$\pi^{\pm}$ FORM FACTORS

F<sub>V</sub>, VECTOR FORM FACTOR

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>0.0254 ±0.0017 OUR AVERAGE</strong></td></tr><tr><td>0.0258 ±0.0017</td><td>65k</td><td>1 BYCHKOV</td><td>09</td><td>PIBE e<sup>+</sup>νγ at rest</td></tr><tr><td>0.014 ±0.009</td><td></td><td>2 BOLOTOV</td><td>90B</td><td>SPEC 17 GeV π<sup>-</sup> → e<sup>+</sup>π<sup>-</sup>eγ</td></tr><tr><td>0.023 <sup>+0.015</sup><sub>-0.013</sub></td><td>98</td><td>EGLI</td><td>89</td><td>SPEC π<sup>+</sup> → e<sup>+</sup>ν<sub>e</sub>e<sup>+</sup>e<sup>-</sup></td></tr></tbody></table>

¹The BYCHKOV 09 $F_A$ and $F_V$ results are highly (anti-)correlated: $F_A + 1.0286 F_V = 0.03853 ± 0.00014$.

²BOLOTOV 90B only determines the absolute value.

$F_A$, AXIAL-VECTOR FORM FACTOR

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.0119 ±0.0001</td><td>65k</td><td>1,2 BYCHKOV</td><td>09</td><td>PIBE e<sup>+</sup>νγ at rest</td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.0115 ±0.0004</td><td>41k</td><td>1,3 FRLEZ</td><td>04</td><td>PIBE π<sup>+</sup> → e<sup>+</sup>νγ at rest</td></tr><tr><td>0.0106 ±0.0060</td><td></td><td>1,4 BOLOTOV</td><td>90B</td><td>SPEC 17 GeV π<sup>-</sup> → e<sup>+</sup>π<sup>-</sup>eγ</td></tr><tr><td>0.021 <sup>+0.011</sup><sub>-0.013</sub></td><td>98</td><td>EGLI</td><td>89</td><td>SPEC π<sup>+</sup> → e<sup>+</sup>ν<sub>e</sub>e<sup>+</sup>e<sup>-</sup></td></tr><tr><td>0.0135 ±0.0016</td><td></td><td>1,4 BAY</td><td>86</td><td>SPEC π<sup>+</sup> → e<sup>+</sup>νγ</td></tr><tr><td>0.006 ±0.003</td><td></td><td>1,4 PIILONEN</td><td>86</td><td>SPEC π<sup>+</sup> → e<sup>+</sup>νγ</td></tr><tr><td>0.011 ±0.003</td><td></td><td>1,4,5 STETZ</td><td>78</td><td>SPEC π<sup>+</sup> → e<sup>+</sup>νγ</td></tr></tbody></table>

¹These values come from fixing the vector form factor at the CVC prediction, $F_V = 0.0259 ± 0.0005$.

²When $F_V$ is released, the BYCHKOV 09 $F_A$ is 0.0117 ± 0.0017, and $F_A$ and $F_V$ results are highly (anti-)correlated: $F_A + 1.0286 F_V = 0.03853 ± 0.00014$.

³The sign of $\gamma = F_A / F_V$ is determined to be positive.

⁴Only the absolute value of $F_A$ is determined.

⁵The result of STETZ 78 has a two-fold ambiguity. We take the solution compatible with later determinations.

VECTOR FORM FACTOR SLOPE PARAMETER a

This is a $F_V(q^2) = F_V(0)$ ($1 + a q^2$)

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.10 ±0.06</td><td>65k</td><td>BYCHKOV</td><td>09</td><td>PIBE e<sup>+</sup>νγ at rest</td></tr></tbody></table>

R, SECOND AXIAL-VECTOR FORM FACTOR

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.059 <sup>+0.009</sup><sub>-0.008</sub></td><td>98</td><td>EGLI</td><td>89</td><td>SPEC π<sup>+</sup> → e<sup>+</sup>ν<sub>e</sub>e<sup>+</sup>e<sup>-</sup></td></tr></tbody></table>

$\pi^{\pm}$ CHARGE RADIUS

The charge radius of the pion $\sqrt{\langle r^2 \rangle}$ is defined in relation to the form factor of the pion electromagnetic vertex, called vector form factor VFF, $F_V^\pi$. The VFF is a function of the squared four-momentum transfer $t$, or $\pi^2$ of the squared c.m. energy $s$, depending on the channel in which the photon exchange takes place. In both cases, it is related to the slope of the VFF at zero, namely

$$ \langle r^2 \rangle = 6 \frac{dF_V(q)}{dq} (q=0) \text{ where } q = t, s. $$

The quantity cannot be measured directly. It can be extracted from the cross sections of three processes: pion electroproduction, $eN \to e\pi\pi$, and pion electron scattering $e^- \to e^+\pi$, for the $t$ channel, and positron electron annihilation into two charged pions, $e^+e^- \to \pi^+\pi^-$, for the $s$ channel. We encode all measurements, but we do not use electroproduction data in averaging because the extraction of the pion radius involves, in this case, theoretical uncertainties that cannot be controlled at the needed level of accuracy. In case of analyses based on the same data set, as ANANTHANARAYAN 17 and COLANGELO 19, which cannot be averaged, we combine the results into a common value, with the uncertainty range chosen to cover both analyses. Note that for consistency the form factor needs to be defined in both channels with the vacuum polarisation removed. For details see COLANGELO 19 or Appendix B of ANANTHANARAYAN 16A.

<table><thead><tr><th>VALUE (fm)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4"><strong>0.659 ±0.004 OUR AVERAGE</strong></td></tr><tr><td>0.656 ±0.005</td><td>1 PDG</td><td>19</td><td>FIT</td></tr><tr><td>0.65 ±0.05</td><td>ESCHRICH</td><td>01</td><td>CNTR π<sup>+</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>0.663 ±0.006</td><td>AMENDOLIA</td><td>86</td><td>CNTR π<sup>+</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>0.663 ±0.023</td><td>DALLY</td><td>82</td><td>CNTR π<sup>+</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.640 ±0.007</td><td>2 CUI</td><td>21A</td><td>FIT</td><td>Fit existing data</td></tr><tr><td>0.655 ±0.004</td><td>3 COLANGELO</td><td>19</td><td>FIT</td><td>Fit existing data</td></tr><tr><td>0.657 ±0.003</td><td>4 ANANTHANA..17</td><td>19</td><td>FIT</td><td>Fit existing data</td></tr><tr><td>0.6603 ±0.0005 ±0.0004</td><td>5 HANHART</td><td>17</td><td>FIT</td><td>Fit existing data</td></tr><tr><td>0.740 ±0.031</td><td>6 LIESENFELD</td><td>99</td><td>CNTR e<sup>+</sup> → e<sup>+</sup>n</td><td></td></tr><tr><td>0.661 ±0.012</td><td>7 BIJNENS</td><td>98</td><td>CNTR χPT extraction</td><td></td></tr><tr><td>0.660 ±0.024</td><td>AMENDOLIA</td><td>84</td><td>CNTR π<sup>+</sup> → π<sup>+</sup>π<sup>-</sup></td><td></td></tr><tr><td>0.711 ±0.009</td><td>6 BEBEK</td><td>78</td><td>CNTR eN → eπN</td><td></td></tr><tr><td>0.678 ±0.004</td><td>8 QUENZER</td><td>78</td><td>CNTR e<sup>+</sup> → e<sup>+</sup>π<sup>+</sup>π<sup>-</sup></td><td></td></tr><tr><td>0.78 ±0.09</td><td>ADYLOV</td><td>77</td><td>CNTR π<sup>+</sup> → π<sup>+</sup>π<sup>-</sup></td><td></td></tr></tbody></table>

$$ 0.74 \quad \begin{array}{c} +0.11 \\ -0.13 \end{array} $$

$$ 0.56 \quad \pm 0.04 $$

$$ \text{BARDIN} \quad 77 \quad \text{CNTR } e\pi \to e\pi^+ n $$

$$ \text{DALLY} \quad 77 \quad \text{CNTR } \pi e \to \pi e $$

¹This value combines the measurements of ANANTHANARAYAN 17 and COLANGELO 19 which are based on the same data set. The uncertainty range is chosen to cover both results.

²CUI 21A perform a fit including spacelike data only. Employ a new mathematical procedure based on interpolation via continued fractions augmented by statistical sampling. Also do not impose the charge conserving normalization condition $F(0) = 1$.

³COLANGELO 19 fit existing $F_V$ data, using an extended Omnes dispersive representation. This analysis is based on the same data set of ANANTHANARAYAN 17. Accordingly, they cannot be averaged. We combine the results into a common value, with the uncertainty range chosen to cover the uncertainty ranges of both analyses.

⁴ANANTHANARAYAN 17 fit existing $F_V$ data, using a mixed phase-modulus dispersive representation. This analysis is based on the same data set of COLANGELO 19. Accordingly, they cannot be averaged. We combine the results into a common value, with the uncertainty range chosen to cover the uncertainty ranges of both analyses.

⁵According to the authors the uncertainty could be underestimated. The value quoted omits the BaBar data AUBERT 09.

⁶The extractions could contain an additional theoretical uncertainty which cannot be sufficiently quantified.

⁷BIJNENS 98 fits existing data.

⁸The extraction is based on a parametrization that does not have correct analytic properties.

$\pi^{\pm}$ REFERENCES

We have omitted some papers that have been superseded by later experiments. The omitted papers may be found in our 1988 edition Physics Letters B204 1 (1988).

