C NP B187 1</td><td>C. Daum et al.</td><td>(AMST, CERN, CRAC, MPIM+)</td></tr><tr><td>RODEBACK</td><td>81 ZPHY C9 9</td><td>S. Rodeback et al.</td><td>(CERN, CDEF, MADR+)</td></tr><tr><td>MAZZUCATO</td><td>79 NP B156 532</td><td>M. Mazzucato et al.</td><td>(CERN, ZEEM, NIJM+)</td></tr><tr><td>VERGEEST</td><td>79 NP B158 265</td><td>J.S.M. Vergeest et al.</td><td>(NIJM, AMST, CERN+)</td></tr><tr><td>GAVILLET</td><td>78 PL 76B 517</td><td>P. Gavillet et al.</td><td>(AMST, CERN, NIJM+)</td></tr><tr><td>CARNEGIE</td><td>77 NP B127 509</td><td>R.K. Carnegie et al.</td><td>(SLAC)</td></tr><tr><td>CARNEGIE</td><td>77B PL 68B 287</td><td>R.K. Carnegie et al.</td><td>(SLAC)</td></tr><tr><td>BRANDENB...</td><td>76 PRL 36 703</td><td>G.W. Brandenburg et al.</td><td>(SLAC) JP</td></tr><tr><td>OTTER</td><td>76 NP B106 77</td><td>G. Otter et al.</td><td>(AACH3, BERL, CERN, LOIC+)</td></tr><tr><td>CRENNELL</td><td>72 PR D6 1220</td><td>D.J. Crennell et al.</td><td>(BNL)</td></tr><tr><td>DAVIS</td><td>72 PR D5 2688</td><td>P.J. Davis et al.</td><td>(BNL)</td></tr><tr><td>FIRESTONE</td><td>72B PR D5 505</td><td>A. Firestone et al.</td><td>(BNL)</td></tr><tr><td>ASTIER</td><td>69 NP B10 65</td><td>A. Astier et al.</td><td>(CDEF, CERN, IPNP, LIVP) JP</td></tr><tr><td>CRENNELL</td><td>67 PRL 19 44</td><td>D.J. Crennell et al.</td><td>(BNL) I</td></tr></tbody></table>

$K_1(1400)$

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

$K_1(1400)$ 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>1463 ± 64</td><td>±68</td><td>7k</td><td>ASNER</td><td>00B</td><td>CLEO ±</td><td>τ<sup>-</sup> → K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>T</sub></td></tr><tr><td>1373 ± 14</td><td>±18</td><td>1</td><td>ASTON</td><td>87</td><td>LASS 0</td><td>11 K<sup>-</sup> p → K<sup>0</sup>π<sup>+</sup>π<sup>-</sup> n</td></tr><tr><td>1392 ± 18</td><td></td><td>BAUBILLIER</td><td>82B</td><td>HBC 0</td><td>8.25 K<sup>-</sup> p → K<sup>0</sup>π<sup>+</sup>π<sup>-</sup> n</td></tr><tr><td>1410 ± 25</td><td></td><td>DAUM</td><td>81C</td><td>CNTR -</td><td>63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr><tr><td>1415 ± 15</td><td></td><td>ETKIN</td><td>80</td><td>MPS 0</td><td>6 K<sup>-</sup> p → K<sup>0</sup>π<sup>+</sup>π<sup>-</sup> n</td></tr><tr><td>1404 ± 10</td><td></td><td>CARNEGIE</td><td>77</td><td>ASPK ±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

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

<table><tbody><tr><td>1418 ± 8</td><td>25k</td><td>3 ABLIKIM</td><td>06C BES2</td><td>J/ψ → K<sup>*</sup>(892)<sup>0</sup> K<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

<table><tbody><tr><td>~ 1350</td><td>4 TORNQVIST</td><td>82B</td><td>RVUE</td><td></td></tr><tr><td>~ 1400</td><td>VERGEEST</td><td>79</td><td>HBC</td><td>-</td></tr><tr><td>~ 1400</td><td>BRANDENB...</td><td>76</td><td>ASPK ±</td><td>4.2 K<sup>-</sup> p → (Kππ)<sup>-</sup> p</td></tr><tr><td>~ 1420</td><td>DAVIS</td><td>72</td><td>HBC +</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr><tr><td>~ 1368</td><td>FIRESTONE</td><td>72B</td><td>DBC +</td><td>12 K<sup>+</sup> d</td></tr></tbody></table>

¹From partial-wave analysis of K<sup>0</sup>π<sup>+</sup>π<sup>-</sup> system.

