# Meson Particle Listings

$f_2(2150)$, $\rho(2150)$

<table><tr><td>HASAN</td><td>94</td><td>PL B334 215</td></tr><tr><td>OAKDEN</td><td>94</td><td>NP A574 731</td></tr><tr><td>SINGOVSKI</td><td>94</td><td>NC A107 1911</td></tr><tr><td>ARMSTRONG</td><td>93C</td><td>PL B307 394</td></tr><tr><td>ARMSTRONG</td><td>89D</td><td>PL B227 186</td></tr><tr><td>MARTIN</td><td>80B</td><td>NP B176 355</td></tr><tr><td>MARTIN</td><td>80C</td><td>NP B169 216</td></tr><tr><td>CUTTS</td><td>78B</td><td>PR D17 16</td></tr><tr><td>DULUDE</td><td>78B</td><td>PL 79B 335</td></tr><tr><td>COUPLAND</td><td>77</td><td>PL 71B 460</td></tr><tr><td>ALSPECTOR</td><td>73</td><td>PRL 30 511</td></tr></table>

<table><tr><td>A. Hasan, D.V. Bugg</td><td>(LOOM)</td></tr><tr><td>M.N. Oakden, M.R. Pennington</td><td>(DURH)</td></tr><tr><td>A.V. Singovsky</td><td>(SERP)</td></tr><tr><td>T.A. Armstrong et al.</td><td>(FNAL, FERR, GENO+)</td></tr><tr><td>T.A. Armstrong, M. Benayoun</td><td>(ATHU, BARI, BIRM+)</td></tr><tr><td>B.R. Martin, D. Morgan</td><td>(LOUQ, RHEL) JP</td></tr><tr><td>A.D. Martin, M.R. Pennington</td><td>(DURH) JP</td></tr><tr><td>D. Cutts et al.</td><td>(STON, WISC)</td></tr><tr><td>R.S. Dulude et al.</td><td>(BROW, MIT, BARI) JP</td></tr><tr><td>M. Coupland et al.</td><td>(LOQM, RHEL)</td></tr><tr><td>J. Alspector et al.</td><td>(RUTG, UPNJ)</td></tr></table>

$\rho(2150)$

$I^G(J^{PC}) = 1^+(1^- -)$

## OMITTED FROM SUMMARY TABLE

This entry was previously called $T_1(2190)$. See the review on "Spec- troscopy of Light Meson Resonances."

## $\rho(2150)$ MASS

### $e^+e^-$ PRODUCED

<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>2044 ±31 ± 4</td><td></td><td>1 ABLIKIM</td><td>23BQ BES3</td><td>e<sup>+</sup>e<sup>-</sup> → a<sub>2</sub>(1320)<sup>+</sup>π<sup>-</sup> +<br>c.c. → ηπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>2095 ± 4</td><td></td><td>2 ACHASOV</td><td>23A SND</td><td>e<sup>+</sup>e<sup>+</sup> → ωπ<sup>0</sup></td></tr><tr><td>2034 ±13 ± 9</td><td></td><td>3 ABLIKIM</td><td>21A BES3</td><td>e<sup>+</sup>e<sup>+</sup> → ωπ<sup>0</sup></td></tr><tr><td>2111 ±43 ±25</td><td></td><td>4 ABLIKIM</td><td>21X BES3</td><td>e<sup>+</sup>e<sup>+</sup> → η'<sup>+</sup>π<sup>-</sup>π<sup>-</sup></td></tr><tr><td>2255 ±17 ±50<br>-18 -41</td><td>1.8k</td><td>5 ABLIKIM</td><td>20F BES3</td><td>ψ(2S) → K<sup>+</sup> K<sup>-</sup>η</td></tr><tr><td>2201 ±19</td><td></td><td>6 LEES</td><td>20 BABR</td><td>e<sup>+</sup>e<sup>+</sup> → K<sup>+</sup> K<sup>-</sup>γ</td></tr><tr><td>2227 ± 9 ± 9</td><td></td><td>7 LEES</td><td>20 RVUE</td><td>e<sup>+</sup>e<sup>+</sup> → K<sup>+</sup> K<sup>-</sup></td></tr><tr><td>2039 ± 8 <sup>+36</sup><sub>-18</sub></td><td></td><td>8 ABLIKIM</td><td>19AQ BES</td><td>J/ψ → K<sup>+</sup> K<sup>-</sup>π<sup>0</sup></td></tr><tr><td>2239.2 ± 7.1 ±11.3</td><td></td><td>9 ABLIKIM</td><td>19L BES3</td><td>e<sup>+</sup>e<sup>+</sup> → K<sup>+</sup> K<sup>-</sup></td></tr><tr><td>2254 ±22</td><td></td><td>10 LEES</td><td>12G BABR</td><td>e<sup>+</sup>e<sup>+</sup> → π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>2150 ±40 ±50</td><td></td><td>AUBERT</td><td>07AU BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> →<br>f<sub>1</sub>(1285) π<sup>-</sup> π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>1990 ±80</td><td></td><td>AUBERT</td><td>07AU BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> → η'<sup>+</sup>π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>2153 ±37</td><td></td><td>BIAGINI</td><td>91 RVUE</td><td>e<sup>+</sup>e<sup>+</sup> → π<sup>+</sup>π<sup>-</sup>, K<sup>+</sup> K<sup>-</sup></td></tr><tr><td>2110 ±50</td><td></td><td>11 CLEGG</td><td>90 RVUE</td><td>e<sup>+</sup>e<sup>+</sup> → 3(π<sup>+</sup>π<sup>-</sup>),<br>2(π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>)</td></tr></tbody></table>

¹ From a fit to the cross section between 2.00 and 3.08 GeV with a coherent sum of a Breit-Wigner resonance and a non-resonant contribution. Could be another state.

² From a vector dominance fit to the Born cross section between 1.05 and 2.0 GeV with $\rho(770)$, $\rho(1570)$, $\rho(1700)$, $\rho(2150)$. The fit also uses SND data from the VEPP-2M collider below 1.02 GeV and from LEES 17H and ABLIKIM 21A above 1.5 GeV.

³ From a fit to the cross section between 2.00 and 3.08 GeV with a coherent sum of Breit-Wigner amplitudes, including contributions from $\rho(770)$, $\rho(1450)$ and $\rho(1700)$. Could be another state.

⁴ From a Breit-Wigner fit to the Born cross section, including an s-dependent continuum amplitude.

⁵ Seen in $\psi(2S)$ decay with branching ratio $\psi(2S) \to X\eta \to K^+K^-\eta = (21.7 \pm 1.9^{+7.7}_{-8.3}) \times 10^{-6}$.

⁶ From the fit to the BABAR data of LEES 13Q assuming a coherent sum of a single Breit-Wigner resonance and a nonresonant contribution. The resonance significance is $3.5 \sigma$.

⁷ From the fit to the BABAR data of LEES 13q and BESIII data of ABLIKIM 19l assuming a coherent sum of a single Breit-Wigner resonance and a nonresonant contribution.

⁸ Could also be another state. Seen in $J/\psi$ decay with branching ratio $J/\psi \to X\pi^0 \to K^+K^-\pi^0 = (6.7 \pm 1.1^{+2.2}_{-1.8}) \times 10^{-6}$.

⁹ The observed structure can be due to both the $\phi(2170)$ and $\rho(2150)$.

¹⁰ Using the GOUNARIS 68 parametrization of the pion form factor leaving the masses and widths of the $\rho(1450)$, $\rho(1700)$, and $\rho(2150)$ resonances as free parameters of the fit.

¹¹ Includes ATKINSON 85.

### $\bar{p}p \to \pi\pi$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>~ 2191</td><td>HASAN</td><td>94</td><td>RVUE $\bar{p}p \to \pi\pi$</td></tr><tr><td>~ 2070</td><td>1 OAKDEN</td><td>94</td><td>RVUE 0.36-1.55 $\bar{p}p \to \pi\pi$</td></tr><tr><td>~ 2170</td><td>2 MARTIN</td><td>80B RVUE</td><td></td></tr><tr><td>~ 2100</td><td>2 MARTIN</td><td>80C RVUE</td><td></td></tr></tbody></table>

¹ See however KLOET 96 who fit $\pi^+\pi^-$ only and find waves only up to $J=3$ to be important but not significantly resonant.

² $I(J^P) = 1(1^-)$ from simultaneous analysis of $p\bar{p} \to \pi^-\pi^+$ and $\pi^0\pi^0$.

### S-CHANNEL $\bar{N}N$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2110 ±35</td><td>1 ANISOVICH 02</td><td>SPEC</td><td>0.6-1.9 p<span style="text-decoration: overline">p</span> → ωπ<sup>0</sup>, ωηπ<sup>0</sup>, π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>~ 2190</td><td>2 CUTTS 78B</td><td>CNTR</td><td>0.97-3 <span style="text-decoration: overline">p</span> → <span style="text-decoration: overline">N</span>N</td></tr><tr><td>2155 ±15</td><td>2,3 COUPLAND 77</td><td>CNTR</td><td>0.7-2.4 <span style="text-decoration: overline">p</span> → <span style="text-decoration: overline">p</span>p</td></tr><tr><td>2193 ± 2</td><td>2,4 ALSPECTOR 73</td><td>CNTR</td><td><span style="text-decoration: overline">p</span>p S channel</td></tr><tr><td>2190 ±10</td><td>5 ABRAMS 70</td><td>CNTR</td><td>S channel <span style="text-decoration: overline">p</span>N</td></tr></tbody></table>

¹ From the combined analysis of ANISOVICH 00J, ANISOVICH 01D, ANISOVICH 01E, and ANISOVICH 02.

² Isospins 0 and 1 not separated.

³ From a fit to the total elastic cross section.

⁴ Referred to as *T* or *T* region by ALSPECTOR 73.

⁵ Seen as bump in $I=1$ state. See also COOPER 68. PEASLEE 75 confirm $\bar{p}p$ results of ABRAMS 70, no narrow structure.

### $\pi^-p \to \omega\pi^0 n$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2140 ±30</td><td>ALDE</td><td>95</td><td>GAM2 38 π<sup>-</sup> p → ωπ<sup>0</sup> n</td></tr><tr><td>2170 ±30</td><td>ALDE</td><td>92C</td><td>GAM4 100 π<sup>-</sup> p → ωπ<sup>0</sup> n</td></tr></tbody></table>

## $\rho(2150)$ WIDTH

### $e^+e^-$ PRODUCED

<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>163 ± 69 ± 24</td><td></td><td>1 ABLIKIM</td><td>23BQ BES3</td><td>e<sup>+</sup>e<sup>-</sup> → a<sub>2</sub>(1320)<sup>+</sup>π<sup>-</sup> +<br>c.c. → ηπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>270 ± 3</td><td></td><td>2 ACHASOV</td><td>23A SND</td><td>e<sup>+</sup>e<sup>-</sup> → ωπ<sup>0</sup></td></tr><tr><td>234 ± 30 ± 25</td><td></td><td>3 ABLIKIM</td><td>21A BES3</td><td>e<sup>+</sup>e<sup>-</sup> → ωπ<sup>0</sup></td></tr><tr><td>135 ± 34 ± 30</td><td></td><td>4 ABLIKIM</td><td>21X BES3</td><td>e<sup>+</sup>e<sup>-</sup> → η'<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>460 ± 54 ±160<br>-48 -90</td><td>1.8k</td><td>5 ABLIKIM</td><td>20F BES3</td><td>ψ(2S) → K<sup>+</sup> K<sup>-</sup>η</td></tr><tr><td>70 ± 38</td><td></td><td>6 LEES</td><td>20 BABR</td><td>e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup> K<sup>-</sup>γ</td></tr><tr><td>127 ± 14 ± 4</td><td></td><td>7 LEES</td><td>20 RVUE</td><td>e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup> K<sup>-</sup></td></tr><tr><td>196 ± 23 ± 25<br>-27</td><td></td><td>8 ABLIKIM</td><td>19AQ BES</td><td>J/ψ → K<sup>+</sup> K<sup>-</sup>π<sup>0</sup></td></tr><tr><td>139.8 ± 12.3 ± 20.6</td><td></td><td>9 ABLIKIM</td><td>19L BES3</td><td>e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup> K<sup>-</sup></td></tr><tr><td>109 ± 76</td><td></td><td>10 LEES</td><td>12G BABR</td><td>e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>350 ± 40 ± 50</td><td></td><td>AUBERT</td><td>07AU BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> →<br>f<sub>1</sub>(1285) π<sup>-</sup> π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>310 ±140</td><td></td><td>AUBERT</td><td>07AU BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> → η'<sup>+</sup>π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>389 ± 79</td><td></td><td>BIAGINI</td><td>91 RVUE</td><td>e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>, K<sup>+</sup> K<sup>-</sup></td></tr><tr><td>410 ±100</td><td></td><td>11 CLEGG</td><td>90 RVUE</td><td>e<sup>+</sup>e<sup>-</sup> → 3(π<sup>+</sup>π<sup>-</sup>),<br>2(π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>)</td></tr></tbody></table>

¹ From a fit to the cross section between 2.00 and 3.08 GeV with a coherent sum of a Breit-Wigner resonance and a non-resonant contribution. Could be another state.

² From a vector dominance fit to the Born cross section between 1.05 and 2.0 GeV with $\rho(770)$, $\rho(1570)$, $\rho(1700)$, $\rho(2150)$. The fit also uses SND data from the VEPP-2M collider below 1.02 GeV and from LEES 17H and ABLIKIM 21A above 1.5 GeV.

³ From a fit to the cross section between 2.00 and 3.08 GeV with a coherent sum of Breit-Wigner amplitudes, including contributions from $\rho(770)$, $\rho(1450)$ and $\rho(1700)$. Could be another state.

⁴ From a Breit-Wigner fit to the Born cross section, including an s-dependent continuum amplitude.

⁵ Seen in $\psi(2S)$ decay with branching ratio $\psi(2S) \to X\eta \to K^+K^-\eta = (21.7 \pm 1.9^{+7.7}_{-8.3}) \times 10^{-6}$.

⁶ From the fit to the BABAR data of LEES 13q assuming a coherent sum of a single Breit-Wigner resonance and a nonresonant contribution. The resonance significance is $3.5 \sigma$.

⁷ From the fit to the BABAR data of LEES 13q and BESIII data of ABLIKIM 19l assuming a coherent sum of a single Breit-Wigner resonance and a nonresonant contribution.

⁸ Could also be another state. Seen in $J/\psi$ decay with branching ratio $J/\psi \to X\pi^0 \to K^+K^-\pi^0 = (6.7 \pm 1.1^{+2.2}_{-1.8}) \times 10^{-6}$.

⁹ The observed structure can be due to both the $\phi(2170)$ and $\rho(2150)$.

¹⁰ Using the GOUNARIS 68 parametrization of the pion form factor leaving the masses and widths of the $\rho(1450)$, $\rho(1700)$, and $\rho(2150)$ resonances as free parameters of the fit.

¹¹ Includes ATKINSON 85.

### $\bar{p}p \to \pi\pi$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>~ 296</td><td>HASAN</td><td>94</td><td>RVUE $\bar{p}p \to \pi\pi$</td></tr><tr><td>~ 40</td><td>1 OAKDEN</td><td>94</td><td>RVUE 0.36-1.55 $\bar{p}p \to \pi\pi$</td></tr><tr><td>~ 250</td><td>2 MARTIN</td><td>80B RVUE</td><td></td></tr><tr><td>~ 200</td><td>2 MARTIN</td><td>80C RVUE</td><td></td></tr></tbody></table>

¹ See however KLOET 96 who fit $\pi^+\pi^-$ only and find waves only up to $J=3$ to be important but not significantly resonant.

² $I(J^P) = 1(1^-)$ from simultaneous analysis of $p\bar{p} \to \pi^-\pi^+$ and $\pi^0\pi^0$.

### S-CHANNEL $\bar{N}N$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>230 ±50</td><td>1 ANISOVICH 02</td><td>SPEC</td><td>0.6-1.9 p<span style="text-decoration: overline">p</span> → ωπ<sup>0</sup>, ωηπ<sup>0</sup>, π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>135 ±75</td><td>2,3 COUPLAND 77</td><td>CNTR</td><td>0.7-2.4 <span style="text-decoration: overline">p</span> → <span style="text-decoration: overline">p</span>p</td></tr><tr><td>98 ± 8</td><td>3 ALSPECTOR 73</td><td>CNTR <span style="text-decoration: overline">p</span>p S channel</td><td></td></tr><tr><td>~ 85</td><td>4 ABRAMS</td><td>70</td><td>CNTR S channel <span style="text-decoration: overline">p</span>N</td></tr></tbody></table>

¹ From the combined analysis of ANISOVICH 00J, ANISOVICH 01D, ANISOVICH 01E, and ANISOVICH 02.

² From a fit to the total elastic cross section.

³ Isospins 0 and 1 not separated.

⁴ Seen as bump in $I=1$ state. See also COOPER 68. PEASLEE 75 confirm $\bar{p}p$ results of ABRAMS 70, no narrow structure.

### $\pi^-p \to \omega\pi^0 n$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>320 ±70</td><td>ALDE</td><td>95</td><td>GAM2 38 π<sup>-</sup> p → ωπ<sup>0</sup> n</td></tr><tr><td>~ 300</td><td>ALDE</td><td>92C</td><td>GAM4 100 π<sup>-</sup> p → ωπ<sup>0</sup> n</td></tr></tbody></table>
## $\rho(2150)$ DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction ($\Gamma_i/\Gamma$)</th></tr></thead><tbody><tr><td>$\Gamma_1$</td><td>e<sup>+</sup>e<sup>-</sup></td></tr><tr><td>$\Gamma_2$</td><td>$\pi^+\pi^-$</td></tr><tr><td>$\Gamma_3$</td><td>K<sup>+</sup>K<sup>-</sup></td></tr><tr><td>$\Gamma_4$</td><td>3($\pi^+\pi^-$)</td></tr><tr><td>$\Gamma_5$</td><td>2($\pi^+\pi^-$, $\pi^0$)</td></tr><tr><td>$\Gamma_6$</td><td>$\eta'\pi^+\pi^-$</td></tr><tr><td>$\Gamma_7$</td><td>$\tilde{\Gamma}_1(1285)\pi^+\pi^-$</td></tr><tr><td>$\Gamma_8$</td><td>$\omega\pi^0$</td></tr><tr><td>$\Gamma_9$</td><td>$\omega\pi^0\eta$</td></tr><tr><td>$\Gamma_{10}$</td><td>$\partial_2(1320)\pi$</td></tr><tr><td>$\Gamma_{11}$</td><td>$\rho\bar{\rho}$</td></tr></tbody></table>

## $\rho(2150)$ $\Gamma(i)\Gamma(e^+e^-)/\Gamma(\text{total})$

$$ \begin{array}{l} \Gamma(\eta'\pi^+\pi^-) \times \Gamma(e^+e^-)/\Gamma_{\text{total}} \\ \text{VALUE (eV)} \qquad \text{DOCUMENT ID} \qquad \text{TECN} \qquad \text{COMMENT} \qquad \Gamma_6\Gamma_1/\Gamma \end{array} $$

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

$$ 23.3 \pm 5.3 \pm 3.3 \qquad 1 \text{ ABLIKIM} \quad 21 \times \text{BES3} \quad e^+e^- \rightarrow \eta'\pi^+\pi^- $$

¹ From a Breit-Wigner fit to the Born cross section interfering constructively with the continuum. For destructive interference the value is 0.64 ± 0.49 ± 0.42 eV.

$$ \begin{array}{l} \Gamma(\omega\pi^0) \times \Gamma(e^+e^-)/\Gamma_{\text{total}} \\ \text{VALUE (eV)} \qquad \text{DOCUMENT ID} \qquad \text{TECN} \qquad \text{COMMENT} \qquad \Gamma_8\Gamma_1/\Gamma \end{array} $$

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

$$ 34 \pm 11 \pm 16 \qquad \text{ABLIKIM} \quad 21 \text{A BES3} \quad e^+e^- \rightarrow \omega\pi^0 $$

$$ \begin{array}{l} \Gamma(\partial_2(1320)\pi) \times \Gamma(e^+e^-)/\Gamma_{\text{total}} \\ \text{VALUE (eV)} \qquad \text{DOCUMENT ID} \qquad \text{TECN} \qquad \text{COMMENT} \qquad \Gamma_{10}\Gamma_1/\Gamma \end{array} $$

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

$$ 34.6 \pm 17.1 \pm 6.0 \qquad 1 \text{ ABLIKIM} \quad 23 \text{BQ BES3} \quad e^+e^- \rightarrow \partial_2(1320)\pi^+\pi^- + \text{c.c.} \rightarrow \eta\pi^+\pi^- $$

¹ From a solution of the fit to the cross section between 2.00 and 3.08 GeV using a coherent sum of a single Breit-Wigner resonance and a non-resonant contribution. $B(\partial_2(1320) \rightarrow \eta\pi) \times B(\eta \rightarrow \gamma\gamma)$ fixed to 0.057. Another solution with equal fit quality gives 137.1 ± 73.3 ± 2.1 eV.

## $\rho(2150)$ $\Gamma(i)\Gamma(e^+e^-)/\Gamma^2(\text{total})$

$$ \begin{array}{l} \Gamma(\tilde{\Gamma}_1(1285)\pi^+\pi^-)/\Gamma_{\text{total}} \times \Gamma(e^+e^-)/\Gamma_{\text{total}} \\ \text{VALUE (units $10^{-7}$)} \qquad \text{DOCUMENT ID} \qquad \text{TECN} \qquad \text{COMMENT} \qquad \Gamma_7/\Gamma \times \Gamma_1/\Gamma \end{array} $$

$$ 3.1 \pm 0.6 \pm 0.5 \qquad 1 \text{ AUBERT} \quad 07 \text{AU BABR} \quad 10.6 e^+e^- \rightarrow \tilde{\Gamma}_1(1285)\pi^+\pi^-\gamma $$

¹ Calculated by us from the reported value of cross section at the peak.

$$ \begin{array}{l} \Gamma(\eta'\pi^+\pi^-)/\Gamma_{\text{total}} \times \Gamma(e^+e^-)/\Gamma_{\text{total}} \\ \text{VALUE (units $10^{-6}$)} \qquad \text{DOCUMENT ID} \qquad \text{TECN} \qquad \text{COMMENT} \qquad \Gamma_6/\Gamma \times \Gamma_1/\Gamma \end{array} $$

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

$$ 4.9 \pm 1.9 \qquad 1 \text{ AUBERT} \quad 07 \text{AU BABR} \quad 10.6 e^+e^- \rightarrow \eta'\pi^+\pi^-\gamma $$

¹ Calculated by us from the reported value of cross section at the peak.

## $\rho(2150)$ REFERENCES

<table><tbody><tr><td>ABLIKIM</td><td>23BQ PR D108 L111101</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ACHASOV</td><td>23A PR D108 092012</td><td>M.N. Achasov et al.</td><td>(SND Collab.)</td></tr><tr><td>ABLIKIM</td><td>21A PL B813 136059</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>21X PR D103 072007</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>20F PR D101 032008</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>LEES</td><td>20 PR D101 012011</td><td>J.P. Lees et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>19AQ PR D100 032004</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>19L PR D99 032001</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>LEES</td><td>17H PR D96 092009</td><td>J.P. Lees et al.</td><td>(BABAR Collab.)</td></tr><tr><td>LEES</td><td>13Q PR D88 032013</td><td>J.P. Lees et al.</td><td>(BABAR Collab.)</td></tr><tr><td>LEES</td><td>12G PR D86 032013</td><td>J.P. Lees et al.</td><td>(BABAR Collab.)</td></tr><tr><td>AUBERT</td><td>07AU PR D76 092005</td><td>B. Aubert et al.</td><td>(BABAR Collab.)</td></tr><tr><td>ANISOVICH</td><td>02 PL B542 8</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>ANISOVICH</td><td>01D PL B508 6</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>ANISOVICH</td><td>01E PL B513 281</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>ANISOVICH</td><td>00J PL B491 47</td><td>A.V. Anisovich et al.</td><td>(RAL, LOQM, PNPI+)</td></tr><tr><td>KLOET</td><td>96 PR D53 6120</td><td>W.M. Kloet, F. Myhrer</td><td>(RUTG, NORD)</td></tr><tr><td>ALDE</td><td>95 ZPHY C66 379</td><td>D.M. Alde et al.</td><td>(GAMS Collab.) JP</td></tr><tr><td>HASAN</td><td>94 PL B334 215</td><td>A. Hasan, D.V. Bugg</td><td>(LOQM)</td></tr><tr><td>OAKDEN</td><td>94 NP A574 731</td><td>M.N. Oakden, M.R. Pennington</td><td>(DURH)</td></tr><tr><td>ALDE</td><td>92C ZPHY C54 553</td><td>D.M. Alde et al.</td><td>(BELG, SERP, KEK, LANL+)</td></tr><tr><td>BIAGINI</td><td>91 NC 104A 363</td><td>M.E. Biagini et al.</td><td>(FRAS, PRAG)</td></tr><tr><td>CLEGG</td><td>90 ZPHY C45 677</td><td>A.B. Clegg, A. Donnachie</td><td>(LANC, MCHS)</td></tr><tr><td>ATKINSON</td><td>85 ZPHY C29 333</td><td>M. Atkinson et al.</td><td>(BONN, CERN, GLAS+)</td></tr><tr><td>MARTIN</td><td>80B NP B176 355</td><td>B.R. Martin, D. Morgan</td><td>(LOUC, RHEL) JP</td></tr><tr><td>MARTIN</td><td>80C NP B169 216</td><td>A.D. Martin, M.R. Pennington</td><td>(DURH)</td></tr><tr><td>CUTTS</td><td>78B PR D17 16</td><td>D. Cutts et al.</td><td>(STON, WISC)</td></tr><tr><td>COUPLAND</td><td>77 PL 71B 460</td><td>M. Coupland et al.</td><td>(LOQM, RHEL)</td></tr><tr><td>PEASLEE</td><td>75 PL 57B 189</td><td>D.C. Peaslee et al.</td><td>(CANB, BARI, BROW+)</td></tr><tr><td>ALSPPECTOR</td><td>73 PRL 30 511</td><td>J. Alpector et al.</td><td>(RUTG, UPNJ)</td></tr><tr><td>ABRAMS</td><td>70 PR D1 1917</td><td>R.J. Abrams et al.</td><td>(BNL)</td></tr><tr><td>COOPER</td><td>68 PRL 20 1059</td><td>W.A. Cooper et al.</td><td>(ANL)</td></tr><tr><td>GOUNARIS</td><td>68 PRL 21 244</td><td>G.J. Gounaris, J.J. Sakurai</td><td></td></tr></tbody></table>

$\phi(2170)$

$\Gamma(G^{PC}) = 0^{-}(1^{-})^{-}$

See the review on "Spectroscopy of Light Meson Resonances."

## $\phi(2170)$ MASS

<table><thead><tr><th>VALUE (MeV)</th><th>EVT$^S$</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>2164 ± 6 OUR AVERAGE</strong></td></tr><tr><td>2178</td><td>±20 ± 5</td><td>1 ABLIKIM</td><td>23AX BES3</td><td>e<sup>+</sup>e<sup>-</sup> → φπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>2190</td><td>±19 ± 37</td><td>2 ABLIKIM</td><td>22L BES3</td><td>2.0-3.08 e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup>π<sup>0</sup></td></tr><tr><td>2176</td><td>±24 ± 3</td><td>3 ABLIKIM</td><td>21A BES3</td><td>e<sup>+</sup>e<sup>-</sup> → ωη</td></tr><tr><td>2163.5</td><td>±6.2 ± 3.0</td><td>4 ABLIKIM</td><td>21T BES3</td><td>e<sup>+</sup>e<sup>-</sup> → φη</td></tr><tr><td>2177.5</td><td>±4.8 ± 19.5</td><td>5 ABLIKIM</td><td>20M BES3</td><td>e<sup>+</sup>e<sup>-</sup> → η'φ</td></tr><tr><td>2126.5</td><td>±16.8 ± 12.4</td><td>6 ABLIKIM</td><td>20S BES3</td><td>e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup>π<sup>0</sup>π<sup>0</sup></td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>2215.7</td><td>± 8.3</td><td>7 LICHARD</td><td>23 RVUE</td><td>e<sup>+</sup>e<sup>-</sup> → T(nS) → φηη</td></tr><tr><td>2169</td><td>± 5 ± 6</td><td>8 ZHU</td><td>23A RVUE</td><td>e<sup>+</sup>e<sup>-</sup> → ηφ</td></tr><tr><td>2273.7</td><td>± 5.7 ± 19.3</td><td>9 ABLIKIM</td><td>21AP BES3</td><td>e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>S K<sup>-</sup>L</td></tr><tr><td>2135</td><td>± 8 ± 9</td><td>95 ABLIKIM</td><td>19L BES3</td><td>e<sup>+</sup>e<sup>-</sup> → ηφf<sub>0</sub>(980)</td></tr><tr><td>2239.2</td><td>± 7.1 ± 11.3</td><td>10 ABLIKIM</td><td>19L BES3</td><td>e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup></td></tr><tr><td>2200</td><td>± 6 ± 5</td><td>471 ABLIKIM</td><td>15H BES3</td><td>J/ψ → ηφπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>2180</td><td>± 8 ± 8</td><td>11,12 LEES</td><td>12F BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>2079</td><td>±13 <sup>+79</sup><sub>-28</sub></td><td>4.8k</td><td>13 SHEN</td><td>10.6 e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>2186</td><td>±10 ± 6</td><td>52 ABLIKIM</td><td>08F BES</td><td>J/ψ → ηφf<sub>0</sub>(980)</td></tr><tr><td>2125</td><td>±22 ± 10</td><td>483 AUBERT</td><td>08S BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> → φηη</td></tr><tr><td>2192</td><td>±14</td><td>116 AUBERT</td><td>07AK BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>2169</td><td>±20</td><td>149 AUBERT</td><td>07AK BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup>π<sup>0</sup>π<sup>0</sup>γ</td></tr><tr><td>2175</td><td>±10 ± 15</td><td>201 12,15 AUBERT, BE</td><td>06D BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

¹ From a fit to the e<sup>+</sup>e<sup>-</sup> cross section between 2.00 and 3.08 GeV with a sum of Breit-Wigner amplitude and a non-resonant contribution.