<table><tbody><tr><td>CUI</td><td>21A</td><td>PL B822 136631</td><td>Z.-F. Cui et al.</td><td>(NJU, ECT, HZDR)</td></tr><tr><td>AGUILAR-AR...</td><td>20A</td><td>PR D102 012001</td><td>A. Aguilar-Arevalo et al.</td><td>(PIENU Collab.)</td></tr><tr><td>COLANGELO</td><td>19</td><td>JHEP 1902 006</td><td>G. Colangelo, M. Hoferichter, P. Stoffer</td><td>(BERN+)</td></tr><tr><td>DAUM</td><td>19</td><td>PL B796 11</td><td>M. Daum, R. Frosch, P.-R. Kettle</td><td>(PSI)</td></tr><tr><td>PDG</td><td>19</td><td>RPP 2019 at pdg.ibl.gov</td><td>M. Tanabashi et al.</td><td>(PDG Collab.)</td></tr><tr><td>ANANTHANA...</td><td>17</td><td>PRL 119 132002</td><td>B. Ananthanarayan, I. Caprini, D. Das</td><td></td></tr><tr><td>HANHART</td><td>17</td><td>EPJ C77 98</td><td>C. Hanhart et al.</td><td></td></tr><tr><td>ANANTHANA...</td><td>16A</td><td>PR D93 116007</td><td>B. Ananthanarayan et al.</td><td></td></tr><tr><td>TRASSINELLI</td><td>16</td><td>PL B759 583</td><td>M. Trassinelli et al.</td><td></td></tr><tr><td>ADOLPH</td><td>15A</td><td>PRL 114 062002</td><td>C. Adolph et al.</td><td>(COMPASS Collab.)</td></tr><tr><td>AGUILAR-AR...</td><td>15</td><td>PRL 115 071801</td><td>A. Aguilar-Arevalo et al.</td><td>(PIENU Collab.)</td></tr><tr><td>HOLSTEIN</td><td>14</td><td>ARNPS 64 51</td><td>B. Holstein, S. Scherer</td><td>(MASA, MAINZ)</td></tr><tr><td>AUBERT</td><td>09</td><td>PR D79 011102</td><td>B. Aubert et al.</td><td>(BABAR Collab.)</td></tr><tr><td>BYCHKOV</td><td>09</td><td>PRL 103 051802</td><td>M. Bychkov et al.</td><td>(PSI PIBETA Collab.)</td></tr><tr><td>FRLEZ</td><td>04</td><td>PRL 93 181804</td><td>E. Frlez et al.</td><td>(PSI PIBETA Collab.)</td></tr><tr><td>POCANIC</td><td>04</td><td>PRL 93 181803</td><td>D. Pocanic et al.</td><td>(PSI PIBETA Collab.)</td></tr><tr><td>ERCHSI</td><td>01</td><td>PL B522 233</td><td>I. Eschrich et al.</td><td>(FNAL SELEX Collab.)</td></tr><tr><td>LIESENFELD</td><td>99</td><td>PL B468 20</td><td>A. Liesenfeld et al.</td><td></td></tr><tr><td>BUNENS</td><td>98</td><td>JHEP 9805 014</td><td>J. Bijens et al.</td><td></td></tr><tr><td>BRESSI</td><td>98</td><td>NP B513 555</td><td>G. Bressi et al.</td><td></td></tr><tr><td>LENZ</td><td>98</td><td>PL B416 50</td><td>S. Lenz et al.</td><td></td></tr><tr><td>ASSAMAGAN</td><td>96</td><td>PR D53 6065</td><td>K.A. Assamagan et al.</td><td>(PSI, ZURI, VILL+)</td></tr><tr><td>KOPTEV</td><td>95</td><td>JETPL 61 877</td><td>V.P. Koptev et al.</td><td>(PNPI)</td></tr><tr><td>NUMAO</td><td>95</td><td>PR D52 4855</td><td>T. Numao et al.</td><td>(TRIU, BRCO)</td></tr><tr><td>ASSAMAGAN</td><td>94</td><td>PL B335 231</td><td>K.A. Assamagan et al.</td><td>(PSI, ZURI, VILL+)</td></tr><tr><td>JECKELMANN</td><td>94</td><td>PL B335 326</td><td>B. Jeckelmann, P.F.A. Goudsmit, H.J. Leisi</td><td>(WABRN+)</td></tr><tr><td>CZAPEK</td><td>93</td><td>PRL 70 17</td><td>G. Czapek et al.</td><td>(BERN, VILL)</td></tr><tr><td>BAROV</td><td>92</td><td>SJNP 55 1644</td><td>V.A. Baranov et al.</td><td>(JINR)</td></tr><tr><td>BRITTON</td><td>92</td><td>PRL 68 3000</td><td>Also</td><td>(TRIU, CARL)</td></tr><tr><td>Also</td><td>92</td><td>PR D49 28</td><td>D.I. Britton et al.</td><td>(TRIU, CARL)</td></tr><tr><td>NUMAO</td><td>92</td><td>MPL A7 3357</td><td>T. Numao</td><td>(TRIU)</td></tr><tr><td>BAROV</td><td>91B</td><td>SJNP 54 790</td><td>V.A. Baranov et al.</td><td>(JINR)</td></tr><tr><td>DAUM</td><td>91</td><td>PL B265 425</td><td>M. Daum et al.</td><td>(VILL)</td></tr><tr><td>BOLOTOV</td><td>90B</td><td>PL B243 308</td><td>V.N. Bolotov et al.</td><td>(INRM)</td></tr><tr><td>EGLI</td><td>89</td><td>PL B717 93</td><td>S. Egli et al.</td><td>(SINDRUM Collab.)</td></tr><tr><td>Also</td><td>88</td><td>PL B204 1</td><td>S. Egli et al.</td><td>(AACH3, ETH, SIN, ZURI)</td></tr><tr><td>PDG</td><td>88</td><td>PR D37 1131</td><td>G.P. Yost et al.</td><td>(LBL+)</td></tr><tr><td>PICCIOTTO</td><td>88</td><td>PR D37 1131</td><td>C.E. Picciotto et al.</td><td>(TRIU, CNRC)</td></tr><tr><td>COHEN</td><td>87</td><td>RMP 59 1121</td><td>E.R. Cohen, B.N. Taylor</td><td>(RISC, NBS)</td></tr><tr><td>KORENCH...</td><td>87</td><td>SJNP 46 192</td><td>S.M. Korenchenko et al.</td><td>(JINR)</td></tr><tr><td>Also</td><td>87</td><td>Also</td><td>Translated from YAF 46 313.</td><td></td></tr><tr><td>AMENDOLIA</td><td>86</td><td>NP B277 168</td><td>S.R. Amendolia et al.</td><td>(CERN NA7 Collab.)</td></tr><tr><td>BAY</td><td>86</td><td>PL B174 445</td><td>A. Bay et al.</td><td>(LAUS, ZURI)</td></tr><tr><td>BRYMAN</td><td>86</td><td>PL B33 1211</td><td>D.A. Bryman et al.</td><td>(TRIU, CNRC)</td></tr><tr><td>Also</td><td>86</td><td>PL 50 7</td><td>D.A. Bryman et al.</td><td>(TRIU, CNRC)</td></tr><tr><td>JECKELMANN</td><td>86B</td><td>NP A457 709</td><td>B. Jeckelmann et al.</td><td>(ETH, FRIB)</td></tr><tr><td>Also</td><td>86B</td><td>PRL 56 1444</td><td>B. Jeckelmann et al.</td><td>(ETH, FRIB)</td></tr><tr><td>PHILONEN</td><td>86</td><td>PRL 57 1402</td><td>L.E. Pillonen et al.</td><td>(LANL, TEMP, CHIC)</td></tr><tr><td>MCFARLANE</td><td>85</td><td>PR D32 547</td><td>W.K. McFarlane et al.</td><td>(TEMP, LANL)</td></tr><tr><td>ABELA</td><td>84</td><td>PL 146B 431</td><td>R. Abela et al.</td><td>(SIN)</td></tr><tr><td>Also</td><td>84</td><td>PL 74B 126</td><td>M. Daum et al.</td><td>(SIN)</td></tr><tr><td>Also</td><td>84</td><td>PR D20 2692</td><td>M. Daum et al.</td><td>(SIN)</td></tr><tr><td>AMENDOLIA</td><td>84</td><td>PL 146B 116</td><td>S.R. Amendolia et al.</td><td>(CERN NA7 Collab.)</td></tr><tr><td>FETSCHER</td><td>84</td><td>PL 140B 117</td><td>W. Fetscher</td><td>(ETH)</td></tr><tr><td>ABELA</td><td>84</td><td>PL 149 413</td><td>R. Abela et al.</td><td>(BASL, KARLK, KARLE)</td></tr><tr><td>CARR</td><td>83</td><td>PRL 51 627</td><td>J. Carr et al.</td><td>(LBL, NWES, TRIU)</td></tr><tr><td>COOPER</td><td>82</td><td>PL 112B 97</td><td>A.M. Cooper et al.</td><td>(RL)</td></tr><tr><td>DALLY</td><td>82</td><td>PRL 48 375</td><td>E.B. Dally et al.</td><td></td></tr><tr><td>LU</td><td>80</td><td>PRL 45 1066</td><td>D.C. Lu et al.</td><td>(YALE, COLU, JHU)</td></tr><tr><td>BEBEK</td><td>78</td><td>PR D17 1693</td><td>C.J. Bebek et al.</td><td></td></tr><tr><td>QUENZER</td><td>78</td><td>PL 76B 512</td><td>A. Quenzer et al.</td><td>(LALO)</td></tr><tr><td>STETZ</td><td>78</td><td>NP B138 285</td><td>A.W. Stetz et al.</td><td>(LBL, UCLA)</td></tr><tr><td>ADYLOV</td><td>77</td><td>NP B128 461</td><td>G.T. Adylov et al.</td><td></td></tr><tr><td>BARDIN</td><td>77</td><td>NP B120 45</td><td>G. Bardin et al.</td><td></td></tr><tr><td>DALLY</td><td>77</td><td>PRL 39 1176</td><td>E.B. Dally et al.</td><td></td></tr><tr><td>CARTER</td><td>76</td><td>PL 37 1380</td><td>A.L. Carter et al.</td><td>(CARL, CNRC, CHIC+)</td></tr><tr><td>KORENCH...</td><td>76B</td><td>JETP 44 35</td><td>S.M. Korenchenko et al.</td><td>(JINR)</td></tr><tr><td>MARUSHEN...</td><td>76</td><td>Translated from ZETF 71 69.</td><td>V.J. Marushenko et al.</td><td>(PNPI)</td></tr><tr><td>Also</td><td>76</td><td>Translated from ZETF 23 80.</td><td>W. Fetscher</td><td>(FNAL)</td></tr><tr><td>Also</td><td>76</td><td>Private Comm.</td><td>A. Smirnov</td><td>(PNPI)</td></tr><tr><td>DUNAITSEV</td><td>73</td><td>SJNP 16 292</td><td>A.F. Dunaitsev et al.</td><td>(SERP)</td></tr><tr><td>AYRES</td><td>71</td><td>PR D3 1051</td><td>D.S. Ayres et al.</td><td>(LRL, UCSB)</td></tr><tr><td>Also</td><td>71</td><td>PR 157 1288</td><td>D.S. Ayres et al.</td><td>(LRL)</td></tr><tr><td>Also</td><td>71</td><td>PRL 21 261</td><td>D.S. Ayres et al.</td><td>(LRL, UCSB)</td></tr><tr><td>Also</td><td>71</td><td>Thesis UCRL 18369</td><td>D.S. Ayres</td><td>(LRL)</td></tr><tr><td>Also</td><td>71</td><td>PRL 23 1267</td><td>A.J. Greenberg et al.</td><td>(LRL, UCSB)</td></tr><tr><td>KORENCH...</td><td>71</td><td>SJNP 13 189</td><td>S.M. Korenchenko et al.</td><td>(JINR)</td></tr><tr><td></td><td></td><td>Translated from YAF 13 339.</td><td></td><td></td></tr></tbody></table>
# Meson Particle Listings

$$\pi^{\pm}, \pi^{0}$$

<table><tr><td>BOOTH</td><td>70</td><td>PL 32B 723</td><td>P.S.L. Booth et al.</td><td>(LIVP)</td></tr><tr><td>DEPOMMIER</td><td>68</td><td>NP B4 189</td><td>P. Depommier et al.</td><td>(CERN)</td></tr><tr><td>PETRUKHIN</td><td>68</td><td>JINR P1 3862</td><td>V.I. Petrukhin et al.</td><td>(JINR)</td></tr><tr><td>HYMAN</td><td>67</td><td>PL 25B 376</td><td>L.G. Hyman et al.</td><td>(ANL, CMU, NWES)</td></tr><tr><td>NORDBERG</td><td>67</td><td>PL 24B 594</td><td>M.E. Nordberg, F. Lobkowicz, R.L. Burman</td><td>(ROCH)</td></tr><tr><td>BARDON</td><td>66</td><td>PRL 16 775</td><td>M. Bardon et al.</td><td>(COLU)</td></tr><tr><td>KINSEY</td><td>66</td><td>PRL 144 1132</td><td>K.F. Kinsey, F. Lobkowicz, M.E. Nordberg</td><td>(ROCH)</td></tr><tr><td>LOBKOWICZ</td><td>66</td><td>PRL 17 548</td><td>F. Lobkowicz et al.</td><td>(ROCH, BNL)</td></tr><tr><td>BACASTOW</td><td>65</td><td>PR 139 B407</td><td>R.B. Bacastow et al.</td><td>(LRL, SLAC)</td></tr><tr><td>BERTRAM</td><td>65</td><td>PR 139 B617</td><td>W.K. Bertram et al.</td><td>(MICH, CMU)</td></tr><tr><td>DUNAITSEV</td><td>65</td><td>JETP 20 58</td><td>A.F. Dunaitsev et al.</td><td>(JINR)</td></tr><tr><td colspan="5">Translated from ZETF 47 84.</td></tr><tr><td>ECKHAUSE</td><td>65</td><td>PL 19 348</td><td>M. Eckhause et al.</td><td>(WILL)</td></tr><tr><td>BARTLETT</td><td>64</td><td>PR 136 B1452</td><td>D. Bartlett et al.</td><td>(COLU)</td></tr><tr><td>DICAPUA</td><td>64</td><td>PR 133 B1333</td><td>M. di Capua et al.</td><td>(COLU)</td></tr><tr><td colspan="5">Also</td></tr><tr><td>DEPOMMIER</td><td>63</td><td>Private Comm.</td><td>L. Pondrom</td><td>(WISC)</td></tr><tr><td>DEPOMMIER</td><td>63B</td><td>PL 7 285</td><td>P. Depommier et al.</td><td>(CERN)</td></tr><tr><td>ANDERSON</td><td>60</td><td>PR 119 2050</td><td>P. Depommier et al.</td><td>(EFI)</td></tr><tr><td>CASTAGNOLI</td><td>58</td><td>PR 112 1779</td><td>H.L. Anderson et al.</td><td>(ROMA)</td></tr></table>

$$\pi^0$$

We have omitted some results that have been superseded by later experiments. The omitted results may be found in our 1988 edition Physics Letters B204 1 (1988).

$$\pi^0 \text{ MASS}$$

The value is calculated from $m_{\pi^{\pm}}$ and $(m_{\pi^{\pm}} - m_{\pi^{0}})$. See also the notes under the $\pi^{\pm}$ Mass Listings.