²From a model-dependent fit with Gaussian background to BRANDENBURG 76 data.

³Systematic errors not estimated.

⁴From a unitarized quark-model calculation.
## $K_1(1400)$ WIDTH

<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><strong>174 ± 13</strong></td><td><strong>OUR AVERAGE</strong></td><td colspan="4">Error includes scale factor of 1.6.</td><td>See the ideogram below.</td></tr><tr><td>300 ± 370<br/>-110 ± 140</td><td>7k</td><td>ASNER</td><td>00B</td><td>CLEO</td><td>±</td><td>τ<sup>-</sup> → K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub></td></tr><tr><td>188 ± 54 ± 60</td><td></td><td><sup>1</sup>ASTON</td><td>87</td><td>LASS</td><td>0</td><td>11 K<sup>-</sup> p → R<sup>0</sup>π<sup>+</sup>π<sup>-</sup> n</td></tr><tr><td>276 ± 65</td><td></td><td>BAUBILLIER</td><td>82B</td><td>HBC</td><td>0</td><td>8.25 K<sup>-</sup> p →<br/>K<sup>0</sup><sub>S</sub>π<sup>+</sup>π<sup>-</sup> n</td></tr><tr><td>195 ± 25</td><td></td><td>DAUM</td><td>81C</td><td>CNTR</td><td>–</td><td>63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr><tr><td>180 ± 10</td><td></td><td>ETKIN</td><td>80</td><td>MPS</td><td>0</td><td>6 K<sup>-</sup> p → R<sup>0</sup>π<sup>+</sup>π<sup>-</sup> n</td></tr><tr><td>142 ± 16</td><td></td><td><sup>2</sup>CARNEGIE</td><td>77</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr><tr><td colspan="7"><strong>• • •</strong> We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>152 ± 16</td><td>25k</td><td><sup>3</sup>ABLIKIM</td><td>06C</td><td>BES2</td><td></td><td>J/ψ →<br/>R<sup>*</sup>(892)0 K<sup>+</sup>π<sup>-</sup></td></tr><tr><td>~ 200</td><td></td><td>VERGEEST</td><td>79</td><td>HBC</td><td>–</td><td>4.2 K<sup>-</sup> p → (Rππ)<sup>-</sup> p</td></tr><tr><td>~ 160</td><td></td><td>BRANDENB...</td><td>76</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr><tr><td>80</td><td></td><td>DAVIS</td><td>72</td><td>HBC</td><td>+</td><td>12 K<sup>+</sup> p</td></tr><tr><td>241 ± 30</td><td></td><td>FIRESTONE</td><td>72B</td><td>DBC</td><td>+</td><td>12 K<sup>+</sup> d</td></tr></tbody></table>

¹ From partial-wave analysis of $K^0\pi^+\pi^-$ system.

² From a model-dependent fit with Gaussian background to BRANDENBURG 76 data.

³ Systematic errors not estimated.

WEIGHTED AVERAGE
174±13 (Error scaled by 1.6)

<figure><img src="image_525.png" /></figure>

(Confidence Level = 0.080)

$K_1(1400)$ width (MeV)

## $K_1(1400)$ DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction (Γ<sub>f</sub>/Γ)</th></tr></thead><tbody><tr><td>Γ<sub>1</sub> K<sup>*</sup>(892)π</td><td>(94 ± 6 ) %</td></tr><tr><td>Γ<sub>2</sub> Kρ</td><td>( 3.0 ± 3.0 ) %</td></tr><tr><td>Γ<sub>3</sub> Kf<sub>0</sub>(1370)</td><td>( 2.0 ± 2.0 ) %</td></tr><tr><td>Γ<sub>4</sub> Kω</td><td>( 1.0 ± 1.0 ) %</td></tr><tr><td>Γ<sub>5</sub> K<sub>0</sub><sup>*</sup>(1430)π</td><td>not seen</td></tr><tr><td>Γ<sub>6</sub> γK<sup>0</sup></td><td>seen</td></tr><tr><td>Γ<sub>7</sub> Kφ</td><td>seen</td></tr></tbody></table>

## $K_1(1400)$ PARTIAL WIDTHS

<table><thead><tr><th>Γ(K<sup>*</sup>(892)π)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th><th>Γ<sub>1</sub></th></tr></thead><tbody><tr><td>117 ± 10</td><td>CARNEGIE</td><td>77</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