² By a simultaneous fit of the $K_S^*(1430)^+K^-$ and $K^*(892)^+K^-$ intermediate channels in a partial-wave analysis, assuming the same structure, modelled with a coherent sum of a nonresonant component and a resonant component by a Breit-Wigner function.

³ From a fit to the cross section between 2.00 and 3.08 GeV with a coherent sum of Breit-Wigner amplitudes, including contributions from $\omega(1420)$ and $\omega(1650)/\phi(1680)$.

⁴ From a fit to the cross section below 3.5 GeV measured by BaBar and BESIII with a coherent sum of two modified Breit-Wigner amplitudes ($\phi(1680)$ and $\phi(2170)$) and a nonresonant term.

⁵ From a fit using a coherent sum of a phase-space modified Breit-Wigner function and a phase-space term.

⁶ By a simultaneous fit of the intermediate channels in a partial-wave analysis, assuming the same structure, modelled with a coherent sum of a nonresonant component and a resonant component by a Breit-Wigner function.

⁷ From a VDM fit to ZHU 23 $\eta\phi\gamma$ data with two resonances, $\phi(1680)$, $\phi(2170)$, and a third resonance with mass 1850.7 ± 5.3 MeV and width 25 ± 35 MeV of 1.7 σ statistical evidence.

⁸ From the analysis of the combined measurements of $\sigma(e^+e^- \rightarrow \eta\phi)$ from BaBar, Belle, BESIII, CMD3. The statistical significance for $\phi(2170)$ is 7.2 σ.

⁹ From a fit to the cross section between 2.00 and 3.08 GeV with a sum of Breit-Wigner amplitude and a nonresonant contribution. The observed structure can be also due to $\rho(2150)$.

¹⁰ The observed structure can be due to both the $\phi(2170)$ and $\rho(2150)$.

¹¹ Fit includes interference with the $\phi(1680)$.

¹² The $\phi f_0(980)$ component.

¹³ From a fit with two incoherent Breit-Wigners.

¹⁴ From the $K^+K^-$ $f_0(980)$ component.

¹⁵ Superseded by LEES 12F.

## $\phi(2170)$ WIDTH

<table><thead><tr><th>VALUE (MeV)</th><th>EVT$^S$</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>106 <sup>+24</sup><sub>-18</sub> OUR AVERAGE</strong></td></tr><tr><td>140</td><td>±36 ± 16</td><td>1 ABLIKIM</td><td>23AX BES3</td><td>e<sup>+</sup>e<sup>-</sup> → φπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>191</td><td>±28 ± 60</td><td>2 ABLIKIM</td><td>22L BES3</td><td>2.0-3.08 e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup>π<sup>0</sup></td></tr><tr><td>89</td><td>±50 ± 5</td><td>3 ABLIKIM</td><td>21A BES3</td><td>e<sup>+</sup>e<sup>-</sup> → ωη</td></tr><tr><td>31.1 <sup>+21.6</sup><sub>-11.6</sub></td><td>± 1.1</td><td>4 ABLIKIM</td><td>21T BES3</td><td>e<sup>+</sup>e<sup>-</sup> → φη</td></tr><tr><td>149.0</td><td>±15.6 ± 8.9</td><td>5 ABLIKIM</td><td>20M BES3</td><td>e<sup>+</sup>e<sup>-</sup> → η'φ</td></tr><tr><td>106.9</td><td>±32.1 ± 28.1</td><td>6 ABLIKIM</td><td>20S BES3</td><td>e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup>π<sup>0</sup>π<sup>0</sup>γ</td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>35</td><td>±23</td><td>7 LICHARD</td><td>23 RVUE</td><td>e<sup>+</sup>e<sup>-</sup> → T(nS) → φηη</td></tr><tr><td>96</td><td>±17 ± 9</td><td>8 ZHU</td><td>23A RVUE</td><td>e<sup>+</sup>e<sup>-</sup> → φη</td></tr><tr><td>86</td><td>±44 ± 51</td><td>9 ABLIKIM</td><td>21AP BES3</td><td>e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>S K<sup>-</sup>L</td></tr><tr><td>104</td><td>±24 ± 12</td><td>95 ABLIKIM</td><td>19L BES3</td><td>e<sup>+</sup>e<sup>-</sup> → ηφf<sub>0</sub>(980)</td></tr><tr><td>139.8</td><td>±12.3 ± 20.6</td><td>10 ABLIKIM</td><td>19L BES3</td><td>e<sup>+</sup>e<sup>-</sup> → K<sup>+</sup>K<sup>-</sup></td></tr><tr><td>104</td><td>±15 ± 15</td><td>471 ABLIKIM</td><td>15H BES3</td><td>J/ψ → ηφπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>77</td><td>±15 ± 10</td><td>11,12 LEES</td><td>12F BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> → φπ<sup>+</sup>π<sup>-</sup>γ</td></tr></tbody></table>
# Meson Particle Listings

## $\phi(2170)$

<table><tbody><tr><td>192</td><td>±23</td><td>+25/61</td><td>4.8k</td><td><sup>13</sup>SHEN</td><td>09 BELL</td><td>10.6 e<sup>+</sup>e<sup>-</sup> →<br>K<sup>+</sup>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>65</td><td>±23</td><td>±17</td><td>52</td><td>ABLIKIM</td><td>08F BES</td><td>J/ψ → ηφ<sub>0</sub>(980)</td></tr><tr><td>61</td><td>±50</td><td>±13</td><td>483</td><td>AUBERT</td><td>08S BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> → Φηγ</td></tr><tr><td>71</td><td>±21</td><td></td><td>116</td><td><sup>14</sup>AUBERT</td><td>07AK BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> →<br>K<sup>+</sup>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>102</td><td>±27</td><td></td><td>149</td><td><sup>14</sup>AUBERT</td><td>07AK BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> →<br>K<sup>+</sup>K<sup>-</sup>π<sub>0</sub>π<sub>0</sub>γ</td></tr><tr><td>58</td><td>±16</td><td>±20</td><td>201</td><td>12,15 AUBERT, BE</td><td>06D BABR</td><td>10.6 e<sup>+</sup>e<sup>-</sup> →<br>K<sup>+</sup>K<sup>-</sup>ππγ</td></tr></tbody></table>

1. From a fit to the $e^+e^-$ cross section between 2.00 and 3.08 GeV with a sum of Breit-Wigner amplitude and a non-resonant contribution.

2. By a simultaneous fit of the $K_2^*(1430)^+K^-$ and $K^*(892)^+K^-$ intermediate channels in a partial-wave analysis, assuming the same structure, modelled with a coherent sum of a nonresonant component and a resonant component by a Breit-Wigner function.

3. From a fit to the cross section between 2.00 and 3.08 GeV with a coherent sum of Breit-Wigner amplitudes, including contributions from $\omega(1420)$ and $\omega(1650)/\phi(1680)$.

4. From a fit to the cross section below 3.5 GeV measured by BaBar and BESIII with a coherent sum of two modified Breit-Wigner amplitudes ($\phi(1680)$ and $\phi(2170)$) and a nonresonant term.

5. From a fit using a coherent sum of a phase-space modified Breit-Wigner function and a phase-space term.

6. By a simultaneous fit of the intermediate channels in a partial-wave analysis, assuming the same structure, modelled with a coherent sum of a nonresonant component and a resonant component by a Breit-Wigner function.

7. From a VDM fit to ZHU 23 $\eta\phi\gamma$ data with two resonances, $\phi(1680)$, $\phi(2170)$, and a third resonance with mass 1850.7 ± 5.3 MeV and width 25 ± 35 MeV of $1.7\sigma$ statistical evidence.

8. From the analysis of the combined measurements of $\sigma(e^+e^- \to \eta\phi)$ from BaBar, Belle, BESIII, CMD3. The statistical significance for $\phi(2170)$ is $7.2\sigma$.

9. From a fit to the cross section between 2.00 and 3.08 GeV with a sum of Breit-Wigner amplitude and a nonresonant contribution. The observed structure can be also due to $\rho(2150)$.

10. The observed structure can be due to both the $\phi(2170)$ and $\rho(2150)$.

11. Fit includes interference with the $\phi(1680)$.

12. From the $\phi f_0(980)$ component.

13. From a fit with two incoherent Breit-Wigners.

14. From the $K^+K^-f_0(980)$ component.

15. Superseded by LEES 12f.

<figure><img src="image_505.png" /></figure>

## $\phi(2170)$ 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></td><td>e<sup>+</sup>e<sup>-</sup></td></tr><tr><td>Γ<sub>2</sub></td><td>Φη</td></tr><tr><td>Γ<sub>3</sub></td><td>ωη</td></tr><tr><td>Γ<sub>4</sub></td><td>Φη'</td></tr><tr><td>Γ<sub>5</sub></td><td>Φππ</td></tr><tr><td>Γ<sub>6</sub></td><td>Φf<sub>0</sub>(980)</td></tr><tr><td>Γ<sub>7</sub></td><td>K<sup>0</sup><sub>S</sub>K<sup>0</sup><sub>L</sub></td></tr><tr><td>Γ<sub>8</sub></td><td>K<sup>+</sup>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>Γ<sub>9</sub></td><td>K<sup>+</sup>K<sup>-</sup>f<sub>0</sub>(980) → K<sup>+</sup>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>Γ<sub>10</sub></td><td>K<sup>+</sup>K<sup>-</sup>π<sup>0</sup>π<sup>0</sup></td></tr><tr><td>Γ<sub>11</sub></td><td>K<sup>+</sup>K<sup>-</sup>f<sub>0</sub>(980) → K<sup>+</sup>K<sup>-</sup>π<sup>0</sup>π<sup>0</sup></td></tr><tr><td>Γ<sub>12</sub></td><td>K<sup>0</sup>K<sup>+</sup>K<sup>-</sup></td></tr><tr><td>Γ<sub>13</sub></td><td>K<sup>*</sup>(892)<sup>0</sup>K<sup>*</sup>(892)<sup>0</sup></td></tr><tr><td>Γ<sub>14</sub></td><td>K<sup>*</sup>(892)<sup>+</sup>K<sup>*</sup>(892)<sup>-</sup></td></tr><tr><td>Γ<sub>15</sub></td><td>K<sup>*</sup>(892)<sup>+</sup>K<sup>-</sup> + c.c.</td></tr><tr><td>Γ<sub>16</sub></td><td>K<sup>+</sup>(1460)<sup>+</sup>K<sup>-</sup> + c.c.</td></tr><tr><td>Γ<sub>17</sub></td><td>K<sub>1</sub>(1270)<sup>+</sup>K<sup>-</sup> + c.c.</td></tr><tr><td>Γ<sub>18</sub></td><td>K<sub>1</sub>(1400)<sup>+</sup>K<sup>-</sup> + c.c.</td></tr><tr><td>Γ<sub>19</sub></td><td>K<sup>0</sup><sub>S</sub>(1430)<sup>+</sup>K<sup>-</sup> + c.c.</td></tr></tbody></table>

## $\phi(2170) \Gamma(\eta) \times \Gamma(e^+e^-) / \Gamma(\text{total})$

$$ \Gamma(\phi\eta) \times \Gamma(e^+e^-) / \Gamma_{\text{total}} \quad \Gamma_{2\Gamma_1/\Gamma} $$

$$ \begin{array}{l} \text{VALUE (eV)} \\ \text{CL}\% \\ \text{EVTS} \end{array} $$

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

0.17 90 1 ZHU 23 BELL $e^+e^- \to \tau(nS) \to \phi\eta\gamma$

0.36 $^{+0.05}_{-0.03}$ ±0.07 to 41 ± 2 ± 6 2 ZHU 23A RVUE $e^+e^- \to \eta\phi$

0.24 $^{+0.12}_{-0.07}$ 3 ABLIKIM 21T BES3 $e^+e^- \to \phi\eta$

1.7 ±0.7 ±1.3 483 AUBERT 08S BABR 10.6 $e^+e^- \to \phi\eta\gamma$

1. From a solution of the fit using a vector meson dominance model with contributions from $\phi(1680)$, $\phi(2170)$ and non resonant contribution with mass and width of $\phi(2170)$ fixed at 2163.5 MeV and 31.1 MeV respectively. Four solutions are found with equal fit quality giving 0.17 eV (solution I and II) and 18.6 eV (III and IV) at 90% CL.

2. From the analysis of the combined measurements of $\sigma(e^+e^- \to \eta\phi)$ from BaBar, Belle, BESIII, CMD3. The statistical significance for $\phi(2170)$ is $7.2\sigma$. Four solutions are found, with equal fit quality: $(0.56^{+0.03}_{-0.02}) \pm 0.07$ eV, $(0.36^{+0.05}_{-0.03}) \pm 0.07$ eV, $(38 \pm 1 \pm 5)$ eV, $(41 \pm 2 \pm 6)$ eV.

3. From a solution of the fit to the cross section below 3.5 GeV measured by BaBar and BESIII with a coherent sum of two modified Breit-Wigner amplitudes ($\phi(1680)$ and $\phi(2170)$) and a nonresonant term. The other solution gives $10.11^{+3.87}_{-3.13}$ eV.

$$ \Gamma(\omega\eta) \times \Gamma(e^+e^-) / \Gamma_{\text{total}} \quad \Gamma_{3\Gamma_1/\Gamma} $$

$$ \begin{array}{l} \text{VALUE (eV)} \\ \text{CL}\% \\ \text{EVTS} \end{array} $$

0.43 $^{+0.15}_{-0.04}$ 1 ABLIKIM 21A BES3 $e^+e^- \to \omega\eta$

1. For constructive interference with $\omega(1420)$ and $\omega(1650)/\phi(1680)$. For destructive interference: $1.25 \pm 0.48 \pm 0.18$ eV.

$$ \Gamma(\phi\eta') \times \Gamma(e^+e^-) / \Gamma_{\text{total}} \quad \Gamma_{4\Gamma_1/\Gamma} $$

$$ \begin{array}{l} \text{VALUE (eV)} \\ \text{CL}\% \\ \text{EVTS} \end{array} $$

7.1 $^{+0.7}_{-0.7}$ 20M BES3 $e^+e^- \to \eta'\phi$

1. From a fit using a coherent sum of a phase-space modified Breit-Wigner function and a phase-space term.

$$ \Gamma(\phi f_0(980)) \times \Gamma(e^+e^-) / \Gamma_{\text{total}} \quad \Gamma_{6\Gamma_1/\Gamma} $$

$$ \begin{array}{l} \text{VALUE (eV)} \\ \text{CL}\% \\ \text{EVTS} \end{array} $$

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

2.3 ±0.3 ±0.3 1,2 LEES 12F BABR 10.6 $e^+e^- \to \phi\pi^+\pi^-\gamma$

2.5 ±0.8 ±0.4 201 2,3 AUBERT, BE 06D BABR 10.6 $e^+e^- \to K^+K^-\pi\pi\gamma$

1. From a fit with constructive interference with the $\phi(1680)$. In a fit with destructive interference, the value is larger by a factor of 12.

2. For $f_0(980) \to \pi\pi$.

3. Superseded by LEES 12f.

$$ \Gamma(K_S^0 K_L^0) \times \Gamma(e^+e^-) / \Gamma_{\text{total}} \quad \Gamma_{7\Gamma_1/\Gamma} $$

$$ \begin{array}{l} \text{VALUE (eV)} \\ \text{CL}\% \\ \text{EVTS} \end{array} $$

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

0.9 ±0.6 ±0.7 1 ABLIKIM 21AP BES3 $e^+e^- \to K_S^0 K_L^0$

1. From a fit to the cross section between 2.00 and 3.08 GeV with a sum of Breit-Wigner amplitude and a nonresonant contribution. The observed structure can be also due to $\rho(2150)$.

$$ \Gamma(K^*(892)^+ K^*(892)^-) \times \Gamma(e^+e^-) / \Gamma_{\text{total}} \quad \Gamma_{14\Gamma_1/\Gamma} $$

$$ \begin{array}{l} \text{VALUE (eV)} \\ \text{CL}\% \\ \text{EVTS} \end{array} $$

1. By a simultaneous fit of the intermediate channels in a partial-wave analysis, assuming the same structure, modelled with a coherent sum of a nonresonant component and a resonant component by a Breit-Wigner function.

$$ \Gamma(K^*(892)^+ K^- + \text{c.c.}) \times \Gamma(e^+e^-) / \Gamma_{\text{total}} \quad \Gamma_{15\Gamma_1/\Gamma} $$

$$ \begin{array}{l} \text{VALUE (eV)} \\ \text{CL}\% \\ \text{EVTS} \end{array} $$

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

1.0 ±0.3 1 ABLIKIM 22L BES3 2.0-3.08 $e^+e^- \to K^+K^-\pi^0\pi^0$

1. From a solution of a simultaneous fit of the $K_2^*(1430)^+K^-$ and $K^*(892)^+K^-$ intermediate channels in a partial-wave analysis, assuming the same structure, modelled with a coherent sum of a nonresonant component and a resonant component by a Breit-Wigner function. The other solution gives 7.1 ± 0.9 eV. Significance 3.7 $\sigma$.

$$ \Gamma(K(1460)^+ K^- + \text{c.c.}) \times \Gamma(e^+e^-) / \Gamma_{\text{total}} \quad \Gamma_{16\Gamma_1/\Gamma} $$

$$ \begin{array}{l} \text{VALUE (eV)} \\ \text{CL}\% \\ \text{EVTS} \end{array} $$

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

3.0 ±3.8 1 ABLIKIM 20s BES3 $e^+e^- \to K^+K^-\pi^0\pi^0$

1. By a simultaneous fit of the intermediate channels in a partial-wave analysis, assuming the same structure, modelled with a coherent sum of a nonresonant component and a resonant component by a Breit-Wigner function.

$$ \Gamma(K_1(1270)^+ K^- + \text{c.c.}) \times \Gamma(e^+e^-) / \Gamma_{\text{total}} \quad \Gamma_{17\Gamma_1/\Gamma} $$

$$ \begin{array}{l} \text{VALUE (eV)} \\ \text{CL}\% \\ \text{EVTS} \end{array} $$

1. By a simultaneous fit of the intermediate channels in a partial-wave analysis, assuming the same structure, modelled with a coherent sum of a nonresonant component and a resonant component by a Breit-Wigner function. A second solution of the fit with equal fit quality gives an upper limit value of 297.6 eV.
$$ \Gamma(K_1(1400)^+ K^- + \text{c.c.}) \times \Gamma(e^+ e^-)/\Gamma_{\text{total}} \quad \Gamma_{18}\Gamma_1/\Gamma $$

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

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

$$ 4.7 \pm 3.3 \qquad 1 \text{ ABLIKIM} \qquad 20s \text{ BES3} \quad e^+ e^- \to K^+ K^- \pi^0 \pi^0 $$

1 By a simultaneous fit of the intermediate channels in a partial-wave analysis, assuming the same structure, modelled with a coherent sum of a nonresonant component and a resonant component by a Breit-Wigner function. A second solution of the fit with equal fit quality gives a value of 98.8 ± 7.8 eV.

$$ \Gamma(K_2^*(1430)^+ K^- + \text{c.c.}) \times \Gamma(e^+ e^-)/\Gamma_{\text{total}} \quad \Gamma_{19}\Gamma_1/\Gamma $$

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

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

$$ 12.6 \pm 2.4 \qquad 1 \text{ ABLIKIM} \qquad 22l \text{ BES3} \quad 2.0-3.08 \ e^+ e^- \to K^+ K^- \pi^0 $$

1 From a solution of a simultaneous fit of the $K_2^*(1430)^+ K^-$ and $K^*(892)^+ K^-$ intermediate channels in a partial-wave analysis, assuming the same structure, modelled with a coherent sum of a nonresonant component and a resonant component by a Breit-Wigner function. The other solution gives 161.1 ± 20.6 eV.

$$ \phi(2170) \Gamma(i)\Gamma(e^+ e^-)/\Gamma^2(\text{total}) $$

$$ \Gamma(\phi\pi\pi)/\Gamma_{\text{total}} \times \Gamma(e^+ e^-)/\Gamma_{\text{total}} \quad \Gamma_5/\Gamma_1/\Gamma $$

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

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

$$ 1.65 \pm 0.15 \pm 0.18 \qquad 4.8k \qquad 1 \text{ SHEN} \qquad 09 \text{ BELL} \quad 10.6 \ e^+ e^- \to K^+ K^- \pi^+ \pi^- \gamma $$

1 Multiplied by 3/2 to take into account the $\phi\pi^0\pi^0$ mode. Using $B(\phi \to K^+K^-) = (49.2 \pm 0.6)%$.

$$ \phi(2170) \text{ BRANCHING RATIOS} $$

$$ \Gamma(\phi\pi\pi)/\Gamma_{\text{total}} \quad \Gamma_5/\Gamma $$

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

seen
1 From a fit to the $e^+ e^-$ cross section between 2.00 and 3.08 GeV with a sum of Breit-Wigner amplitude and a non-resonant contribution.

$$ \Gamma(K^+ K^- f_0(980) \to K^+ K^- \pi^+ \pi^-)/\Gamma_{\text{total}} \quad \Gamma_9/\Gamma $$

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

seen
AUBERT 07AK BABR 10.6 $e^+ e^-$ $\to K^+ K^- \pi^+ \pi^- \gamma$

$$ \Gamma(K^+ K^- f_0(980) \to K^+ K^- \pi^0 \pi^0)/\Gamma_{\text{total}} \quad \Gamma_{11}/\Gamma $$

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

seen
AUBERT 07AK BABR 10.6 $e^+ e^-$ $\to K^+ K^- \pi^0 \pi^0 \gamma$

$$ \Gamma(K^0 K^\pm \pi^\mp)/\Gamma_{\text{total}} \quad \Gamma_{12}/\Gamma $$

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

not seen
AUBERT 07AK BABR 10.6 GeV $e^+ e^-$

$$ \Gamma(K^*(892)^0 K^*(892)^0)/\Gamma_{\text{total}} \quad \Gamma_{13}/\Gamma $$

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

not seen
ABLIKIM 10C BES2 $J/\psi \to \eta K^+ \pi^- K^- \pi^+$

$$ \phi(2170) \text{ REFERENCES} $$

<table><tr><td>ABLIKIM</td><td>23AX PR D108 032011</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>LICHARD</td><td>23 PR D108 092005</td><td>P. Lichard</td><td>(OPAV, CTUP)</td></tr><tr><td>ZHU</td><td>23 PR D107 012006</td><td>W. Zhu et al.</td><td>(BELLE Collab.)</td></tr><tr><td>ZHU</td><td>23A CP C47 113003</td><td>W. Zhu, X. Wang</td><td>(RVUE)</td></tr><tr><td>ABLIKIM</td><td>22L JHEP 2207 045</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>21A</td><td>PL B813 136059</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>21AP</td><td>PR D104 092014</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>21T</td><td>PR D104 032007</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>20M</td><td>PR D102 012008</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>20S</td><td>PRL 124 112001</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>19I PR D99 012014</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>19L PR D99 032001</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>15H</td><td>PR D91 052017</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>LEES</td><td>12F PR D86 012008</td><td>J.P. Lees et al.</td><td>(BABAR Collab.)</td></tr><tr><td>ABLIKIM</td><td>10C PL B685 27</td><td>M. Ablikim et al.</td><td>(BES II Collab.)</td></tr><tr><td>SHEN</td><td>09 PR D80 031101</td><td>C.P. Shen et al.</td><td>(BELLE Collab.)</td></tr><tr><td>ABLIKIM</td><td>08F PRL 100 102003</td><td>M. Ablikim et al.</td><td>(BES Collab.)</td></tr><tr><td>AUBERT</td><td>08S PR D77 092002</td><td>B. Aubert et al.</td><td>(BABAR Collab.)</td></tr><tr><td>AUBERT</td><td>07AK PR D76 012008</td><td>B. Aubert et al.</td><td>(BABAR Collab.)</td></tr><tr><td>AUBERT, BE</td><td>06D PR D74 091103</td><td>B. Aubert et al.</td><td>(BABAR Collab.)</td></tr></table>

$$ f_0(2200) $$

$$ I^G(J^{PC}) = 0^+(2++ \text{ or } 4++) $$

OMITTED FROM SUMMARY TABLE

Seen in $K_S^0 K_S^0$ (AUGUSTIN 88), $K^+ K^-$ (ABLIKIM 05Q) and $\eta\eta$ (BINON 05) system. Not seen in $\Gamma(1S)$ radiative decays (BARU 89).

$$ f_0(2200) \text{ MASS} $$

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

2187 ± 14 OUR AVERAGE

$$ 2170 \pm 20 \frac{+10}{-15} $$

$$ 2197 \pm 17 \qquad 1 \text{ AUGUSTIN} \qquad 88 \text{ DM2} \quad \frac{J/\psi \to \gamma K_S^0 K_S^0}{\gamma \pi^+ \pi^- K^+ K^-} $$

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

<table><tr><td>2200 ± 25</td><td>SARANTSEV</td><td>21</td><td>RVUE</td><td>J/ψ(1S) → γ (ππ, K<sup>+</sup>K<sup>-</sup>, ηη, ωφ)</td></tr><tr><td>2206 ± 12 ± 8</td><td>381</td><td>2,3 DOBBS</td><td>15</td><td>J/ψ → γK<sup>+</sup>K<sup>-</sup></td></tr><tr><td>2188 ± 17 ± 16</td><td>203</td><td>2,3 DOBBS</td><td>15</td><td>ψ(2S) → γK<sup>+</sup>K<sup>-</sup></td></tr><tr><td>2210 ± 50</td><td>4 BINON</td><td></td><td>05</td><td>GAMS 33 π<sup>-</sup> p → ηηη</td></tr><tr><td>~ 2122</td><td>HASAN</td><td></td><td>94</td><td>RVUE p → ππ</td></tr><tr><td>~ 2321</td><td>HASAN</td><td></td><td>94</td><td>RVUE p → ππ</td></tr></table>

1 Cannot determine spin to be 0.

2 Using CLEO-c data but not authorized by the CLEO Collaboration.

3 From a fit to a Breit-Wigner line shape with fixed $\Gamma = 238$ MeV.

4 First solution, PWA is ambiguous.

$$ f_0(2200) \text{ WIDTH} $$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4">210 ± 40 OUR AVERAGE</td></tr><tr><td>220 ± 60 <sup>+40</sup><sub>-45</sub></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>201 ± 51</td><td>5 AUGUSTIN</td><td>88 DM2</td><td>J/ψ → γK<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup></td></tr></tbody></table>

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

<table><tr><td>150 ± 30</td><td>SARANTSEV</td><td>21</td><td>RVUE</td><td>J/ψ(1S) → γ (ππ, K<sup>+</sup>K<sup>-</sup>, ηη, ωφ)</td></tr><tr><td>380 ± 90</td><td>6 BINON</td><td>05</td><td>GAMS</td><td>33 π<sup>-</sup> p → ηηη</td></tr><tr><td>~ 273</td><td>HASAN</td><td>94</td><td>RVUE p → ππ</td><td></td></tr><tr><td>~ 223</td><td>HASAN</td><td>94</td><td>RVUE p → ππ</td><td></td></tr></table>

5 Cannot determine spin to be 0.

6 First solution, PWA is ambiguous.

$$ f_0(2200) \text{ REFERENCES} $$

<table><tr><td>SARANTSEV</td><td>21</td><td>PL B816 136227</td><td>A.V. Sarantsev et al.</td><td>(BONN, PNPI)</td></tr><tr><td>DOBBS</td><td>15</td><td>PR D91 052006</td><td>S. Dobbs et al.</td><td>(NWES)</td></tr><tr><td>ABLIKIM</td><td>05Q</td><td>PR D72 092002</td><td>M. Ablikim et al.</td><td>(BES Collab.)</td></tr><tr><td>BINON</td><td>05</td><td>PAN 68 960</td><td>F. Binon et al.</td><td></td></tr><tr><td>HASAN</td><td>94</td><td>PL B334 215</td><td>A. Hasan, D.V. Bugg</td><td>(LOQM)</td></tr><tr><td>BARU</td><td>89</td><td>ZPHY C42 505</td><td>S.E. Baru et al.</td><td>(NOVO)</td></tr><tr><td>AUGUSTIN</td><td>88</td><td>PRL 60 2238</td><td>J.E. Augustin et al.</td><td>(DM2 Collab.)</td></tr></table>

$$ f_j(2220) $$

$$ I^G(J^{PC}) = 0^+(2++ \text{ or } 4++) $$

OMITTED FROM SUMMARY TABLE

See our mini-review in the 2004 edition of this Review, PDG 04.

$$ f_j(2220) \text{ MASS} $$

<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>2231.1 ± 3.5 OUR AVERAGE</td><td></td><td>BAI</td><td>96B BES</td><td>e<sup>+</sup> e<sup>-</sup> → J/ψ → γπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>2230 ± <sup>+6</sup><sub>-7</sub> ± 16</td><td></td><td>BAI</td><td>96B BES</td><td>e<sup>+</sup> e<sup>-</sup> → J/ψ → γK<sup>+</sup>K<sup>-</sup></td></tr><tr><td>2232 ± <sup>+8</sup><sub>-7</sub> ± 15</td><td></td><td>BAI</td><td>96B BES</td><td>e<sup>+</sup> e<sup>-</sup> → J/ψ → γK<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup></td></tr><tr><td>2235 ± 4 ± 5</td><td></td><td>BAI</td><td>96B BES</td><td>e<sup>+</sup> e<sup>-</sup> → J/ψ → γp p̄</td></tr><tr><td>2209 ± <sup>+17</sup><sub>-15</sub> ± 10</td><td></td><td>ASTON</td><td>88F LASS</td><td>11 K<sup>-</sup> p → K<sup>+</sup>K<sup>-</sup>Λ</td></tr><tr><td>2230 ± 20</td><td></td><td>BOLONKIN</td><td>88 SPEC</td><td>40 π<sup>-</sup> p → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup> n</td></tr><tr><td>2220 ± 10</td><td>1 ALDE</td><td>86B GA24</td><td>38-100 πp → ηηη'</td></tr><tr><td>2230 ± 6 ± 14</td><td>BALTRUSAIT...86D</td><td>MRK3</td><td>e<sup>+</sup> e<sup>-</sup> → γK<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup></td></tr><tr><td>2232 ± 7 ± 7</td><td>BALTRUSAIT...86D</td><td>MRK3</td><td>e<sup>+</sup> e<sup>-</sup> → γK<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup></td></tr></tbody></table>