<table><tr><td>VALUE (MeV)</td><td>DOCUMENT ID</td></tr><tr><td>134.9768 ± 0.0005</td><td>OUR FIT</td></tr></table>

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

Measurements with an error > 0.01 MeV have been omitted.

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>4.5936 ± 0.0005</strong></td><td><strong>OUR FIT</strong></td><td></td><td></td></tr><tr><td><strong>4.5936 ± 0.0005</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td></tr><tr><td>4.59364 ± 0.00048</td><td>CRAWFORD</td><td>91</td><td>CNTR $\pi^- p \rightarrow \pi^0 n, n$ TOF</td></tr><tr><td>4.5930 ± 0.0013</td><td>CRAWFORD</td><td>86</td><td>CNTR $\pi^- p \rightarrow \pi^0 n, n$ TOF</td></tr><tr><td colspan="4">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>4.59366 ± 0.00048</td><td>CRAWFORD</td><td>88b</td><td>CNTR See CRAWFORD 91</td></tr><tr><td>4.6034 ± 0.0052</td><td>VASILEVSKY</td><td>66</td><td>CNTR</td></tr><tr><td>4.6056 ± 0.0055</td><td>CZIRR</td><td>63</td><td>CNTR</td></tr></tbody></table>

$$\pi^0 \text{ MEAN LIFE}$$

Most experiments measure the $\pi^0$ width which we convert to a lifetime. ATHERTON 85 is the only direct measurement of the $\pi^0$ lifetime. The two Primakoff measurements from 1970 have been excluded from our average because they suffered model-related systematics unknown at the time. More information on the $\pi^0$ lifetime can be found in BERNSTEIN 13.

<table><thead><tr><th>VALUE (10<sup>-17</sup> s)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>8.43 ± 0.13</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>8.337 ± 0.056 ± 0.112</td><td></td><td>1 LARIN</td><td>20</td><td>PRMX Primakoff effect</td></tr><tr><td>8.5 ± 1.1</td><td></td><td>2 BYCHKOV</td><td>09</td><td>PIBE $\pi^+ \rightarrow e^+ \nu \gamma$ at rest</td></tr><tr><td>8.4 ± 0.5 ± 0.5</td><td>1182</td><td>3 WILLIAMS</td><td>88</td><td>CBAL $e^+ e^- \rightarrow e^+ e^- \pi^0$</td></tr><tr><td>8.97 ± 0.22 ± 0.17</td><td></td><td>ATHERTON</td><td>85</td><td>CNTR Direct measurement</td></tr><tr><td>8.2 ± 0.4</td><td></td><td>4 BROWMAN</td><td>74</td><td>CNTR Primakoff effect</td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>8.32 ± 0.15 ± 0.18</td><td></td><td>5 LARIN</td><td>11</td><td>PRMX Primakoff effect</td></tr><tr><td>5.6 ± 0.6</td><td></td><td>BELLETTINI</td><td>70</td><td>CNTR Primakoff effect</td></tr><tr><td>9 ± 0.68</td><td></td><td>KRYSHKIN</td><td>70</td><td>CNTR Primakoff effect</td></tr><tr><td>7.3 ± 1.1</td><td></td><td>BELLETTINI</td><td>65b</td><td>CNTR Primakoff effect</td></tr></tbody></table>

$$\pi^0 \text{ DECAY MODES}$$

For decay limits to particles which are not established, see the appropriate Search sections ($A^0$ (axion) and Other Light Boson ($\chi^0$) Searches, etc.).

<table><thead><tr><th>Mode</th><th>Fraction ($\Gamma_i/\Gamma$)</th><th>Scale factor/<br>Confidence level</th></tr></thead><tbody><tr><td>$\Gamma_1$</td><td>(98.823 ± 0.034) %</td><td>S=1.5</td></tr><tr><td>$\Gamma_2$</td><td>( 1.174 ± 0.035) %</td><td>S=1.5</td></tr><tr><td>$\Gamma_3$</td><td>( 1.82 ± 0.29) × 10<sup>-9</sup></td><td></td></tr></tbody></table>

<table><tr><td>$\Gamma_4$</td><td>$e^+ e^- e^- e^-$</td><td>( 3.34 ± 0.16) × 10<sup>-5</sup></td></tr><tr><td>$\Gamma_5$</td><td>$e^+ e^-$</td><td>( 6.46 ± 0.33) × 10<sup>-8</sup></td></tr><tr><td>$\Gamma_6$</td><td>$4\gamma$</td><td>< 2 × 10<sup>-8</sup> CL=90%</td></tr><tr><td>$\Gamma_7$</td><td>invisible</td><td>< 4.4 × 10<sup>-9</sup> CL=90%</td></tr><tr><td>$\Gamma_8$</td><td>$\nu_e \bar{\nu}_e e$</td><td>< 1.7 × 10<sup>-6</sup> CL=90%</td></tr><tr><td>$\Gamma_9$</td><td>$\nu_\mu \bar{\nu}_\mu \mu$</td><td>< 1.6 × 10<sup>-6</sup> CL=90%</td></tr><tr><td>$\Gamma_{10}$</td><td>$\nu_\tau \bar{\nu}_\tau \tau$</td><td>< 2.1 × 10<sup>-6</sup> CL=90%</td></tr><tr><td>$\Gamma_{11}$</td><td>$\gamma \nu \bar{\nu} \nu$</td><td>< 1.9 × 10<sup>-7</sup> CL=90%</td></tr></table>

### Charge conjugation (C) or Lepton Family number (LF) violating modes

<table><tr><td>$\Gamma_{12}$</td><td>$3\gamma$</td><td>C</td><td>< 3.1 × 10<sup>-8</sup> CL=90%</td></tr><tr><td>$\Gamma_{13}$</td><td>$\mu^+ e^-$</td><td>LF</td><td>< 3.8 × 10<sup>-10</sup> CL=90%</td></tr><tr><td>$\Gamma_{14}$</td><td>$\mu^- e^+$</td><td>LF</td><td>< 3.2 × 10<sup>-10</sup> CL=90%</td></tr><tr><td>$\Gamma_{15}$</td><td>$\mu^+ e^- + \mu^- e^+$</td><td>LF</td><td>< 3.6 × 10<sup>-10</sup> CL=90%</td></tr></table>

### CONSTRAINED FIT INFORMATION

An overall fit to 2 branching ratios uses 6 measurements and one constraint to determine 3 parameters. The overall fit has a $\chi^2 = 4.6$ for 4 degrees of freedom.

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

$$\begin{array}{c|ccc} x_2 & -100 & 0 & -1 \\ x_4 & 0 & x_1 & x_2 \end{array}$$

$$\pi^0 \text{ BRANCHING RATIOS}$$

$$\Gamma(e^+ e^- \gamma)/\Gamma(2\gamma) \qquad \Gamma_2/\Gamma_1$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>1.188 ± 0.035</strong></td><td><strong>OUR FIT</strong></td><td></td><td></td><td></td></tr><tr><td><strong>1.188 ± 0.034</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td colspan="5">Error includes scale factor of 1.5.</td></tr><tr><td colspan="5">Error includes scale factor of 1.4. See the ideogram below.</td></tr><tr><td>1.140 ± 0.024</td><td>± 0.033</td><td>12.5k</td><td>1 BEDDALL</td><td>08 ALEP $e^+ e^- \rightarrow Z \rightarrow$ hadrons</td></tr><tr><td>1.25 ± 0.04</td><td></td><td></td><td>SCHARDT</td><td>81 SPEC $\pi^- p \rightarrow n\pi^0$</td></tr><tr><td>1.166 ± 0.047</td><td></td><td>3k</td><td>2 SAMIOS</td><td>61 HBC $\pi^- p \rightarrow n\pi^0$</td></tr><tr><td>1.17 ± 0.15</td><td></td><td>27</td><td>BUDAGOV</td><td>60 HBC</td></tr></tbody></table>

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

<table><tr><td>1.1559 ± 0.047 ± 0.0106</td><td>60k</td><td>3 ABOUZAID</td><td>19 KTEV $K_L \rightarrow 3\pi^0$ in flight</td></tr><tr><td>1.196</td><td></td><td>JOSEPH</td><td>60 THEO QED calculation</td></tr></table>

### WEIGHTED AVERAGE

<figure><img src="image_431.png" /></figure>

$$\Gamma(\gamma \text{ positronium})/\Gamma(2\gamma) \qquad \Gamma_3/\Gamma_1$$

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>1.84 ± 0.29</strong></td><td>277</td><td>AFANASYEV</td><td>90 CNTR pC 70 GeV</td><td></td></tr></tbody></table>

<footnote n="1">1 LARIN 20 reported this lifetime value from a measurement of $\Gamma(\pi^0 \rightarrow \gamma\gamma) = 7.802 \pm 0.052 \pm 0.105$ eV, combining data from PrimEx-II on 12C and 28Si targets with previous PrimEx-I LARIN 11 measurements. This result supersedes LARIN 11.</footnote>

<footnote n="2">2 BYCHKOV 09 obtains this using the conserved-vector-current relation between the vector form factor $F_V$ and the $\pi^0$ lifetime.</footnote>

<footnote n="3">3 WILLIAMS 88 gives $\Gamma(\gamma\gamma) = 7.7 \pm 0.5 \pm 0.5$ eV. We give here $\tau = \hbar/\Gamma(\text{total})$.</footnote>

<footnote n="4">4 BROWMAN 74 gives a $\pi^0$ width $\Gamma = 8.02 \pm 0.42$ eV. The mean life is $\hbar/\Gamma$.</footnote>

<footnote n="5">5 LARIN 11 reported $\Gamma(\pi^0 \rightarrow \gamma\gamma) = 7.82 \pm 0.14 \pm 0.17$ eV which we converted to mean life $\tau = \hbar/\Gamma(\text{total})$.</footnote>

<footnote n="1">1 BEDDALL 08 value is obtained from ALEPH archived data.</footnote>

<footnote n="2">2 SAMIOS 61 value uses a Panofsky ratio = 1.62.</footnote>

<footnote n="3">3 ABOUZAID 19 measured a value of $(0.3920 \pm 0.0016 \pm 0.0036)\%$ from 1999 KTEV data in $K_L \rightarrow 3\pi^0 \rightarrow 5\gamma e^+ e^-$ decays, normalised to $K_L \rightarrow 3\pi^0$, for $m(e^e) > 15$ MeV and then extrapolated it to the full $m(e^e)$ range using the Mikaelian and Smith predictions for the mass spectrum.</footnote>
$\Gamma(e^+e^-e^-)/\Gamma(2\gamma)$

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

3.38±0.16 OUR FIT

3.38±0.16 OUR AVERAGE

<table><tr><td>3.46±0.19</td><td>30.5k</td><td>1 ABOUZAID</td><td>08D</td><td>KTEV</td><td>$K_L^0 \to \pi^0 \pi^0 \pi^0 \pi^0$</td></tr><tr><td>3.18±0.30</td><td>146</td><td>2 SAMIOS</td><td>62B</td><td>HBC</td><td></td></tr></table>

¹This ABOUZAID 08d value includes all radiative final states. The error includes both statistical and systematic errors. The correlation between the Dalitz-pair planes gives a direct measurement of the $\pi^0$ parity. The $\pi^0 2\gamma^*$ form factor is measured and limits are placed on a scalar contribution to the decay.

²SAMIOS 62B value uses a Panofsky ratio = 1.62.

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

Experimental results are listed; branching ratios corrected for radiative effects are given in the footnotes. BERMAN 60 found $B(\pi^0 \to e^+e^-) \ge 4.69 \times 10^{-8}$ via an exact QED calculation.

<table><thead><tr><th>VALUE (units 10<sup>-8</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="6"><strong>6.46±0.33 OUR AVERAGE</strong></td></tr></tbody></table>

<table><tr><td>6.44±0.25±0.22</td><td>794</td><td>1 ABOUZAID</td><td>07</td><td>KTEV</td><td>$K_L^0 \to 3\pi^0$ in flight</td></tr><tr><td>6.9±2.3±0.6</td><td>21</td><td>2 DESHPANDE</td><td>93</td><td>SPEC</td><td>$K^+ \to \pi^+\pi^0$</td></tr><tr><td>7.6<sup>+2.9</sup><sub>-2.8</sub></td><td>8</td><td>3 MCFARLAND</td><td>93</td><td>SPEC</td><td>$K_L^0 \to 3\pi^0$ in flight</td></tr></table>

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

<table><tr><td>6.09±0.40±0.24</td><td>275</td><td>4 ALAVI-HARATI99C</td><td>SPEC</td><td>0</td><td>Repl. by ABOUZAID 07</td></tr></table>

¹ABOUZAID 07 result is for $m_{e^+e^-}/m_{\pi^0} > 0.95$. With radiative corrections the result becomes $(7.48 \pm 0.29 \pm 0.25) \times 10^{-8}$.