<table><thead><tr><th>Γ(Kρ)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th><th>Γ<sub>2</sub></th></tr></thead><tbody><tr><td>2 ± 1</td><td>CARNEGIE</td><td>77</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

<table><thead><tr><th>Γ(Kω)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th><th>Γ<sub>4</sub></th></tr></thead><tbody><tr><td>23 ± 12</td><td>CARNEGIE</td><td>77</td><td>ASPK</td><td>±</td><td>13 K<sup>±</sup> p → (Kππ)<sup>±</sup> p</td></tr></tbody></table>

<table><thead><tr><th>Γ(γK<sup>0</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>280.8 ± 23.2 ± 40.4</td><td>ALAVI-HARATI02B</td><td>KTEV</td><td>K + A → K<sup>*</sup> + A</td></tr></tbody></table>

## $K_1(1400)$ BRANCHING RATIOS

<table><thead><tr><th>Γ(K<sup>*</sup>(892)π)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.94 ± 0.06</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr></tbody></table>

¹ Average from low and high t data.

<table><thead><tr><th>Γ(Kρ)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.03 ± 0.03</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr></tbody></table>

¹ Average from low and high t data.

<table><thead><tr><th>Γ(Kf<sub>0</sub>(1370))/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.02 ± 0.02</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr></tbody></table>

¹ Average from low and high t data.

<table><thead><tr><th>Γ(Kω)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.01 ± 0.01</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr></tbody></table>

¹ Average from low and high t data.

<table><thead><tr><th>Γ(Kφ)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>seen</td><td>24k</td><td>1 AAIJ</td><td>21E LHCB B<sup>+</sup> → J/ψφK<sup>+</sup></td></tr></tbody></table>

¹ From an amplitude analysis of the decay B<sup>+</sup> → J/ψφK<sup>+</sup> with a significance of 9.2 σ.

<table><thead><tr><th>Γ(K<sub>0</sub><sup>*</sup>(1430)π)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>not seen</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr></tbody></table>

¹ Average from low and high t data.

<table><thead><tr><th>D-wave/S-wave RATIO FOR K<sub>1</sub>(1400)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.04 ± 0.01</td><td>1 DAUM</td><td>81C</td><td>CNTR 63 K<sup>-</sup> p → K<sup>-</sup>2πp</td></tr></tbody></table>

¹ Average from low and high t data.

## $K_1(1400)$ REFERENCES

<table><tbody><tr><td>AAIJ</td><td>21E PRL 127 082001</td><td>R. Aaij et al.</td><td>(LHCb Collab.)</td></tr><tr><td>ABLIKIM</td><td>06C PL B633 681</td><td>M. Ablikim et al.</td><td>(BES Collab.)</td></tr><tr><td>ALAVI-HARATI</td><td>02B PRL 89 072001</td><td>A. Alavi-Harati et al.</td><td>(FNAL KtV Collab.)</td></tr><tr><td>ASNER</td><td>00B PR D62 072006</td><td>D.M. Asner et al.</td><td>(CLEO Collab.)</td></tr><tr><td>ASTON</td><td>87 NP B292 693</td><td>D. Aston et al.</td><td>(SLAC, NAGO, CINC, INUS)</td></tr><tr><td>BAUBILLIER</td><td>82B NP B202 21</td><td>M. Baubillier et al.</td><td>(BIRM, CERN, GLAS+)</td></tr><tr><td>TORNQVIST</td><td>82B NP B203 268</td><td>N.A. Tornqvist</td><td>(HELS)</td></tr><tr><td>DAUM</td><td>81C NP B187 1</td><td>C. Daum et al.</td><td>(AMST, CERN, CRAC, MPIM+)</td></tr><tr><td>ETKIN</td><td>80 PR D22 42</td><td>A. Etkin et al.</td><td>(BNL, CUNY) JP</td></tr><tr><td>VERGEEST</td><td>79 NP B158 265</td><td>J.S.M. Vergeest et al.</td><td>(NIJM, AMST, CERN+)</td></tr><tr><td>CARNEGIE</td><td>77 NP B127 509</td><td>R.K. Carnegie et al.</td><td>(SLAC)</td></tr><tr><td>BRANDENB...</td><td>76 PRL 36 703</td><td>G.W. Brandenburg et al.</td><td>(SLAC) JP</td></tr><tr><td>DAVIS</td><td>72 PR D5 2688</td><td>P.J. Davis et al.</td><td>(LBL)</td></tr><tr><td>FIRESTONE</td><td>72B PR D5 505</td><td>A. Firestone et al.</td><td>(LBL)</td></tr></tbody></table>

$$K^*(1410)$$

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

$$K^*(1410) \text{ T-MATRIX POLE } \sqrt{s}$$

Note that $\Gamma = -2 \operatorname{Im}(\sqrt{s})$.