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

$$ 2223.9 \pm 2.5 \qquad 2 \text{ VLADIMIRSK...08} \qquad \text{SPEC} \quad 40 \pi^- p \to K_S^0 K_S^0 n + m\pi^0 $$

$$ 2246 \pm 36 \qquad \text{BAI} \qquad 98\text{BES} \qquad J/\psi \to \gamma\pi^0\pi^0 \quad K_S^0 \quad K_S^0 n $$

1 ALDE 86b uses data from both the GAMS-2000 and GAMS-4000 detectors.

2 $J^{PC} = 2^+$. Systematic uncertainties not evaluated

$$ f_j(2220) \text{ WIDTH} $$

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

23 ± 8 OUR AVERAGE

<table><tr><td>19 ± 13</td><td>11 ± 12</td><td>74</td><td>BAI</td><td>96B BES</td><td>e<sup>+</sup> e<sup>-</sup> → J/ψ → γπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>20 ± 20</td><td>15 ± 17</td><td>46</td><td>BAI</td><td>96B BES</td><td>e<sup>+</sup> e<sup>-</sup> → J/ψ → γK<sup>+</sup>K<sup>-</sup></td></tr><tr><td>20 ± 25</td><td>16 ± 14</td><td>23</td><td>BAI</td><td>96B BES</td><td>e<sup>+</sup> e<sup>-</sup> → J/ψ → γK<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup></td></tr><tr><td>15 ± 12</td><td>9 ± 9</td><td>32</td><td>BAI</td><td>96B BES</td><td>e<sup>+</sup> e<sup>-</sup> → J/ψ → γp p̄</td></tr></table>

$$ 60 \pm 107 \qquad 57 \qquad \text{ASTON} \qquad 88\text{F LASS} \qquad 11 K^- p \to K^+ K^- \Lambda $$

$$ 80 \pm 30 \qquad \text{BOLONKIN} \qquad 88 \text{ SPEC} \qquad 40 \pi^- p \to K_S^0 K_S^0 n $$
<table><tr><td>26<sup>+</sup><sub>-16</sub> 20<sup>±</sup>17</td><td>93</td><td>BALTRUSAIT..86D</td><td>MRK3</td><td>e<sup>+</sup>e<sup>-</sup> → γK<sup>+</sup>K<sup>-</sup></td></tr><tr><td>18<sup>+</sup><sub>-15</sub> 23<sup>±</sup>10</td><td>23</td><td>BALTRUSAIT..86D</td><td>MRK3</td><td>e<sup>+</sup>e<sup>-</sup> → γK<sup>0</sup><sub>S</sub>K<sup>0</sup><sub>S</sub></td></tr></table>

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

<table><tr><td>8.6 ± 2.5</td><td>1</td><td>VLADIMIRSK...08</td><td>SPEC</td><td>40 π<sup>-</sup> p → K<sup>0</sup><sub>S</sub>K<sup>0</sup><sub>S</sub> n<br>+mπ<sup>0</sup></td></tr><tr><td>&lt;80</td><td>90</td><td>ALDE</td><td>87c</td><td>GAM2 38 π<sup>-</sup> p → η'ηn</td></tr></table>

1 $J^PC = 2^{++}$. Systematic uncertainties not evaluated

### $f_j(2220)$ DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction ($\Gamma_j/\Gamma$)</th></tr></thead><tbody><tr><td>$\Gamma_1$</td><td>not seen</td></tr><tr><td>$\Gamma_2$</td><td>not seen</td></tr><tr><td>$\Gamma_3$</td><td>not seen</td></tr><tr><td>$\Gamma_4$</td><td>not seen</td></tr><tr><td>$\Gamma_5$</td><td>not seen</td></tr><tr><td>$\Gamma_6$</td><td>seen</td></tr><tr><td>$\Gamma_7$</td><td>not seen</td></tr><tr><td>$\Gamma_8$</td><td>not seen</td></tr></tbody></table>

### $f_j(2220)$ $\Gamma(i)\Gamma(\gamma\gamma)/\Gamma(\text{total})$

<table><thead><tr><th colspan="2">$\Gamma(K\bar{K}) \times \Gamma(\gamma\gamma)/\Gamma_{\text{total}}$</th><th colspan="4">$\Gamma_3\Gamma_5/\Gamma$</th></tr><tr><th>VALUE (eV)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th><th></th></tr></thead><tbody><tr><td>&lt; 1.4</td><td>95</td><td>1</td><td>ACCIARRI</td><td>01H</td><td>γγ → K<sup>0</sup><sub>S</sub>K<sup>0</sup><sub>S</sub> E<sup>ee</sup>cm= 91, 183–209 GeV</td></tr></tbody></table>

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

<table><tr><td>&lt; 5.6</td><td>95</td><td>1</td><td>GODANG</td><td>97</td><td>CLE2</td><td>γγ → K<sup>0</sup><sub>S</sub>K<sup>0</sup><sub>S</sub></td></tr><tr><td>&lt; 86</td><td>95</td><td>1</td><td>ALBRECHT</td><td>90G</td><td>ARG</td><td>γγ → K<sup>+</sup>K<sup>-</sup></td></tr><tr><td>&lt;1000</td><td>95</td><td>2</td><td>ALTHOFF</td><td>85B</td><td>TASS</td><td>γγ, K<sup>π</sup>K<sup>π</sup></td></tr></table>

<table><thead><tr><th colspan="2">$\Gamma(\pi\pi) \times \Gamma(\gamma\gamma)/\Gamma_{\text{total}}$</th><th colspan="4">$\Gamma_1\Gamma_5/\Gamma$</th></tr><tr><th>VALUE (eV)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th><th></th></tr></thead><tbody><tr><td>&lt;2.5</td><td>95</td><td>ALAM</td><td>98C</td><td>CLE2</td><td>γγ → π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

1 Assuming $J^P = 2^+$.

2 True for $J^P = 0^+$ and $J^P = 2^+$.

### $f_j(2220)$ $\Gamma(i)\Gamma(p\bar{p})/\Gamma^2(\text{total})$

<table><thead><tr><th colspan="2">$\Gamma(p\bar{p})/\Gamma_{\text{total}} \times \Gamma(\pi\pi)/\Gamma_{\text{total}}$</th><th colspan="4">$\Gamma_4/\Gamma \times \Gamma_1/\Gamma$</th></tr><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th><th></th></tr></thead><tbody><tr><td>&lt;18</td><td>95</td><td>1</td><td>AMSLER</td><td>01</td><td>CBAR</td><td>1.4–1.5 p<bar>p → π<sup>0</sup>π<sup>0</sup></td></tr></tbody></table>

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

<table><tr><td>&lt;(11–42)</td><td>99</td><td>2</td><td>HASAN</td><td>96</td><td>SPEC</td><td>1.35–1.55 p<bar>p → π<sup>+</sup>π<sup>-</sup></td></tr></table>

<table><thead><tr><th colspan="2">$\Gamma(p\bar{p})/\Gamma_{\text{total}} \times \Gamma(\phi\phi)/\Gamma_{\text{total}}$</th><th colspan="4">$\Gamma_4/\Gamma \times \Gamma_7/\Gamma$</th></tr><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th><th></th></tr></thead><tbody><tr><td>&lt;6</td><td>95</td><td>3</td><td>EVANGELIS...</td><td>98</td><td>SPEC</td><td>1.1–2.0 p<bar>p → φφ</td></tr></tbody></table>

<table><thead><tr><th colspan="2">$\Gamma(p\bar{p})/\Gamma_{\text{total}} \times \Gamma(\eta\eta)/\Gamma_{\text{total}}$</th><th colspan="4">$\Gamma_4/\Gamma \times \Gamma_8/\Gamma$</th></tr><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th><th></th></tr></thead><tbody><tr><td>&lt;4</td><td>95</td><td>1</td><td>AMSLER</td><td>01</td><td>CBAR</td><td>1.4–1.5 p<bar>p → ηη</td></tr></tbody></table>

1 For $J^P = 2^+$ in the mass range 2222–2240 MeV and the total width between 10 and 20 MeV.

2 For $J^P = 2^+$ and $J^P = 4^+$ in the mass range 2220–2245 MeV and the total width of 15 MeV.

3 For $J^P = 2^+$, the mass of 2235 MeV and the total width of 15 MeV.

### $f_j(2220)$ BRANCHING RATIOS

<table><thead><tr><th colspan="2">$\Gamma(\pi\pi)/\Gamma_{\text{total}}$</th><th colspan="4">$\Gamma_1/\Gamma$</th></tr><tr><th>VALUE</th><th>DOCUMENT ID</th><th>COMMENT</th><th></th><th></th><th></th></tr></thead><tbody><tr><td>not seen</td><td>1 DOBBS</td><td>15</td><td>J/ψ → γππ</td><td></td><td></td></tr><tr><td>not seen</td><td>1 DOBBS</td><td>15</td><td>ψ(25) → γππ</td><td></td><td></td></tr></tbody></table>

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

<table><thead><tr><th colspan="2">$\Gamma(K\bar{K})/\Gamma_{\text{total}}$</th><th colspan="4">$\Gamma_3/\Gamma$</th></tr><tr><th>VALUE</th><th>DOCUMENT ID</th><th>COMMENT</th><th></th><th></th><th></th></tr></thead><tbody><tr><td>not seen</td><td>1 DOBBS</td><td>15</td><td>J/ψ → γK<sup>π</sup>K<sup>-</sup></td><td></td><td></td></tr><tr><td>not seen</td><td>1 DOBBS</td><td>15</td><td>ψ(25) → γK<sup>π</sup>K<sup>-</sup></td><td></td><td></td></tr></tbody></table>

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

<table><thead><tr><th colspan="2">$\Gamma(\pi\pi)/\Gamma(K\bar{K})$</th><th colspan="4">$\Gamma_1/\Gamma_3$</th></tr><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th><th></th><th></th></tr></thead><tbody><tr><td>1.0 ± 0.5</td><td>BAI</td><td>96B</td><td>BES</td><td>e<sup>+</sup>e<sup>-</sup> → J/ψ → γ2π, K<sup>π</sup>K<sup>-</sup></td><td></td><td></td></tr></tbody></table>

<table><thead><tr><th colspan="2">$\Gamma(p\bar{p})/\Gamma_{\text{total}}$</th><th colspan="4">$\Gamma_4/\Gamma$</th></tr><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th><th></th></tr></thead></table>

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

<table><tr><td>not seen</td><td></td><td>1</td><td>AUBERT</td><td>07AV</td><td>BABR</td><td>B → p<bar>p>K(*)</td></tr><tr><td>not seen</td><td></td><td></td><td>WANG</td><td>05A</td><td>BELL</td><td>B<sup>+</sup> → p<bar>p>K<sup>+</sup></td></tr><tr><td>&lt;3.0</td><td>95</td><td>2</td><td>EVANGELIS...</td><td>97</td><td>SPEC</td><td>1.96–2.40 p<bar>p → K<sup>0</sup><sub>S</sub>K<sup>0</sup><sub>S</sub></td></tr><tr><td>&lt;1.1</td><td>99.7</td><td>3</td><td>BARNES</td><td>93</td><td>SPEC</td><td>1.3–1.57 p<bar>p → K<sup>0</sup><sub>S</sub>K<sup>0</sup><sub>S</sub></td></tr><tr><td>&lt;2.6</td><td>99.7</td><td>3</td><td>BARDIN</td><td>87</td><td>CNTR</td><td>1.3–1.5 p<bar>p → K<sup>+</sup>K<sup>-</sup></td></tr><tr><td>&lt;3.6</td><td>99.7</td><td>3</td><td>SCULLI</td><td>87</td><td>CNTR</td><td>1.29–1.55 p<bar>p → K<sup>+</sup>K<sup>-</sup></td></tr></table>

1 Assuming $\Gamma < 30$ MeV.

2 Assuming $\Gamma \sim 20$ MeV, $J^P = 2^+$ and $B(f_j(2220) \rightarrow K\bar{K}) = 100\%$.

3 Assuming $\Gamma = 30–35$ MeV, $J^P = 2^+$ and $B(f_j(2220) \rightarrow K\bar{K}) = 100\%$.

<table><thead><tr><th colspan="2">$\Gamma(p\bar{p})/\Gamma(K\bar{K})$</th><th colspan="4">$\Gamma_4/\Gamma_3$</th></tr><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th><th></th></tr></thead><tbody><tr><td>0.17 ± 0.09</td><td></td><td>BAI</td><td>96B</td><td>BES</td><td>e<sup>+</sup>e<sup>-</sup> → J/ψ → γp<bar>p, K<sup>π</sup>K<sup>-</sup></td></tr></tbody></table>

### $f_j(2220)$ REFERENCES

<table><tr><td>DOBBS</td><td>15</td><td>PR</td><td>D91 052006</td><td>S. Dobbs et al.</td><td>(NWES)</td></tr><tr><td>VLADIMIRSK...</td><td>08</td><td>PAN</td><td>71 2129</td><td>V.V. Vladimirsky et al.</td><td>(ITEP)</td></tr><tr><td></td><td></td><td>Translated from</td><td>YAF 71 2166.</td><td></td><td></td></tr><tr><td>AUBERT</td><td>07AV</td><td>PR</td><td>D76 092004</td><td>B. Aubert et al.</td><td>(BABAR Collab.)</td></tr><tr><td>WANG</td><td>05A</td><td>PL</td><td>B617 141</td><td>M.-Z. Wang et al.</td><td>(BELLE Collab.)</td></tr><tr><td>PDG</td><td>04</td><td>PL</td><td>B592 1</td><td>S. Eidelman et al.</td><td>(PDG Collab.)</td></tr><tr><td>ACCIARRI</td><td>01H</td><td>PL</td><td>B501 173</td><td>M. Acciarri et al.</td><td>(L3 Collab.)</td></tr><tr><td>AMSLER</td><td>01</td><td>PL</td><td>B520 175</td><td>C. Amsler et al.</td><td>(Crystal Barrel Collab.)</td></tr><tr><td>ALAM</td><td>98C</td><td>PL</td><td>81 3328</td><td>M.S. Alam et al.</td><td>(CLEO Collab.)</td></tr><tr><td>BAI</td><td>98H</td><td>PL</td><td>81 1179</td><td>J.Z. Bai et al.</td><td>(BES Collab.)</td></tr><tr><td>EVANGELIS...</td><td>98</td><td>PR</td><td>D57 5370</td><td>C. Evangelista et al.</td><td>(JETSET Collab.)</td></tr><tr><td>EVANGELIS...</td><td>97</td><td>PR</td><td>D56 3803</td><td>C. Evangelista et al.</td><td>(LEAR Collab.)</td></tr><tr><td>GODANG</td><td>97</td><td>PL</td><td>79 3829</td><td>R. Godang et al.</td><td>(CLEO Collab.)</td></tr><tr><td>BAI</td><td>96B</td><td>PL</td><td>76 3502</td><td>J.Z. Bai et al.</td><td>(BES Collab.)</td></tr><tr><td>HASAN</td><td>96</td><td>PL</td><td>388 376</td><td>A. Hasan, D.V. Bugg</td><td>(BRUN, LOQM)</td></tr><tr><td>BARNES</td><td>93</td><td>PL</td><td>B309 469</td><td>P.D. Barnes et al.</td><td>(PS185 Collab.)</td></tr><tr><td>ALBRECHT</td><td>90G</td><td>ZPHY</td><td>C48 183</td><td>H. Albrecht et al.</td><td>(ARGUS Collab.)</td></tr><tr><td>ASTON</td><td>88F</td><td>PL</td><td>B215 199</td><td>D. Aston et al.</td><td>(SLAC, NAGO, CINC, INUS) JP</td></tr><tr><td>BOLONKIN</td><td>88</td><td>NP</td><td>B309 426</td><td>B.V. Bolonkin et al.</td><td>(ITEP, SERP)</td></tr><tr><td>ALDE</td><td>87C</td><td>SJNP</td><td>45 255</td><td>D. Alde et al.</td><td></td></tr><tr><td>BARDIN</td><td>87</td><td>PL</td><td>B195 292</td><td>Translated from</td><td>YAF 45 405.</td></tr><tr><td>SCULLI</td><td>87</td><td>PL</td><td>56 1715</td><td>G. Bardin et al.</td><td>(SACL, FERR, CERN, PADO+)</td></tr><tr><td>ALDE</td><td>86B</td><td>PL</td><td>B177 120</td><td>J. Sculli et al.</td><td>(NYU, BNL)</td></tr><tr><td>HALTRUSAIT...</td><td>86D</td><td>PL</td><td>56 107</td><td>D.M. Alde et al.</td><td>(SERP, BELG, LANL, LAPP)</td></tr><tr><td>ALTHOFF</td><td>85B</td><td>ZPHY</td><td>C29 189</td><td>R.M. Baltrusaitis et al.</td><td>(CIT, UCSC, ILL, SLAC+)</td></tr><tr><td></td><td></td><td></td><td></td><td>M. Althoff et al.</td><td>(TASSO Collab.)</td></tr></table>

### OTHER RELATED PAPERS

DEL-AMO-SA... 100 PRL 105 172001

J. del Amo Sanchez et al. (BABAR Collab.)

### $\omega(2220)$

$$\omega(2220) = I^G(J^PC) = 0^{--}$$

OMITTED FROM SUMMARY TABLE

### $\omega(2220)$ MASS

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2232 ± 19 ± 27</td><td>1 ABLIKIM</td><td>23G</td><td>BES3 2.0–3.1 e<sup>+</sup>e<sup>-</sup> → ωππ</td></tr><tr><td>2250 ± 25 ± 27</td><td>2 ABLIKIM</td><td>23G</td><td>BES3 2.0–3.1 e<sup>+</sup>e<sup>-</sup> → ωπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>2222 ± 7 ± 2</td><td>3 ABLIKIM</td><td>22I</td><td>BES3 2.0–3.8 e<sup>+</sup>e<sup>-</sup> → ωπ<sup>0</sup>π<sup>0</sup></td></tr><tr><td>2205 ± 30</td><td>4 ANISOVICH</td><td>02B</td><td>SPEC 0.6–1.9 p<bar>p → ωη, ωπ<sup>0</sup>π<sup>0</sup></td></tr></tbody></table>

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



1 From a fit to $\omega\pi^+\pi^-$ and $\omega\pi^0\pi^0$ with a Breit-Wigner resonance interfering with the continuum. Supersedes ABLIKIM 221.

2 From a fit to $\omega\pi^+\pi^-$ with a Breit-Wigner resonance interfering with the continuum.

3 From the fit to the cross section by the coherent sum of resonant component parametrized by a modified Breit-Wigner amplitude and a phase-space contribution for the continuum.

4 From the combined analysis of ANISOVICH 00D, ANISOVICH 01C, and ANISOVICH 02B.

### $\omega(2220)$ WIDTH

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>93 ± 53 ± 20</td><td>5 ABLIKIM</td><td>23G</td><td>BES3 2.0–3.1 e<sup>+</sup>e<sup>-</sup> → ωππ</td></tr><tr><td>125 ± 43 ± 15</td><td>6 ABLIKIM</td><td>23G</td><td>BES3 2.0–3.1 e<sup>+</sup>e<sup>-</sup> → ωπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>59 ± 30 ± 6</td><td>7 ABLIKIM</td><td>22I</td><td>BES3 2.0–3.8 e<sup>+</sup>e<sup>-</sup> → ωπ<sup>0</sup>π<sup>0</sup></td></tr><tr><td>350 ± 90</td><td>8 ANISOVICH</td><td>02B</td><td>SPEC 0.6–1.9 p<bar>p → ωη, ωπ<sup>0</sup>π<sup>0</sup></td></tr></tbody></table>

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



5 From a fit to $\omega\pi^+\pi^-$ and $\omega\pi^0\pi^0$ with a Breit-Wigner resonance interfering with the continuum. Supersedes ABLIKIM 221.

6 From a fit to $\omega\pi^+\pi^-$ with a Breit-Wigner resonance interfering with the continuum.

7 From the fit to the cross section by the coherent sum of resonant component parametrized by a modified Breit-Wigner amplitude and a phase-space contribution for the continuum.

8 From the combined analysis of ANISOVICH 00D, ANISOVICH 01C, and ANISOVICH 02B.
## $\omega(2220)$ DECAY MODES

<table><thead><tr><th>Mode</th><th></th><th>Fraction (Γ<sub>i</sub>/Γ)</th></tr></thead><tbody><tr><td>Γ<sub>1</sub></td><td>ωππ</td><td>seen</td></tr><tr><td>Γ<sub>2</sub></td><td>ωπ<sup>+</sup>π<sup>-</sup></td><td>seen</td></tr><tr><td>Γ<sub>3</sub></td><td>ωπ<sup>0</sup>π<sup>0</sup></td><td>seen</td></tr><tr><td>Γ<sub>4</sub></td><td>e<sup>+</sup>e<sup>-</sup></td><td>seen</td></tr></tbody></table>

## $\omega(2220)$ $\Gamma(i)\Gamma(e^+e^-)/\Gamma(\text{total})$

$$ \Gamma(\omega\pi^0\pi^0) \times \Gamma(e^+e^-)/\Gamma_{\text{total}} \qquad \Gamma_3\Gamma_4/\Gamma $$

VALUE (eV) DOCUMENT ID TECN COMMENT

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

$$ 0.3 \pm 0.1 \pm 0.1 \qquad 9 \text{ ABLIKIM} \quad 22i \quad \text{BES3} \quad 2.0-3.8 \ e^+e^- \rightarrow \omega\pi^0\pi^0 $$

⁹Superseded by ABLIKIM 23G.

$$ \Gamma(\omega\pi^+\pi^-) \times \Gamma(e^+e^-)/\Gamma_{\text{total}} \qquad \Gamma_2\Gamma_4/\Gamma $$

VALUE (eV) DOCUMENT ID TECN COMMENT

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

$$ 0.9 \pm 0.4 \pm 0.4 \qquad 10 \text{ ABLIKIM} \quad 23g \quad \text{BES3} \quad 2.0-3.1 \ e^+e^- \rightarrow \omega\pi^+\pi^- $$

¹⁰From a fit to $\omega\pi^+\pi^-$ with a Breit-Wigner resonance interfering with the continuum. Solution with constructive interference: 52.9 $\pm$ 17.0 $\pm$ 13.1 eV.

$$ \Gamma(\omega\pi\pi) \times \Gamma(e^+e^-)/\Gamma_{\text{total}} \qquad \Gamma_1\Gamma_4/\Gamma $$

VALUE (eV) DOCUMENT ID TECN COMMENT

$$ 0.9 \pm 0.5 \pm 0.2 \qquad 11 \text{ ABLIKIM} \quad 23g \quad \text{BES3} \quad 2.0-3.1 \ e^+e^- \rightarrow \omega\pi\pi $$

¹¹From a fit to $\omega\pi^+\pi^-$ and $\omega\pi^0\pi^0$ with a Breit-Wigner resonance interfering with the continuum. Solution with constructive interference: 61.1 $\pm$ 32.1 $\pm$ 15.4 eV. Supersedes ABLIKIM 22i.

## $\omega(2220)$ REFERENCES

ABLIKIM 23G JHEP 2301 111 M. Ablikim et al. (BESIII Collab.)

Also JHEP 2303 093 (erratum). M. Ablikim et al. (BESIII Collab.)

ABLIKIM 22i PR D105 032005 M. Ablikim et al. (BESIII Collab.)

ANISOVICH 02B PL B542 19 A.V. Anisovich et al. (BESIII Collab.)

ANISOVICH 01C PL B507 23 A.V. Anisovich et al. (BESIII Collab.)

ANISOVICH 00D PL B476 15 A.V. Anisovich et al. (BESIII Collab.)

## $\eta(2225)$

$$ I^G(J^{PC}) = 0^+(0^-) $$

## OMITTED FROM SUMMARY TABLE

Seen in $J/\psi \rightarrow \gamma\phi\phi$. Possibly seen in $B \rightarrow \phi\phi K$ by LEES 11A.

### $\eta(2225)$ 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 colspan="5"><strong>2221<sup>+13</sup><sub>-10</sub> OUR AVERAGE</strong></td></tr></tbody></table>

<table><tbody><tr><td>2216<sup>+4</sup><sub>-5</sub><sup>+21</sup><sup>-11</sup></td><td>1 ABLIKIM</td><td>16N</td><td>BES3</td><td>J/ψ → γK<sup>+</sup>K<sup>-</sup>K<sup>+</sup>K<sup>-</sup></td></tr><tr><td>2240<sup>+30</sup><sub>-20</sub><sup>+30</sup><sup>-20</sup></td><td>196 ± 19</td><td>ABLIKIM</td><td>08i</td><td>BES</td><td>J/ψ → γK<sup>+</sup>K<sup>-</sup>K<sub>S</sub><sup>0</sup>K<sub>L</sub><sup>0</sup></td></tr><tr><td>2230 ± 25 ± 15</td><td>BAI</td><td>90b</td><td>MRK3</td><td>J/ψ → γK<sup>+</sup>K<sup>-</sup>K<sup>+</sup>K<sup>-</sup></td></tr><tr><td>2214 ± 20 ± 13</td><td>BAI</td><td>90b</td><td>MRK3</td><td>J/ψ → γK<sup>+</sup>K<sup>-</sup>K<sub>S</sub><sup>0</sup>K<sub>L</sub><sup>0</sup></td></tr></tbody></table>

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

~ 2220 BISELLO 86b DM2 J/ψ → γK<sup>+</sup>K<sup>-</sup>K<sup>+</sup>K<sup>-</sup> ¹From a partial wave analysis of $J/\psi \rightarrow \gamma\phi\phi$ that also finds significant signals for $\eta(2100)$, 0<sup>-</sup> + phase space, $f_0(2100)$, $f_2(2010)$, $f_2(2300)$, $f_2(2340)$, and a previously unseen 0<sup>-</sup> + state $X(2500)$ (M = 2470<sup>+15</sup><sub>-19</sub> 23 MeV, $\Gamma = 230<sup>+64</sup><sub>-35</sub> 33 MeV).

### $\eta(2225)$ 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"><strong>185<sup>+40</sup><sub>-20</sub> OUR AVERAGE</strong></td></tr></tbody></table>

<table><tbody><tr><td>185<sup>+12</sup><sub>-14</sub><sup>+43</sup><sup>-17</sup></td><td>1 ABLIKIM</td><td>16N</td><td>BES3</td><td>J/ψ → γK<sup>+</sup>K<sup>-</sup>K<sup>+</sup>K<sup>-</sup></td></tr><tr><td>190 ± 30<sup>+60</sup><sub>-40</sub></td><td>196 ± 19</td><td>ABLIKIM</td><td>08i</td><td>BES</td><td>J/ψ → γK<sup>+</sup>K<sup>-</sup>K<sub>S</sub><sup>0</sup>K<sub>L</sub><sup>0</sup></td></tr><tr><td>150<sup>+300</sup><sub>-60</sub><sup>+60</sup></td><td>BAI</td><td>90b</td><td>MRK3</td><td>J/ψ → γK<sup>+</sup>K<sup>-</sup>K<sup>+</sup>K<sup>-</sup></td></tr></tbody></table>

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

~ 80 BISELLO 86b DM2 J/ψ → γK<sup>+</sup>K<sup>-</sup>K<sup>+</sup>K<sup>-</sup> ¹From a partial wave analysis of $J/\psi \rightarrow \gamma\phi\phi$ that also finds significant signals for $\eta(2100)$, 0<sup>-</sup> + phase space, $f_0(2100)$, $f_2(2010)$, $f_2(2300)$, $f_2(2340)$, and a previously unseen 0<sup>-</sup> + state $X(2500)$ (M = 2470<sup>+15</sup><sub>-19</sub> 23 MeV, $\Gamma = 230<sup>+64</sup><sub>-35</sub> 33 MeV).

### $\eta(2225)$ REFERENCES

ABLIKIM 16N PR D93 112011 M. Ablikim (BESIII Collab.)

LEES 11A PR D84 012001 J.P. Lees et al. (BABAR Collab.)

ABLIKIM 08i PL B662 330 M. Ablikim et al. (BES Collab.)

BAI 90B PRL 65 1309 Z. Bai et al. (Mark III Collab.)

BISELLO 86B PL B179 294 D. Bisello et al. (DM2 Collab.)

## $\rho_3(2250)$

$$ I^G(J^{PC}) = 1^+(3^-) $$

## OMITTED FROM SUMMARY TABLE

Contains results mostly from formation experiments. For further production experiments see the Further States entry. See also $\rho(2150)$, $\tilde{\rho}_2(2150)$, $\tilde{\rho}_4(2300)$, $\rho_5(2350)$.

## $\rho_3(2250)$ 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>2248 ± 17<sup>+59</sup><sub>-5</sub></td><td>1.8k</td><td>1 ABLIKIM</td><td>20F</td><td>BES3</td><td>ψ(2S) → K<sup>+</sup>K<sup>-</sup>η</td></tr><tr><td>~ 2232</td><td></td><td>HASAN</td><td>94</td><td>RVUE</td><td>$\bar{\rho}p \rightarrow \pi\pi$</td></tr><tr><td>~ 2090</td><td></td><td>2 OAKDEN</td><td>94</td><td>RVUE</td><td>0.36-1.55 $\bar{\rho}p \rightarrow \pi\pi$</td></tr><tr><td>~ 2250</td><td></td><td>3 MARTIN</td><td>80B</td><td>RVUE</td><td></td></tr><tr><td>~ 2300</td><td></td><td>3 MARTIN</td><td>80C</td><td>RVUE</td><td></td></tr><tr><td>~ 2140</td><td></td><td>4 CARTER</td><td>78B</td><td>CNTR 0</td><td>0.7-2.4 $\bar{\rho}p \rightarrow K^-K^+$</td></tr><tr><td>~ 2150</td><td></td><td>5 CARTER</td><td>77</td><td>CNTR</td><td>0.7-2.4 $\bar{\rho}p \rightarrow \pi\pi$</td></tr></tbody></table>

¹Seen in $\psi(2S)$ decay with branching ratio $\psi(2S) \rightarrow X\eta \rightarrow K^+K^-\eta = (1.9 \pm 0.4_{-1.3}^{+0.5}) \times 10^{-6}$.