²The DESHPANDE 93 result with bremstrahlung radiative corrections is $(8.0 \pm 2.6 \pm 0.6) \times 10^{-8}$.

³The MCFARLAND 93 result is for $B[\pi^0 \to e^+e^-]$, $(m_{e^+e^-}/m_{\pi^0})^2 > 0.95]$. With radiative corrections it becomes $(8.8^{+4.5}_{-3.2} \pm 0.6) \times 10^{-8}$.

⁴ALAVI-HARATI 99C quote result for $B[\pi^0 \to e^+e^-]$, $(m_{e^+e^-}/m_{\pi^0})^2 > 0.95]$ to minimize radiative contributions from $\pi^0 \to e^+e^-\gamma$. After radiative corrections they obtain $(7.04 \pm 0.46 \pm 0.28) \times 10^{-8}$.

$\Gamma(e^+e^-)/\Gamma(2\gamma)$

<table><thead><tr><th>VALUE (units 10<sup>-7</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="6"><strong>• • • We do not use the following data for averages, fits, limits, etc.</strong></td></tr></tbody></table>

<table><tr><td>&lt;1.3</td><td>90</td><td>NIEBUHR</td><td>89</td><td>SPEC</td><td>$\pi^- p \to \pi^0 n$ at rest</td></tr><tr><td>&lt;5.3</td><td>90</td><td>ZEPHAT</td><td>87</td><td>SPEC</td><td>$\pi^- p \to \pi^0 n$<br>0.3 GeV/c</td></tr><tr><td>1.7 ±0.6 ±0.3</td><td>59</td><td>FRANK</td><td>83</td><td>SPEC</td><td>$\pi^- p \to n\pi^0$</td></tr><tr><td>1.8 ±0.6</td><td>58</td><td>MISCHKE</td><td>82</td><td>SPEC</td><td>See FRANK 83</td></tr><tr><td>2.23<sup>+2.40</sup><sub>-1.10</sub></td><td>90</td><td>FISCHER</td><td>78B</td><td>SPRK</td><td>$K^+ \to \pi^+\pi^0$</td></tr></table>

$\Gamma(4\gamma)/\Gamma_{\text{total}}$

<table><thead><tr><th>VALUE (units 10<sup>-8</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt; 2</td><td>90</td><td>MCDONOUGH 88</td><td>CBOX</td><td>$\pi^- p$ at rest</td><td></td></tr></tbody></table>

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

<table><tr><td>&lt;160</td><td>90</td><td>BOLOTOV</td><td>86C</td><td>CALO</td><td></td></tr><tr><td>&lt;440</td><td>90</td><td>0</td><td>AUERBACH</td><td>80</td><td>CNTR</td></tr></table>

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

The limits apply to all "invisible" channels, including in particular neutrino-antineutrino final states, obtained with laboratory experiments. Astrophysical and cosmological limits exist and are many orders of magnitude lower, but they are model dependent.

<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; 4.4 × 10<sup>-9</sup></td><td>90</td><td>CORTINA-GIL</td><td>21C</td><td>SPEC</td><td>$K^+ \to \pi^+\pi^0(\gamma)$</td></tr></tbody></table>

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

<table><tr><td>&lt; 0.27 × 10<sup>-6</sup></td><td>90</td><td>ARTAMONOV</td><td>05A</td><td>B949</td><td>$K^+ \to \pi^+\pi^0$</td></tr><tr><td>&lt; 0.83 × 10<sup>-6</sup></td><td>90</td><td>ATIYA</td><td>91</td><td>B787</td><td>$K^+ \to \pi^+\nu\bar{\nu}'$</td></tr><tr><td>&lt;24 × 10<sup>-6</sup></td><td>90</td><td>HERCZEG</td><td>81</td><td>RVUE</td><td>$K^+ \to \pi^+\nu\bar{\nu}'$</td></tr></table>

$\Gamma(\nu_e\bar{\nu}_e)/\Gamma_{\text{total}}$

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;1.7</td><td>90</td><td>DORENBOS...</td><td>88</td><td>CHRM</td><td>Beam dump, prompt $\nu$</td></tr></tbody></table>

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

<table><tr><td>&lt;3.1</td><td>90</td><td>1 HOFFMAN</td><td>88</td><td>RVUE</td><td>Beam dump, prompt $\nu$</td></tr></table>

¹HOFFMAN 88 analyzes data from a 400-GeV BEBC beam-dump experiment.

$\Gamma(\nu_{\mu}\bar{\nu}_{\mu})/\Gamma_{\text{total}}$

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;1.6</td><td>90</td><td>8.7</td><td>AUERBACH</td><td>04</td><td>LSND 800 MeV p on Cu</td></tr><tr><td>&lt;3.1</td><td>90</td><td>1 HOFFMAN</td><td>88</td><td>RVUE</td><td>Beam dump, prompt $\nu$</td></tr></tbody></table>

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

<table><tr><td>&lt;7.8</td><td>90</td><td>DORENBOS...</td><td>88</td><td>CHRM</td><td>Beam dump, prompt $\nu$</td></tr></table>

¹HOFFMAN 88 analyzes data from a 400-GeV BEBC beam-dump experiment.

$\Gamma(\nu_{\tau}\bar{\nu}_{\tau})/\Gamma_{\text{total}}$

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;2.1</td><td>90</td><td>1 HOFFMAN</td><td>88</td><td>RVUE</td><td>Beam dump, prompt $\nu$</td></tr></tbody></table>

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

<table><tr><td>&lt;4.1</td><td>90</td><td>DORENBOS...</td><td>88</td><td>CHRM</td><td>Beam dump, prompt $\nu$</td></tr></table>

¹HOFFMAN 88 analyzes data from a 400-GeV BEBC beam-dump experiment.

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

Standard Model prediction is $6 \times 10^{-18}$.

<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;1.9 × 10<sup>-7</sup></td><td>90</td><td>CORTINA-GIL</td><td>19</td><td>SPEC</td><td>$K^+ \to \pi^+\gamma\nu\bar{\nu}$</td></tr></tbody></table>

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

<table><tr><td>&lt;6 × 10<sup>-4</sup></td><td>90</td><td>ATIYA</td><td>92</td><td>CNTR</td><td>$K^+ \to \gamma\nu\bar{\nu}\pi^+$</td></tr></table>

$\Gamma(3\gamma)/\Gamma_{\text{total}}$

Forbidden by C invariance.

<table><thead><tr><th>VALUE (units 10<sup>-8</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt; 3.1</td><td>90</td><td>MCDONOUGH 88</td><td>CBOX</td><td>$\pi^- p$ at rest</td><td></td></tr></tbody></table>

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

<table><tr><td>&lt; 38</td><td>90</td><td>0</td><td>HIGHLAND</td><td>80</td><td>CNTR</td></tr><tr><td>&lt;150</td><td>90</td><td>0</td><td>AUERBACH</td><td>78</td><td>CNTR</td></tr><tr><td>&lt;490</td><td>90</td><td>0</td><td>1 DUCLOS</td><td>65</td><td>CNTR</td></tr><tr><td>&lt;490</td><td>90</td><td>1</td><td>KUTIN</td><td>65</td><td>CNTR</td></tr></table>

¹These experiments give $B(3\gamma/2\gamma) < 5.0 \times 10^{-6}$.

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

Forbidden by lepton family number conservation.

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt; 0.38</td><td>90</td><td>0</td><td>APPEL</td><td>00</td><td>SPEC</td><td>$K^+ \to \pi^+\mu^+e^-$</td></tr></tbody></table>

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

<table><tr><td>&lt;16</td><td>90</td><td>LEE</td><td>90</td><td>SPEC</td><td>$K^+ \to \pi^+\mu^+e^-$</td></tr><tr><td>&lt;78</td><td>90</td><td>CAMPAGNARI</td><td>88</td><td>SPEC</td><td>See LEE 90</td></tr></table>

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

Forbidden by lepton family 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;3.2 × 10<sup>-10</sup></td><td>90</td><td>ALIBERTI</td><td>21</td><td>NA62</td><td>$K^+ \to \pi^+\mu^+e^-$</td></tr></tbody></table>

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

<table><tr><td>&lt;3.4 × 10<sup>-9</sup></td><td>90</td><td>APPEL</td><td>00B</td><td>B865</td><td>$K^+ \to \pi^+\mu^+e^-$</td></tr></table>

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

Forbidden by lepton family number conservation.

<table><thead><tr><th>VALUE (units 10<sup>-9</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt; 0.36</td><td>90</td><td>ABOUZAID</td><td>08C</td><td>KTEV</td><td>$K_L^0 \to 2\pi^0 \mu^\pm e^\pm$</td></tr></tbody></table>

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

<table><tr><td>&lt; 17.2</td><td>90</td><td>KROLAK</td><td>94</td><td>E799</td><td>$\ln K_L^0 \to 3\pi^0$</td></tr><tr><td>&lt;140</td><td>90</td><td>HERCZEG</td><td>84</td><td>RVUE</td><td>$K^+ \to \pi^+\mu e$</td></tr><tr><td>&lt; 2 × 10<sup>-6</sup></td><td>90</td><td>HERCZEG</td><td>84</td><td>THEO</td><td>$\mu^- \to e^- \text{conversion}$</td></tr><tr><td>&lt; 70</td><td>90</td><td>BRYMAN</td><td>82</td><td>RVUE</td><td>$K^+ \to \pi^+\mu e$</td></tr></table>

$\pi^0$ ELECTROMAGNETIC FORM FACTOR

The amplitude for the process $\pi^0 \to e^+e^-\gamma$ contains a form factor $F(x)$ at the $\pi^0\gamma\gamma$ vertex, where $x = [m_{e^+e^-}/m_{\pi^0}]^2$. The parameter $a$ in the linear expansion $F(x) = 1 + ax$ is listed below.

All the measurements except that of BEHREND 91 are in the time-like region of momentum transfer.

LINEAR COEFFICIENT OF $\pi^0$ ELECTROMAGNETIC FORM FACTOR

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>3.35± 0.31 OUR AVERAGE</strong></td></tr><tr><td>3.68 ± 0.51±0.25</td><td>1.1M</td><td>LAZZERONI</td><td>17</td><td>SPEC</td><td>$K^\pm \to \pi^0 \pi^\pm; \pi^0 \to e^+e^-\gamma$</td></tr><tr><td>2.6 ± 2.4 ± 4.8</td><td>7.5k</td><td>FARZANPAY</td><td>92</td><td>SPEC</td><td>$\pi^- p \to \pi^0 n$ at rest</td></tr><tr><td>2.5 ± 1.4 ± 2.6</td><td>54k</td><td>MEIJDREEDREES92B</td><td></td><td>SPEC</td><td>$\pi^- p \to \pi^0 n$ at rest</td></tr><tr><td>3.26± 0.26±0.26</td><td>127</td><td>1 BEHREND</td><td>91</td><td>CELL</td><td>$e^+ e^- \to e^+ e^- \pi^0$</td></tr><tr><td>-11 ± 3 ± 8</td><td>32k</td><td>FONVIEILLE</td><td>89</td><td>SPEC</td><td>Radiation corr.</td></tr></tbody></table>

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

<table><tr><td>12</td><td>+ 5</td><td>2 TUPPER</td><td>83</td><td>THEO</td><td>FISCHER 78 data</td></tr><tr><td>10</td><td>± 3</td><td>3 FISCHER</td><td>78</td><td>SPEC</td><td>Radiation corr.</td></tr><tr><td>1</td><td>±11</td><td>DEVONS</td><td>69</td><td>OSPK</td><td>No radiation corr.</td></tr><tr><td>-15</td><td>±10</td><td>KOBRAK</td><td>61</td><td>HBC</td><td>No radiation corr.</td></tr><tr><td>-24</td><td>±16</td><td>SAMIOS</td><td>61</td><td>HBC</td><td>No radiation corr.</td></tr></table>

¹BEHREND 91 estimates that their systematic error is of the same order of magnitude as their statistical error, and so we have included a systematic error of this magnitude. The value of $a$ is obtained by extrapolation from the region of large space-like momentum transfer assuming vector dominance.

²TUPPER 83 is a theoretical analysis of FISCHER 78 including 2-photon exchange in the corrections.