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

(1368 ± 38) - i (106<sup>+48</sup><sub>-59</sub>) OUR ESTIMATE

(1368 ± 38) - i (106<sup>+48</sup><sub>-59</sub>) 1 PELAEZ 17 RVUE πK → πK

¹ Reanalysis of ESTABROOKS 78 and ASTON 88 satisfying Forward Dispersion Relations and using sequences of Pade approximants.

## $K^*(1410)$ 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>1414 ± 15</td><td>OUR AVERAGE</td><td colspan="4">Error includes scale factor of 1.3.</td></tr><tr><td>1380 ± 21 ± 19</td><td></td><td>ASTON</td><td>88</td><td>LASS</td><td>0</td><td>11 K<sup>-</sup> p → K<sup>-</sup>π<sup>+</sup> n</td></tr><tr><td>1420 ± 7 ± 10</td><td></td><td>ASTON</td><td>87</td><td>LASS</td><td>0</td><td>11 K<sup>-</sup> p → R<sup>0</sup>π<sup>+</sup>π<sup>-</sup> n</td></tr></tbody></table>

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

<table><tbody><tr><td>1437 ± 8 ± 16</td><td>190k</td><td>1 AAIJ</td><td>16N LHCB</td><td>D<sup>0</sup> → (K<sup>0</sup><sub>S</sub>π<sup>∓</sup>)K<sup>±</sup></td></tr><tr><td>1426 ± 8 ± 24</td><td>190k</td><td>2 AAIJ</td><td>16N LHCB</td><td>D<sup>0</sup> → K<sup>0</sup><sub>S</sub>(K<sup>±</sup>π<sup>∓</sup>)</td></tr><tr><td>1276 ± 7<sup>2</sup><sub>77</sub></td><td></td><td>3,4 BOITO</td><td>09 RVUE</td><td>τ<sup>-</sup> → K<sup>0</sup><sub>S</sub>π<sup>-</sup>ν<sub>τ</sub></td></tr><tr><td>1367 ± 54</td><td></td><td>BIRD</td><td>89 LASS</td><td>11 K<sup>-</sup> p → R<sup>0</sup>π<sup>-</sup> p</td></tr><tr><td>1474 ± 25</td><td></td><td>BAUBILLIER</td><td>82B HBC</td><td>8.25 K<sup>-</sup> p → R<sup>0</sup>2πn</td></tr><tr><td>1500 ± 30</td><td></td><td>ETKIN</td><td>80 MPS</td><td>6 K<sup>-</sup> p → R<sup>0</sup>π<sup>+</sup>π<sup>-</sup> n</td></tr></tbody></table>

¹ Using a parametrization for the Kπ S-wave similar to ASTON 88 with fixed resonance width.

² Using a Kπ S-wave parametrization with resonant and non-resonant contributions.

³ From the pole position of the Kπ vector form factor in the complex s-plane and using EPIFANOV 07 data.

⁴ Systematic uncertainties not estimated.

## $K^*(1410)$ WIDTH

<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>232 ± 21</td><td>OUR AVERAGE</td><td colspan="4">Error includes scale factor of 1.1.</td></tr><tr><td>176 ± 52 ± 22</td><td></td><td>ASTON</td><td>88</td><td>LASS</td><td>0</td><td>11 K<sup>-</sup> p → K<sup>-</sup>π<sup>+</sup> n</td></tr><tr><td>240 ± 18 ± 12</td><td></td><td>ASTON</td><td>87</td><td>LASS</td><td>0</td><td>11 K<sup>-</sup> p → R<sup>0</sup>π<sup>+</sup>π<sup>-</sup> n</td></tr></tbody></table>
# Meson Particle Listings