²See however KLOET 96 who fit $\pi^+\pi^-$ only and find waves only up to $J = 3$ to be important but not significantly resonant.

³$I(J^P) = 1(3^-)$ from simultaneous analysis of $p\bar{p} \rightarrow \pi^-\pi^+$ and $\pi^0\pi^0$.

⁴$I = 0, 1, J^P = 3^-$ from Barrelet-zero analysis.

⁵$I(J^P) = 1(3^-)$ from amplitude analysis.

<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>2260 ± 20</td><td></td><td>6 ANISOVICH</td><td>02</td><td>SPEC</td><td>0.6-1.9 $\bar{\rho}p \rightarrow \omega\pi^0$, $\omega\eta\pi^0$, $\pi^+\pi^-$</td></tr><tr><td>~ 2190</td><td></td><td>7 CUTTS</td><td>78b</td><td>CNTR</td><td>0.97-3 $\bar{\rho}p \rightarrow \bar{N}N$</td></tr><tr><td>2155 ± 15</td><td></td><td>7.8 COUPLAND</td><td>7</td><td>CNTR 0</td><td>0.7-2.4 $\bar{\rho}p \rightarrow \bar{\rho}p$</td></tr><tr><td>2193 ± 2</td><td></td><td>7.9 ALSPECTOR</td><td>73</td><td>CNTR</td><td>$\bar{\rho}p$ S channel</td></tr><tr><td>2190 ± 10</td><td></td><td>10 ABRAMS</td><td>70</td><td>CNTR</td><td>S channel $\bar{N}N$</td></tr></tbody></table>

⁶From the combined analysis of ANISOVICH 00J, ANISOVICH 01D, ANISOVICH 01E, and ANISOVICH 02.
⁷Iospins 0 and 1 not separated.
⁸From a fit to the total elastic cross section.
⁹Referred to as T or $\bar{T}$ region by ALSPECTOR 73.
¹⁰Seen as bump in $I = 1$ state. See also COOPER 68. PEASLEE 75 confirm $\bar{\rho}p$ results of ABRAMS 70, no narrow structure.

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

<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>2290 ± 20 ± 30</td><td></td><td>AMELIN</td><td>00</td><td>VES</td><td>37 $\pi^-p \rightarrow \eta\pi^+\pi^-n$</td></tr></tbody></table>

## $\rho_3(2250)$ 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>185<sup>+31</sup><sub>-26</sub><sup>+17</sup><sup>-103</sup></td><td>1.8k</td><td>11 ABLIKIM</td><td>20F</td><td>BES3</td><td>ψ(2S) → K<sup>+</sup>K<sup>-</sup>η</td></tr><tr><td>~ 220</td><td></td><td>HASAN</td><td>94</td><td>RVUE</td><td>$\bar{\rho}p \rightarrow \pi\pi$</td></tr><tr><td>~ 60</td><td></td><td>12 OAKDEN</td><td>94</td><td>RVUE</td><td>0.36-1.55 $\bar{\rho}p \rightarrow \pi\pi$</td></tr><tr><td>~ 250</td><td></td><td>13 MARTIN</td><td>80B</td><td>RVUE</td><td></td></tr><tr><td>~ 200</td><td></td><td>13 MARTIN</td><td>80C</td><td>RVUE</td><td></td></tr><tr><td>~ 150</td><td></td><td>14 CARTER</td><td>78B</td><td>CNTR 0</td><td>0.7-2.4 $\bar{\rho}p \rightarrow K^-K^+$</td></tr><tr><td>~ 200</td><td></td><td>15 CARTER</td><td>77</td><td>CNTR 0</td><td>0.7-2.4 $\bar{\rho}p \rightarrow \pi\pi$</td></tr></tbody></table>

¹¹Seen in $\psi(2S)$ decay with branching ratio $\psi(2S) \rightarrow X\eta \rightarrow K^+K^-\eta = (1.9 \pm 0.4_{-1.3}^{+0.5}) \times 10^{-6}$.

¹²See however KLOET 96 who fit $\pi^+\pi^-$ only and find waves only up to $J = 3$ to be important but not significantly resonant.

¹³$I(J^P) = 1(3^-)$ from simultaneous analysis of $p\bar{p} \rightarrow \pi^-\pi^+$ and $\pi^0\pi^0$.

¹⁴$I = 0, 1, J^P = 3^-$ from Barrelet-zero analysis.

¹⁵$I(J^P) = 1(3^-)$ from amplitude analysis.

<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>160 ± 25</td><td></td><td>16 ANISOVICH</td><td>02</td><td>SPEC</td><td>0.6-1.9 $\bar{\rho}p \rightarrow \omega\pi^0$, $\omega\eta\pi^0$, $\pi^+\pi^-$</td></tr><tr><td>135 ± 75</td><td></td><td>17,18 COUPLAND</td><td>77</td><td>CNTR 0</td><td>0.7-2.4 $\bar{\rho}p \rightarrow \bar{\rho}p$</td></tr><tr><td>98 ± 8</td><td></td><td>18 ALSPECTOR</td><td>73</td><td>CNTR</td><td>$\bar{\rho}p$ S channel</td></tr><tr><td>~ 85</td><td></td><td>19 ABRAMS</td><td>70</td><td>CNTR</td><td>S channel $\bar{N}N$</td></tr></tbody></table>

¹⁶From the combined analysis of ANISOVICH 00J, ANISOVICH 01D, ANISOVICH 01E, and ANISOVICH 02.
¹⁷From a fit to the total elastic cross section.
¹⁸Iospins 0 and 1 not separated.
¹⁹Seen as bump in $I = 1$ state. See also COOPER 68. PEASLEE 75 confirm $\bar{\rho}p$ results of ABRAMS 70, no narrow structure.
Other processes

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>230 ± 50 ± 80</td><td>AMELIN</td><td>00</td><td>VES 37 π<sup>-</sup> p → ηπ<sup>+</sup> π<sup>-</sup> n</td></tr></tbody></table>

$\rho_3(2250)$ REFERENCES

<table><tr><td>ABLIKIM</td><td>20F</td><td>PR D101 032008</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ANISOVICH</td><td>02</td><td>PL B542 8</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>ANISOVICH</td><td>01D</td><td>PL B508 6</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>ANISOVICH</td><td>01E</td><td>PL B513 281</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>AMELIN</td><td>00</td><td>NP A668 83</td><td>D. Amelin et al.</td><td>(VES Collab.)</td></tr><tr><td>ANISOVICH</td><td>00J</td><td>PL B491 47</td><td>A.V. Anisovich et al.</td><td>(RAL, LOQM, PNP+)</td></tr><tr><td>KLOET</td><td>96</td><td>PR D53 6120</td><td>W.M. Kloet, F. Myhrer</td><td>(RUTG, NORD)</td></tr><tr><td>HASAN</td><td>94</td><td>PL B334 215</td><td>A. Hasan, D.V. Bugg</td><td>(LOQM)</td></tr><tr><td>OAKDEN</td><td>94</td><td>NP A574 731</td><td>M.N. Oakden, M.R. Pennington</td><td>(DURH)</td></tr><tr><td>MARTIN</td><td>80B</td><td>NP B176 355</td><td>B.R. Martin, D. Morgan</td><td>(LOUC, RHEL) JP</td></tr><tr><td>MARTIN</td><td>80C</td><td>NP B169 216</td><td>A.D. Martin, M.R. Pennington</td><td>(DURH) JP</td></tr><tr><td>CARTER</td><td>78B</td><td>NP B141 467</td><td>A.A. Carter</td><td>(LOQM)</td></tr><tr><td>CUTTS</td><td>78B</td><td>PR D17 16</td><td>D. Cutts et al.</td><td>(STON, WISC)</td></tr><tr><td>CARTER</td><td>77</td><td>PL 67B 117</td><td>A.A. Carter et al.</td><td>(LOQM, RHEL) JP</td></tr><tr><td>COUPLAND</td><td>77</td><td>PL 71B 460</td><td>M. Coupland et al.</td><td>(LOQM, RHEL)</td></tr><tr><td>PEASLEE</td><td>75</td><td>PL 57B 189</td><td>D.C. Peaslee et al.</td><td>(CANB, BARI, BROW+)</td></tr><tr><td>ALSPECTOR</td><td>73</td><td>PRL 30 511</td><td>J. Alspector et al.</td><td>(RUTG, UPNJ)</td></tr><tr><td>ABRAMS</td><td>70</td><td>PR D1 1917</td><td>R.J. Abrams et al.</td><td>(BNL)</td></tr><tr><td>COOPER</td><td>68</td><td>PRL 20 1059</td><td>W.A. Cooper et al.</td><td>(ANL)</td></tr></table>

$f_2(2300)$

$$f_2(2300) = 0^{+}(2^{++})$$

$f_2(2300)$ MASS

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2297 ± 28</td><td>1 ETKIN</td><td>88</td><td>MPS 22 π<sup>-</sup> p → φφn</td></tr><tr><td>2262 ± 4 ± 28</td><td>2 ABLIKIM</td><td>21AI BES3</td><td>3.51-4.60 e<sup>+</sup> e<sup>-</sup> → φΛπ</td></tr><tr><td>2243<sup>+7</sup><sub>-3</sub></td><td>3 UEHARA</td><td>13</td><td>BELL γγ → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup></td></tr><tr><td>2270 ± 12</td><td>VLADIMIRSK...06</td><td>SPEC</td><td>40 π<sup>-</sup> p → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup> n</td></tr><tr><td>2327 ± 9 ± 6</td><td>ABE</td><td>04</td><td>BELL 10.6 e<sup>+</sup> e<sup>-</sup> → e<sup>+</sup> e<sup>-</sup> K<sup>+</sup> K<sup>-</sup></td></tr><tr><td>2331 ± 10</td><td>BOOTH</td><td>86</td><td>OMEG 85 π<sup>-</sup> Be → 2φBe</td></tr><tr><td>2220<sup>+90</sup><sub>-20</sub></td><td>LINDENBAUM</td><td>84</td><td>RVUE</td></tr><tr><td>2320 ± 40</td><td>ETKIN</td><td>82</td><td>MPS 22 π<sup>-</sup> p → 2φn</td></tr></tbody></table>

¹Includes data of ETKIN 85. The percentage of the resonance going into $φφ 2^{++} S_2$, $D_2$, and $D_0$ is $6 \pm 15/5$, $25 \pm 18/14$, and $69 \pm 16/27$, respectively.

²Threshold enhancement in $Λ\bar{Λ}$, preferred $JPC$ are $2^{++}$, $2^{−−}$, or $1^{++}$. Could be another state.

³Spin 2 preferred, tentatively assigned to $f_2(2300)$.

$f_2(2300)$ WIDTH

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>149 ± 41</td><td>1 ETKIN</td><td>88</td><td>MPS 22 π<sup>-</sup> p → φφn</td></tr><tr><td>72 ± 5 ± 43</td><td>2 ABLIKIM</td><td>21AI BES3</td><td>3.51-4.60 e<sup>+</sup> e<sup>-</sup> → φΛπ</td></tr><tr><td>145 ± 12<sup>+27</sup><sub>-34</sub></td><td>3 UEHARA</td><td>13</td><td>BELL γγ → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup></td></tr><tr><td>90 ± 29</td><td>VLADIMIRSK...06</td><td>SPEC</td><td>40 π<sup>-</sup> p → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup> n</td></tr><tr><td>275 ± 36 ± 20</td><td>ABE</td><td>04</td><td>BELL 10.6 e<sup>+</sup> e<sup>-</sup> → e<sup>+</sup> e<sup>-</sup> K<sup>+</sup> K<sup>-</sup></td></tr><tr><td>133 ± 50</td><td>BOOTH</td><td>86</td><td>OMEG 85 π<sup>-</sup> Be → 2φBe</td></tr><tr><td>200 ± 50</td><td>LINDENBAUM</td><td>84</td><td>RVUE</td></tr><tr><td>220 ± 70</td><td>ETKIN</td><td>82</td><td>MPS 22 π<sup>-</sup> p → 2φn</td></tr></tbody></table>

¹Includes data of ETKIN 85.

²Threshold enhancement in $Λ\bar{Λ}$, preferred $JPC$ are $2^{++}$, $2^{−−}$, or $1^{++}$. Could be another state.

³Spin 2 preferred, tentatively assigned to $f_2(2300)$.

$f_2(2300)$ 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> φφ</td><td>seen</td></tr><tr><td>Γ<sub>2</sub> K<sub>Λ</sub></td><td>seen</td></tr><tr><td>Γ<sub>3</sub> γγ</td><td>seen</td></tr><tr><td>Γ<sub>4</sub> ΛΛ</td><td>seen</td></tr></tbody></table>

$f_2(2300) Γ(i)Γ(γγ)/Γ(total)$

<table><thead><tr><th>Γ(ΛK) × Γ(γγ)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>3.2<sup>+0.5</sup><sub>-0.4</sub> ± 1.3</td><td>UEHARA</td><td>13</td><td>BELL γγ → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup></td></tr><tr><td>44 ± 6 ± 12</td><td>1 ABE</td><td>04</td><td>BELL 10.6 e<sup>+</sup> e<sup>-</sup> → e<sup>+</sup> e<sup>-</sup> K<sup>+</sup> K<sup>-</sup></td></tr></tbody></table>

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

$3.2 \pm 0.4 \pm 2.2$

$44 \pm 6 \pm 12$

¹Assuming spin 2.

$f_2(2340)$ BRANCHING RATIOS

<table><thead><tr><th>Γ(φφ)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>seen</td><td>BOOTH</td><td>86</td><td>OMEG 85 π<sup>-</sup> Be → 2φBe</td></tr><tr><td>seen</td><td>ETKIN</td><td>82</td><td>MPS 22 π<sup>-</sup> p → 2φn</td></tr></tbody></table>

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>seen</td><td>BOOTH</td><td>86</td><td>OMEG 85 π<sup>-</sup> Be → 2φBe</td></tr><tr><td>seen</td><td>ETKIN</td><td>82</td><td>MPS 22 π<sup>-</sup> p → 2φn</td></tr></tbody></table>

<table><thead><tr><th>Γ(KK)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>seen</td><td>VLADIMIRSK...06</td><td>SPEC</td><td>40 π<sup>-</sup> p → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup> n</td></tr><tr><td>seen</td><td>ABE</td><td>04</td><td>BELL 10.6 e<sup>+</sup> e<sup>-</sup> → e<sup>+</sup> e<sup>-</sup> K<sup>+</sup> K<sup>-</sup></td></tr></tbody></table>

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>seen</td><td>ABE</td><td>04</td><td>BELL 10.6 e<sup>+</sup> e<sup>-</sup> → e<sup>+</sup> e<sup>-</sup> K<sup>+</sup> K<sup>-</sup></td></tr></tbody></table>

<table><thead><tr><th>Γ(γγ)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>seen</td><td>UEHARA</td><td>13</td><td>BELL γγ → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup></td></tr></tbody></table>

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>seen</td><td>UEHARA</td><td>13</td><td>BELL γγ → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup></td></tr></tbody></table>

<table><thead><tr><th>Γ(ΛΛ)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>seen</td><td>1 ABLIKIM</td><td>21AI BES3</td><td>3.51-4.60 e<sup>+</sup> e<sup>-</sup> → φΛπ</td></tr></tbody></table>

¹Threshold enhancement in $Λ\bar{Λ}$, preferred $JPC$ are $2^{++}$, $2^{−−}$, or $1^{++}$. Could be another state.

$f_2(2300)$ REFERENCES

<table><tr><td>ABLIKIM</td><td>21AI PR D104 052006</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>UEHARA</td><td>13 PTEP 2013 123C01</td><td>S. Uehara et al.</td><td>(BELLE Collab.)</td></tr><tr><td>VLADIMIRSK...06</td><td>PAN 69 493<br>Translated from YAF 69 515</td><td>V.V. Vladimirsky et al.</td><td>(ITEP, Moscow)</td></tr><tr><td>ABE</td><td>04 EPJ C32 323</td><td>K. Abe et al.</td><td>(BELLE Collab.)</td></tr><tr><td>ETKIN</td><td>88 PL B201 568</td><td>A. Etkin et al.</td><td>(BNL, CUNY)</td></tr><tr><td>BOOTH</td><td>86 NP B273 677</td><td>P.S.L. Booth et al.</td><td>(LIVP, GLAS, CERN)</td></tr><tr><td>ETKIN</td><td>85 PL 165B 217</td><td>A. Etkin et al.</td><td>(BNL, CUNY)</td></tr><tr><td>LINDENBAUM</td><td>84 CNPP 13 285</td><td>S.J. Lindenbaum</td><td>(CUNY)</td></tr><tr><td>ETKIN</td><td>82 PRL 49 1620</td><td>A. Etkin et al.</td><td>(BNL, CUNY)</td></tr></table>

$f_4(2300)$

$$f_4(JPC) = 0^{+}(4^{++})$$

OMITTED FROM SUMMARY TABLE

This entry was previously called $U_0(2350)$. Contains results mostly from formation experiments. For further production experiments see the Further States entry. See also $\rho(2150)$, $f_2(2150)$, $\rho_3(2250)$, $\rho_5(2350)$.

$f_4(2300)$ MASS

<table><thead><tr><th>p → ππ or KK</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>~ 2314</td><td>HASAN</td><td>94</td><td>RVUE p → ππ</td></tr><tr><td>~ 2300</td><td>1 MARTIN</td><td>80B</td><td>RVUE</td></tr><tr><td>~ 2300</td><td>1 MARTIN</td><td>80C</td><td>RVUE</td></tr><tr><td>~ 2340</td><td>2 CARTER</td><td>78B</td><td>CNTR 0.7-2.4 p → K<sup>-</sup> K<sup>+</sup></td></tr><tr><td>~ 2330</td><td>DULUDE</td><td>78B</td><td>OSPK 1-2 p → π<sup>0</sup> π<sup>0</sup></td></tr><tr><td>~ 2310</td><td>3 CARTER</td><td>77</td><td>CNTR 0.7-2.4 p → ππ</td></tr></tbody></table>

¹$I(J^P) = 0(4^+)$ from simultaneous analysis of $p\bar{p} → π^-π^+$ and $π^0π^0$.

²$I(J^P) = 0(4^+)$ from Barrelet-zero analysis.

³$I(J^P) = 0(4^+)$ from amplitude analysis.

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>~ 2283 ± 17</td><td>4 ANISOVICH</td><td>00J SPEC</td><td></td></tr><tr><td>~ 2380</td><td>5 CUTTS</td><td>78B</td><td>CNTR 0.97-3 p → N̄N</td></tr><tr><td>2345 ± 15</td><td>5.6 COUPLAND</td><td>77</td><td>CNTR 0.7-2.4 p → p̄p</td></tr><tr><td>2359 ± 2</td><td>5.7 ALSPECTOR</td><td>73</td><td>CNTR p̄p S channel</td></tr><tr><td>2375 ± 10</td><td>ABRAMS</td><td>70</td><td>CNTR S channel N̄N</td></tr></tbody></table>

⁴From the combined analysis of ANISOVICH 99C and ANISOVICH 99F on $p\bar{p} → η\pi^0\pi^0$, $\pi^0\pi^0$, $ηη$, $ηη'$, $\pi^+\pi^-$.

⁵Isospins 0 and 1 not separated.

⁶From a fit to the total elastic cross section.

⁷Referred to as U or U region by ALSPECTOR 73.

<table><thead><tr><th>π<sup>-</sup> p → ηππn</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2330 ± 20 ± 40</td><td>AMELIN</td><td>00</td><td>VES 37 π<sup>-</sup> p → ηπ<sup>+</sup> π<sup>-</sup> n</td></tr></tbody></table>

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

$2330 \pm 20 \pm 40$

<table><thead><tr><th>pp CENTRAL PRODUCTION</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2320 ± 60 OUR ESTIMATE</td><td>1 ABLIKIM</td><td>00</td><td>VES 37 π<sup>-</sup> p → ηπ<sup>+</sup> π<sup>-</sup> n</td></tr></tbody></table>

<table><thead><tr><th>2320 ± 60 OUR ESTIMATE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2332 ± 15</td><td>BARBERIS</td><td>00F</td><td>450 p̄p → p̄ωωp̄S</td></tr></tbody></table>
## f₄(2300) WIDTH

### $\bar{p}p \to \pi\pi \text{ or } \bar{K}K$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>~ 278</td><td>8 HASAN</td><td>94</td><td>RVUE $\bar{p}p \to \pi\pi$</td></tr><tr><td>~ 200</td><td>8 MARTIN</td><td>80c</td><td>RVUE</td></tr><tr><td>~ 150</td><td>9 CARTER</td><td>78b</td><td>CNTR 0.7-2.4 $\bar{p}p \to K^- K^+$</td></tr><tr><td>~ 210</td><td>10 CARTER</td><td>77</td><td>CNTR 0.7-2.4 $\bar{p}p \to \pi\pi$</td></tr></tbody></table>

8 $I(J^P) = 0(4^+)$ from simultaneous analysis of $p\bar{p} \to \pi^-\pi^+$ and $\pi^0\pi^0$.

9 $I(J^P) = 0(4^+)$ from Barrelet-zero analysis.

10 $I(J^P) = 0(4^+)$ from amplitude analysis.

### S-CHANNEL $\bar{p}p \text{ or } \bar{N}N$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>310 ± 25</td><td>11 ANISOVICH</td><td>00J</td><td>SPEC</td></tr><tr><td>135<sup>+150</sup><sub>-65</sub></td><td>12,13 COUPLAND</td><td>77</td><td>CNTR 0.7-2.4 $\bar{p}p \to \bar{p}p$</td></tr><tr><td>165<sup>+18</sup><sub>-8</sub></td><td>13 ALSPECTOR</td><td>73</td><td>CNTR $\bar{p}p S$ channel</td></tr><tr><td>~ 190</td><td>ABRAMS</td><td>70</td><td>CNTR $S$ channel $\bar{N}N$</td></tr></tbody></table>

11 From the combined analysis of ANISOVICH 99c and ANISOVICH 99f on $\bar{p}p \to \eta\pi^0\pi^0$, $\pi^0\pi^0$, $\eta\eta$, $\eta\eta'$, $\pi^+\pi^-$.

12 From a fit to the total elastic cross section.

13 Isospins 0 and 1 not separated.

### $\pi^- p \to \eta\pi\pi n$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>~ 235 ± 50</td><td>40 AMELIN</td><td>00</td><td>VES 37 $\pi^- p \to \eta\pi^+\pi^- n$</td></tr></tbody></table>

### pp CENTRAL PRODUCTION

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>COMMENT</th></tr></thead><tbody><tr><td>250 ± 80</td><td>OUR ESTIMATE</td><td></td></tr><tr><td>260 ± 57</td><td>BARBERIS</td><td>00F 450 $\bar{p}p \to p_f \omega\omega p_S$</td></tr></tbody></table>

## f₄(2300) 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> ρρ</td><td>seen</td></tr><tr><td>Γ<sub>2</sub> ωω</td><td>seen</td></tr><tr><td>Γ<sub>3</sub> ηππ</td><td>seen</td></tr><tr><td>Γ<sub>4</sub> ππ</td><td>seen</td></tr><tr><td>Γ<sub>5</sub> K<span style="text-decoration: overline">K</span></td><td>seen</td></tr><tr><td>Γ<sub>6</sub> N<span style="text-decoration: overline">N</span></td><td>seen</td></tr></tbody></table>

## f₄(2300) BRANCHING RATIOS

### $\Gamma(\rho p)/\Gamma(\omega\omega)$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>COMMENT</th></tr></thead><tbody><tr><td>• • •</td><td></td><td>We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>2.8 ± 0.5</td><td>BARBERIS</td><td>00F 450 $\bar{p}p \to p_f \omega\omega p_S$</td></tr></tbody></table>

## f₄(2300) REFERENCES

<table><tbody><tr><td>AMELIN</td><td>00</td><td>NP A668 83</td><td>D. Amelin et al. (VES Collab.)</td></tr><tr><td>ANISOVICH</td><td>00J</td><td>PL B491 47</td><td>A.V. Anisovich et al. (RAL, LOQM, PNPI+)</td></tr><tr><td>BARBERIS</td><td>00F</td><td>PL B484 198</td><td>D. Barberis et al. (WA 102 Collab.)</td></tr><tr><td>ANISOVICH</td><td>99C</td><td>PL B452 173</td><td>A.V. Anisovich et al.</td></tr><tr><td>ANISOVICH</td><td>99F</td><td>NP A651 253</td><td>A.V. Anisovich et al.</td></tr><tr><td>HASAN</td><td>94</td><td>PL B334 215</td><td>A. Hasan, D.V. Bugg (LOQM)</td></tr><tr><td>MARTIN</td><td>80B</td><td>NP B176 355</td><td>B.R. Martin, D. Morgan (LOUC, RHEL) JP</td></tr><tr><td>MARTIN</td><td>80C</td><td>NP B169 216</td><td>A.D. Martin, M.R. Pennington (DURH) JP</td></tr><tr><td>CARTER</td><td>78B</td><td>NP B141 467</td><td>A.A. Carter (LOQM)</td></tr><tr><td>CUTTS</td><td>78B</td><td>PR D17 16</td><td>D. Cutts et al. (STON, WISC)</td></tr><tr><td>DULUBE</td><td>78B</td><td>PL 79B 335</td><td>R.S. Dulube et al. (BROW, MIT, BARI) JP</td></tr><tr><td>CARTER</td><td>77</td><td>PL 67B 117</td><td>A.A. Carter et al. (LOQM, RHEL) JP</td></tr><tr><td>COUPLAND</td><td>77</td><td>PL 71B 460</td><td>M. Coupland et al. (LOQM, RHEL)</td></tr><tr><td>ALSPECTOR</td><td>73</td><td>PRL 30 511</td><td>J. Alspector et al. (RUTG, UPNJ)</td></tr><tr><td>ABRAMS</td><td>70</td><td>PR D1 1917</td><td>R.J. Abrams et al. (BNL)</td></tr></tbody></table>

## f₀(2330)

$$I^G(J^{PC}) = 0^+(2^+ +^-)$$

OMITTED FROM SUMMARY TABLE

## f₀(2330) MASS

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>• • •</td><td></td><td></td><td>We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>2312 ± 7<sup>+7</sup><sub>-3</sub></td><td>1 ABLIKIM</td><td>22AS BES3</td><td>$J/\psi(1S) \to \gamma\eta'$</td></tr><tr><td>2312 ± 2<sup>+10</sup><sub>-0</sub></td><td>2 ABLIKIM</td><td>22C BES3</td><td>$J/\psi \to \gamma\eta'\eta' \to 4/5\gamma2(\pi^+\pi^-)$</td></tr><tr><td>2419 ± 64</td><td>3 RODAS</td><td>22 RVUE</td><td>$J/\psi(1S) \to \gamma(\pi\pi, K\bar{K})$</td></tr></tbody></table>

<table><tbody><tr><td>2340 ± 20</td><td>SARANTSEV</td><td>21 RVUE</td><td>$J/\psi(1S) \to \gamma(\pi\pi, K\bar{K}, \eta\eta, \omega\phi)$</td></tr><tr><td>2314 ± 25</td><td>4 BUGG</td><td>04A RVUE</td><td></td></tr><tr><td>2337 ± 14</td><td>ANISOVICH</td><td>00J SPEC</td><td>$2.0 \bar{p}p \to \pi\pi, \eta\eta$</td></tr><tr><td>~ 2321</td><td>HASAN</td><td>94 RVUE</td><td>$\bar{p}p \to \pi\pi$</td></tr></tbody></table>

1 From a Breit-Wigner fit involving 9 resonances and a resonating exotic $\eta_1(1855) \to \eta\eta' P$-wave.

2 From a partial wave analysis of the systems $(\gamma X)$, with $X \to \eta'\eta'$, $(\eta' X)$, with $X \to \eta\eta'$ in the decay $J/\psi \to \gamma\eta'\eta'$. The intermediate resonance X is parametrized by a constant-width, relativistic Breit-Wigner.

3 T-matrix pole from coupled channel K-matrix fit to data on $J/\psi \to \gamma\pi^0\pi^0$ (AB-LIKIM 15AE) and $J/\psi \to \gamma K_S^0 K_S^0$ (ABLIKIM 18AA).

4 Partial wave analysis of the data on $p\bar{p} \to \bar{K}\Lambda$ from BARNES 00.

## f₀(2330) WIDTH

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>• • •</td><td></td><td></td><td>We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>65 ± 10<sup>+3</sup><sub>-12</sub></td><td>1 ABLIKIM</td><td>22AS BES3</td><td>$J/\psi(1S) \to \gamma\eta\eta'$</td></tr><tr><td>134 ± 5<sup>+30</sup><sub>-9</sub></td><td>2 ABLIKIM</td><td>22C BES3</td><td>$J/\psi \to \gamma\eta'\eta' \to 4/5\gamma2(\pi^+\pi^-)$</td></tr><tr><td>274 ± 94</td><td>3 RODAS</td><td>22 RVUE</td><td>$J/\psi(1S) \to \gamma(\pi\pi, K\bar{K})$</td></tr><tr><td>165 ± 25</td><td>SARANTSEV</td><td>21 RVUE</td><td>$J/\psi(1S) \to \gamma(\pi\pi, K\bar{K}, \eta\eta, \omega\phi)$</td></tr><tr><td>144 ± 20</td><td>4 BUGG</td><td>04A RVUE</td><td></td></tr><tr><td>217 ± 33</td><td>ANISOVICH</td><td>00J SPEC</td><td>$2.0 \bar{p}p \to \pi\pi, \eta\eta$</td></tr><tr><td>~ 223</td><td>HASAN</td><td>94 RVUE</td><td>$\bar{p}p \to \pi\pi$</td></tr></tbody></table>

1 From a Breit-Wigner fit involving 9 resonances and a resonating exotic $\eta_1(1855) \to \eta\eta' P$-wave.

2 From a partial wave analysis of the systems $(\gamma X)$, with $X \to \eta'\eta'$, $(\eta' X)$, with $X \to \eta\eta'$ in the decay $J/\psi \to \gamma\eta'\eta'$. The intermediate resonance X is parametrized by a constant-width, relativistic Breit-Wigner.