³The FISCHER 78 error is statistical only. The result without radiation corrections is $+0.05 \pm 0.03$.
## $\pi^0$ REFERENCES

We have omitted some papers that have been superseded by later experiments. The omitted papers may be found in our 1988 edition Physics Letters **B204** 1 (1988).

<table><tbody><tr><td>ALIBERTI</td><td>21</td><td>PRL 127 131802</td><td>R. Aliberti et al.</td><td>(NA62 Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>21C</td><td>JHEP 2102 201</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>LARIN</td><td>20</td><td>SCI 368 506</td><td>I. Larin et al.</td><td>(PrimEx II Collab.)</td></tr><tr><td>ABOUZAID</td><td>19</td><td>PRL 0100 032003</td><td>E. Abouzaid et al.</td><td>(KTeV Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>19</td><td>JHEP 1905 182</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>LAZZERONI</td><td>17</td><td>PL B768 38</td><td>C. Lazzeroni et al.</td><td>(NA62 Collab.)</td></tr><tr><td>BERNSTEIN</td><td>13</td><td>RMP 85 49</td><td>A.M. Bernstein, B. R. Holstein</td><td>(AMHT, MIT)</td></tr><tr><td>LARIN</td><td>11</td><td>PRL 106 162303</td><td>I. Larin et al.</td><td>(PrimEx Collab.)</td></tr><tr><td>BYCHKOV</td><td>09</td><td>PRL 103 051802</td><td>M. Bychkov et al.</td><td>(PSI PIBETA Collab.)</td></tr><tr><td>ABOUZAID</td><td>08C</td><td>PRL 100 131803</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>ABOUZAID</td><td>08D</td><td>PRL 100 182001</td><td>E. Abouzaid et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>BEDDALL</td><td>08</td><td>EPJ C54 365</td><td>A. Beddall, A. Beddall</td><td>(UGAZ)</td></tr><tr><td>ABOUZAID</td><td>08</td><td>PRL D75 0120004</td><td>E. Abouzaid et al.</td><td>(KTeV Collab.)</td></tr><tr><td>ARTAMONOV</td><td>05A</td><td>PRL D72 091102</td><td>A.V. Artamonov et al.</td><td>(BNL E949 Collab.)</td></tr><tr><td>AUERBACH</td><td>04</td><td>PRL 92 091801</td><td>L.B. Auerbach et al.</td><td>(L5ND Collab.)</td></tr><tr><td>APPEL</td><td>00</td><td>PRL 85 2450</td><td>R. Appel et al.</td><td>(BNL 865 Collab.)</td></tr><tr><td>Also</td><td></td><td>Thesis, Yale Univ.</td><td>D.R. Bergman</td><td></td></tr><tr><td>Also</td><td></td><td>Thesis, Univ. Zurich</td><td>S. Pislat</td><td></td></tr><tr><td>APPEL</td><td>00B</td><td>PRL 85 2877</td><td>R. Appel et al.</td><td>(BNL 865 Collab.)</td></tr><tr><td>ALAVI-HARATI</td><td>99C</td><td>PRL 83 922</td><td>A. Alavi-Harati et al.</td><td>(FNAL KTeV Collab.)</td></tr><tr><td>KROLAK</td><td>94</td><td>PL B320 407</td><td>P. Krolak et al.</td><td>(EFI, UCLA, COLO, ELMT+)</td></tr><tr><td>DESHPANDE</td><td>93</td><td>PRL 71 27</td><td>A. Deshpande et al.</td><td>(BNL E851 Collab.)</td></tr><tr><td>MCFARLAND</td><td>93</td><td>PRL 71 31</td><td>K.S. McFarland et al.</td><td>(EFI, UCLA, COLO+)</td></tr><tr><td>ATIYA</td><td>92</td><td>PRL 69 733</td><td>M.S. ATIYA et al.</td><td>(BNL, LANL, PRIN+)</td></tr><tr><td>FARZANPAY</td><td>92</td><td>PL B278 413</td><td>F. Farzanpay et al.</td><td>(ORST, TRIU, BRCO+)</td></tr><tr><td>MEIJDERDREES</td><td>92B</td><td>PRL D45 1439</td><td>R. Meijer Drees et al.</td><td>(PSI SINDRUM-I Collab.)</td></tr><tr><td>ATIYA</td><td>91</td><td>PRL 66 2189</td><td>M.S. ATIYA et al.</td><td>(BNL, LANL, PRIN+)</td></tr><tr><td>BEHREND</td><td>91</td><td>ZPHY C49 401</td><td>H.J. Behrend et al.</td><td>(CELLO Collab.)</td></tr><tr><td>CRAWFORD</td><td>91</td><td>PRL D43 46</td><td>J.F. Crawford et al.</td><td>(VILL, UVA)</td></tr><tr><td>AFANASYEV</td><td>90</td><td>PL B236 116</td><td>L.G. Afanasyev et al.</td><td>(JINR, MOSU, SERP)</td></tr><tr><td>Also</td><td></td><td>SJPN 51 664</td><td>L.G. Afanasyev et al.</td><td>(JINR)</td></tr><tr><td>LEE</td><td>90</td><td>PRL 64 165</td><td>A.M. Lee et al.</td><td>(BNL, FNAL, VILL, WASH+)</td></tr><tr><td>FONVEILLE</td><td>89</td><td>H. Fonveille et al.</td><td>C. Fonveille et al.</td><td>(CLER, LYON, SACL)</td></tr><tr><td>NIEBUHR</td><td>89</td><td>PRL D40 2796</td><td>C. Niebuhr et al.</td><td>(SINDRUM Collab.)</td></tr><tr><td>CAMPAGNARI</td><td>88</td><td>PRL 61 2062</td><td>C. Campagnari et al.</td><td>(BNL, FNAL, PSI+)</td></tr><tr><td>CRAWFORD</td><td>88B</td><td>PL B213 391</td><td>J.F. Crawford et al.</td><td>(PSI, UVA)</td></tr><tr><td>DORENBOS...</td><td>88</td><td>ZPHY C40 497</td><td>J. Dorenbosch et al.</td><td>(CHARM Collab.)</td></tr><tr><td>HOFFMAN</td><td>88</td><td>PRL 208 149</td><td>C.M. Hoffman</td><td>(BNL, LANL, PRIN+)</td></tr><tr><td>MCDONOUGH</td><td>88</td><td>PRL D38 2121</td><td>J.M. McDonough et al.</td><td>(TEMP, LANL, CHIC)</td></tr><tr><td>PDG</td><td>88</td><td>PL B204 1</td><td>G.P. Yost et al.</td><td>(LBL+)</td></tr><tr><td>WILLIAMS</td><td>88</td><td>PRL D38 1365</td><td>D.A. Williams et al.</td><td>(Crystal Ball Collab.)</td></tr><tr><td>ZEPHAT</td><td>87</td><td>JP G13 1375</td><td>A.G. Zephat et al.</td><td>(OMICRON Collab.)</td></tr><tr><td>BOLOTOV</td><td>86C</td><td>JETPL 43 520</td><td>V.N. Bolotov et al.</td><td>(INRM)</td></tr><tr><td>CRAWFORD</td><td>86</td><td>PRL 56 1043</td><td>J.F. Crawford et al.</td><td>(SIN, UVA)</td></tr><tr><td>ATHERTON</td><td>85</td><td>PL 158B 81</td><td>H.W. Atherton et al.</td><td>(CERN, ISU, LUND+)</td></tr><tr><td>HERCZEG</td><td>84</td><td>PRL D29 1954</td><td>P. Herczeg, C.M. Hoffman</td><td>(LANL)</td></tr><tr><td>FRANK</td><td>83</td><td>PRL D28 423</td><td>J.S. Frank et al.</td><td>(LANL, ARZS)</td></tr><tr><td>TUPPER</td><td>83</td><td>PRL D28 2905</td><td>G.B. Tupper, T.R. Grose, M.A. Samuel</td><td>(OKSU)</td></tr><tr><td>BRYMAN</td><td>82</td><td>PRL D26 2538</td><td>D.A. Bryman</td><td>(TRIU)</td></tr><tr><td>MISCHKE</td><td>82</td><td>PRL 48 1153</td><td>R.E. Mischke et al.</td><td>(LANL, ARZS)</td></tr><tr><td>HERCZEG</td><td>81</td><td>PL 100B 347</td><td>P. Herczeg, C.M. Hoffman</td><td>(LANL)</td></tr><tr><td>SCHARDT</td><td>81</td><td>PRL D23 539</td><td>M.A. Schardt et al.</td><td>(ARZS, LANL)</td></tr><tr><td>AUERBACH</td><td>80</td><td>PRL 31 317</td><td>L.B. Auerbach et al.</td><td>(TEMP, LASL)</td></tr><tr><td>HIGHLAND</td><td>80</td><td>PRL 44 628</td><td>V.L. Highland et al.</td><td>(TEMP, LASL)</td></tr><tr><td>AUERBACH</td><td>78</td><td>PRL 41 275</td><td>L.B. Auerbach et al.</td><td>(TEMP, LASL)</td></tr><tr><td>FISCHER</td><td>78B</td><td>PL 73B 359</td><td>J. Fischer et al.</td><td>(GEVA, SACL)</td></tr><tr><td>FISCHER</td><td>78</td><td>PL 73B 364</td><td>J. Fischer et al.</td><td>(GEVA, SACL)</td></tr><tr><td>BROWMAN</td><td>74</td><td>PRL 33 1400</td><td>A. Brownman et al.</td><td>(CORN, BING)</td></tr><tr><td>BELLETTINI</td><td>70</td><td>NC 66A 243</td><td>G. Bellettini et al.</td><td>(PISA, BONN)</td></tr><tr><td>KRYSHKIN</td><td>70</td><td>JETP 30 1037</td><td>V.I. Kryshkin, A.G. Sterligov, Y.U. Povsh</td><td>(TMSK)</td></tr><tr><td>DEVONS</td><td>69</td><td>PRL 184 1356</td><td>S. Devons et al.</td><td>(COLU, ROMA)</td></tr><tr><td>VASILEVSKY</td><td>66</td><td>PL 23 281</td><td>L.M. Vasilevsky et al.</td><td>(JINR)</td></tr><tr><td>BELLETTINI</td><td>65B</td><td>NC 40A 1139</td><td>G. Bellettini et al.</td><td>(PISA, FIRZ)</td></tr><tr><td>DUCLOS</td><td>65</td><td>PL 19 253</td><td>J. Duclos et al.</td><td>(CERN, HEID)</td></tr><tr><td>KUTIN</td><td>65</td><td>JETPL 2 243</td><td>V.M. Kutjin, V.I. Petrukhin, Y.D. Prokoshkin</td><td>(JINR)</td></tr><tr><td>CZIRR</td><td>63</td><td>PL 130 341</td><td>J.B. Czirr</td><td>(LRL)</td></tr><tr><td>SAMIOS</td><td>62B</td><td>PRL 126 1844</td><td>N.P. Samios et al.</td><td>(COLU, BNL)</td></tr><tr><td>KOBRAK</td><td>61</td><td>NC 20 1115</td><td>H. Kobrak</td><td>(EFI)</td></tr><tr><td>SAMIOS</td><td>61</td><td>PRL 121 275</td><td>N.P. Samios</td><td>(COLU, BNL)</td></tr><tr><td>BERMAN</td><td>60</td><td>NC 18 1192</td><td>S. Berman, D. Geffen</td><td></td></tr><tr><td>BUDAGOV</td><td>60</td><td>JETP 11 755</td><td>V.A. Budagov et al.</td><td>(JINR)</td></tr><tr><td>JOSEPH</td><td>60</td><td>NC 16 997</td><td>D.W. Joseph</td><td>(EFI)</td></tr></tbody></table>

## $\eta$

We have omitted some results that have been superseded by later experiments. The omitted results may be found in our 1988 edition Physics Letters **B204** (1988).

## $\eta$ MASS

Recent measurements resolve the obvious inconsistency in previous $\eta$ mass measurements in favor of the higher value first reported by NA48 (LAI 02). We use only precise measurements consistent with this higher mass value for our $\eta$ mass average.