## K*(1410), K⁰*(1430)

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

<table><tr><td>210 ± 20 ± 60</td><td>190k</td><td>1 AAIJ</td><td>16N</td><td>LHCB</td><td>D<sup>0</sup> → (K<sup>0</sup><sub>S</sub>π<sup>∓</sup>)K<sup>±</sup></td></tr><tr><td>270 ± 20 ± 40</td><td>190k</td><td>1 AAIJ</td><td>16N</td><td>LHCB</td><td>D<sup>0</sup> → K<sup>0</sup><sub>S</sub>(K<sup>±</sup>π<sup>∓</sup>)</td></tr><tr><td>198<sup>+</sup> 61 / 87</td><td></td><td>2,3 BOITO</td><td>09</td><td>RVUE</td><td>τ<sup>−</sup> → K<sup>0</sup><sub>S</sub>π<sup>−</sup>ν<sub>τ</sub></td></tr><tr><td>114 ± 101</td><td></td><td>BIRD</td><td>89</td><td>LASS</td><td>11 K<sup>−</sup>p → R<sup>0</sup>π<sup>−</sup>p</td></tr><tr><td>275 ± 65</td><td></td><td>BAUBILLIER</td><td>82b</td><td>HBC</td><td>8.25 K<sup>−</sup>p → R<sup>0</sup>2πn</td></tr><tr><td>500 ± 100</td><td></td><td>ETKIN</td><td>80</td><td>MPS</td><td>6 K<sup>−</sup>p → R<sup>0</sup>π<sup>+</sup>π<sup>−</sup>n</td></tr></table>

¹ Using a $K\pi$ S-wave parametrization with resonant and non-resonant contributions.

² From the pole position of the $K\pi$ vector form factor in the complex s-plane and using EPIFANOV 07 data.

³ Systematic uncertainties not estimated.

## K*(1410) DECAY MODES

<table><thead><tr><th>Mode</th><th></th><th>Fraction (Γ<sub>i</sub>/Γ)</th><th>Confidence level</th></tr></thead><tbody><tr><td>Γ<sub>1</sub></td><td>K*(892) π</td><td>&gt; 40 %</td><td>95%</td></tr><tr><td>Γ<sub>2</sub></td><td>Kπ</td><td>( 6.6±1.3) %</td><td></td></tr><tr><td>Γ<sub>3</sub></td><td>Kρ</td><td>&lt; 7 %</td><td>95%</td></tr><tr><td>Γ<sub>4</sub></td><td>γK<sup>0</sup></td><td>&lt; 2.3 × 10<sup>−4</sup></td><td>90%</td></tr><tr><td>Γ<sub>5</sub></td><td>Kφ</td><td>seen</td><td></td></tr></tbody></table>

## K*(1410) PARTIAL WIDTHS

<table><thead><tr><th>Γ(γK<sup>0</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>VALUE (keV)</td><td></td><td></td><td></td><td></td></tr><tr><td><b>&lt;52.9</b></td><td>90</td><td>ALAVI-HARATI02B</td><td>KTEV</td><td>K + A → K* + A</td></tr></tbody></table>

## K*(1410) BRANCHING RATIOS

<table><thead><tr><th>Γ(K<sub>p</sub>)/Γ(K*(892)π)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>&lt;0.17</b></td><td>95</td><td>ASTON</td><td>84</td><td>LASS</td><td>11 K<sup>−</sup>p → R<sup>0</sup>2πn</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sub>π</sub>)/Γ(K*(892)π)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>&lt;0.16</b></td><td>95</td><td>ASTON</td><td>84</td><td>LASS</td><td>11 K<sup>−</sup>p → R<sup>0</sup>2πn</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sub>π</sub>)/Γ<sub>total</sub></th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>0.066±0.010±0.008</b></td><td></td><td>ASTON</td><td>88</td><td>LASS</td><td>11 K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sub>φ</sub>)/Γ<sub>total</sub></th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>seen</td><td>24k</td><td>1 AAIJ</td><td>21E</td><td>LHCB</td><td>B<sup>+</sup> → J/ψφK<sup>+</sup></td></tr></tbody></table>

¹ From an amplitude analysis of the decay $B^+ \to J/\psi\phi K^+$ with a significance of 7.7 $\sigma$.