3 T-matrix pole from coupled channel K-matrix fit to data on $J/\psi \to \gamma\pi^0\pi^0$ (AB-LIKIM 15AE) and $J/\psi \to \gamma K_S^0 K_S^0$ (ABLIKIM 18AA).

4 Partial wave analysis of the data on $p\bar{p} \to \bar{K}\Lambda$ from BARNES 00.

## f₀(2330) REFERENCES

<table><tbody><tr><td>ABLIKIM</td><td>22AS PR D106 072012</td><td>M. Ablikim et al. (BESIII Collab.)</td></tr><tr><td>Also</td><td>PR D107 079901</td><td>(errat.) M. Ablikim et al. (BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>PR D105 072002</td><td>M. Ablikim et al. (BESIII Collab.)</td></tr><tr><td>RODAS</td><td>22 EPJ C82 80</td><td>A. Rodas et al. (JPAC Collab.)</td></tr><tr><td>SARANTSEV</td><td>21 PL B816 136227</td><td>A.V. Sarantsev et al. (BONN, PNPI)</td></tr><tr><td>ABLIKIM</td><td>18AA PR D98 072003</td><td>M. Ablikim et al. (BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>15AE PR D92 052003</td><td>M. Ablikim et al. (BESIII Collab.)</td></tr><tr><td>BUGG</td><td>04 EPJ C36 161</td><td>D.V. Bugg</td></tr><tr><td>ANISOVICH</td><td>00J PL B491 47</td><td>A.V. Anisovich et al. (RAL, LOQM, PNPI+)</td></tr><tr><td>BARNES</td><td>00 PR C62 055203</td><td>P.D. Barnes et al. (LOQM)</td></tr><tr><td>HASAN</td><td>94 PL B334 215</td><td>A. Hasan, D.V. Bugg</td></tr></tbody></table>

## f₂(2340)

$$I^G(J^{PC}) = 0^+(2^+ +^-)$$

## f₂(2340) 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>2346<sup>+21</sup><sub>-10</sub> OUR AVERAGE</td><td></td><td></td><td></td><td></td></tr><tr><td>2346 ± 8<sup>+22</sup><sub>-6</sub></td><td>1 ABLIKIM</td><td>22c BES3</td><td>$J/\psi \to \gamma\eta'\eta' \to 4/5\gamma2(\pi^+\pi^-)$</td></tr><tr><td>2362<sup>+31+140</sup><sub>-30-63</sub></td><td>5.5k</td><td>13N BES3</td><td>$e^+ e^- \to J/\psi \to \gamma\eta\eta$</td></tr><tr><td>2339 ± 55</td><td>3 ETKIN</td><td>88 MPS</td><td>$2\pi^- p \to \phi\phi n$</td></tr><tr><td>• • •</td><td></td><td></td><td>We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>2350 ± 7</td><td>80k</td><td>4 UMAN</td><td>$06 E835 5.2 \bar{p}p \to \eta\eta\pi^0$</td></tr><tr><td>2392 ± 10</td><td></td><td>BOOTH</td><td>$86 OMEG 85 $\pi^- \text{Be} \to 2\phi\text{Be}$</td></tr><tr><td>2360 ± 20</td><td></td><td>LINDENBAUM</td><td>84 RVUE</td></tr></tbody></table>

1 From a partial wave analysis of the systems $(\gamma X)$, with $X \to \eta'\eta'$, $(\eta' X)$, with $X \to \eta\eta'$ in the decay $J/\psi \to \gamma\eta'\eta'$. The intermediate resonance X is parametrized by a constant-width, relativistic Breit-Wigner.

2 From partial wave analysis including all possible combinations of 0$^{++}$, 2$^{++}$, and 4$^{++}$ resonances.

3 Includes data of ETKIN 85. The percentage of the resonance going into $\phi\phi 2^{++} S_2$, $D_2$, and $D_0$ is 37 $\pm 19$, 4 $^{+12}$, and 59 $^{+21}$, respectively.

4 Statistical error only.

## f₂(2340) 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>331<sup>+27</sup><sub>-18</sub> OUR AVERAGE</td><td></td><td></td><td></td><td></td></tr><tr><td>332 ± 14<sup>+26</sup><sub>-12</sub></td><td>1 ABLIKIM</td><td>22C BES3</td><td>$J/\psi \to \gamma\eta'\eta' \to 4/5\gamma2(\pi^+\pi^-)$</td></tr><tr><td>334<sup>+62</sup><sub>-54</sub></td><td>5.5k</td><td>13N BES3</td><td>$e^+ e^- \to J/\psi \to \gamma\eta\eta$</td></tr><tr><td>319<sup>+81</sup><sub>-69</sub></td><td>3 ETKIN</td><td>88 MPS</td><td>$2\pi^- p \to \phi\phi n$</td></tr></tbody></table>
• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>218 ± 16</td><td>80k</td><td>4 UMAN</td><td>06</td><td>E835</td><td>5.2 p̄p → ηηπ°</td></tr><tr><td>198 ± 50</td><td></td><td>BOOTH</td><td>86</td><td>OMEG</td><td>85 π⁻ Be → 2φBe</td></tr><tr><td>150<sup>+150</sup><sub>-50</sub></td><td></td><td>LINDENBAUM</td><td>84</td><td>RVUE</td><td></td></tr></table>

¹ From a partial wave analysis of the systems (γX), with X → η'η', and (η'X), with X → γη'η' in the decay J/ψ → γη'η'. The intermediate resonance X is parametrized by a constant-width, relativistic Breit-Wigner.

² From partial wave analysis including all possible combinations of 0<sup>++</sup>, 2<sup>++</sup>, and 4<sup>++</sup> resonances.

³ Includes data of ETKIN 85.

⁴ Statistical error only.

$f_2(2340)$ 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> φφ</td><td>seen</td></tr><tr><td>Γ<sub>2</sub> ηη</td><td>seen</td></tr><tr><td>Γ<sub>3</sub> η'η'</td><td>seen</td></tr></tbody></table>

$f_2(2340)$ BRANCHING RATIOS

<table><thead><tr><th>Γ(ηη)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>VALUE</td><td></td><td></td><td></td></tr><tr><td>seen</td><td>UMAN</td><td>06</td><td>E835</td></tr></tbody></table>

<table><thead><tr><th>Γ(η'η')/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>VALUE</td><td></td><td></td><td></td></tr><tr><td>seen</td><td>1 ABLIKIM</td><td>22c</td><td>BES3</td></tr></tbody></table>

¹ From a partial wave analysis of the systems (γX), with X → η'η', and (η'X), with X → γη'η' in the decay J/ψ → γη'η'. The intermediate resonance X is parametrized by a constant-width, relativistic Breit-Wigner.

$f_2(2340)$ REFERENCES

<table><tr><td>ABLIKIM</td><td>22C</td><td>PR D105 072002</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>13N</td><td>PR D87 092009</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>UMAN</td><td>06</td><td>PR D73 052009</td><td>I. Uman et al.</td><td>(FNAL E835)</td></tr><tr><td>ETKIN</td><td>88</td><td>PL B201 568</td><td>A. Etkin et al.</td><td>(BNL, CUNY)</td></tr><tr><td>BOOTH</td><td>86</td><td>NP B273 677</td><td>P.S.L. Booth et al.</td><td>(LIVP, GLAS, CERN)</td></tr><tr><td>ETKIN</td><td>85</td><td>PL 165B 217</td><td>A. Etkin et al.</td><td>(BNL, CUNY)</td></tr><tr><td>LINDENBAUM</td><td>84</td><td>CNP 13 285</td><td>S.J. Lindenbaum</td><td>(CUNY)</td></tr></table>

$\rho_5(2350)$

$I^G(J^{PC}) = 1^+(5^-)$

OMITTED FROM SUMMARY TABLE

This entry was previously called $U_1(2400)$. See also $\rho(2150)$, $f_2(2150)$, $\rho_3(2250)$, $f_4(2300)$.

$\rho_5(2350)$ MASS

$\pi^{-}p \rightarrow \omega\pi^{0}n$

<table><tr><td>VALUE (MeV)</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr><tr><td>2330 ± 35</td><td>ALDE</td><td>95</td><td>GAM2</td></tr></table>

$\bar{p}p \rightarrow \pi\pi \text{ or } \bar{K}K$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>~ 2303</td><td>HASAN</td><td>94</td><td>RVUE</td><td>p̄p → ππ</td></tr><tr><td>~ 2300</td><td>1 MARTIN</td><td>80B</td><td>RVUE</td><td></td></tr><tr><td>~ 2250</td><td>1 MARTIN</td><td>80C</td><td>RVUE</td><td></td></tr><tr><td>~ 2500</td><td>2 CARTER</td><td>78B</td><td>CNTR 0</td><td>0.7-2.4 p̄p → K⁻K⁺</td></tr><tr><td>~ 2480</td><td>3 CARTER</td><td>77</td><td>CNTR 0</td><td>0.7-2.4 p̄p → ππ</td></tr></tbody></table>

$\bar{S}$-CHANNEL $\bar{N}N$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>2300 ± 45</td><td>4 ANISOVICH</td><td>02</td><td>SPEC</td><td>0.6-1.9 p̄p → ωπ°, ωηπ°, π⁺π⁻</td></tr><tr><td>2295 ± 30</td><td>ANISOVICH</td><td>00J</td><td>SPEC</td><td></td></tr><tr><td>~ 2380</td><td>5 CUTTS</td><td>78B</td><td>CNTR</td><td>0.97-3 p̄p → N̄N</td></tr><tr><td>2345 ± 15</td><td>5,6 COUPLAND</td><td>77</td><td>CNTR 0</td><td>0.7-2.4 p̄p → p̄p</td></tr><tr><td>2359 ± 2</td><td>5,7 ALSPECTOR</td><td>73</td><td>CNTR</td><td>p̄p S channel</td></tr><tr><td>2350 ± 10</td><td>8 ABRAMS</td><td>70</td><td>CNTR</td><td>S channel N̄N</td></tr><tr><td>2360 ± 25</td><td>9 OH</td><td>70B</td><td>HDBC -0</td><td>p̄(pn), K⁺K²π</td></tr></tbody></table>

$\pi^{-}p \rightarrow K^{+}K^{-}n$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>2307 ± 6</td><td>ALPER</td><td>80</td><td>CNTR 0</td><td>62 π⁻ p → K⁺K⁻n</td></tr><tr><td>1 I(J<sup>P</sup>) = 1(5<sup>-</sup>)</td><td></td><td></td><td></td><td>from simultaneous analysis of p̄p → π⁻π⁺ and π°π°.</td></tr></tbody></table>

²I = 0(1); J<sup>P</sup> = 5⁻ from Barrelet-zero analysis.

³I(J<sup>P</sup>) = 1(5⁻) from amplitude analysis.

⁴ From the combined analysis of ANISOVICH 00J, ANISOVICH 01D, ANISOVICH 01E, and ANISOVICH 02.

⁵ Ispoons 0 and 1 not separated.

⁶ From a fit to the total elastic cross section.

⁷ Referred to as U or U region by ALSPECTOR 73.

⁸ For I = 1 N̄N.

⁹ No evidence for this bump seen in the p̄p data of CHAPMAN 71B. Narrow state not confirmed by OH 73 with more data.

$\rho_5(2350)$ WIDTH

$\pi^{-}p \rightarrow \omega\pi^{0}n$

<table><tr><td>VALUE (MeV)</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr><tr><td>400 ± 100</td><td>ALDE</td><td>95</td><td>GAM2</td></tr></table>

$\bar{p}p \rightarrow \pi\pi \text{ or } \bar{K}K$

<table><tr><td>VALUE (MeV)</td><td>DOCUMENT ID</td><td>TECN</td><td>CHG</td><td>COMMENT</td></tr><tr><td>~ 169</td><td>HASAN</td><td>94</td><td>RVUE</td><td>p̄p → ππ</td></tr><tr><td>~ 250</td><td>10 MARTIN</td><td>80B</td><td>RVUE</td><td></td></tr><tr><td>~ 300</td><td>10 MARTIN</td><td>80C</td><td>RVUE</td><td></td></tr><tr><td>~ 150</td><td>11 CARTER</td><td>78B</td><td>CNTR 0</td><td>0.7-2.4 p̄p → K⁻K⁺</td></tr><tr><td>~ 210</td><td>12 CARTER</td><td>77</td><td>CNTR 0</td><td>0.7-2.4 p̄p → ππ</td></tr></table>

$\bar{S}$-CHANNEL $\bar{N}N$

<table><tr><td>VALUE (MeV)</td><td>DOCUMENT ID</td><td>TECN</td><td>CHG</td><td>COMMENT</td></tr><tr><td>260 ± 75</td><td>13 ANISOVICH</td><td>02</td><td>SPEC</td><td>0.6-1.9 p̄p → ωπ°, ωηπ°, π⁺π⁻</td></tr><tr><td>235<sup>+</sup><sub>-65</sub></td><td>ANISOVICH</td><td>00J</td><td>SPEC</td><td></td></tr><tr><td>135<sup>+150</sup><sub>-65</sub></td><td>14,15 COUPLAND</td><td>77</td><td>CNTR 0</td><td>0.7-2.4 p̄p → p̄p</td></tr><tr><td>165<sup>+</sup><sub>-18</sub></td><td>15 ALSPECTOR</td><td>73</td><td>CNTR</td><td>p̄p S channel</td></tr><tr><td>&lt; 60</td><td>16 OH</td><td>70B</td><td>HDBC -0</td><td>p̄(pn), K⁺K²π</td></tr><tr><td>~ 140</td><td>ABRAMS</td><td>67C</td><td>CNTR</td><td>S channel p̄N</td></tr></table>

$\pi^{-}p \rightarrow K^{+}K^{-}n$

<table><tr><td>VALUE (MeV)</td><td>DOCUMENT ID</td><td>TECN</td><td>CHG</td><td>COMMENT</td></tr><tr><td>245 ± 20</td><td>ALPER</td><td>80</td><td>CNTR 0</td><td>62 π⁻ p → K⁺K⁻n</td></tr></table>

¹⁰I(J<sup>P</sup>) = 1(5⁻) from simultaneous analysis of p̄p → π⁻π⁺ and π°π°.

¹¹I = 0(1); J<sup>P</sup> = 5⁻ from Barrelet-zero analysis.

¹²I(J<sup>P</sup>) = 1(5⁻) from amplitude analysis.

¹³ From the combined analysis of ANISOVICH 00J, ANISOVICH 01D, ANISOVICH 01E, and ANISOVICH 02.

¹⁴ From a fit to the total elastic cross section.

¹⁵ Ispoons 0 and 1 not separated.

¹⁶ No evidence for this bump seen in the p̄p data of CHAPMAN 71B. Narrow state not confirmed by OH 73 with more data.

$\rho_5(2350)$ REFERENCES

<table><tr><td>ANISOVICH</td><td>02</td><td>PL B542 8</td><td>A.V. Anisovich et al.</td></tr><tr><td>ANISOVICH</td><td>01D</td><td>PL B508 6</td><td>A.V. Anisovich et al.</td></tr><tr><td>ANISOVICH</td><td>01E</td><td>PL B513 281</td><td>A.V. Anisovich et al.</td></tr><tr><td>ANISOVICH</td><td>00J</td><td>PL B491 47</td><td>A.V. Anisovich et al. (RAL, LOQM, PNPI+)</td></tr><tr><td>ALDE</td><td>95</td><td>ZPHY C66 379</td><td>(GAMS Collab.) JP (LOQM)</td></tr><tr><td>HASAN</td><td>94</td><td>PL B304 215</td><td>A. Hasan, D.V. Bugg (LOQM)</td></tr><tr><td>ALPER</td><td>80</td><td>PL 94B 422</td><td>B. Alper et al. (AMST, CERN, CRAC, MPIM+)</td></tr><tr><td>MARTIN</td><td>80B</td><td>NP B176 355</td><td>B.R. Martin, D. Morgan (LOUC, RHEL) JP</td></tr><tr><td>MARTIN</td><td>80C</td><td>NP B169 216</td><td>A.D. Martin, M.R. Pennington (DURH) JP</td></tr><tr><td>CARTER</td><td>78B</td><td>NP B141 467</td><td>(LOQM)</td></tr><tr><td>CUTTS</td><td>78B</td><td>PR D17 16</td><td>(STON, WISC)</td></tr><tr><td>CARTER</td><td>77</td><td>PL 67B 117</td><td>(LOQM, RHEL) JP</td></tr><tr><td>COUPLAND</td><td>77</td><td>PL 71B 460</td><td>(LOQM, RHEL)</td></tr><tr><td>ALSPECTOR</td><td>73</td><td>PL 30 511</td><td>(RUTG, UPNJ)</td></tr><tr><td>OH</td><td>73</td><td>NP B51 57</td><td>(MSU)</td></tr><tr><td>CHAPMAN</td><td>71B</td><td>PR D4 1275</td><td>(MICH)</td></tr><tr><td>ABRAMS</td><td>70</td><td>PR D1 1917</td><td>(BNL)</td></tr><tr><td>OH</td><td>70B</td><td>PL 24 1257</td><td>(MSU)</td></tr><tr><td>ABRAMS</td><td>67C</td><td>PL 18 1209</td><td>(BNL)</td></tr></table>

$X(2370)$

$I^G(J^{PC}) = ??(???)$

OMITTED FROM SUMMARY TABLE

$X(2370)$ MASS

<table><thead><tr><th>VALUE (MeV)</th><th>EVENTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2357 ± 17</td><td>OUR AVERAGE</td><td></td><td></td><td>Error includes scale factor of 2.7.</td></tr><tr><td>2341.6 ± 6.5 ± 5.7</td><td>1 ABLIKIM</td><td>20Q</td><td>BES3</td><td>J/ψ → γK̄K̄η'</td></tr><tr><td>2376.3 ± 8.7<sup>+3.2</sup><sub>-4.3</sub></td><td>ABLIKIM</td><td>11C</td><td>BES3</td><td>J/ψ → γπ⁺π⁻η'</td></tr></tbody></table>

¹ The state observed by ABLIKIM 11c at 2120 MeV is not observed with 90% CL upper limit of 1.49 × 10⁻⁵ for J/ψ → γX(2120) → γK⁺K⁻η' and 6.38 × 10⁻⁶ for K°S K°S η'.
X(2370) WIDTH

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>114 + 12 / -10</strong> OUR AVERAGE</td><td></td><td></td><td></td></tr><tr><td>117 ± 10 ± 8</td><td>1 ABLIKIM</td><td>20Q BES3</td><td>J/ψ → γK<sup>-</sup>Kη'</td></tr><tr><td>83 ± 17 + 44 / - 6</td><td>ABLIKIM</td><td>11c BES3</td><td>J/ψ → γπ<sup>+</sup>π<sup>-</sup>η'</td></tr></tbody></table>

¹ The state observed by ABLIKIM 11c at 2120 MeV is not observed with 90% CL upper limit of 1.49 × 10⁻⁵ for J/ψ → γX(2120) → γK⁺K⁻η' and 6.38 × 10⁻⁶ for K⁰_S K⁰_S η'.

X(2370) DECAY MODES

<table><thead><tr><th></th><th>Mode</th><th>Fraction (Γ<sub>f</sub>/Γ)</th></tr></thead><tbody><tr><td>Γ<sub>1</sub></td><td>K<sup>+</sup> K<sup>-</sup>η'</td><td>seen</td></tr><tr><td>Γ<sub>2</sub></td><td>K<sup>0</sup><sub>S</sub> K<sup>0</sup><sub>S</sub>η'</td><td>seen</td></tr><tr><td>Γ<sub>3</sub></td><td>π<sup>+</sup> π<sup>-</sup>η'</td><td>seen</td></tr><tr><td>Γ<sub>4</sub></td><td>ηηη'</td><td>not seen</td></tr></tbody></table>

X(2370) BRANCHING RATIOS

<table><thead><tr><th>Γ(K<sup>+</sup> K<sup>-</sup>η')/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>VALUE</td><td></td><td></td><td></td></tr><tr><td>seen</td><td>ABLIKIM</td><td>20Q BES3</td><td>J/ψ → γK<sup>+</sup> K<sup>-</sup>η'</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>0</sup><sub>S</sub> K<sup>0</sup><sub>S</sub>η')/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>VALUE</td><td></td><td></td><td></td></tr><tr><td>seen</td><td>ABLIKIM</td><td>20Q BES3</td><td>J/ψ → γK<sup>0</sup><sub>S</sub> K<sup>0</sup><sub>S</sub>η'</td></tr></tbody></table>

<table><thead><tr><th>Γ(π<sup>+</sup> π<sup>-</sup>η')/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>VALUE</td><td></td><td></td><td></td></tr><tr><td>seen</td><td>ABLIKIM</td><td>11c BES3</td><td>J/ψ → γπ<sup>+</sup> π<sup>-</sup>η'</td></tr></tbody></table>

<table><thead><tr><th>Γ(ηηη')/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>VALUE</td><td></td><td></td><td></td></tr><tr><td>not seen</td><td>1 ABLIKIM</td><td>21c BES3</td><td>J/ψ(1S) → γηηη'</td></tr></tbody></table>

X(2370) REFERENCES

<table><tr><td>ABLIKIM</td><td>21C</td><td>PR D103 012009</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>20Q</td><td>EPJ C80 746</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>11C</td><td>PRL 106 072002</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr></table>

$$f_0(2470)$$

$$I^G(J^{PC}) = 0^{+}(0^{++})$$

OMITTED FROM SUMMARY TABLE

Seen by ABLIKIM 22c with a significance of 5.2 σ in a partial-wave analysis of the systems (γX), X → η'η' and (η'X), X → γη' in the decay J/ψ → γη'η'.

f₀(2470) MASS

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2470 ± 4 + 4 / - 6</td><td>1 ABLIKIM</td><td>22c BES3</td><td>J/ψ → γη'η' → 4/5γ2(π<sup>+</sup> π<sup>-</sup>)</td></tr></tbody></table>

¹ From a partial wave analysis of the systems (γX), with X → η'η', and (η'X), with X → γη' in the decay J/ψ → γη'η'. The intermediate resonance X is parametrized by a constant-width, relativistic Breit-Wigner.

f₀(2470) WIDTH

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>75 ± 9 + 11 / - 8</td><td>1 ABLIKIM</td><td>22c BES3</td><td>J/ψ → γη'η' → 4/5γ2(π<sup>+</sup> π<sup>-</sup>)</td></tr></tbody></table>

¹ From a partial wave analysis of the systems (γX), with X → η'η', and (η'X), with X → γη' in the decay J/ψ → γη'η'. The intermediate resonance X is parametrized by a constant-width, relativistic Breit-Wigner.

f₀(2470) DECAY MODES

<table><thead><tr><th></th><th>Mode</th><th>Fraction (Γ<sub>f</sub>/Γ)</th></tr></thead><tbody><tr><td>Γ<sub>1</sub></td><td>η'η'</td><td>seen</td></tr></tbody></table>

<table><thead><tr><th>Γ(η'η')/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>VALUE</td><td></td><td></td><td></td></tr><tr><td>seen</td><td>1 ABLIKIM</td><td>22c BES3</td><td>J/ψ → γη'/η' → 4/5γ2(π<sup>+</sup> π<sup>-</sup>)</td></tr></tbody></table>

¹ From a partial wave analysis of the systems (γX), with X → η'η', and (η'X), with X → γη' in the decay J/ψ → γη'η'. The intermediate resonance X is parametrized by a constant-width, relativistic Breit-Wigner.

f₀(2470) REFERENCES

<table><tr><td>ABLIKIM</td><td>22C PR D105 072002</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr></table>

$$f_6(2510)$$

$$I^G(J^{PC}) = 0^{+}(6^{++})$$

OMITTED FROM SUMMARY TABLE

Needs confirmation.

f₀(2510) MASS

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2470 ± 50 OUR AVERAGE</td><td>Error includes scale factor of 2.1.</td><td></td><td></td></tr><tr><td>2420 ± 30</td><td>ALDE</td><td>98 GAM4</td><td>100 π<sup>-</sup> p → π<sup>0</sup>π<sup>0</sup> n</td></tr><tr><td>2510 ± 30</td><td>BINON</td><td>84B GAM2</td><td>38 π<sup>-</sup> p → n2π<sup>0</sup></td></tr></tbody></table>

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

<table><tr><td>2485 ± 40</td><td>1 ANISOVICH</td><td>00J SPEC</td><td>1.92-2.41 pπ</td></tr></table>

¹ From the combined analysis of ANISOVICH 99c, ANISOVICH 99f, ANISOVICH 99j, ANISOVICH 99k, and ANISOVICH 00b.

f₀(2510) WIDTH

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>260 ± 40 OUR AVERAGE</td><td></td><td></td><td></td></tr><tr><td>270 ± 60</td><td>ALDE</td><td>98 GAM4</td><td>100 π<sup>-</sup> p → π<sup>0</sup>π<sup>0</sup> n</td></tr><tr><td>240 ± 60</td><td>BINON</td><td>84B GAM2</td><td>38 π<sup>-</sup> p → n2π<sup>0</sup></td></tr></tbody></table>

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

<table><tr><td>410 ± 90</td><td>2 ANISOVICH</td><td>00J SPEC</td><td>1.92-2.41 pπ</td></tr></table>

² From the combined analysis of ANISOVICH 99c, ANISOVICH 99f, ANISOVICH 99j, ANISOVICH 99k, and ANISOVICH 00b.

f₀(2510) DECAY MODES

<table><thead><tr><th></th><th>Mode</th><th>Fraction (Γ<sub>f</sub>/Γ)</th></tr></thead><tbody><tr><td>Γ<sub>1</sub></td><td>ππ</td><td>(6.0 ± 1.0) %</td></tr></tbody></table>

f₀(2510) BRANCHING RATIOS

<table><thead><tr><th>Γ(ππ)/Γ<sub>total</sub></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.06 ± 0.01</td><td>3 BINON</td><td>83c GAM2</td><td>38 π<sup>-</sup> p → n4γ</td></tr></tbody></table>

³ Assuming one pion exchange and using data of BOLOTOV 74.

f₀(2510) REFERENCES

<table><tr><td>ANISOVICH</td><td>00B NP A662 319</td><td>A.V. Anisovich et al.</td><td>(RAL, LOQM, PNPI+)</td></tr><tr><td>ANISOVICH</td><td>00J PL B491 47</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>ANISOVICH</td><td>99C PL B452 173</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>ANISOVICH</td><td>99F NP A651 253</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>ANISOVICH</td><td>99J PL B471 271</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>ANISOVICH</td><td>99K PL B468 309</td><td>A.V. Anisovich et al.</td><td></td></tr><tr><td>ALDE</td><td>98 EPJ A3 361</td><td>D. Alde et al.</td><td>(GAM4 Collab.)</td></tr><tr><td>Also</td><td>PAN 62 405</td><td>D. Alde et al.</td><td>(GAMS Collab.)</td></tr><tr><td></td><td>Translated from YAF 62 446.</td><td></td><td></td></tr><tr><td>BINON</td><td>84B LNC 39 41</td><td>F.G. Binon et al.</td><td>(SERP, BELG, LAPP) JP</td></tr><tr><td>BINON</td><td>83C SJNP 38 723</td><td>F.G. Binon et al.</td><td>(SERP, BRUX+)</td></tr></table>

<table><tr><td>BOLOTOV</td><td>74 PL 52B 489</td><td>V.N. Bolotov et al.</td><td>(SERP)</td></tr></table>
STRANGE MESONS
(S = ±1, C = B = 0)

$K^{+} = u\bar{s}, K^{0} = d\bar{s}, \bar{K}^{0} = \bar{d}s, K^{-} = \bar{u}s, \text{ similarly for } K^{*\pm}\text{s}$

$K^{\pm}$

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

CHARGED KAON MASS

Revised 1994 by T.G. Trippe (LBNL).

The average of the six charged kaon mass measurements which we use in the Particle Listings is

$$m_{K^{\pm}} = 493.677 \pm 0.013 \text{ MeV (S = 2.4)}, \quad (1)$$

where the error has been increased by the scale factor S. The large scale factor indicates a serious disagreement between different input data. The average before scaling the error is

$$\begin{gathered} m_{K^{\pm}} = 493.677 \pm 0.005 \text{ MeV,} \\ \chi^2 = 22.9 \text{ for 5 D.F., Prob. } = 0.04\%, \quad (2) \end{gathered}$$

where the high $\chi^2$ and correspondingly low $\chi^2$ probability further quantify the disagreement.

The main disagreement is between the two most recent and precise results,

$$\begin{gathered} m_{K^{\pm}} = 493.696 \pm 0.007 \text{ MeV} \qquad \text{DENISOV 91} \\ m_{K^{\pm}} = 493.636 \pm 0.011 \text{ MeV (S = 1.5)} \qquad \text{GALL 88} \\ \text{Average} = 493.679 \pm 0.006 \text{ MeV} \\ \chi^2 = 21.2 \text{ for 1 D.F., Prob. } = 0.0004\%, \quad (3) \end{gathered}$$

both of which are measurements of x-ray energies from kaonic atoms. Comparing the average in Eq. (3) with the overall average in Eq. (2), it is clear that DENISOV 91 [1] and GALL 88 [2] dominate the overall average, and that their disagreement is responsible for most of the high $\chi^2$.

The GALL 88 measurement was made using four different kaonic atom transitions, $K^{-} \text{Pb} (9 \to 8)$, $K^{-} \text{Pb} (11 \to 10)$, $K^{-} \text{W} (9 \to 8)$, and $K^{-} \text{W} (11 \to 10)$. The $m_{K^{\pm}}$ values they obtain from each of these transitions is shown in the Particle Listings and in Fig. 1. Their $K^{-} \text{Pb} (9 \to 8)$ $m_{K^{\pm}}$ is below and somewhat inconsistent with their other three transitions. The average of their four measurements is

$$\begin{gathered} m_{K^{\pm}} = 493.636 \pm 0.007, \\ \chi^2 = 7.0 \text{ for 3 D.F., Prob. } = 7.2\%. \quad (4) \end{gathered}$$

This is a low but acceptable $\chi^2$ probability so, to be conservative, GALL 88 scaled up the error on their average by S=1.5 to obtain their published error ±0.011 shown in Eq. (3) above and used in the Particle Listings average.