<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>547.862±0.017 OUR AVERAGE</strong></td></tr><tr><td>547.865±0.031±0.062</td><td></td><td>NIKOLAEV</td><td>14</td><td>CRYB γp → pη</td></tr><tr><td>547.873±0.005±0.027</td><td>1M</td><td>GOSLAWSKI</td><td>12</td><td>SPEC dp → <sup>3</sup>He η</td></tr><tr><td>547.874±0.007±0.029</td><td></td><td>AMBROSINO</td><td>07B</td><td>KLOE e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td></tr><tr><td>547.785±0.017±0.057</td><td>16k</td><td>MILLER</td><td>07</td><td>CLEO ψ(25) → J/ψη</td></tr><tr><td>547.843±0.030±0.041</td><td>1134</td><td>LAI</td><td>02</td><td>NA48 η → 3π<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>547.311±0.028±0.032</td><td></td><td><sup>1</sup>ABDEL-BARY</td><td>05</td><td>SPEC dp → <sup>3</sup>He η</td></tr><tr><td>547.12±0.06±0.25</td><td></td><td>KRUSCHE</td><td>95D</td><td>SPEC γp → ηp, threshold</td></tr></tbody></table>

<table><tbody><tr><td>547.30</td><td>±0.15</td><td>PLOUIN</td><td>92</td><td>SPEC dp → <sup>3</sup>He η</td></tr><tr><td>547.45</td><td>±0.25</td><td>DUANE</td><td>74</td><td>SPEC π<sup>-</sup> p → n neutrals</td></tr><tr><td>548.2</td><td>±0.65</td><td>FOSTER</td><td>65C</td><td>HBC</td></tr><tr><td>549.0</td><td>±0.7</td><td>FOELSCHE</td><td>64</td><td>HBC</td></tr><tr><td>548.0</td><td>±1.0</td><td>ALFF-...</td><td>62</td><td>HBC</td></tr><tr><td>549.0</td><td>±1.2</td><td>BASTIEN</td><td>62</td><td>HBC</td></tr></tbody></table>

¹ABDEL-BARY 05 disagrees significantly with recent measurements of similar or better precision. See comment in the header.

## $\eta$ WIDTH

This is the partial decay rate $\Gamma(\eta \to \gamma\gamma)$ divided by the fitted branching fraction for that mode. See the note at the start of the $\Gamma(2\gamma)$ data block, next below.

VALUE (keV)
1.31±0.05 OUR FIT

DOCUMENT ID

## $\eta$ DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction (f<sub>i</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th></tr></thead><tbody><tr><td colspan="3"><strong>Neutral modes</strong></td></tr><tr><td>Γ<sub>1</sub> neutral modes</td><td>(71.96±0.30) %</td><td>S=1.3</td></tr><tr><td>Γ<sub>2</sub> 2γ</td><td>(39.36±0.18) %</td><td>S=1.1</td></tr><tr><td>Γ<sub>3</sub> 3π<sup>0</sup></td><td>(32.57±0.21) %</td><td>S=1.2</td></tr><tr><td>Γ<sub>4</sub> π<sup>0</sup>2γ</td><td>(2.55±0.22) × 10<sup>-4</sup></td><td></td></tr><tr><td>Γ<sub>5</sub> 2π<sup>0</sup>2γ</td><td>&lt; 1.2 × 10<sup>-3</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>6</sub> 4γ</td><td>&lt; 2.8 × 10<sup>-4</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>7</sub> invisible</td><td>&lt; 1.0 × 10<sup>-4</sup></td><td>CL=90%</td></tr><tr><td colspan="3"><strong>Charged modes</strong></td></tr><tr><td>Γ<sub>8</sub> charged modes</td><td>(28.04±0.30) %</td><td>S=1.3</td></tr><tr><td>Γ<sub>9</sub> π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>(23.02±0.25) %</td><td>S=1.2</td></tr><tr><td>Γ<sub>10</sub> π<sup>+</sup>π<sup>-</sup>γ</td><td>(4.28±0.07) %</td><td>S=1.1</td></tr><tr><td>Γ<sub>11</sub> e<sup>+</sup>e<sup>-</sup>γ</td><td>(6.9 ± 0.4) × 10<sup>-3</sup></td><td>S=1.2</td></tr><tr><td>Γ<sub>12</sub> μ<sup>+</sup>μ<sup>-</sup>γ</td><td>(3.1 ± 0.4) × 10<sup>-4</sup></td><td></td></tr><tr><td>Γ<sub>13</sub> e<sup>+</sup>e<sup>-</sup></td><td>&lt; 7 × 10<sup>-7</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>14</sub> μ<sup>+</sup>μ<sup>-</sup></td><td>(5.8 ± 0.8) × 10<sup>-6</sup></td><td></td></tr><tr><td>Γ<sub>15</sub> 2e<sup>+</sup>2e<sup>-</sup></td><td>(2.40±0.22) × 10<sup>-5</sup></td><td></td></tr><tr><td>Γ<sub>16</sub> π<sup>+</sup>π<sup>-</sup> e<sup>+</sup>e<sup>-</sup> (γ)</td><td>(2.68±0.11) × 10<sup>-4</sup></td><td></td></tr><tr><td>Γ<sub>17</sub> e<sup>+</sup>e<sup>-</sup> μ<sup>+</sup>μ<sup>-</sup></td><td>&lt; 1.6 × 10<sup>-4</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>18</sub> 2μ<sup>+</sup>2μ<sup>-</sup></td><td>(5.0 ± 1.3) × 10<sup>-9</sup></td><td></td></tr><tr><td>Γ<sub>19</sub> μ<sup>+</sup>μ<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td><td>&lt; 3.6 × 10<sup>-4</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>20</sub> π<sup>+</sup>e<sup>-</sup> νe + c.c.</td><td>&lt; 1.7 × 10<sup>-4</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>21</sub> π<sup>+</sup>π<sup>-</sup>2γ</td><td>&lt; 2.1 × 10<sup>-3</sup></td><td></td></tr><tr><td>Γ<sub>22</sub> π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>γ</td><td>&lt; 6 × 10<sup>-4</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>23</sub> π<sup>0</sup>μ<sup>+</sup>μ<sup>-</sup>γ</td><td>&lt; 3 × 10<sup>-6</sup></td><td>CL=90%</td></tr></tbody></table>

## Charge conjugation (C), Parity (P), Charge conjugation × Parity (CP), or Lepton Family number (LF) violating modes

<table><tbody><tr><td>Γ<sub>24</sub> π<sup>0</sup>γ</td><td>C</td><td>[a] &lt; 9 × 10<sup>-5</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>25</sub> π<sup>+</sup>π<sup>-</sup></td><td>P,CP</td><td>&lt; 4.4 × 10<sup>-6</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>26</sub> 2π<sup>0</sup></td><td>P,CP</td><td>&lt; 3.5 × 10<sup>-4</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>27</sub> 2π<sup>0</sup>γ</td><td>C</td><td>&lt; 5 × 10<sup>-4</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>28</sub> 3π<sup>0</sup>γ</td><td>C</td><td>&lt; 6 × 10<sup>-5</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>29</sub> 3γ</td><td>C</td><td>&lt; 1.6 × 10<sup>-5</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>30</sub> 4π<sup>0</sup></td><td>P,CP</td><td>&lt; 6.9 × 10<sup>-7</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>31</sub> π<sup>0</sup>e<sup>+</sup>e<sup>-</sup></td><td>C</td><td>[b] &lt; 8 × 10<sup>-6</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>32</sub> π<sup>0</sup>μ<sup>+</sup>μ<sup>-</sup></td><td>C</td><td>[b] &lt; 5 × 10<sup>-6</sup></td><td>CL=90%</td></tr><tr><td>Γ<sub>33</sub> μ<sup>+</sup>e<sup>-</sup> + μ<sup>-</sup> e<sup>+</sup></td><td>LF</td><td>&lt; 6 × 10<sup>-6</sup></td><td>CL=90%</td></tr></tbody></table>

[a] Forbidden by angular momentum conservation.

[b] C parity forbids this to occur as a single-photon process.

## CONSTRAINED FIT INFORMATION

An overall fit to 2 decay rate and 22 branching ratios uses 54 measurements and one constraint to determine 9 parameters. The overall fit has a $\chi^2 = 46.2$ for 46 degrees of freedom.

The following off-diagonal array elements are the correlation coefficients $\langle\delta x_i\delta x_j\rangle/(\delta x_i\delta x_j)$, in percent, from the fit to the branching fractions, $x_i \equiv \Gamma_i/\Gamma_{\text{total}}$. The fit constrains the $x_i$ whose labels appear in this array to sum to one.
<table><thead><tr><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>x<sub>3</sub></td><td>12</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>x<sub>4</sub></td><td>4</td><td>0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>x<sub>9</sub></td><td>-69</td><td>-76</td><td>-3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>x<sub>10</sub></td><td>-48</td><td>-52</td><td>-2</td><td>53</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>x<sub>11</sub></td><td>-8</td><td>-7</td><td>0</td><td>-4</td><td>-3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>x<sub>12</sub></td><td>-1</td><td>-1</td><td>0</td><td>0</td><td>0</td><td>0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>x<sub>16</sub></td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Γ</td><td>-13</td><td>-1</td><td>-32</td><td>9</td><td>6</td><td>1</td><td>0</td><td>0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>x<sub>2</sub></td><td>x<sub>3</sub></td><td>x<sub>4</sub></td><td>x<sub>9</sub></td><td>x<sub>10</sub></td><td>x<sub>11</sub></td><td>x<sub>12</sub></td><td>x<sub>16</sub></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<table><thead><tr><th>Mode</th><th></th><th>Rate (keV)</th><th>Scale factor</th></tr></thead><tbody><tr><td>Γ<sub>2</sub></td><td>2γ</td><td>0.515 ± 0.018</td><td></td></tr><tr><td>Γ<sub>3</sub></td><td>3π<sup>0</sup></td><td>0.426 ± 0.015</td><td></td></tr><tr><td>Γ<sub>4</sub></td><td>π<sup>0</sup>2γ</td><td>(3.34 ± 0.28 ) × 10<sup>-4</sup></td><td></td></tr><tr><td>Γ<sub>9</sub></td><td>π<sup>+</sup> π<sup>-</sup> π<sup>0</sup></td><td>0.301 ± 0.011</td><td></td></tr><tr><td>Γ<sub>10</sub></td><td>π<sup>+</sup> π<sup>-</sup> γ</td><td>0.0559 ± 0.0022</td><td></td></tr><tr><td>Γ<sub>11</sub></td><td>e<sup>+</sup> e<sup>-</sup> γ</td><td>0.0090 ± 0.0006</td><td>1.2</td></tr><tr><td>Γ<sub>12</sub></td><td>μ<sup>+</sup> μ<sup>-</sup> γ</td><td>(4.1 ± 0.5 ) × 10<sup>-4</sup></td><td></td></tr><tr><td>Γ<sub>16</sub></td><td>π<sup>+</sup> π<sup>-</sup> e<sup>+</sup> e<sup>-</sup> (γ)</td><td>(3.50 ± 0.19 ) × 10<sup>-4</sup></td><td></td></tr></tbody></table>

η DECAY RATES

Γ(2γ) Γ<sub>2</sub>
See the table immediately above giving the fitted decay rates. Following the advice of NEFKENS 02, we have removed the Primakoff-effect measurement from the average. See also the "Note on the Decay Width Γ(η → γγ)," in our 1994 edition, Phys. Rev. D50, 1 August 1994, Part I, p. 1451, for a discussion of the various measurements.

<table><thead><tr><th>VALUE (keV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>0.515±0.018 OUR FIT</strong></td></tr><tr><td colspan="5"><strong>0.516±0.018 OUR AVERAGE</strong></td></tr><tr><td>0.520±0.020±0.013</td><td>BABUSCI</td><td>13A</td><td>KLOE</td><td>e<sup>+</sup>e<sup>-</sup> → e<sup>+</sup>e<sup>-</sup>η</td></tr><tr><td>0.51 ± 0.12 ± 0.05</td><td>36</td><td>BARU</td><td>90</td><td>MD1</td><td>e<sup>+</sup>e<sup>-</sup> → e<sup>+</sup>e<sup>-</sup>η</td></tr><tr><td>0.490±0.010±0.048</td><td>2287</td><td>ROE</td><td>90</td><td>ASP</td><td>e<sup>+</sup>e<sup>-</sup> → e<sup>+</sup>e<sup>-</sup>η</td></tr><tr><td>0.514±0.017±0.035</td><td>1295</td><td>WILLIAMS</td><td>88</td><td>CBAL</td><td>e<sup>+</sup>e<sup>-</sup> → e<sup>+</sup>e<sup>-</sup>η</td></tr><tr><td>0.53 ± 0.04 ± 0.04</td><td>BARTEL</td><td>85E</td><td>JADE</td><td>e<sup>+</sup>e<sup>-</sup> → e<sup>+</sup>e<sup>-</sup>η</td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.476±0.062</td><td>1 RODRIGUES</td><td>08</td><td>CNTR</td><td>Reanalysis</td></tr><tr><td>0.64 ± 0.14 ± 0.13</td><td>AIHARA</td><td>86</td><td>TPC</td><td>e<sup>+</sup>e<sup>-</sup> → e<sup>+</sup>e<sup>-</sup>η</td></tr><tr><td>0.56 ± 0.16</td><td>56</td><td>WEINSTEIN</td><td>83</td><td>CBAL</td><td>e<sup>+</sup>e<sup>-</sup> → e<sup>+</sup>e<sup>-</sup>η</td></tr><tr><td>0.324±0.046</td><td>BROWMAN</td><td>74B</td><td>CNTR</td><td>Primakoff effect</td></tr><tr><td>1.00 ± 0.22</td><td>2 BEMPORAD</td><td>67</td><td>CNTR</td><td>Primakoff effect</td></tr></tbody></table>

1 RODRIGUES 08 uses a more sophisticated calculation for the inelastic background due to incoherent photoproduction to reanalyze the η photoproduction data on Be and Cu at 9 GeV from BROWMAN 74B. This brings the value of Γ(η → 2γ) in line with direct measurements of the width. The error here is only statistical.