## K*(1410) REFERENCES

<table><tr><td>AAIJ</td><td>21E</td><td>PRL 127 082001</td><td>R. Aaij et al.</td><td>(LHCb Collab.)</td></tr><tr><td>PELAEZ</td><td>17</td><td>EPJ C77 91</td><td>J.R. Pelaez, A.Rodas, J.R. de Elvira</td><td></td></tr><tr><td>AAIJ</td><td>16N</td><td>PR D93 052018</td><td>R. Aaij et al.</td><td>(LHCb Collab.)</td></tr><tr><td>BOITO</td><td>09</td><td>EPJ C59 821</td><td>D.R. Boito, R. Escribano, M. Jamin</td><td></td></tr><tr><td>EPIFANOV</td><td>07</td><td>PL B654 65</td><td>D. Epifanov et al.</td><td>(BELLE Collab.)</td></tr><tr><td>ALAVI-HARATI 02B</td><td>07</td><td>PRL 89 072001</td><td>A. Alavi-Harati et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>BIRD</td><td>89</td><td>SLAC-332</td><td>P.F. Bird</td><td>(SLAC)</td></tr><tr><td>ASTON</td><td>88</td><td>NP B296 493</td><td>D. Aston et al.</td><td>(SLAC, NAGO, CINC, INUS)</td></tr><tr><td>ASTON</td><td>87</td><td>NP B292 693</td><td>D. Aston et al.</td><td>(SLAC, NAGO, CINC, INUS)</td></tr><tr><td>ASTON</td><td>84</td><td>PL 149B 258</td><td>D. Aston et al.</td><td>(SLAC, CARL, OTTA) JP</td></tr><tr><td>BAUBILLIER</td><td>82B</td><td>PR B202 21</td><td>M. Baubiller et al.</td><td>(BIRM, CERN, GLAS+)</td></tr><tr><td>ETKIN</td><td>80</td><td>PR D22 42</td><td>A. Etkin et al.</td><td>(BNL, CUNY) JP</td></tr><tr><td>ESTABROOKS</td><td>78</td><td>NP B133 490</td><td>P.G. Estabrooks et al.</td><td>(MCGI, CARL, DURH+)</td></tr></table>

$$K_0^*(1430)$$

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

## K⁰*(1430) T-MATRIX POLE $\sqrt{s}$

Note that $\Gamma = -2 \, \mathrm{Im}(\sqrt{s})$.

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

### (1431 ± 6) - i (110 ± 19) OUR ESTIMATE

<table><tr><td>(1431 ± 6) - i (110 ± 19)</td><td>1 PELAEZ</td><td>17</td><td>RVUE</td><td>πK → πK</td></tr></table>

¹ Reanalysis of ESTABROOKS 78 and ASTON 88 satisfying Forward Dispersion Relations and using sequences of Pade approximants.