<figure><img src="image_506.png" /><figcaption>Figure 1: Ideogram of $m_{K^{\pm}}$ mass measurements. GALL 88 and CHENG 75 measurements are shown separately for each transition they measured.</figcaption></figure>

The ideogram in Fig. 1 shows that the DENISOV 91 measurement and the GALL 88 $K^{-} \text{Pb} (9 \to 8)$ measurement yield two well-separated peaks. One might suspect the GALL 88 $K^{-} \text{Pb} (9 \to 8)$ measurement since it is responsible both for the internal inconsistency in the GALL 88 measurements and the disagreement with DENISOV 91.

To see if the disagreement could result from a systematic problem with the $K^{-} \text{Pb} (9 \to 8)$ transition, we have separated the CHENG 75 [3] data, which also used $K^{-} \text{Pb}$, into its separate transitions. Figure 1 shows that the CHENG 75 and GALL 88 $K^{-} \text{Pb} (9 \to 8)$ values are consistent, suggesting the possibility of a common effect such as contaminant nuclear $\gamma$ rays near the $K^{-} \text{Pb} (9 \to 8)$ transition energy, although the CHENG 75 errors are too large to make a strong conclusion. The average of all 13 measurements has a $\chi^2$ of 52.6 as shown in Fig. 1 and the first line of Table 1, yielding an unacceptable $\chi^2$ probability of 0.00005%. The second line of Table 1 excludes both the GALL 88 and CHENG 75 measurements of the $K^{-} \text{Pb} (9 \to 8)$ transition and yields a $\chi^2$ probability of 43%. The third [fourth] line of Table 1 excludes only the GALL 88 $K^{-} \text{Pb} (9 \to 8)$ [DENISOV 91] measurement and yields a $\chi^2$ probability of 20% [8.6%]. Table 1 shows that removing both measurements of the $K^{-} \text{Pb} (9 \to 8)$ transition produces the most consistent set of data, but that excluding only the GALL 88 $K^{-} \text{Pb} (9 \to 8)$ transition or DENISOV 91 also produces acceptable probabilities.
<table><caption>**Table 1:** $m_{K^{\pm}}$ averages for some combinations of Fig. 1 data.</caption><thead><tr><th>m<sub>K&plusmn;</sub> (MeV)</th><th>&chi;<sup>2</sup></th><th>D.F.</th><th>Prob. (%)</th><th>Measurements used</th></tr></thead><tbody><tr><td>493.664 &plusmn; 0.004</td><td>52.6</td><td>12</td><td>0.00005</td><td>all 13 measurements</td></tr><tr><td>493.690 &plusmn; 0.006</td><td>10.1</td><td>10</td><td>43</td><td>no K<sup>-</sup>Pb(9&rarr;8)</td></tr><tr><td>493.687 &plusmn; 0.006</td><td>14.6</td><td>11</td><td>20</td><td>no GALL 88 K<sup>-</sup>Pb(9&rarr;8)</td></tr><tr><td>493.642 &plusmn; 0.006</td><td>17.8</td><td>11</td><td>8.6</td><td>no DENISOV 91</td></tr></tbody></table>

Yu.M. Ivanov, representing DENISOV 91, has estimated corrections needed for the older experiments because of improved $^{192}$Ir and $^{198}$Au calibration γ-ray energies. He estimates that CHENG 75 and BACKENSTOSS 73 [4] $m_{K^{\pm}}$ values could be raised by about 15 keV and 22 keV, respectively. With these estimated corrections, Table 1 becomes Table 2. The last line of Table 2 shows that if such corrections are assumed, then GALL 88 K$^-$ Pb (9 → 8) is inconsistent with the rest of the data even when DENISOV 91 is excluded. Yu.M. Ivanov warns that these are rough estimates. Accordingly, we do not use Table 2 to reject the GALL 88 K$^-$ Pb (9 → 8) transition, but we note that a future reanalysis of the CHENG 75 data could be useful because it might provide supporting evidence for such a rejection.

<table><caption>**Table 2:** $m_{K^{\pm}}$ averages for some combinations of Fig. 1 data after raising CHENG 75 and BACKENSTOSS 73 values by 0.015 and 0.022 MeV respectively.</caption><thead><tr><th>m<sub>K&plusmn;</sub> (MeV)</th><th>&chi;<sup>2</sup></th><th>D.F.</th><th>Prob. (%)</th><th>Measurements used</th></tr></thead><tbody><tr><td>493.666 &plusmn; 0.004</td><td>53.9</td><td>12</td><td>0.00003</td><td>all 13 measurements</td></tr><tr><td>493.693 &plusmn; 0.006</td><td>9.0</td><td>10</td><td>53</td><td>no K<sup>-</sup>Pb(9&rarr;8)</td></tr><tr><td>493.690 &plusmn; 0.006</td><td>11.5</td><td>11</td><td>40</td><td>no GALL 88 K<sup>-</sup>Pb(9&rarr;8)</td></tr><tr><td>493.645 &plusmn; 0.006</td><td>23.0</td><td>11</td><td>1.8</td><td>no DENISOV 91</td></tr></tbody></table>

The GALL 88 measurement uses a Ge semiconductor spectrometer which has a resolution of about 1 keV, so they run the risk of some contaminant nuclear γ rays. Studies of γ rays following stopped π$^-$ and Σ$^-$ absorption in nuclei (unpublished) do not show any evidence for contaminants according to GALL 88 spokesperson, B.L. Roberts. The DENISOV 91 measurement uses a crystal diffraction spectrometer with a resolution of 6.3 eV for radiation at 22.1 keV to measure the 4f-3d transition in K$^-$ $^{12}$C. The high resolution and the light nucleus reduce the probability for overlap by contaminant γ rays, compared with the measurement of GALL 88. The DENISOV 91 measurement is supported by their high-precision measurement of the 4d-2p transition energy in π$^-$ $^{12}$C, which is good agreement with the calculated energy.

While we suspect that the GALL 88 K$^-$ Pb (9 → 8) measurements could be the problem, we are unable to find clear grounds for rejecting it. Therefore, we retain their measurement in the average and accept the large scale factor until further information can be obtained from new measurements and/or from reanalysis of GALL 88 and CHENG 75 data.

We thank B.L. Roberts (Boston Univ.) and Yu.M. Ivanov (Petersburg Nuclear Physics Inst.) for their extensive help in understanding this problem.

## References

1. A.S. Denisov, et al. [DENISOV 91], Sov. Phys. JETP Lett. **54**, 558 (1991).

2. K.P. Gall, et al. [GALL 88], Phys. Rev. Lett. **60**, 186 (1988).

3. S.C. Cheng, et al. [CHENG 75], Nucl. Phys. **A254**, 381 (1975).

4. G. Backenstoss, et al. [BACKENSTOSS 73], Phys. Lett. **43B**, 431 (1973).

### K$^{\pm}$ MASS

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>493.677&plusmn;0.015</strong> OUR FIT</td><td>Error includes scale factor of 2.8.</td><td></td><td></td><td></td></tr><tr><td><strong>493.677&plusmn;0.013</strong> OUR AVERAGE</td><td>Error includes scale factor of 2.4.</td><td></td><td></td><td>See the ideogram below.</td></tr><tr><td>493.696&plusmn;0.007</td><td><sup>1</sup> DENISOV</td><td>91</td><td>CNTR</td><td>K<sup>-</sup>Pb (9&rarr;8)</td></tr><tr><td>493.636&plusmn;0.011</td><td><sup>2</sup> GALL</td><td>88</td><td>CNTR</td><td>K<sup>-</sup>Pb (11&rarr;10)</td></tr><tr><td>493.640&plusmn;0.054</td><td>LUM</td><td>81</td><td>CNTR</td><td>K<sup>-</sup>W (9&rarr;8)</td></tr><tr><td>493.670&plusmn;0.029</td><td>BARKOV</td><td>79</td><td>EMUL &plusmn;</td><td>e<sup>+</sup>e<sup>-</sup> &rarr; K<sup>+</sup>K<sup>-</sup></td></tr><tr><td>493.657&plusmn;0.020</td><td><sup>2</sup> CHENG</td><td>75</td><td>CNTR</td><td>K<sup>-</sup>Pb (11&rarr;10)</td></tr><tr><td>493.691&plusmn;0.040</td><td>BACKENSTO...</td><td>73</td><td>CNTR</td><td>K<sup>-</sup>Pb (9&rarr;8)</td></tr><tr><td>&bull; &bull; &bull;</td><td colspan="4">We do not use the following data for averages, fits, limits, etc. &bull; &bull; &bull;</td></tr><tr><td>493.631&plusmn;0.007</td><td>GALL</td><td>88</td><td>CNTR</td><td>K<sup>-</sup>Pb (9&rarr;8)</td></tr><tr><td>493.675&plusmn;0.026</td><td>GALL</td><td>88</td><td>CNTR</td><td>K<sup>-</sup>Pb (11&rarr;10)</td></tr><tr><td>493.709&plusmn;0.073</td><td>GALL</td><td>88</td><td>CNTR</td><td>K<sup>-</sup>W (9&rarr;8)</td></tr><tr><td>493.806&plusmn;0.095</td><td>GALL</td><td>88</td><td>CNTR</td><td>K<sup>-</sup>W (11&rarr;10)</td></tr><tr><td>493.640&plusmn;0.022&plusmn;0.008</td><td><sup>3</sup> CHENG</td><td>75</td><td>CNTR</td><td>K<sup>-</sup>Pb (9&rarr;8)</td></tr><tr><td>493.658&plusmn;0.019&plusmn;0.012</td><td><sup>3</sup> CHENG</td><td>75</td><td>CNTR</td><td>K<sup>-</sup>Pb (10&rarr;9)</td></tr><tr><td>493.638&plusmn;0.035&plusmn;0.016</td><td><sup>3</sup> CHENG</td><td>75</td><td>CNTR</td><td>K<sup>-</sup>Pb (11&rarr;10)</td></tr><tr><td>493.753&plusmn;0.042&plusmn;0.021</td><td><sup>3</sup> CHENG</td><td>75</td><td>CNTR</td><td>K<sup>-</sup>Pb (12&rarr;11)</td></tr><tr><td>493.742&plusmn;0.081&plusmn;0.027</td><td><sup>3</sup> CHENG</td><td>75</td><td>CNTR</td><td>K<sup>-</sup>Pb (13&rarr;12)</td></tr></tbody></table>

WEIGHTED AVERAGE
493.677&plusmn;0.013 (Error scaled by 2.4)

<figure><img src="image_507.png" /></figure>

### m<sub>K&plusmn;</sub> - m<sub>K&minus;</sub>

Test of CPT.

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>-0.032&plusmn;0.090</td><td>1.5M</td><td><sup>1</sup> FORD</td><td>72</td><td>ASPK &plusmn;</td></tr></tbody></table>

<footnote n="1">¹Error increased from 0.0059 based on the error analysis in IVANOV 92.</footnote>

<footnote n="2">²This value is the authors' combination of all of the separate transitions listed for this paper.</footnote>

<footnote n="3">³The CHENG 75 values for separate transitions were calculated from their Table 7 transition energies. The first error includes a 20% systematic error in the noncircular contaminant shift. The second error is due to a ±5 eV uncertainty in the theoretical transition energies.</footnote>

<footnote n="1">¹FORD 72 uses $m_{\pi^+} - m_{\pi^-} = +28 \pm 70$ keV.</footnote>
## $K^{\pm}$ MEAN LIFE

<table><thead><tr><th>VALUE (10<sup>-8</sup> s)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="6"><strong>1.2380 &plusmn; 0.0020 OUR FIT</strong> Error includes scale factor of 1.8.</td></tr><tr><td colspan="6"><strong>1.2379 &plusmn; 0.0021 OUR AVERAGE</strong> Error includes scale factor of 1.9. See the ideogram below.</td></tr><tr><td>1.2347 &plusmn; 0.0030</td><td>15M</td><td>1 AMBROSINO</td><td>08</td><td>KLOE &plusmn; &phi; &rarr; K<sup>+</sup> K<sup>-</sup></td><td></td></tr><tr><td>1.2451 &plusmn; 0.0030</td><td>250k</td><td>KOPTEV</td><td>95</td><td>CNTR</td><td>K at rest, U target</td></tr><tr><td>1.2368 &plusmn; 0.0041</td><td>150k</td><td>KOPTEV</td><td>95</td><td>CNTR</td><td>K at rest, Cu target</td></tr><tr><td>1.2380 &plusmn; 0.0016</td><td>3M</td><td>OTT</td><td>71</td><td>CNTR +</td><td>K at rest</td></tr><tr><td>1.2272 &plusmn; 0.0036</td><td></td><td>LOBKOWICZ</td><td>69</td><td>CNTR +</td><td>K in flight</td></tr><tr><td>1.2443 &plusmn; 0.0038</td><td></td><td>FITCH</td><td>65B</td><td>CNTR +</td><td>K at rest</td></tr></tbody></table>

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

<table><tr><td>1.2415 &plusmn; 0.0024</td><td>400k</td><td>2 KOPTEV</td><td>95</td><td>CNTR</td><td>K at rest</td></tr><tr><td>1.221 &plusmn; 0.011</td><td></td><td>FORD</td><td>67</td><td>CNTR &plusmn;</td><td></td></tr><tr><td>1.231 &plusmn; 0.011</td><td></td><td>BOYARSKI</td><td>62</td><td>CNTR +</td><td></td></tr></table>

¹Result obtained by averaging the decay length and decay time analyses taking correlations into account.

²KOPTEV 95 report this weighted average of their U-target and Cu-target results, where they have weighted by $1/\sigma$ rather than $1/\sigma^2$.

<figure><img src="image_508.png" /><figcaption>### WEIGHTED AVERAGE
1.2379±0.0021 (Error scaled by 1.9)</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.

$$ (\tau_{K^+} - \tau_{K^-}) / \tau_{\text{average}} $$

This quantity is a measure of CPT invariance in weak interactions.

<table><thead><tr><th>VALUE (%)</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.10 &plusmn; 0.09 OUR AVERAGE</strong></td><td colspan="2">Error includes scale factor of 1.2.</td></tr><tr><td>-0.4 &plusmn; 0.4</td><td>AMBROSINO</td><td>08 KLOE</td></tr><tr><td>0.090 &plusmn; 0.078</td><td>LOBKOWICZ</td><td>69 CNTR</td></tr><tr><td>0.47 &plusmn; 0.30</td><td>FORD</td><td>67 CNTR</td></tr></tbody></table>

See the related review(s):

Rare Kaon Decays

## $K^{\pm}$ DECAY MODES

$K^{\pm}$ modes are charge conjugates of the modes below.

<table><thead><tr><th>Mode</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th></tr></thead><tbody><tr><td colspan="3"><strong>Leptonic and semileptonic modes</strong></td></tr><tr><td>Γ<sub>1</sub></td><td>e<sup>+</sup>ν<sub>e</sub> (1.582 ± 0.007) × 10<sup>-5</sup></td><td></td></tr><tr><td>Γ<sub>2</sub></td><td>μ<sup>+</sup>ν<sub>μ</sub> (63.56 ± 0.11) %</td><td>S=1.2</td></tr><tr><td>Γ<sub>3</sub></td><td>π<sup>0</sup> e<sup>+</sup>ν<sub>e</sub> (5.07 ± 0.04) %</td><td>S=2.1</td></tr><tr><td colspan="3">Called K<sub>e3</sub><sup>+</sup>.</td></tr><tr><td>Γ<sub>4</sub></td><td>π<sup>0</sup> μ<sup>+</sup>ν<sub>μ</sub> (3.352 ± 0.034) %</td><td>S=1.9</td></tr><tr><td colspan="3">Called K<sub>μ3</sub><sup>+</sup>.</td></tr><tr><td>Γ<sub>5</sub></td><td>π<sup>0</sup> π<sup>0</sup> e<sup>+</sup>ν<sub>e</sub> (2.55 ± 0.04) × 10<sup>-5</sup></td><td>S=1.1</td></tr><tr><td>Γ<sub>6</sub></td><td>π<sup>+</sup> π<sup>-</sup> e<sup>+</sup>ν<sub>e</sub> (4.247 ± 0.024) × 10<sup>-5</sup></td><td></td></tr><tr><td>Γ<sub>7</sub></td><td>π<sup>+</sup> π<sup>-</sup> μ<sup>+</sup>ν<sub>μ</sub> (1.4 ± 0.9) × 10<sup>-5</sup></td><td></td></tr><tr><td>Γ<sub>8</sub></td><td>π<sup>0</sup> π<sup>0</sup> π<sup>0</sup> e<sup>+</sup>ν<sub>e</sub> &lt; 3.5 × 10<sup>-6</sup></td><td>CL=90%</td></tr><tr><td colspan="3"><strong>Hadronic modes</strong></td></tr><tr><td>Γ<sub>9</sub></td><td>π<sup>+</sup> π<sup>0</sup> (20.67 ± 0.08) %</td><td>S=1.2</td></tr><tr><td>Γ<sub>10</sub></td><td>π<sup>+</sup> π<sup>0</sup> π<sup>0</sup> (1.760 ± 0.023) %</td><td>S=1.1</td></tr><tr><td>Γ<sub>11</sub></td><td>π<sup>+</sup> π<sup>+</sup> π<sup>-</sup> (5.583 ± 0.024) %</td><td></td></tr></tbody></table>

## Leptonic and semileptonic modes with photons

<table><tr><td>Γ<sub>12</sub></td><td>μ<sup>+</sup>ν<sub>μ</sub>γ (a,b) (6.2 ± 0.8) × 10<sup>-3</sup></td><td></td></tr><tr><td>Γ<sub>13</sub></td><td>μ<sup>+</sup>ν<sub>μ</sub>γ (SD<sup>+</sup>) (c,d) (1.33 ± 0.22) × 10<sup>-5</sup></td><td></td></tr><tr><td>Γ<sub>14</sub></td><td>μ<sup>+</sup>ν<sub>μ</sub>γ (SD<sup>+</sup>INT) (c,d) &lt; 2.7 × 10<sup>-5</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>15</sub></td><td>μ<sup>+</sup>ν<sub>μ</sub>γ (SD<sup>-</sup> + SD<sup>-INT</sup>) (c,d) &lt; 2.6 × 10<sup>-4</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>16</sub></td><td>e<sup>+</sup>ν<sub>e</sub>γ (1.03 ± 0.14) × 10<sup>-5</sup></td><td></td></tr><tr><td>Γ<sub>17</sub></td><td>π<sup>0</sup> e<sup>+</sup>ν<sub>e</sub>γ (a,b) (2.698 ± 0.033) × 10<sup>-4</sup></td><td></td></tr><tr><td>Γ<sub>18</sub></td><td>π<sup>0</sup> e<sup>+</sup>ν<sub>e</sub>γ (SD) (c,d) &lt; 5.3 × 10<sup>-5</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>19</sub></td><td>π<sup>0</sup> μ<sup>+</sup>ν<sub>μ</sub>γ (a,b) (1.25 ± 0.25) × 10<sup>-5</sup></td><td></td></tr><tr><td>Γ<sub>20</sub></td><td>π<sup>0</sup> π<sup>0</sup> e<sup>+</sup>ν<sub>e</sub>γ &lt; 5 × 10<sup>-6</sup></td><td>CL=90%</td></tr></table>

## Hadronic modes with photons or $\ell\bar{\ell}$ pairs

<table><tr><td>Γ<sub>21</sub></td><td>π<sup>+</sup> π<sup>0</sup>γ (INT) (–4.2 ± 0.9) × 10<sup>-6</sup></td><td></td></tr><tr><td>Γ<sub>22</sub></td><td>π<sup>+</sup> π<sup>0</sup>γ (DE) (a,e) (6.0 ± 0.4) × 10<sup>-6</sup></td><td></td></tr><tr><td>Γ<sub>23</sub></td><td>π<sup>+</sup> π<sup>0</sup> e<sup>+</sup> e<sup>-</sup> (a,e) (4.24 ± 0.14) × 10<sup>-6</sup></td><td></td></tr><tr><td>Γ<sub>24</sub></td><td>π<sup>+</sup> π<sup>0</sup>γ (a,b) (7.6 ± 6.0<sub>-3.0</sub>) × 10<sup>-6</sup></td><td></td></tr><tr><td>Γ<sub>25</sub></td><td>π<sup>+</sup> π<sup>+</sup> π<sup>-</sup>γ (a,b) (7.1 ± 0.5) × 10<sup>-6</sup></td><td></td></tr><tr><td>Γ<sub>26</sub></td><td>π<sup>+</sup>γγ (a) (1.01 ± 0.06) × 10<sup>-6</sup></td><td></td></tr><tr><td>Γ<sub>27</sub></td><td>π<sup>+</sup>3γ (a) &lt; 1.0 × 10<sup>-4</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>28</sub></td><td>π<sup>+</sup> e<sup>+</sup> e<sup>-</sup>γ (a) (1.19 ± 0.13) × 10<sup>-8</sup></td><td></td></tr></table>

## Leptonic modes with $\ell\bar{\ell}$ pairs

<table><tr><td>Γ<sub>29</sub></td><td>e<sup>+</sup>ν<sub>e</sub>ν<sub>ν</sub> &lt; 6 × 10<sup>-5</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>30</sub></td><td>μ<sup>+</sup>ν<sub>μ</sub>ν<sub>ν</sub> &lt; 1.0 × 10<sup>-6</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>31</sub></td><td>e<sup>+</sup>ν<sub>e</sub> e<sup>+</sup> e<sup>-</sup> (2.48 ± 0.20) × 10<sup>-8</sup></td><td></td></tr><tr><td>Γ<sub>32</sub></td><td>μ<sup>+</sup>ν<sub>μ</sub> e<sup>+</sup> e<sup>-</sup> (7.06 ± 0.31) × 10<sup>-8</sup></td><td></td></tr><tr><td>Γ<sub>33</sub></td><td>e<sup>+</sup>ν<sub>e</sub> μ<sup>+</sup> μ<sup>-</sup> (1.7 ± 0.5) × 10<sup>-8</sup></td><td></td></tr><tr><td>Γ<sub>34</sub></td><td>μ<sup>+</sup>ν<sub>μ</sub> μ<sup>+</sup> μ<sup>-</sup> &lt; 4.1 × 10<sup>-7</sup></td><td>CL=90%</td></tr></table>

## Lepton family number (LF), Lepton number (L), $\Delta S = \Delta Q (SQ)$ violating modes, or $\Delta S = 1$ weak neutral current (SI) modes

<table><tr><td>Γ<sub>35</sub></td><td>π<sup>+</sup> π<sup>+</sup> e<sup>-</sup>ν<sub>e</sub> SQ &lt; 1.3 × 10<sup>-8</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>36</sub></td><td>π<sup>+</sup> π<sup>+</sup> μ<sup>-</sup>ν<sub>μ</sub> SQ &lt; 3.0 × 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>37</sub></td><td>π<sup>+</sup> e<sup>+</sup> e<sup>-</sup> S1 (3.00 ± 0.09) × 10<sup>-7</sup></td><td></td></tr><tr><td>Γ<sub>38</sub></td><td>π<sup>+</sup> μ<sup>+</sup> μ<sup>-</sup> S1 (9.17 ± 0.14) × 10<sup>-8</sup></td><td>S=1.8</td></tr><tr><td>Γ<sub>39</sub></td><td>π<sup>+</sup> e<sup>+</sup> e<sup>-</sup> e<sup>+</sup> e<sup>-</sup> &lt; 1.4 × 10<sup>-8</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>40</sub></td><td>π<sup>+</sup>ν<sub>ν</sub> S1 (1.14 ± 0.40<sub>-0.33</sub>) × 10<sup>-10</sup></td><td></td></tr><tr><td>Γ<sub>41</sub></td><td>π<sup>+</sup> π<sup>0</sup>ν<sub>ν</sub> S1 &lt; 4.3 × 10<sup>-5</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>42</sub></td><td>μ<sup>-</sup> e<sup>+</sup> e<sup>+</sup> LF &lt; 8.1 × 10<sup>-11</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>43</sub></td><td>μ<sup>+</sup>ν<sub>e</sub> LF [f] &lt; 4 × 10<sup>-3</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>44</sub></td><td>π<sup>+</sup> μ<sup>+</sup> e<sup>-</sup> LF &lt; 1.3 × 10<sup>-11</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>45</sub></td><td>π<sup>+</sup> μ<sup>-</sup> e<sup>+</sup> LF &lt; 6.6 × 10<sup>-11</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>46</sub></td><td>π<sup>-</sup> μ<sup>+</sup> e<sup>+</sup> L &lt; 4.2 × 10<sup>-11</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>47</sub></td><td>π<sup>-</sup> e<sup>+</sup> e<sup>+</sup> L &lt; 5.3 × 10<sup>-11</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>48</sub></td><td>π<sup>-</sup> μ<sup>+</sup> μ<sup>+</sup> L &lt; 4.2 × 10<sup>-11</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>49</sub></td><td>π<sup>-</sup> π<sup>0</sup> e<sup>+</sup> e<sup>+</sup> L &lt; 8.5 × 10<sup>-10</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>50</sub></td><td>μ<sup>+</sup>ν<sub>e</sub> L [f] &lt; 3.3 × 10<sup>-3</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>51</sub></td><td>π<sup>0</sup> e<sup>+</sup>ν<sub>e</sub> L &lt; 3 × 10<sup>-3</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>52</sub></td><td>π<sup>+</sup>γ [g] &lt; 2.3 × 10<sup>-9</sup></td><td>CL=90%</td></tr></table>

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

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

[c] Structure-dependent part.

[d] See the review on "Form Factors for Radiative Pion and Kaon Decays" for definitions and details.

[e] Direct-emission branching fraction.

[f] Derived from an analysis of neutrino-oscillation experiments.

[g] Violates angular-momentum conservation.

## CONSTRAINED FIT INFORMATION

An overall fit to the mean life, a decay rate, and 15 branching ratios uses 35 measurements and one constraint to determine 8 parameters. The overall fit has a $\chi^2 = 53.4$ for 28 degrees of freedom.

The following off-diagonal array elements are the correlation coefficients $\langle\delta p_i; \delta p_j\rangle/(\delta p_i; \delta p_j)$, in percent, from the fit to parameters $p_i$, including the branching fractions, $x_i \equiv \Gamma_i/\Gamma_{\text{total}}$. The fit constrains the $x_i$ whose labels appear in this array to sum to one.
<table><tr><td>x<sub>3</sub></td><td>-66</td></tr><tr><td>x<sub>4</sub></td><td>-64 89</td></tr><tr><td>x<sub>5</sub></td><td>-12 -5 -5</td></tr><tr><td>x<sub>9</sub></td><td>-67 0 -1 -6</td></tr><tr><td>x<sub>10</sub></td><td>-13 -6 -5 91 -6</td></tr><tr><td>x<sub>11</sub></td><td>-14 -6 -6 2 -7 2</td></tr><tr><td>Γ</td><td>3 1 1 0 2 0 -24</td></tr><tr><td></td><td>x<sub>2</sub> x<sub>3</sub> x<sub>4</sub> x<sub>5</sub> x<sub>9</sub> x<sub>10</sub> x<sub>11</sub></td></tr></table>

<table><thead><tr><th>Mode</th><th>Rate (10<sup>8</sup> s<sup>-1</sup>)</th><th>Scale factor</th></tr></thead><tbody><tr><td>Γ<sub>2</sub> μ<sup>+</sup>ν<sub>μ</sub></td><td>0.5134 ± 0.0012</td><td>1.5</td></tr><tr><td>Γ<sub>3</sub> π<sup>0</sup>e<sup>+</sup>ν<sub>e</sub><br>Called K<sub>e3</sub><sup>+</sup></td><td>0.0410 ± 0.0004</td><td>2.1</td></tr><tr><td>Γ<sub>4</sub> π<sup>0</sup>μ<sup>+</sup>ν<sub>μ</sub><br>Called K<sub>μ3</sub><sup>+</sup></td><td>0.02707 ± 0.00028</td><td>1.9</td></tr><tr><td>Γ<sub>5</sub> π<sup>0</sup>π<sup>0</sup>e<sup>+</sup>ν<sub>e</sub></td><td>(2.059 ± 0.029 ) × 10<sup>-5</sup></td><td>1.1</td></tr><tr><td>Γ<sub>9</sub> π<sup>+</sup>π<sup>0</sup></td><td>0.1670 ± 0.0007</td><td>1.3</td></tr><tr><td>Γ<sub>10</sub> π<sup>+</sup>π<sup>0</sup>π<sup>0</sup></td><td>0.01421 ± 0.00018</td><td>1.1</td></tr><tr><td>Γ<sub>11</sub> π<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td><td>0.04510 ± 0.00019</td><td></td></tr></tbody></table>

## K$^{\pm}$ DECAY RATES

$$\Gamma(\mu^{+} \nu_{\mu})$$

$$\text{VALUE (10}^{6}\text{s}^{-1}) \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{CHG}$$

$$51.34 \pm 0.12 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.5.}$$

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

51.2 ± 0.8 FORD 67 CNTR ±

$$\Gamma_2$$

$$\Gamma(\pi^{+} \pi^{+} \pi^{-})$$

$$\text{VALUE (10}^{6}\text{s}^{-1}) \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{CHG}$$

$$4.510 \pm 0.019 \text{ OUR FIT}$$

$$4.511 \pm 0.024 \quad 1 \text{ FORD} \quad 70 \text{ ASPK}$$

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

4.529 ± 0.032 3.2M 1 FORD 70 ASPK

4.496 ± 0.030 1 FORD 67 CNTR ±

$$\Gamma_{11}$$

¹ First FORD 70 value is second FORD 70 combined with FORD 67.