2 BEMPORAD 67 gives Γ(2γ) = 1.21 ± 0.26 keV assuming Γ(2γ)/Γ(total) = 0.314.

Bemporad private communication gives Γ(2γ)<sup>2</sup>/Γ(total) = 0.380 ± 0.083. We evaluate this using Γ(2γ)/Γ(total) = 0.38 ± 0.01. Not included in average because the uncertainty resulting from the separation of the coulomb and nuclear amplitudes has apparently been underestimated.

<table><thead><tr><th>Γ(π<sup>0</sup>2γ)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.334±0.028 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td><strong>0.33 ± 0.03</strong></td><td>1200</td><td>NEFKENS</td><td>14</td><td>CRYB γp → ηp</td></tr></tbody></table>

η BRANCHING RATIOS

Neutral modes

<table><thead><tr><th>Γ(neutral modes)/Γ<sub>total</sub></th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.7196±0.0030 OUR FIT</td><td>Error includes scale factor of 1.3.</td><td></td><td></td><td></td></tr><tr><td>0.705 ± 0.008</td><td>16k</td><td>BASILE</td><td>71D</td><td>CMR MM spectrometer</td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.79 ± 0.08</td><td>BUNIATOV</td><td>67</td><td>OSPK</td><td></td></tr></tbody></table>

<table><thead><tr><th>Γ(2γ)/Γ<sub>total</sub></th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>39.36±0.18 OUR FIT</strong></td><td>Error includes scale factor of 1.1.</td><td></td><td></td><td></td></tr><tr><td colspan="5"><strong>39.53±0.33 OUR AVERAGE</strong></td></tr><tr><td>39.86±0.04±0.99</td><td>2m</td><td>1 ABLIKIM</td><td>21AM BES3</td><td>J/ψ → γη</td></tr><tr><td>39.49±0.17±0.30</td><td>65k</td><td>ABEGG</td><td>96</td><td>SPEC pd → 3Heη</td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>38.45±0.40±0.36</td><td>14k</td><td>2 LOPEZ</td><td>07</td><td>CLEO ψ(2S) → J/ψη</td></tr></tbody></table>

1 ABLIKIM 21AM normalize the branching ratio (η → γγ) to B(J/ψ → γη), which they measured absolutely.

2 Not independent of other results listed for LOPEZ 07. Assuming decays of η → γγ, 3π<sup>0</sup>, π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>, π<sup>+</sup>π<sup>-</sup>γ, and e<sup>+</sup>e<sup>-</sup>γ account for all η decays within a contribution of 0.3% to the systematic error.

<table><thead><tr><th colspan="2">Γ(2γ)/Γ(neutral modes)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="2"><strong>0.5470±0.0018 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="2"><strong>0.548 ± 0.023 OUR AVERAGE</strong></td><td>Error includes scale factor of 1.5.</td><td></td><td></td><td></td></tr><tr><td>0.535 ± 0.018</td><td>BUTTRAM</td><td>70</td><td>OSPK</td><td></td><td></td></tr><tr><td>0.59 ± 0.033</td><td>BUNIATOV</td><td>67</td><td>OSPK</td><td></td><td></td></tr><tr><td colspan="6">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.52 ± 0.09</td><td>88</td><td>ABROSIMOV</td><td>80</td><td>HLBC</td><td></td></tr><tr><td>0.60 ± 0.14</td><td>113</td><td>KENDALL</td><td>74</td><td>OSPK</td><td></td></tr><tr><td>0.57 ± 0.09</td><td></td><td>STRUGALSKI</td><td>71</td><td>HLBC</td><td></td></tr><tr><td>0.579 ± 0.052</td><td></td><td>FELDMAN</td><td>67</td><td>OSPK</td><td></td></tr><tr><td>0.416 ± 0.044</td><td></td><td>DIGIUGNO</td><td>66</td><td>CNTR</td><td>Error doubled</td></tr><tr><td>0.44 ± 0.07</td><td></td><td>GRUNHAUS</td><td>66</td><td>OSPK</td><td></td></tr><tr><td>0.39 ± 0.06</td><td>1 JONES</td><td>66</td><td>CNTR</td><td></td><td></td></tr></tbody></table>

1 This result from combining cross sections from two different experiments.

<table><thead><tr><th colspan="2">Γ(3π<sup>0</sup>)/Γ<sub>total</sub></th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="2"><strong>32.57±0.21 OUR FIT</strong></td><td>Error includes scale factor of 1.2.</td><td></td><td></td><td></td></tr><tr><td colspan="2"><strong>31.96±0.07±0.84</strong></td><td>280k</td><td>1 ABLIKIM</td><td>21AM BES3</td><td>J/ψ → γη</td></tr><tr><td colspan="6">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>34.03±0.56±0.49</td><td>1821</td><td>2 LOPEZ</td><td>07</td><td>CLEO</td><td>ψ(2S) → J/ψη</td></tr></tbody></table>

1 ABLIKIM 21AM normalize the branching ratio (η → 3π<sup>0</sup>) to B(J/ψ → γη), which they measured absolutely.

2 Not independent of other results listed for LOPEZ 07. Assuming decays of η → γγ, 3π<sup>0</sup>, π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>, π<sup>+</sup>π<sup>-</sup>γ, and e<sup>+</sup>e<sup>-</sup>γ account for all η decays within a contribution of 0.3% to the systematic error.

<table><thead><tr><th colspan="2">Γ(3π<sup>0</sup>)/Γ(neutral modes)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="2"><strong>0.4526±0.0019 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="2"><strong>0.439 ± 0.024</strong></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="6">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.44 ± 0.08</td><td>75</td><td>ABROSIMOV</td><td>80</td><td>HLBC</td><td></td></tr><tr><td>0.32 ± 0.09</td><td></td><td>STRUGALSKI</td><td>71</td><td>HLBC</td><td></td></tr><tr><td>0.41 ± 0.033</td><td></td><td>BUNIATOV</td><td>67</td><td>OSPK</td><td>Not indep. of Γ(2γ)/Γ(neutral modes)</td></tr><tr><td>0.177 ± 0.035</td><td></td><td>FELDMAN</td><td></td><td>OSPK</td><td></td></tr><tr><td>0.209 ± 0.054</td><td></td><td>DIGIUGNO</td><td>66</td><td>CNTR</td><td>Error doubled</td></tr><tr><td>0.29 ± 0.10</td><td></td><td>GRUNHAUS</td><td>66</td><td>OSPK</td><td></td></tr></tbody></table>

<table><thead><tr><th colspan="2">Γ(3π<sup>0</sup>)/Γ(2γ)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="2"><strong>0.827±0.006 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="2"><strong>0.829±0.007 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>0.884±0.022±0.019</td><td>1821</td><td>LOPEZ</td><td>07</td><td>CLEO</td><td>ψ(2S) → J/ψη</td></tr><tr><td>0.817±0.012±0.032</td><td>17.4k</td><td>1 AKHMETSHIN 05</td><td>CMD2</td><td>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td><td></td></tr><tr><td>0.826±0.024</td><td></td><td>ACHASOV</td><td>00D</td><td>SND</td><td>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td></tr><tr><td>0.832±0.005±0.012</td><td></td><td>KRUSCHE</td><td>95D</td><td>SPEC</td><td>γp → ηp, threshold</td></tr><tr><td>0.841±0.034</td><td></td><td>AMSLER</td><td>93</td><td>CBAR</td><td>ρp → π<sup>+</sup>π<sup>-</sup>η at rest</td></tr><tr><td>0.822±0.009</td><td></td><td>ALDE</td><td>84</td><td>GAM2</td><td></td></tr><tr><td colspan="6">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.796±0.016±0.016</td><td></td><td>ACHASOV</td><td>00</td><td>SND</td><td>See ACHASOV 00D</td></tr><tr><td>0.91 ± 0.14</td><td></td><td>COX</td><td>70B</td><td>HBC</td><td></td></tr><tr><td>0.75 ± 0.09</td><td></td><td>DEVONS</td><td>70</td><td>OSPK</td><td></td></tr><tr><td>0.88 ± 0.16</td><td></td><td>BALTAY</td><td>67D</td><td>DBC</td><td></td></tr><tr><td>1.1 ± 0.2</td><td></td><td>CENCE</td><td>67</td><td>OSPK</td><td></td></tr><tr><td>1.25 ± 0.39</td><td></td><td>BACCI</td><td>63</td><td>CNTR</td><td>Inverse BR reported</td></tr></tbody></table>

1 Uses result from AKHMETSHIN 01B.

<table><thead><tr><th colspan="2">Γ(π<sup>0</sup>2γ)/Γ<sub>total</sub></th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="2"><strong>2.55±0.22 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="2"><strong>2.21±0.24±0.47</strong></td><td>≈ 500</td><td>1 PRAKHOV</td><td>08</td><td>CRYB π<sup>-</sup>p → ηn ≈ threshold</td></tr><tr><td colspan="6">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>3.5 ± 0.7 ± 0.6</td><td>1.6k</td><td>2.3 PRAKHOV</td><td>05</td><td>CRYB</td><td>See PRAKHOV 08</td></tr><tr><td>&lt;8.4</td><td>90</td><td>ACHASOV</td><td>01D</td><td>SND</td><td>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td></tr><tr><td>&lt;30</td><td>90</td><td>DAVYDOV</td><td>81</td><td>GAM2</td><td>π<sup>-</sup>p → ηn</td></tr></tbody></table>

1 PRAKHOV 08 is a reanalysis of the data of PRAKHOV 05, using the first time the invariant-mass spectrum of the two photons.

2 Normalized using Γ(η → 2γ)/Γ = 0.3943 ± 0.0026.

3 This measurement and the independent analysis of the same data by KNECHT 04 both imply a lower value of Γ(π<sup>0</sup>2γ) than the one obtained by ALDE 84 from Γ(π<sup>0</sup>2γ)/Γ(2γ).

<table><thead><tr><th colspan="2">Γ(π<sup>0</sup>2γ)/Γ(2γ)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="2"><strong>0.65±0.06 OUR FIT</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="2"><strong>1.8 ± 0.4</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="6">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>2.5 ± 0.6</td><td>70</td><td>BINON</td><td>82</td><td>GAM2</td><td></td><td>See ALDE 84</td></tr></tbody></table>
$$\Gamma(\pi^0 2\gamma)/\Gamma(3\pi^0)$$

$$\Gamma_4/\Gamma_3$$

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

### 7.8±0.7 OUR FIT

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

$$8.3±2.8±1.4 \qquad 1 \text{ KNECHT} \qquad 04 \text{ CRYB} \quad \pi^- p \to n\eta$$

¹Independent analysis of same data as PRAKHOV 05.

$$\Gamma(2\pi^0 2\gamma)/\Gamma_{\text{total}}$$

$$\Gamma_5/\Gamma$$

<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;1.2 × 10<sup>-3</sup></td><td>90</td><td>1 NEFKENS</td><td>05A CRYB</td><td>p(720 MeV/c) π<sup>-</sup> → nη</td></tr></tbody></table>

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

$$<4.0 × 10^{-3} \qquad 90 \qquad \text{BLIK} \qquad 07 \qquad \text{GAM4} \quad \pi^- p \to \eta n$$

¹Measurement is done in limited γγ energy range.

$$\Gamma(4\gamma)/\Gamma_{\text{total}}$$

$$\Gamma_6/\Gamma$$

<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;2.8 × 10<sup>-4</sup></td><td>90</td><td>BLIK</td><td>07 GAM4</td><td>π<sup>-</sup> p → ηn</td></tr></tbody></table>

$$\Gamma(\text{invisible})/\Gamma(2\gamma)$$

$$\Gamma_7/\Gamma_2$$

<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;2.6 × 10<sup>-4</sup></td><td>90</td><td>1 ABLIKIM</td><td>13 BES3</td><td>J/ψ → φη</td></tr></tbody></table>

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

$$<1.65 × 10^{-3} \qquad 90 \qquad 2 \text{ ABLIKIM} \qquad 06Q \text{ BES2} \qquad J/ψ \to \phiη$$

¹Based on 225M J/ψ decays.