## K⁰*(1430) MASS

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1425 ± 50</td><td>OUR ESTIMATE</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>1493 ± 4 ± 7</td><td>1 AAIJ</td><td>23AH LHCB</td><td>B<sup>+</sup> → K<sup>+</sup>(K<sup>0</sup><sub>S</sub>Kπ)</td></tr><tr><td>1449 ± 17 ± 2</td><td>2 LEES</td><td>21A BABR</td><td>η<sub>C</sub>(1S) → η'K<sup>+</sup>K<sup>−</sup></td></tr><tr><td>1438 ± 8 ± 4</td><td>3 LEES</td><td>14E BABR</td><td>η<sub>C</sub>(1S) → K<sup>+</sup>K<sup>−</sup>η/π<sup>0</sup></td></tr><tr><td>1427 ± 4 ± 13</td><td>4 BUGG</td><td>10 RVUE</td><td>S-matrix pole</td></tr><tr><td>1466.6 ± 0.7 ± 3.4</td><td>5 BONVICINI</td><td>08A CLEO</td><td>D<sup>+</sup> → K<sup>−</sup>π<sup>+</sup>π<sup>+</sup></td></tr><tr><td>~ 1412</td><td>6 LINK</td><td>07 FOCS</td><td>D<sup>+</sup> → K<sup>−</sup>K<sup>+</sup>π<sup>+</sup></td></tr><tr><td>1461.0 ± 4.0 ± 2.1</td><td>7 LINK</td><td>07B FOCS</td><td>D<sup>+</sup> → K<sup>−</sup>π<sup>+</sup>π<sup>+</sup></td></tr><tr><td>1406 ± 29</td><td>8 BUGG</td><td>06 RVUE</td><td>Kp → K<sup>−</sup>π<sup>+</sup>n</td></tr><tr><td>1435 ± 6</td><td>9 ZHOU</td><td>06 RVUE</td><td>Kp → K<sup>−</sup>π<sup>+</sup>n</td></tr><tr><td>1455 ± 20 ± 15</td><td>ABLIKIM</td><td>05Q BES2</td><td>ψ(2S) → γπ<sup>+</sup>π<sup>−</sup>K<sup>+</sup>K<sup>−</sup></td></tr><tr><td>1456 ± 8</td><td>10 ZHENG</td><td>04 RVUE</td><td>K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td></tr><tr><td>~ 1419</td><td>11 BUGG</td><td>03 RVUE</td><td>11 K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td></tr><tr><td>~ 1440</td><td>12 LI</td><td>03 RVUE</td><td>11 K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td></tr><tr><td>1459 ± 9</td><td>13 AITALA</td><td>02 E791</td><td>D<sup>+</sup> → K<sup>−</sup>π<sup>+</sup>π<sup>+</sup></td></tr><tr><td>~ 1440</td><td>14 JAMIN</td><td>00 RVUE</td><td>Kp → Kp</td></tr><tr><td>1436 ± 8</td><td>15 BARBERIS</td><td>98E OMEG</td><td>450 pp → pfρS K<sup>+</sup>K<sup>−</sup>π<sup>+</sup>π<sup>−</sup></td></tr><tr><td>1415 ± 25</td><td>11 ANISOVICH</td><td>97C RVUE</td><td>11 K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td></tr><tr><td>~ 1450</td><td>16 TORNQVIST</td><td>96 RVUE</td><td>ππ → ππ, K<sup>+</sup>K, Kπ</td></tr><tr><td>1412 ± 6</td><td>17 ASTON</td><td>88 LASS</td><td>11 K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td></tr><tr><td>~ 1430</td><td>17 BAUBILLIER</td><td>84B HBC</td><td>8.25 K<sup>−</sup>p → R<sup>0</sup>π<sup>−</sup>p</td></tr><tr><td>~ 1425</td><td>18 ESTABROOKS 78</td><td>SPEC</td><td>13 K<sup>±</sup>p → K<sup>±</sup>π<sup>±</sup>(n,Δ)</td></tr><tr><td>~ 1450.0</td><td>18 MARTIN</td><td>78</td><td>K<sup>±</sup>p → K<sup>0</sup>Sπp</td></tr></table>

¹ From Dalitz plot analyses of $\eta_C(1S, 2S) \to K_S^0 K^+ \pi^- + \text{c.c.}$.

² Using a $K\pi-K\eta'$ coupled channel Breit-Wigner function.

³ Using both $\eta \to \gamma\gamma$ and $\eta \to \pi^+\pi^-\pi^0$. From a likelihood scan in the presence of several interfering scalar-meson resonances with fixed width $\Gamma(K_0^*(1430)) = 210$ MeV.

⁴ S-Matrix pole. Supersedes BUGG 06. Combined analysis of ASTON 88, ABLIKIM 06c, AITALA 06, and LINK 09 using an s-dependent width with couplings to $K\pi$ and $K\eta'$, and the Adler zero near thresholds.

⁵ From the isobar model with a complex pole for the $\kappa$.

⁶ Using a non-parametric analysis.

⁷ A Breit-Wigner mass and width.

⁸ S-matrix pole. Reanalysis of ASTON 88, AITALA 02, and ABLIKIM 06c including the $\kappa$ with an s-dependent width and an Adler zero near threshold.

⁹ S-matrix pole. Using ASTON 88 and assuming $K_0^*(700)$, $K_0^*(1950)$.

¹⁰ Using ASTON 88 and assuming $K_0^*(700)$.

¹¹ T-matrix pole. Reanalysis of ASTON 88 data.

¹² Breit-Wigner fit. Using ASTON 88.

¹³ Assuming a low-mass scalar $K\pi$ resonance, $\kappa(700)$.

¹⁴ T-matrix pole. Using data from ESTABROOKS 78 and ASTON 88.

¹⁵ $J^P$ not determined, could be $K_0^*(1430)$.

¹⁶ T-matrix pole.

¹⁷ Uses a model for the background, without this background they get a mass 1340 MeV, where the phase shift passes 90°.

¹⁸ Mass defined by pole position. From elastic $K\pi$ partial-wave analysis.