## K$^{+}$ BRANCHING RATIOS

### Leptonic and semileptonic modes

$$\Gamma(e^{+} \nu_{e}) / \Gamma(\mu^{+} \nu_{\mu})$$

$$\Gamma_1 / \Gamma_2$$

See the note on "Decay Constants of Charged Pseudoscalar Mesons" in the $D_s^+$ Listings.

$$\text{VALUE (units 10}^{-5}) \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{CHG}$$

$$2.488 \pm 0.009 \text{ OUR AVERAGE}$$

2.488 ± 0.007 ± 0.007 150k ¹ LAZZERONI 13 NA62 ±

2.493 ± 0.025 ± 0.019 13.8k ² AMBROSINO 09E KLOE ±

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

2.487 ± 0.011 ± 0.007 60k ³ LAZZERONI 11 NA62 +

2.51 ± 0.15 404 HEINTZE 76 SPEC +

2.37 ± 0.17 534 HEARD 75B SPEC +

2.42 ± 0.42 112 CLARK 72 OSPK +

¹ LAZZERONI 13 uses full data sample collected from 2007 to 2008. This ratio is defined to be fully inclusive, including internal-bremsstrahlung.

² The ratio is defined to include internal-bremsstrahlung, ignoring direct-emission contribu- tions. AMBROSINO 09E determined the ratio from the measurement of $\Gamma(K \to e\nu(\gamma), E_{\gamma} < 10 \text{ MeV}) / \Gamma(K \to \mu\nu(\gamma))$. 89.8% of $K \to e\nu(\gamma)$ events had $E_{\gamma} < 10 \text{ MeV}$.

³ This ratio is defined to be fully inclusive, including internal-bremsstrahlung.

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

$$\Gamma_2 / \Gamma$$

See the note on "Decay Constants of Charged Pseudoscalar Mesons" in the $D_s^+$ Listings.

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

$$63.56 \pm 0.11 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.2.}$$

$$63.60 \pm 0.16 \text{ OUR AVERAGE}$$

63.66 ± 0.09 ± 0.15 865k ¹ AMBROSINO 06A KLOE +

63.24 ± 0.44 62k CHIANG 72 OSPK + 1.84 GeV/c K$^{+}$

¹ Fully inclusive. Used tagged kaons from $\phi$ decays.

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

$$\Gamma_3 / \Gamma$$

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

$$5.07 \pm 0.04 \text{ OUR FIT} \quad \text{Error includes scale factor of 2.1.}$$

$$4.94 \pm 0.05 \text{ OUR AVERAGE}$$

4.965 ± 0.038 ± 0.037 1 AMBROSINO 08A KLOE ±

4.86 ± 0.10 3516 CHIANG 72 OSPK + 1.84 GeV/c K$^{+}$

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

4.7 ± 0.3 429 SHAKLEE 64 HLBC +

5.0 ± 0.5 ROE 61 HLBC +

¹ Depends on K$^{+}$ lifetime $\tau$. AMBROSINO 08A uses PDG 06 value of $\tau = (1.2385 \pm 0.0024) \times 10^{-8}$ sec. The correlation between $K_{e3}^{+}$ and $K_{\mu3}^{+}$ branching fraction mea- surements is 62.7%.

$$\Gamma(\pi^0 e^+ \nu_e) / \Gamma(\mu^+ \nu_\mu)$$

$$\text{VALUE (10}^{6}\text{s}^{-1}) \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{CHG}$$

$$0.0790 \pm 0.0008 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.9.}$$

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

0.069 ± 0.006 350 ZELLER 69 ASPK +

0.0775 ± 0.0033 960 BOTTERILL 68c ASPK +

0.069 ± 0.006 561 GARLAND 68 ASPK +

0.0791 ± 0.0054 295 ¹ AUERBACH 67 OSPK +

¹ AUERBACH 67 changed from 0.0797 ± 0.0054. See comment with ratio $\Gamma(\pi^0 \mu^+ \nu_\mu) / \Gamma(\mu^+ \nu_\mu)$. The value 0.0785 ± 0.0025 given in AUERBACH 67 is an average of AUERBACH 67 $\Gamma(\pi^0 e^+ \nu_e) / \Gamma(\mu^+ \nu_\mu)$ and CESTER 66 $\Gamma(\pi^0 e^+ \nu_e) / [\Gamma(\mu^+ \nu_\mu) + \Gamma(\pi^+ \nu_\mu)]$.

$$\Gamma(\pi^0 e^+ \nu_e) / [\Gamma(\mu^+ \nu_\mu) + \Gamma(\pi^+ \nu_\mu)]$$

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

$$6.02 \pm 0.06 \text{ OUR FIT} \quad \text{Error includes scale factor of 2.1.}$$

$$6.02 \pm 0.15 \text{ OUR AVERAGE}$$

6.16 ± 0.22 5110 ESCHSTRUTH 68 OSPK +

5.89 ± 0.21 1679 CESTER 66 OSPK +

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

5.92 ± 0.65 ¹ WEISSENBERG 76 SPEC +

¹ Value calculated from WEISSENBERG 76 ($\pi^0 e\nu$, $\mu\nu$), and ($\pi\pi^0$) values to eliminate dependence on our 1974 ($\pi 2\pi^0$) and ($\pi\pi^+ \pi^-$) fractions.

$$\Gamma(\pi^0 e^+ \nu_e) / [\Gamma(\mu^0 \mu^+ \nu_\mu) + \Gamma(\pi^+ \pi^0) + \Gamma(\pi^+ \pi^0 \pi^0)]$$

$$\text{VALUE (10}^{6}\text{s}^{-1}) \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{CHG}$$

$$0.1967 \pm 0.0016 \text{ OUR FIT} \quad \text{Error includes scale factor of 2.5.}$$

$$0.1962 \pm 0.0008 \pm 0.0035 \quad 71k \quad \text{SHER} \quad 03 \quad \text{B865 +}$$

$$\Gamma_3 / (\Gamma_2 + \Gamma_9)$$

$$\Gamma(\pi^0 e^+ \nu_e) / \Gamma(\pi^+ \pi^0)$$

$$\text{VALUE (10}^{6}\text{s}^{-1}) \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{CHG} \quad \text{COMMENT}$$

$$0.2454 \pm 0.0023 \text{ OUR FIT} \quad \text{Error includes scale factor of 2.6.}$$

$$0.2467 \pm 0.0011 \text{ OUR AVERAGE} \quad \text{Error includes scale factor of 1.1.}$$

0.2423 ± 0.0015 ± 0.0037 31k UVAROV 14 ISTR - ISTRA+

0.2470 ± 0.0009 ± 0.0004 87k BATLEY 07A NA48 ±

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

0.221 ± 0.012 786 ¹ LUCAS 73b HBC - Dalitz pairs only

¹ LUCAS 73b gives $N(K_{e3}) = 786 \pm 3.1\%$, $N(2\pi) = 3564 \pm 3.1\%$. We use these values to obtain quoted result.

$$\Gamma(\pi^0 e^+ \nu_e) / \Gamma(\pi^+ \pi^+ \pi^-)$$

$$\text{VALUE (10}^{6}\text{s}^{-1}) \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{CHG}$$

$$0.908 \pm 0.009 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.6.}$$

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

0.867 ± 0.027 2768 BARMIN 87 XEBC +

0.856 ± 0.040 2827 BRAUN 75 HLBC +

0.850 ± 0.019 4385 ¹ HAIDT 71 HLBC +

0.846 ± 0.021 4385 ¹ EICH TEN 68 HLBC +

0.94 ± 0.09 854 BELLOTTI 67b HLBC +

0.90 ± 0.06 230 BORREANI 64 HLBC +

$$\Gamma_3 / \Gamma_{11}$$

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

$$\text{VALUE (10}^{6}\text{s}^{-1}) \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{CHG} \quad \text{COMMENT}$$

$$3.352 \pm 0.034 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.9.}$$

$$3.24 \pm 0.04 \text{ OUR AVERAGE}$$

3.233 ± 0.029 ± 0.026 1 AMBROSINO 08A KLOE ±

3.33 ± 0.16 2345 CHIANG 72 OSPK + 1.84 GeV/c K$^{+}$

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

2.8 ± 0.4 ² TAYLOR 59 EMUL +

¹ Depends on K$^{+}$ lifetime $\tau$. AMBROSINO 08A uses PDG 06 value of $\tau = (1.2385 \pm 0.0024) \times 10^{-8}$ sec. The correlation between $K_{e3}^{+}$ and $K_{\mu3}^{+}$ branching fraction mea- surements is 62.7%.

² Earlier experiments not averaged.

$$\Gamma(\pi^0 \mu^+ \nu_\mu) / \Gamma(\mu^+ \nu_\mu)$$

$$\text{VALUE (10}^{6}\text{s}^{-1}) \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{CHG}$$

$$0.0527 \pm 0.0006 \text{ OUR FIT} \quad \text{Error includes scale factor of 1.6.}$$

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

0.054 ± 0.009 240 ZELLER 69 ASPK +

0.0480 ± 0.0037 424 ¹ GARLAND 68 OSPK +

0.0486 ± 0.0040 307 ² AUERBACH 67 OSPK +

¹ GARLAND 68 changed from 0.055 ± 0.004 in agreement with $\mu$-spectrum calculation of GAILLARD 70 appendix B. L.G.Pondrom, (private communication 73).

² AUERBACH 67 changed from 0.0602 ± 0.0046 by erratum which brings the $\mu$-spectrum calculation into agreement with GAILLARD 70 appendix B.
$$ \Gamma(\pi^{+} \pi^{0} \pi^{0})/\Gamma(\pi^{+} \pi^{0}) \qquad \Gamma_{10}/\Gamma_{9} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.0851 ±0.0012</td><td>OUR FIT</td><td colspan="4">Error includes scale factor of 1.1.</td></tr></tbody></table>

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

0.081 ±0.005 574 1 LUCAS 73B HBC - Dalitz pairs only

1 LUCAS 73B gives N(π2π0) = 574 ± 5.9%, N(2π) = 3564 ± 3.1%. We quote 0.5N(π2π0)/N(2π) where 0.5 is because only Dalitz pair π0's were used.

$$ \Gamma(\pi^{+} \pi^{0} \pi^{0})/\Gamma(\pi^{+} \pi^{+} \pi^{-}) \qquad \Gamma_{10}/\Gamma_{11} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.315 ±0.004</td><td>OUR FIT</td><td colspan="4">Error includes scale factor of 1.1.</td></tr><tr><td>0.303 ±0.009</td><td></td><td>2027</td><td>BISI</td><td>65</td><td>BC + HBC+HLBC</td></tr></tbody></table>

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

0.393 ±0.099 17 YOUNG 65 EMUL +

$$ \Gamma(\pi^{+} \pi^{+} \pi^{-})/\Gamma_{\text{total}} \qquad \Gamma_{11}/\Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead></table>

5.583 ±0.024 OUR FIT

5.565 ±0.031 ±0.025 68k 1 BABUSCI 14b KLOE +

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

5.56 ±0.20 2330 2 CHIANG 72 OSPK + 1.84 GeV/c K+

5.34 ±0.21 693 3 PANDOULAS 70 EMUL +

5.71 ±0.15 DEMARCO 65 HBC

6.0 ±0.4 44 YOUNG 65 EMUL +

5.54 ±0.12 2332 CALLAHAN 64 HLBC +

5.1 ±0.2 540 SHAKLEE 64 HLBC +

5.7 ±0.3 ROE 61 HLBC +

1 Inclusive of final-state radiation. Result obtained from averaging two branching ratios: one from a sample with K⁻ → µν(γ) tagging and another with K⁻ → π⁻π⁰(γ) tagging.

2 Value is not independent of CHIANG 72 Γ(μ⁺νμ⁻)/Γ<sub>total</sub>, Γ(π⁺π⁰)/Γ<sub>total</sub>, Γ(π⁺π⁰νμ⁻)/Γ<sub>total</sub>, and Γ(π⁰e⁺νe⁻)/Γ<sub>total</sub>.

3 Includes events of TAYLOR 59.

## Leptonic and semileptonic modes with photons

$$ \Gamma(\mu^{+} \nu_{\mu} \gamma)/\Gamma_{\text{total}} \qquad \Gamma_{12}/\Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead></table>

6.2 ±0.8 OUR AVERAGE

6.6 ±1.5 1,2 DEMIDOV 90 XEBC P(μ) <231.5 MeV/c

6.0 ±0.9 BARMIN 88 HLBC + P(μ) <231.5 MeV/c

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

3.5 ±0.8 2,3 DEMIDOV 90 XEBC E(γ) > 20 MeV

3.2 ±0.5 57 4 BARMIN 88 HLBC + E(γ) > 20 MeV

5.4 ±0.3 5 AKIBA 85 SPEC P(μ) <231.5 MeV/c

1 P(μ) cut given in DEMIDOV 90 paper, 235.1 MeV/c, is a misprint according to authors (private communication).

2 DEMIDOV 90 quotes only inner bremsstrahlung (IB) part.

3 Not independent of above DEMIDOV 90 value. Cuts differ.

4 Not independent of above BARMIN 88 value. Cuts differ.

5 Assumes μ-e universality and uses constraints from K → eνγ.

$$ \Gamma(\mu^{+} \nu_{\mu} \gamma(\text{SD}^{+}))/\Gamma_{\text{total}} \qquad \Gamma_{13}/\Gamma $$

Structure-dependent part with +γ helicity (SD⁺ term). See the “Note on π⁺ → ℓ⁺νγ and K⁺ → ℓ⁺νγ Form Factors” in the π⁺ section of the Particle Data Listings above.

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>1.33 ±0.12 ±0.18</td><td>2588</td><td>1 ADLER</td><td>00B</td><td>B787</td></tr></tbody></table>

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

<3.0 90 AKIBA 85 SPEC

1 ADLER 00B obtains the branching ratio by extrapolating the measurement in the kinematic region E<sub>μ</sub> > 137 MeV, E<sub>γ</sub> > 90 MeV to the full SD<sup>+</sup> phase-space. Also reports |F<sub>V</sub> + F<sub>A</sub>| = 0.165 ± 0.007 ± 0.011 and -0.04 < F<sub>V</sub> - F<sub>A</sub> < 0.24 at 90% CL.

$$ \Gamma(\mu^{+} \nu_{\mu} \gamma(\text{SD}^{+}\text{INT}))/\Gamma_{\text{total}} \qquad \Gamma_{14}/\Gamma $$

Interference term between internal Bremsstrahlung and SD⁺ term. See the “Note on π⁺ → ℓ⁺νγ and K⁺ → ℓ⁺νγ Form Factors” in the π⁺ section of the Particle Data Listings above.

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><2.7</td><td>90</td><td>AKIBA</td><td>85 SPEC</td></tr></tbody></table>

$$ \Gamma(\mu^{+} \nu_{\mu} \gamma(\text{SD}^{-} + \text{SD}^{+}\text{INT}))/\Gamma_{\text{total}} \qquad \Gamma_{15}/\Gamma $$

Sum of structure-dependent part with -γ helicity (SD⁻ term) and interference term between internal Bremsstrahlung and SD⁻ term. See the “Note on π⁺ → ℓ⁺νγ and K⁺ → ℓ⁺νγ Form Factors” in the π⁺ section of the Particle Data Listings above.

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><2.6</td><td>90</td><td>1 AKIBA</td><td>85 SPEC</td></tr></tbody></table>

1 Assumes μ-e universality and uses constraints from K → eνγ.

$$ \Gamma(e^{+} \nu_{e} \gamma)/\Gamma(\mu^{+} \nu_{\mu}) \qquad \Gamma_{16}/\Gamma_{2} $$

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.62 ±0.22</td><td>OUR AVERAGE</td><td colspan="4">Error includes scale factor of 3.9.</td></tr></tbody></table>

1.98 ±0.11 95 1 KOBAYASHI 23 E36 E<sub>γ</sub> in 10-250 MeV, p<sub>e</sub> > 200 MeV/c

1.483 ±0.066 ±0.013 1.4k 2 AMBROSINO 09E KLOE ± E<sub>γ</sub> in 10-250 MeV, p<sub>e</sub> > 200 MeV/c

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

1.85 ±0.11 ±0.07 574 3,4 ITO 22 E36 + E<sub>γ</sub> in 10-250 MeV, p<sub>e</sub> > 200 MeV/c

1 KOBAYASHI 23 observed 95 ± 10 K<sup>SD+</sup><sub>e2γ(γ)</sub> events and derived B(K<sup>SD+</sup><sub>e2γ(γ)</sub>)/B(K<sub>e2(γ)</sub>) = 1.25 ± 0.14 ± 0.08. The authors obtained the R<sub>γ</sub> value (1.98 ± 0.11) × 10<sup>-5</sup> by averaging KOBAYASHI 23 with ITO 22 after updating the ITO 22 result to include internal bremsstrahlung process in the acceptance calculation.

2 AMBROSINO 09E measured the differential width dR<sub>γ</sub>/dE<sub>γ</sub> = (1/Γ(K → μν)) (dΓ(K → eνγ)/dE<sub>γ</sub>). Result obtained by integrating the differential width over E<sub>γ</sub> from 10 to 250 MeV.

3 ITO 22 result derived from B(K<sup>SD+</sup><sub>e2γ(γ)</sub>)/B(K<sub>e2(γ)</sub>) = 1.12 ± 0.07 ± 0.04.

4 superseded by KOBAYASHI 2023

$$ \Gamma(\pi^{0} e^{+} \nu_{e} \gamma)/\Gamma(\pi^{0} e^{+} \nu_{e}) \qquad \Gamma_{17}/\Gamma_{3} $$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead></table>

5.32 ±0.05 OUR AVERAGE

5.33 ±0.03 ±0.04 130k 1 CORTINA-GIL 23D NA62 + E<sub>γ</sub> > 10 MeV, 0.6 < cos(θ<sub>eγ</sub>) < 0.9

5.32 ±0.10 ±0.12 7248 2 POLYARUSH 21 OKA + E<sub>γ</sub> > 10 MeV, 0.6 < cos(θ<sub>eγ</sub>) < 0.9

4.7 ±0.2 ±0.3 1456 3 AKIMENKO 07 ISTR - E<sub>γ</sub> > 10 MeV, 0.6 < cos(θ<sub>eγ</sub>) < 0.9

4.6 ±0.8 82 4 BARMIN 91 XEBC E<sub>γ</sub> > 10 MeV, 0.6 < cos(θ<sub>eγ</sub>) < 0.9

5.6 ±0.4 192 5 BOLOTOV 86B CALO - E<sub>γ</sub> > 10 MeV

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

18.1 ±0.3 ±0.7 4476 3 AKIMENKO 07 ISTR - E<sub>γ</sub> > 10 MeV, θ<sub>eγ</sub> > 10°

6.3 ±0.2 ±0.3 3 AKIMENKO 07 ISTR - E<sub>γ</sub> > 30 MeV, θ<sub>eγ</sub> > 20°

15.1 ±2.5 82 4 BARMIN 91 XEBC E<sub>γ</sub> > 10 MeV, cos(θ<sub>eγ</sub>) < 0.98

4.8 ±2.0 16 6 LJUNG 73 HLBC + E<sub>γ</sub> > 30 MeV

2.2 ±1.5 1.0 6 LJUNG 73 HLBC + E<sub>γ</sub> > 30 MeV

7.6 ±2.8 13 7 ROMANO 71 HLBC E<sub>γ</sub> > 10 MeV

5.3 ±2.2 7 ROMANO 71 HLBC + E<sub>γ</sub> > 30 MeV

12 ±8 BELLOTTI 67 HLBC E<sub>γ</sub> > 30 MeV

1 CORTINA-GIL 23D provides values for three kinematic regions. For averaging, we use value with E<sub>γ</sub> > 10 MeV and 0.6 < cos(θ<sub>eγ</sub>) < 0.9.

2 POLYARUSH 21 provides values for three kinematic regions. For averaging, we use value with E<sub>γ</sub> > 10 MeV and 0.6 < cos(θ<sub>eγ</sub>) < 0.9.

3 AKIMENKO 07 provides values for three kinematic regions. For averaging, we use value with E<sub>γ</sub> > 10 MeV and 0.6 < cos(θ<sub>eγ</sub>) < 0.9.

4 BARMIN 91 quotes branching ratio Γ(K → eπ⁰νγ)/Γ<sub>all</sub>. The measured normalization is Γ(K → eπ⁰νγ) + Γ(K → π⁺π⁺π⁻). For comparison with other experiments we used Γ(K → eπ⁰νγ)/Γ<sub>all</sub> = 0.0482 to calculate the values quoted here.

5 cos(θ<sub>eγ</sub>) between 0.6 and 0.9.

6 First LJUNG 73 value is for cos(θ<sub>eγ</sub>) < 0.9, second value is for cos(θ<sub>eγ</sub>) between 0.6 and 0.9 for comparison with ROMANO 71.

7 Both ROMANO 71 values are for cos(θ<sub>eγ</sub>) between 0.6 and 0.9. Second value is for comparison with second LJUNG 73 value. We use lowest E<sub>γ</sub> cut for Summary Table value. See ROMANO 71 for E<sub>γ</sub> dependence.

2 POLYARUSH 21 provides values for three kinematic regions. For averaging, we use value with E<sub>γ</sub> > 10 MeV and 0.6 < cos(θ<sub>eγ</sub>) < 0.9.

3 AKIMENKO 07 provides values for three kinematic regions. For averaging, we use value with E<sub>γ</sub> > 10 MeV and 0.6 < cos(θ<sub>eγ</sub>) < 0.9.

4 BARMIN 91 quotes branching ratio Γ(K → eπ⁰νγ)/Γ<sub>all</sub>. The measured normalization is Γ(K → eπ⁰νγ) + Γ(K → π⁺π⁺π⁻). For comparison with other experiments we used Γ(K → eπ⁰νγ)/Γ<sub>all</sub> = 0.0482 to calculate the values quoted here.

5 cos(θ<sub>eγ</sub>) between 0.6 and 0.9.

6 First LJUNG 73 value is for cos(θ<sub>eγ</sub>) < 0.9, second value is for cos(θ<sub>eγ</sub>) between 0.6 and 0.9 for comparison with ROMANO 71.

7 Both ROMANO 71 values are for cos(θ<sub>eγ</sub>) between 0.6 and 0.9. Second value is for comparison with second LJUNG 73 value. We use lowest E<sub>γ</sub> cut for Summary Table value. See ROMANO 71 for E<sub>γ</sub> dependence.

$$ \Gamma(\pi^{0} e^{+} \nu_{e} \gamma(\text{SD}^{+}))/\Gamma_{\text{total}} \qquad \Gamma_{18}/\Gamma $$

Structure-dependent part.

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td><5.3</td><td>90</td><td>BOLOTOV</td><td>86B</td><td>CALO -</td></tr></tbody></table>

$$ \Gamma(\pi^{0} \mu^{+} \nu_{\mu} \gamma)/\Gamma_{\text{total}} \qquad \Gamma_{19}/\Gamma $$

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

1.25 ±0.25 OUR AVERAGE

1.10 ±0.32 ±0.05 23 1 ADLER 10 B787 30 < E<sub>γ</sub> < 60 MeV

1.46 ±0.22 ±0.32 153 2 TCHIKILEV 07 ISTR - 30 < E<sub>γ</sub> < 60 MeV

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

2.4 ±0.5 ±0.6 125 SHIMIZU 06 K470 + E<sub>γ</sub> > 30 MeV;

Θ<sub>μγ</sub> > 20°

<6.1 90 0 LJUNG 73 HLBC + E(γ) > 30 MeV

1 Value obtained from B(K<sup>+</sup> → π<sup>0</sup>μ<sup>+</sup>ν<sub>μ</sub>γ) = (2.51 ± 0.74 ± 0.12) × 10<sup>-5</sup> obtained in the kinematic region E<sub>γ</sub> > 20 MeV, and then theoretical K<sub>μ3γ</sub> spectrum has been used. Also B(K<sup>+</sup> → π<sup>0</sup>μ<sup>+</sup>ν<sub>μ</sub>γ) = (1.58 ± 0.46 ± 0.08) × 10<sup>-5</sup>, for E<sub>γ</sub> > 30 MeV and θ<sub>μγ</sub> > 20°, was determined.

2 Obtained from measuring B(K<sub>μ3γ</sub>) / B(K<sub>μ3</sub>) and using PDG 02 value B(K<sub>μ3</sub>) = 3.27%. B(K<sub>μ3γ</sub>) = (8.82 ± 0.94 ± 0.86) × 10<sup>-5</sup> is obtained for 5 MeV < E<sub>γ</sub> < 30 MeV.
$$ \Gamma(\pi^{+}\pi^{+}e^{-}\nu_{e})/\Gamma(\pi^{+}\pi^{-}e^{+}\nu_{e}) $$

Test of $\Delta S = \Delta Q$ rule.

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>SPEC</th></tr></thead><tbody><tr><td>&lt; 3</td><td>90</td><td>3</td><td>1 BLOCH</td><td>76</td><td></td></tr></tbody></table>

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

<130. 95 0 BOURQUIN 71 ASPK

¹BLOCH 76 quotes 3.6 × 10⁻⁴ at CL = 95%, we convert.

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

Test of $\Delta S = \Delta Q$ rule.

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>&lt;3.0</td><td>95</td><td>0</td><td>BIRGE</td><td>65</td><td>FBC +</td></tr></tbody></table>

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

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

<table><thead><tr><th>VALUE (units 10<sup>-7</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>3.00±0.09 OUR AVERAGE</td><td></td><td></td><td></td><td></td></tr><tr><td>3.11±0.04±0.12</td><td>7253</td><td>1 BATLEY</td><td>09</td><td>NA48 ±</td></tr><tr><td>2.94±0.05±0.14</td><td>10300</td><td>2 APPEL</td><td>99</td><td>SPEC +</td></tr><tr><td>2.75±0.23±0.13</td><td>500</td><td>3 ALLIEGRO</td><td>92</td><td>SPEC +</td></tr><tr><td>2.7 ± 0.5</td><td>41</td><td>4 BLOCH</td><td>75</td><td>SPEC +</td></tr></tbody></table>

¹Value extrapolated from a measurement in the region $z = (m_{ee}/m_{K})^{2} > 0.08$. BATEY 09 also evaluated the shape of the form factor using four different theoretical models.

²APPEL 97 establishes vector nature of this decay and determines form factor $f(Z) = f_{0}(1 + \delta Z)$, $Z = M_{ee}^{2}/m_{K}^{2}$, $\delta = 2.14 \pm 0.13 \pm 0.15$. Also reports constraints on scalar and tensor interactions: $|f_{S}| < 6.6 \times 10^{-5}$, $|f_{T}| < 3.7 \times 10^{-4}$ at 90% C.L.

³ALLIEGRO 92 assumes a vector interaction with a form factor given by $\lambda = 0.105 \pm 0.035 \pm 0.015$ and a correlation coefficient of $-0.82$.

⁴BLOCH 75 assumes a vector interaction.

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

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

<table><thead><tr><th>VALUE (units 10<sup>-8</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>9.17±0.14 OUR AVERAGE</td><td></td><td>Error</td><td>includes scale factor of 1.8.</td><td></td><td></td><td></td></tr><tr><td>9.15±0.06±0.05</td><td>28k</td><td>1 CORTINA-GIL</td><td>22A NA62</td><td></td><td></td><td>2017-18 data</td></tr><tr><td>9.62±0.21±0.13</td><td>3120</td><td>2 BATLEY</td><td>11A NA48 ±</td><td></td><td></td><td>2003-04 data</td></tr><tr><td>9.8 ± 1.0 ± 0.5</td><td>110</td><td>3 PARK</td><td>02 HYCP ±</td><td></td><td></td><td></td></tr><tr><td>9.22±0.60±0.49</td><td>402</td><td>4 MA</td><td>00 B865 +</td><td></td><td></td><td></td></tr><tr><td>5.0 ± 0.4 ± 0.9</td><td>207</td><td>5 ADLER</td><td>97C B787 +</td><td></td><td></td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>9.7 ± 1.2 ± 0.4</td><td>65</td><td>PARK</td><td>02 HYCP +</td></tr><tr><td>10.0 ± 1.9 ± 0.7</td><td>35</td><td>PARK</td><td>02 HYCP -</td></tr><tr><td>&lt;23</td><td>90</td><td>ATIYA</td><td>89 B787 +</td></tr></tbody></table>

¹CORTINA-GIL 22A also studies the form factor $f(z)$ dependence of the decay, described via single photon exchange: assuming a linear form factor including $\pi-\pi$ rescattering, $W_{\pi\pi}$, as in DAMBROSIO 98A, finding $f(z) = G_{F} m_{K}^{2} (a_{+} + b_{+} z) + W_{\pi\pi}(z)$, $a_{+} = -0.575 \pm 0.013$, $b_{+} = -0.722 \pm 0.043$.

²BATLEY 11A also studies the form factor $f(z)$ dependence of the decay, described via single photon exchange: i) assuming a linear form factor, $f(z) = f_{0}(1 + \delta z)$, $z = (M_{\mu\mu}/m_{K})^{2}$, finding $f_{0} = 0.470 \pm 0.040$ and $\delta = 3.11 \pm 0.57$ and ii) assuming a linear form factor including $\pi-\pi$ rescattering, $W_{\pi\pi}$, as in DAMBROSIO 98A, finding $f(z) = G_{F} m_{K}^{2} (a_{+} + b_{+} z) + W_{\pi\pi}(z)$, $a_{+} = -0.575 \pm 0.039$, $b_{+} = -0.813 \pm 0.145$.

³PARK 02 “+” result comes from combining $K^{+} \rightarrow \pi^{+}\mu^{+}\mu^{-}$ and $K^{-} \rightarrow \pi^{-}\mu^{+}\mu^{-}$, assuming CP is conserved.

⁴MA 00 establishes vector nature of this decay and determines form factor $f(z) = f_{0}(1 + \delta z)$, $z = (M_{\mu\mu}/m_{K})^{2}$, $\delta = 2.45 \pm 0.30 \pm 0.95$.

⁵ADLER 97C gives systematic error 0.7 × 10⁻⁸ and theoretical uncertainty 0.6 × 10⁻⁸, which we combine in quadrature to obtain our second error.

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

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>&lt;1.4 × 10<sup>-8</sup></td><td>90</td><td>1 CORTINA-GIL 23B</td><td>NA62</td><td>+</td></tr></tbody></table>

¹Quoted limit is obtained using data collected from 2017 to 2018. CORTINA-GIL 23B also reports upper limits at 90% C.L. at the level of 10⁻⁹ for the branching ratios of two prompt decay chains involving pair-production of hidden-sector mediators: $K^{+} \rightarrow \pi^{+}a\bar{a}$, $a \rightarrow e^{+}e^{-}$ and $K^{+} \rightarrow \pi^{+}S$, $S \rightarrow XX$, $X \rightarrow e^{+}e^{-}$.

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

Test for $\Delta S = 1$ weak neutral current. Allowed by higher-order electroweak interactions. Branching ratio values are extrapolated from the momentum or energy regions shown in the comments assuming Standard Model phase space except for those labeled “Scalar” or “Tensor” to indicate the assumed non-Standard-Model interaction.

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

¹.14+0.40 -0.33 OUR AVERAGE

1.06+0.41 -0.35 20 ¹CORTINA-GIL 21B NA62 +

1.73+1.15 -1.05 7 ²ARTAMONOV 08 B949 + 140< P<sub>π</sub> < 199 MeV, 211< P<sub>π</sub> < 229 MeV

$$ \Gamma_{35}/\Gamma_{6} $$

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

<table><tbody><tr><td>0.48+0.72 -0.48</td><td>90</td><td>3 CORTINA-GIL</td><td>20C NA62 +</td></tr><tr><td>11</td><td>90</td><td>4 CORTINA-GIL</td><td>19b NA62 + decay-in-flight</td></tr><tr><td>7.89+9.26 -5.10</td><td>3</td><td>5 ARTAMONOV</td><td>08 B949 + 140< P<sub>π</sub> < 199 MeV</td></tr><tr><td>&lt; 22</td><td>90</td><td>6 ADLER</td><td>04 B787 + 211< P<sub>π</sub> < 229 MeV</td></tr><tr><td>&lt; 27</td><td>90</td><td>ADLER</td><td>04 B787 + Scalar</td></tr><tr><td>&lt; 18</td><td>90</td><td>ADLER</td><td>04 B787 + Tensor</td></tr><tr><td>1.47+1.30 -0.89</td><td>3</td><td>7 ANISIMOVSK...</td><td>04 B949 + 211< P<sub>π</sub> < 229 MeV</td></tr><tr><td>1.57+1.75 -0.82</td><td>2</td><td>ADLER</td><td>02 B787 + P<sub>π</sub> > 211 MeV/c</td></tr><tr><td>&lt; 42</td><td>90</td><td>ADLER</td><td>02 C B787 + 140< P<sub>π</sub> < 195 MeV</td></tr><tr><td>&lt; 47</td><td>90</td><td>8 ADLER</td><td>02 C B787 + Scalar</td></tr><tr><td>&lt; 25</td><td>90</td><td>8 ADLER</td><td>02 C B787 + Tensor</td></tr><tr><td>1.5+3.4 -1.2</td><td>1</td><td>ADLER</td><td>00 B787 In ADLER 02</td></tr><tr><td>4.2+9.7 -3.5</td><td>1</td><td>ADLER</td><td>97 B787</td></tr><tr><td>&lt; 24</td><td>90</td><td>ADLER</td><td>96 B787</td></tr><tr><td>&lt; 75</td><td>90</td><td>ATIYA</td><td>93 B787 + T<sub>(π)</sub> 115-127 MeV</td></tr><tr><td>&lt; 52</td><td>90</td><td>9 ATIYA</td><td>93 B787 +</td></tr><tr><td>&lt; 170</td><td>90</td><td>ATIYA</td><td>93B B787 + T<sub>(π)</sub> 60-100 MeV</td></tr><tr><td>&lt; 340</td><td>90</td><td>ATIYA</td><td>90 B787 +</td></tr><tr><td>&lt;1400</td><td>90</td><td>ASANO</td><td>81B CNTR + T<sub>(π)</sub> 116-127 MeV</td></tr></tbody></table>

¹CORTINA-GIL 218 analysis of the NA62 data taken in 2016–2018 observed 20 candidate events with an expected background of 7 events. The achieved single event sensitivity is (0.839 ± 0.054) × 10⁻¹¹. The quoted branching ratio includes result from CORTINA-GIL 20C which observed two candidate events. This provides evidence for the very rare $K^{+} \rightarrow \pi^{+}\nu\bar{\nu}$ decay, observed with a significance of 3.4 σ. Search for a feebly interacting scalar or pseudo-scalar particle X in the decay $K^{+} \rightarrow \pi^{+}X$ was performed and an upper limit from < 3 × 10⁻¹¹ to < 6 × 10⁻¹¹ at the 90% C.L. was set for an invisible particle with a mass of 0–110 MeV/c².

²Value obtained combining ANISIMOVSKY 04, ADLER 04, and the present ARTAMONOV 08 results.

³CORTINA-GIL 20C analysis of the NA62 data taken in 2017 observed two candidate events with an expected background of 1.5 events. The achieved single event sensitivity is (0.389 ± 0.024) × 10⁻¹⁰. The quoted branching ratio includes result from CORTINA-GIL 19b which observed one candidate event. The corresponding upper limit B($K^{+} \rightarrow \pi^{+}\nu\bar{\nu}$) < 1.78 × 10⁻¹⁰ at 90% C.L. Superseded by CORTINA-GIL 21B.

⁴Based on a sample of 1.21 × 10¹¹ $K^{+}$ decays collected in 2016. One signal candidate is observed while the expected background is 0.152 events. The single-event-sensitivity is estimated to be 3.15 × 10⁻¹⁰.

⁵Observed 3 events with an estimated background of 0.93 ± 0.17+0.32-0.24. Signal-to-background ratio for each of these 3 events is 0.20, 0.42, and 0.47.

⁶Value obtained combining the previous result ADLER 02C with 1 event and the present result with 0 events to obtain an expected background 1.22 ± 0.24 events and 1 event observed.

⁷Value obtained combining the previous E787 result ADLER 02 with 2 events and the present E949 with 1 event. The additional event has a signal-to-background ratio 0.9. Superseded by ARTAMONOV 08.

⁸Superseded by ADLER 04.

⁹Combining ATIYA 93 and ATIYA 93B results. Superseded by ADLER 96.

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

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

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>&lt;4.3</td><td>90</td><td>1 ADLER</td><td>01 SPEC</td></tr></tbody></table>

¹Search region defined by 90 MeV/c < P<sub>π</sub> < 188 MeV/c and 135 MeV < E<sub>π0</sub> < 180 MeV.

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

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>&lt;8.1 × 10<sup>-11</sup></td><td>90</td><td>1 CORTINA-GIL 23</td><td>NA62</td></tr></tbody></table>

¹Performed using the dataset collected by the NA62 experiment at CERN from 2016 to 2018.

$$ \Gamma(\mu^{-}\nu e^{+}e^{+})/\Gamma(\pi^{+}\pi^{-}e^{+}\nu_{e}) $$

Test of lepton family number conservation.

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>&lt;0.5</td><td>90</td><td>0</td><td>1 DIAMANT-...</td><td>76 SPEC +</td><td>+</td></tr></tbody></table>

¹DIAMANT-BERGER 76 quotes this result times our 1975 $\pi^{+}\pi^{-}e\nu$ BR ratio.

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

Forbidden by lepton family number conservation.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;0.004</td><td>90</td><td>0</td><td>1 LYONS</td><td>81 HLBC</td><td>200 GeV K<sup>+</sup> narrow band ν beam</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;0.012</td><td>90</td><td>1 COOPER</td><td>82 HLBC</td><td>Wideband ν beam</td></tr></tbody></table>

¹COOPER 82 and LYONS 81 limits on $\nu_{e}$ observation are here interpreted as limits on lepton family number violation in the absence of mixing.
# Meson Particle Listings

## K$^{\pm}$

### Γ(π$^{+}$μ$^{+}$e$^{-}$)/Γ$_{total}$

Test of lepton family number conservation.

<table><thead><tr><th>VALUE (units 10<sup>-10</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>&lt;0.13</td><td>90</td><td>1 SHER</td><td>05</td><td>RVUE +</td></tr><tr><td>&lt;0.21</td><td>90</td><td>SHER</td><td>05</td><td>B865 +</td></tr><tr><td>&lt;0.39</td><td>90</td><td>APPEL</td><td>00</td><td>B865 +</td></tr><tr><td>&lt;2.1</td><td>90</td><td>LEE</td><td>90</td><td>SPEC +</td></tr></tbody></table>

¹This result combines SHER 05 1998 data, APPEL 00 1996 data, and data from BERGMAN 97 and PISLAK 97 theses, all from BNL-E865, with LEE 90 BNL-E777 data.

### Γ(π$^{+}$μ$^{-}$e$^{+}$)/Γ$_{total}$

Test of lepton family number conservation.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>&lt; 6.6 × 10<sup>-11</sup></td><td>90</td><td>ALIBERTI</td><td>21</td><td>NA62 +</td></tr><tr><td>&lt; 5.2 × 10<sup>-10</sup></td><td>90</td><td>APPEL</td><td>00B</td><td>B865 +</td></tr><tr><td>&lt;70 × 10<sup>-10</sup></td><td>90</td><td>1 DIAMANT-...</td><td>76</td><td>SPEC +</td></tr></tbody></table>

¹Measurement actually applies to the sum of the π$^{+}$μ$^{-}$e$^{+}$ and π$^{-}$μ$^{+}$e$^{+}$ modes.

### Γ(π$^{-}$μ$^{+}$e$^{+}$)/Γ$_{total}$

Test of total lepton number conservation.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>&lt; 4.2 × 10<sup>-11</sup></td><td>90</td><td>ALIBERTI</td><td>21</td><td>NA62 +</td></tr><tr><td>&lt; 5.0 × 10<sup>-10</sup></td><td>90</td><td>APPEL</td><td>00B</td><td>B865 +</td></tr><tr><td>&lt;70 × 10<sup>-10</sup></td><td>90</td><td>1 DIAMANT-...</td><td>76</td><td>SPEC +</td></tr></tbody></table>

¹Measurement actually applies to the sum of the π$^{+}$μ$^{-}$e$^{+}$ and π$^{-}$μ$^{+}$e$^{+}$ modes.

### Γ(π$^{-}$e$^{+}$e$^{+}$)/Γ$_{total}$

Test of total lepton number conservation.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;5.3 × 10<sup>-11</sup></td><td>90</td><td>1 CORTINA-GIL 22</td><td>NA62 +</td><td>decay-in-flight</td><td></td></tr><tr><td>&lt;2.2 × 10<sup>-10</sup></td><td>90</td><td>2 CORTINA-GIL 19A</td><td>NA62 +</td><td>decay-in-flight</td><td></td></tr><tr><td>&lt;6.4 × 10<sup>-10</sup></td><td>90</td><td>APPEL</td><td>00B</td><td>B865 +</td><td></td></tr><tr><td>&lt;9.2 × 10<sup>-9</sup></td><td>90</td><td>DIAMANT-...</td><td>76</td><td>SPEC +</td><td></td></tr><tr><td>&lt;1.5 × 10<sup>-5</sup></td><td></td><td>CHANG</td><td>68</td><td>HBC -</td><td></td></tr></tbody></table>

¹CORTINA-GIL 22 uses the complete dataset collected by the NA62 experiment at CERN from 2016 to 2018. Supersedes CORTINA-GIL 19A.

²CORTINA-GIL 19A results are obtained with 2017 data.

### Γ(π$^{-}$μ$^{+}$μ$^{+}$)/Γ$_{total}$

Forbidden by total lepton number conservation.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;4.2 × 10<sup>-11</sup></td><td>90</td><td>1 CORTINA-GIL 19A</td><td>NA62 +</td><td>decay-in-flight</td><td></td></tr><tr><td>&lt;8.6 × 10<sup>-11</sup></td><td>90</td><td>2 BATLEY</td><td>17</td><td>NA48 ±</td><td></td></tr><tr><td>&lt;1.1 × 10<sup>-9</sup></td><td>90</td><td>BATLEY</td><td>11A</td><td>NA48 ±</td><td></td></tr><tr><td>&lt;3.0 × 10<sup>-9</sup></td><td>90</td><td>APPEL</td><td>00B</td><td>B865 +</td><td></td></tr><tr><td>&lt;1.5 × 10<sup>-4</sup></td><td>90</td><td>3 LITTENBERG</td><td>92</td><td>HBC</td><td></td></tr></tbody></table>

¹CORTINA-GIL 19A results are obtained with 2017 data.

²BATLEY 17 result is based on data taken in 2003 to 2004. Limits for two-body resonance X in K$^{\pm}$ → πμμ decays are also reported.

³LITTENBERG 92 is from retroactive data analysis of CHANG 68 bubble chamber data.

### Γ(π$^{-}$π$^{0}$e$^{+}$e$^{+}$)/Γ$_{total}$

Test of total lepton number conservation.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;8.5 × 10<sup>-10</sup></td><td>90</td><td>1 CORTINA-GIL 22</td><td>NA62</td><td>decay-in-flight</td><td></td></tr></tbody></table>

¹CORTINA-GIL 22 uses the complete dataset collected by the NA62 experiment at CERN from 2016 to 2018.

### Γ(μ$^{+}$ν̄e)/Γ$_{total}$

Forbidden by total lepton number conservation.

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;3.3</td><td>90</td><td>1 COOPER</td><td>82</td><td>HLBC Wideband ν beam</td></tr></tbody></table>

¹COOPER 82 limit on ν̄e observation is here interpreted as a limit on lepton number violation in the absence of mixing.

### Γ(π$^{0}$e$^{+}$ν̄e)/Γ$_{total}$

Forbidden by total lepton number conservation.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;0.003</td><td>90</td><td>1 COOPER</td><td>82</td><td>HLBC Wideband ν beam</td></tr></tbody></table>

¹COOPER 82 limit on ν̄e observation is here interpreted as a limit on lepton number violation in the absence of mixing.

### Γ$_{44}$/Γ

### Γ$_{45}$/Γ

### Γ$_{46}$/Γ

### Γ$_{47}$/Γ

### Γ$_{48}$/Γ

### Γ$_{49}$/Γ

### Γ$_{50}$/Γ

### Γ$_{51}$/Γ

### Γ(π$^{+}$γ)/Γ$_{total}$

Violates angular momentum conservation and gauge invariance. Current interest in this decay is as a search for non-commutative space-time effects as discussed in ARTAMONOV 05 and for exotic physics such as a vacuum expectation value of a new vector field, non-local Superstring effects, or departures from Lorentz invariance, as discussed in ADLER 02B.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>&lt; 2.3 × 10<sup>-9</sup></td><td>90</td><td>ARTAMONOV 05</td><td>B949</td><td>+</td></tr><tr><td>&lt; 360 × 10<sup>-9</sup></td><td>90</td><td>ADLER</td><td>02B</td><td>B787 +</td></tr><tr><td>&lt;1400 × 10<sup>-9</sup></td><td>90</td><td>ASANO</td><td>82</td><td>CNTR +</td></tr><tr><td>&lt;4000 × 10<sup>-9</sup></td><td>90</td><td>1 KLEMS</td><td>71</td><td>OSPK +</td></tr></tbody></table>

¹Test of model of Selleri, Nuovo Cimento 60A 291 (1969).

## CPT VIOLATION TESTS IN K$^{\pm}$ DECAYS

$$ \Delta = (\Gamma(K^{+}) - \Gamma(K^{-})) / (\Gamma(K^{+}) + \Gamma(K^{-})) $$

### Δ(K$^{\pm}$ → μ$^{\pm}$ν$_{μ}$) RATE DIFFERENCE/SUM

<table><thead><tr><th>VALUE (%)</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>-0.27±0.21</td><td>FORD</td><td>67</td></tr></tbody></table>

### Δ(K$^{\pm}$ → π$^{\pm}$π$^{0}$) RATE DIFFERENCE/SUM

<table><thead><tr><th>VALUE (%)</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>0.4±0.6</td><td>HERZO</td><td>69</td></tr></tbody></table>

## CP VIOLATION TESTS IN K$^{\pm}$ DECAYS

$$ \Delta = (\Gamma(K^{+}) - \Gamma(K^{-})) / (\Gamma(K^{+}) + \Gamma(K^{-})) $$

### Δ(K$^{\pm}$ → π$^{\pm}$e$^{+}$e$^{-}$) RATE DIFFERENCE/SUM

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>-2.2±1.5±0.6</td><td>1 BATLEY</td><td>09</td></tr></tbody></table>

¹This implies an upper limit of 2.1 × 10$^{-2}$ at 90% CL.

### Δ(K$^{\pm}$ → π$^{\pm}$μ$^{+}$μ$^{-}$) RATE DIFFERENCE/SUM

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>0.010±0.023 OUR AVERAGE</td><td>1 BATLEY</td><td>11A</td></tr><tr><td>0.011±0.023</td><td>PARK</td><td>02</td></tr><tr><td>-0.02 ±0.11 ±0.04</td><td>HYCP</td><td></td></tr></tbody></table>

¹This corresponds to the asymmetry upper limit of < 2.9 × 10$^{-2}$ at 90% CL.

### Δ(K$^{\pm}$ → π$^{\pm}$π$^{0}$γ) RATE DIFFERENCE/SUM

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.0± 1.2 OUR AVERAGE</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.0± 1.0±0.6</td><td>1M</td><td>1 BATLEY</td><td>10A</td><td>NA48</td><td></td></tr><tr><td>4 ±29</td><td>2461</td><td>SMITH</td><td>76</td><td>WIRE ±</td><td>E<sub>π</sub> 55-90 MeV</td></tr><tr><td>5 ±20</td><td>4000</td><td>ABRAMS</td><td>73B</td><td>ASPK ±</td><td>E<sub>π</sub> 51-100 MeV</td></tr></tbody></table>

¹This value implies the upper bound for this asymmetry 1.5 × 10$^{-3}$ at 90% CL.

### Δ(K$^{\pm}$ → π$^{\pm}$π$^{+}$π$^{-}$) RATE DIFFERENCE/SUM

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>0.04±0.06</td><td>1 FORD</td><td>70</td><td>ASPK</td><td></td></tr><tr><td>-0.01±0.08</td><td>2 SMITH</td><td>73</td><td>ASPK ±</td><td></td></tr><tr><td>0.05±0.07</td><td>3.2M</td><td>1 FORD</td><td>70</td><td>ASPK</td><td></td></tr><tr><td>-0.25±0.45</td><td>1 FLETCHER</td><td>67</td><td>OSPK</td><td></td></tr><tr><td>-0.02±0.11</td><td>1 FORD</td><td>67</td><td>CNTR</td><td></td></tr></tbody></table>

¹First FORD 70 value is second FORD 70 combined with FORD 67.

²SMITH 73 value of K$^{\pm}$ → π$^{\pm}$π$^{+}$π$^{-}$ rate difference is derived from SMITH 73 value of K$^{\pm}$ → π$^{\pm}$2π$^{0}$ rate difference.

### Δ(K$^{\pm}$ → π$^{\pm}$π$^{0}$π$^{0}$) RATE DIFFERENCE/SUM

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>-0.02±0.28 OUR AVERAGE</td><td></td><td></td><td></td><td></td></tr><tr><td>0.04±0.29</td><td>SMITH</td><td>73</td><td>ASPK ±</td><td></td></tr><tr><td>-0.6 ±0.9</td><td>HERZO</td><td>69</td><td>OSPK</td><td></td></tr></tbody></table>

## T VIOLATION TESTS IN K$^{+}$ AND K$^{-}$ DECAYS

### P$_{T}$ in K$^{+}$ → π$^{0}$μ$^{+}$ν$_{μ}$

T-violating muon polarization. Sensitive to new sources of CP violation beyond the Standard Model.

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th></tr></thead><tbody><tr><td>-1.7±2.3±1.1</td><td>1 ABE</td><td>04F</td><td>K246</td><td>+</td></tr></tbody></table>

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

<table><tr><td>-4.2±4.9±0.9</td><td>3.9M</td><td>ABE</td><td>99S</td><td>K246</td><td>+</td></tr></table>

¹Includes three sets of data: 96-97 (ABE 99s), 98, and 99-00 totaling about three times the ABE 99s data sample. Corresponds to P$_{T}$ < 5.0 × 10$^{-3}$ at 90% CL.
$P_T$ in $K^+ \to \mu^+ \nu_\mu \gamma$

T-violating muon polarization. Sensitive to new sources of CP violation beyond the Standard Model.

$$ \frac{\text{VALUE (units } 10^{-2})}{-0.64 \pm 1.85 \pm 0.10} \frac{\text{EVTS}}{114k} $$

$$ \frac{\text{DOCUMENT ID}}{1 \text{ ANISIMOVSK...03}} \frac{\text{TECN}}{K246} \frac{\text{CHG}}{+} $$

¹ Muons stopped and polarization measured from decay to positrons.

Im($\xi$) in $K^+ \to \pi^0 \mu^+ \nu_\mu$ DECAY (from transverse $\mu$ pol.)

Test of $T$ reversal invariance.

$$ \frac{\text{VALUE}}{-0.006 \pm 0.008} \frac{\text{EVTS}}{\text{OUR AVERAGE}} \frac{\text{DOCUMENT ID}}{1 \text{ ABE}} \frac{\text{TECN}}{04F K246} \frac{\text{CHG}}{+} \frac{\text{COMMENT}}{+} $$

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

$$ -0.013 \pm 0.016 \pm 0.003 \quad 3.9M \quad \text{ABE} \quad 99\text{s CNTR} + p_T K^+ \text{ at rest} $$

¹ Includes three sets of data: 96-97 (ABE 99s), 98, and 99-00 totaling about three times the ABE 99s data sample. Corresponds to Im($\xi$) < 0.016 at 90% CL.

DALITZ PLOT PARAMETERS FOR $K \to 3\pi$ DECAYS

Revised 1999 by T.G. Trippe (LBNL).

The Dalitz plot distribution for $K^\pm \to \pi^\pm \pi^\pm \pi^\mp$, $K^\pm \to \pi^0 \pi^0 \pi^\pm$, and $K_L^0 \to \pi^+ \pi^- \pi^0$ can be parameterized by a series expansion such as that introduced by Weinberg [1]. We use the form

$$ \begin{aligned} |M|^2 & \propto 1 + g \frac{(s_3 - s_0)}{m_{\pi^+}^2} + h \left[ \frac{s_3 - s_0}{m_{\pi^+}^2} \right]^2 \\ & + j \frac{(s_2 - s_1)}{m_{\pi^+}^2} + k \left[ \frac{s_2 - s_1}{m_{\pi^+}^2} \right]^2 \\ & + f \frac{(s_2 - s_1)}{m_{\pi^+}^2} \frac{(s_3 - s_0)}{m_{\pi^+}^2} + \dots, \end{aligned} \quad (1) $$

where $m_{\pi^+}^2$ has been introduced to make the coefficients $g$, $h$, $j$, and $k$ dimensionless, and

$$ \begin{aligned} s_i &= (P_K - P_i)^2 = (m_K - m_i)^2 - 2m_K T_i, \quad i = 1, 2, 3, \\ s_0 &= \frac{1}{3} \sum_i s_i = \frac{1}{3}(m_K^2 + m_1^2 + m_2^2 + m_3^2). \end{aligned} $$

Here the $P_i$ are four-vectors, $m_i$ and $T_i$ are the mass and kinetic energy of the $i^{th}$ pion, and the index 3 is used for the odd pion.

The coefficient $g$ is a measure of the slope in the variable $s_3$ (or $T_3$) of the Dalitz plot, while $h$ and $k$ measure the quadratic dependence on $s_3$ and $(s_2 - s_1)$, respectively. The coefficient $j$ is related to the asymmetry of the plot and must be zero if CP invariance holds. Note also that if CP is good, $g$, $h$, and $k$ must be the same for $K^+ \to \pi^+ \pi^+ \pi^-$ as for $K^- \to \pi^- \pi^- \pi^+$.

Since different experiments use different forms for $|M|^2$, in order to compare the experiments we have converted to $g$, $h$, $j$, and $k$ whatever coefficients have been measured. Where such conversions have been done, the measured coefficient $a_y$, $a_t$, $a_u$, or $a_v$ is given in the comment at the right. For definitions of these coefficients, details of this conversion, and discussion of the data, see the April 1982 version of this note [2].

References

1. S. Weinberg, Phys. Rev. Lett. **4**, 87 (1960).

2. Particle Data Group, Phys. Lett. **111B**, 69 (1982).

ENERGY DEPENDENCE OF $K^\pm$ DALITZ PLOT

$$ \begin{aligned} |\text{matrix element}|^2 &= 1 + gu + h\nu^2 + kv^2 \\ \text{where } u &= (s_3 - s_0) / m_{\pi^+}^2 \text{ and } v = (s_2 - s_1) / m_{\pi^-}^2 \end{aligned} $$

LINEAR COEFFICIENT $g$ FOR $K^\pm \to \pi^\pm \pi^+ \pi^-$

Some experiments use Dalitz variables $x$ and $y$. In the comments we give $a_y$ is coefficient of $y$ term. See note above on "Dalitz Plot Parameters for $K \to 3\pi$ Decays," For discussion of the conversion of $a_y$ to $g$, see the earlier version of the same note in the Review published in Physics Letters **111B** 70 (1982).

$$ \begin{array}{lccccccc} \text{VALUE} & \text{EVTS} & \text{DOCUMENT ID} & \text{TECN} & \text{CHG} & \text{COMMENT} \\ \hline -0.21134 \pm 0.00017 & 471M & 1 \text{ BATLEY} & 07B & NA48 & \pm \\ \hline \bullet \bullet \bullet & \text{We do not use the following data for averages, fits, limits, etc.} & \bullet \bullet \end{array} $$

¹ Final state strong interaction and radiative corrections not included in the fit.

² Quadratic dependence is required by $K_L^0$ experiments.

³ HOFFMASTER 72 includes GRAUMAN 70 data.

⁴ Emulsion data added — all events included by HOFFMASTER 72.

⁵ Experiments with large errors not included in average.

⁶ Also includes DBC events.

⁷ No radiative corrections included.

QUADRATIC COEFFICIENT $h$ FOR $K^\pm \to \pi^\pm \pi^+ \pi^-$

$$ \frac{\text{VALUE (units } 10^{-2})}{1.848 \pm 0.040} \frac{\text{EVTS}}{471M} \frac{\text{DOCUMENT ID}}{1 \text{ BATLEY}} \frac{\text{TECN}}{07B} \frac{\text{CHG}}{NA48} \pm $$

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

$$ \begin{array}{lccccccc} & & & & & & \\ -0.06 & \pm & 1.43 & 225k & \text{DEVAUX} & 77 & \text{SPEC} + \\ 1.87 & \pm & 0.62 & 750k & \text{FORD} & 72 & \text{ASPK} + \\ 1.25 & \pm & 0.62 & 750k & \text{FORD} & 72 & \text{ASPK} - \\ -0.9 & \pm & 1.4 & 39819 & \text{HOFFMASTER72} & \text{HLBC} + \\ -0.1 & \pm & 1.2 & 50919 & \text{MAST} & 69 & \text{HBC} - \\ & & & & & & \\ \hline \end{array} $$

¹ Final state strong interaction and radiative corrections not included in the fit.

QUADRATIC COEFFICIENT $k$ FOR $K^\pm \to \pi^\pm \pi^+ \pi^-$

$$ \frac{\text{VALUE (units } 10^{-3})}{-4.63 \pm 0.14} \frac{\text{EVTS}}{471M} \frac{\text{DOCUMENT ID}}{1 \text{ BATLEY}} \frac{\text{TECN}}{07B} \frac{\text{CHG}}{NA48} \pm $$

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

$$ \begin{array}{lccccccc} & & & & & & \\ -20.5 & \pm & 3.9 & 225k & \text{DEVAUX} & 77 & \text{SPEC} + \\ -7.5 & \pm & 1.9 & 750k & \text{FORD} & 72 & \text{ASPK} + \\ -8.3 & \pm & 1.9 & 750k & \text{FORD} & 72 & \text{ASPK} - \\ -10.5 & \pm & 4.5 & 39819 & \text{HOFFMASTER72} & \text{HLBC} + \\ -14 & \pm & 12 & 50919 & \text{MAST} & 69 & \text{HBC} - \\ & & & & & & \\ \hline \end{array} $$

¹ Final state strong interaction and radiative corrections not included in the fit.

$(g_+ - g_-) / (g_+ + g_-)$ FOR $K^\pm \to \pi^\pm \pi^+ \pi^-$

This is a CP violating asymmetry between linear coefficients $g_+$ for $K^+ \to \pi^+ \pi^+ \pi^-$ decay and $g_-$ for $K^- \to \pi^- \pi^- \pi^-$ decay.

$$ \frac{\text{VALUE (units } 10^{-4})}{-1.5 \pm 1.5 \pm 1.6} \frac{\text{EVTS}}{3.1G} \frac{\text{DOCUMENT ID}}{1 \text{ BATLEY}} \frac{\text{TECN}}{07E NA48} $$

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

$$ \begin{array}{lccccccc} & & & & & & \\ 1.7 \pm 2.1 \pm 2.0 & 1.7G & 2 \text{ BATLEY} & 06 & NA48 \\ -70.0 \pm 53 & 3.2M & \text{FORD} & 70 & \text{ASPK} \\ & & & & & & \\ \hline \end{array} $$

¹ BATLEY 07E includes data from BATLEY 06. Uses quadratic parametrization and value $g_+ + g_- = 2g$ from BATLEY 07B. This measurement neglects any possible charge asymmetries in higher order slope parameters $h$ or $k$.

² This measurement neglects any possible charge asymmetries in higher order slope parameters $h$ or $k$.

LINEAR COEFFICIENT $g$ FOR $K^\pm \to \pi^\pm \pi^0 \pi^0$

Unless otherwise stated, all experiments include terms quadratic in $(s_3 - s_0) / m_{\pi^+}^2$. See note above on "Dalitz Plot Parameters for $K \to 3\pi$ Decays."

See BATUSOV 98 for a discussion of the discrepancy between their result and others, especially BOLOTOV 86. At this time we have no way to resolve the discrepancy so we depend on the large scale factor as a warning.

$$ \frac{\text{VALUE}}{0.626 \pm 0.007} \frac{\text{EVTS}}{\text{OUR AVERAGE}} \frac{\text{DOCUMENT ID}}{1 \text{ AKOPDZHAN...05B}} \frac{\text{TECN}}{TNF} \frac{\text{CHG}}{\pm} \frac{\text{COMMENT}}{+} $$