## K⁰*(1430) WIDTH

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><b>270 ± 80 OUR ESTIMATE</b></td></tr><tr><td>215 ± 7 ± 4</td><td>1 AAIJ</td><td>23AH LHCB</td><td>B<sup>+</sup> → K<sup>+</sup>(K<sup>0</sup><sub>S</sub>Kπ)</td><td></td></tr><tr><td>210 ± 20 ± 12</td><td>2 LEES</td><td>14E BABR</td><td>η<sub>C</sub>(1S) → K<sup>+</sup>K<sup>−</sup>η/π<sup>0</sup></td><td></td></tr><tr><td>270 ± 10 ± 40</td><td>3 BUGG</td><td>10 RVUE</td><td>S-matrix pole</td><td></td></tr><tr><td>174.2 ± 1.9 ± 3.2</td><td>4 BONVICINI</td><td>08A CLEO</td><td>D<sup>+</sup> → K<sup>−</sup>π<sup>+</sup>π<sup>+</sup></td><td></td></tr><tr><td>~ 500</td><td>5 LINK</td><td>07 FOCS</td><td>D<sup>+</sup> → K<sup>−</sup>K<sup>+</sup>π<sup>+</sup></td><td></td></tr><tr><td>177.0 ± 8.0 ± 3.4</td><td>6 LINK</td><td>07B FOCS</td><td>D<sup>+</sup> → K<sup>−</sup>π<sup>+</sup>π<sup>+</sup></td><td></td></tr><tr><td>350 ± 40</td><td>7 BUGG</td><td>06 RVUE</td><td>Kp → K<sup>−</sup>π<sup>+</sup>n</td><td></td></tr><tr><td>288 ± 22</td><td>8 ZHOU</td><td>06 RVUE</td><td>Kp → K<sup>−</sup>π<sup>+</sup>n</td><td></td></tr><tr><td>270 ± 45</td><td>ABLIKIM</td><td>05Q BES2</td><td>ψ(2S) → γπ<sup>+</sup>π<sup>−</sup>K<sup>+</sup>K<sup>−</sup></td><td></td></tr><tr><td>217 ± 31</td><td>9 ZHENG</td><td>04 RVUE</td><td>K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td><td></td></tr><tr><td>~ 316</td><td>10 BUGG</td><td>03 RVUE</td><td>11 K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td><td></td></tr><tr><td>~ 350</td><td>11 LI</td><td>03 RVUE</td><td>11 K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td><td></td></tr><tr><td>175 ± 17</td><td>12 AITALA</td><td>02 E791</td><td>D<sup>+</sup> → K<sup>−</sup>π<sup>+</sup>π<sup>+</sup></td><td></td></tr><tr><td>~ 300</td><td>13 JAMIN</td><td>00 RVUE</td><td>Kp → Kp</td><td></td></tr><tr><td>196 ± 45</td><td>14 BARBERIS</td><td>98E OMEG</td><td>450 pp → pfρS K<sup>+</sup>K<sup>−</sup>π<sup>+</sup>π<sup>−</sup></td><td></td></tr><tr><td>330 ± 50</td><td>10 ANISOVICH</td><td>97C RVUE</td><td>11 K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td><td></td></tr><tr><td>~ 320</td><td>15 TORNQVIST</td><td>96 RVUE</td><td>ππ → ππ, K<sup>+</sup>K, Kπ</td><td></td></tr><tr><td>294 ± 23</td><td>17 ASTON</td><td>88 LASS</td><td>11 K<sup>−</sup>p → K<sup>−</sup>π<sup>+</sup>n</td><td></td></tr><tr><td>~ 200</td><td>17 BAUBILLIER</td><td>84B HBC</td><td>8.25 K<sup>−</sup>p → R<sup>0</sup>π<sup>−</sup>p</td><td></td></tr><tr><td>200 to 300</td><td>18 ESTABROOKS 78</td><td>ASPK</td><td>13 K<sup>±</sup>p → K<sup>±</sup>π<sup>±</sup>(n,Δ)</td><td></td></tr></tbody></table>

¹ From Dalitz plot analyses of $\eta_C(1S, 2S) \to K_S^0 K^+ \pi^- + \text{c.c.}$.

² Using both $\eta \to \gamma\gamma$ and $\eta \to \pi^+\pi^-\pi^0$. From a likelihood scan in the presence of several interfering scalar-meson resonances with fixed mass $M(K_0^*(1430)) = 1435$ MeV.

³ S-Matrix pole. Supersedes BUGG 06. Combined analysis of ASTON 88, ABLIKIM 06c, AITALA 06, and LINK 09 using an s-dependent width with couplings to $K\pi$ and $K\eta'$, and the Adler zero near thresholds.

⁴ From the isobar model with a complex pole for the $\kappa$.