²Based on 58M J/ψ decays.

### Charged modes

$$\Gamma(\text{charged modes})/\Gamma_{\text{total}}$$

$$\Gamma_8/\Gamma = (\Gamma_9 + \Gamma_{10} + \Gamma_{11} + \Gamma_{12} + \Gamma_{16})/\Gamma$$

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

0.2804±0.0030 OUR FIT Error includes scale factor of 1.3.

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

$$\Gamma_9/\Gamma$$

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

23.02±0.25 OUR FIT Error includes scale factor of 1.2.

$$23.04±0.03±0.54 \qquad 60k \qquad 1 \text{ ABLIKIM} \qquad 21 \text{ AMBES3} \qquad J/ψ \to \gammaη$$

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

$$22.60±0.35±0.29 \qquad 3915 \qquad 2 \text{ LOPEZ} \qquad 07 \text{ CLEO} \quad \psi(2S) \to J/ψη$$

¹ ABLIKIM 21AM normalize the branching ratio (η → π⁺π⁻π⁰) to B(J/ψ → γη), which they measured absolutely.

² Not independent of other results listed for LOPEZ 07. Assuming decays of η → γγ, 3π⁰, π⁺π⁻π⁰, π⁺π⁻γ, and e⁺e⁻γ account for all η decays within a contribution of 0.3% to the systematic error.

$$\Gamma(\text{neutral modes})/\Gamma(\pi^+\pi^-\pi^0)$$

$$\Gamma_1/\Gamma = (\Gamma_2 + \Gamma_3 + \Gamma_4)/\Gamma$$

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

3.13±0.05 OUR FIT Error includes scale factor of 1.3.

### 3.26±0.30 OUR AVERAGE

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2.54±1.89</td><td>74</td><td>KENDALL</td><td>74 OSPK</td><td></td></tr><tr><td>3.4 ±1.1</td><td>29</td><td>AGUILAR...</td><td>72B HBC</td><td></td></tr><tr><td>2.83±0.80</td><td>70</td><td>1 BLOODWO...</td><td>72B HBC</td><td></td></tr><tr><td>3.6 ±0.6</td><td>244</td><td>FLATTE</td><td>67B HBC</td><td></td></tr><tr><td>2.89±0.56</td><td>50</td><td>ALFF...</td><td>66 HBC</td><td></td></tr><tr><td>3.6 ±0.8</td><td>50</td><td>KRAEMER</td><td>64 DBC</td><td></td></tr><tr><td>3.8 ±1.1</td><td>50</td><td>PAULI</td><td>64 DBC</td><td></td></tr></tbody></table>

¹Error increased from published value 0.5 by Bloodworth (private communication).

$$\Gamma(2\gamma)/\Gamma(\pi^+\pi^-\pi^0)$$

$$\Gamma_2/\Gamma$$

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

1.710±0.025 OUR FIT Error includes scale factor of 1.2.

### 1.70 ±0.04 OUR AVERAGE

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.704±0.032±0.026</td><td>3915</td><td>1 LOPEZ</td><td>07 CLEO</td><td>ψ(2S) → J/ψη</td></tr><tr><td>1.61 ±0.14</td><td>60E BES2</td><td>ABLIKIM</td><td>06E BES2</td><td>e⁺e⁻ → J/ψ → γη</td></tr><tr><td>1.78 ±0.10 ±0.13</td><td>1077</td><td>AMSLER</td><td>95 CBAR</td><td>p̅p → π⁺π⁻π⁻ at rest</td></tr><tr><td>1.72 ±0.25</td><td>401</td><td>BAGLIN</td><td>69 HLBC</td><td></td></tr><tr><td>1.61 ±0.39</td><td></td><td>FOSTER</td><td>65 HBC</td><td></td></tr></tbody></table>

¹LOPEZ 07 reports Γ(η → π⁺π⁻π⁰) / Γ(η → 2γ) = Γ<sub>9</sub>/Γ<sub>2</sub> = 0.587 ± 0.011 ± 0.009.

$$\Gamma(3\pi^0)/\Gamma(\pi^+\pi^-\pi^0)$$

$$\Gamma_3/\Gamma$$

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

1.415±0.023 OUR FIT Error includes scale factor of 1.2.

### 1.48 ±0.05 OUR AVERAGE

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.46 ±0.03 ±0.09</td><td>ACHASOV</td><td>06A SND</td><td>e⁺e⁻ → ηγ</td><td></td></tr><tr><td>1.52 ±0.04 ±0.08</td><td>23k</td><td>1 AKHMETSHIN 01B</td><td>CMD2</td><td>e⁺e⁻ → φ → γη</td></tr><tr><td>1.44 ±0.09 ±0.10</td><td>1627</td><td>AMSLER</td><td>95 CBAR</td><td>p̅p → π⁺π⁻π⁻ at rest</td></tr><tr><td>1.50 ±0.15</td><td>199</td><td>BAGLIN</td><td>69 HLBC</td><td></td></tr><tr><td>1.47 ±0.20</td><td></td><td>BULLOCK</td><td>68 HLBC</td><td></td></tr></tbody></table>

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

$$1.3 \pm 0.4 \qquad \text{BAGLIN} \qquad 67B \qquad \text{HLBC}$$

$$0.90 \pm 0.24 \qquad \text{FOSTER} \qquad 65 \qquad \text{HBC}$$

$$2.0 \pm 1.0 \qquad \text{FOELSCHE} \qquad 64 \qquad \text{HBC}$$

$$0.83 \pm 0.32 \qquad \text{CRAWFORD} \qquad 63 \qquad \text{HBC}$$

¹AKHMETSHIN 01B uses results from AKHMETSHIN 99F.

$$\Gamma(\pi^+\pi^-\pi^0)/[\Gamma(2\gamma) + \Gamma(3\pi^0)]$$

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

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

0.320 ±0.005 OUR FIT Error includes scale factor of 1.2.

$$0.304 \pm 0.012 \qquad \text{ACHASOV} \qquad 00D SND \qquad e⁺e⁻ → φ → γη$$

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

$$0.3141 \pm 0.0081 \pm 0.0058 \qquad \text{ACHASOV} \qquad 00B SND \qquad \text{See ACHASOV 00D}$$

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

$$\Gamma_{10}/\Gamma$$

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

4.28±0.07 OUR FIT Error includes scale factor of 1.1.

$$4.39±0.02±0.10 \qquad 200k \qquad 1 \text{ ABLIKIM} \qquad 21 \text{ AMBES3} \qquad J/ψ \to γη$$

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

$$3.96±0.14±0.14 \qquad 859 \qquad 2 \text{ LOPEZ} \qquad 07 \text{ CLEO} \quad \psi(2S) \to J/ψη$$

¹ ABLIKIM 21AM normalize the branching ratio (η → π⁺π⁻γ) to B(J/ψ → γη), which they measured absolutely.

² Not independent of other results listed for LOPEZ 07. Assuming decays of η → γγ, 3π⁰, π⁺π⁻π⁰, π⁺π⁻γ, and e⁺e⁻γ account for all η decays within a contribution of 0.3% to the systematic error.

$$\Gamma(\pi^+\pi^-\gamma)/\Gamma(\pi^+\pi^-\pi^0)$$

$$\Gamma_{10}/\Gamma_9$$

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

0.1858±0.0025 OUR FIT Error includes scale factor of 1.1.

$$0.1856±0.0005±0.0028 \qquad 200k \qquad \text{BABUSCI} \qquad 13 \text{ KLEO} \quad e⁺e⁻ → φ → γη$$

$$0.175 ± 0.007 ± 0.006 \qquad 859 \qquad \text{LOPEZ} \qquad 07 \text{ CLEO} \quad \psi(2S) \to J/ψη$$

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

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.209 ± 0.004</td><td>18k</td><td>THALER</td><td>73 ASPK</td><td></td></tr><tr><td>0.201 ± 0.006</td><td>7250</td><td>GORMLEY</td><td>70 ASPK</td><td></td></tr><tr><td>0.28 ± 0.04</td><td></td><td>BALTAY</td><td>67B DBC</td><td></td></tr><tr><td>0.25 ± 0.035</td><td></td><td>LITCHFIELD</td><td>67 DBC</td><td></td></tr><tr><td>0.30 ± 0.06</td><td></td><td>CRAWFORD</td><td>66 HBC</td><td></td></tr><tr><td>0.196 ± 0.041</td><td></td><td>FOSTER</td><td>65C HBC</td><td></td></tr></tbody></table>

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

$$\Gamma_{11}/\Gamma$$

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

6.9 ±0.04 OUR FIT Error includes scale factor of 1.2.

6.7 ±0.5 OUR AVERAGE Error includes scale factor of 1.2.

$$6.6 ± 0.4 ± 0.4 \qquad 1345 \qquad \text{BERGHAUSER 11} \qquad \text{SPEC} \quad \gamma p \to pη$$

$$7.8 ± 0.5 ± 0.8 \qquad 435 ± 31 \qquad \text{BERLOWSKI} \qquad 08 \text{ WASA} \quad p d \to ^3\text{He}η$$

$$5.15±0.62±0.74 \qquad 283 \qquad \text{ACHASOV} \qquad 01B \text{ SND} \quad e^+e^- → φ → γη$$

$$7.10±0.64±0.46 \qquad 323 \qquad \text{AKHMETSHIN 01} \qquad \text{CMD2} \quad e^+e^- → φ → γη$$

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

$$9.4 ± 0.7 ± 0.5 \qquad 172 \qquad 1 \text{ LOPEZ} \qquad 07 \text{ CLEO} \quad \psi(2S) \to J/ψη$$

¹Not independent of other results listed for LOPEZ 07. Assuming decays of η → γγ, 3π⁰, π⁺π⁻π⁰, π⁺π⁻γ, and e⁺e⁻γ account for all η decays within a contribution of 0.3% to the systematic error.

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

$$\Gamma_{11}/\Gamma_{10}$$

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

0.161±0.010 OUR FIT Error includes scale factor of 1.2.

$$0.237±0.021±0.015 \qquad 172 \qquad \text{LOPEZ} \qquad 07 \text{ CLEO} \quad \psi(2S) \to J/ψη$$

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

$$\Gamma_{11}/\Gamma_9$$

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

2.90±0.19 OUR FIT Error includes scale factor of 1.3.

$$2.1 ± 0.5 \qquad 80 \qquad \text{JANE} \qquad 75B \qquad \text{OSPK} \quad \text{See the erratum}$$

$$\Gamma(\text{neutral modes})/\Gamma(\pi^+\pi^-\pi^0) + \Gamma(\pi^+\pi^-\gamma) + \Gamma(e^+e^-\gamma)$$

$$\Gamma_1/(\Gamma_9+\Gamma_{10}+\Gamma_{11}) = (\Gamma_2+\Gamma_3+\Gamma_4)/(\Gamma_9+\Gamma_{10}+\Gamma_{11})$$

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

2.57±0.04 OUR FIT Error includes scale factor of 1.3.

$$2.64±0.23 \qquad \text{BALTAY} \qquad 67B \qquad \text{DBC}$$

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

$$4.5 ± 1.0 \qquad 280 \qquad 1 \text{ JAMES} \qquad 66 \qquad \text{HBC}$$

$$3.20±1.26 \qquad 53 \qquad 1 \text{ BASTIEN} \qquad 62 \qquad \text{HBC}$$

$$2.5 ± 1.0 \qquad 10 \qquad 1 \text{ PICKUP} \qquad 62 \qquad \text{HBC}$$

¹These experiments are not used in the averages as they do not separate clearly η → π⁺π⁻π⁰ and η → π⁺π⁻γ from each other. The reported values thus probably contain some unknown fraction of η → π⁺π⁻γ.

$$\Gamma(2\gamma)/[\Gamma(\pi^+\pi^-\pi^0) + \Gamma(\pi^+\pi^-\gamma) + \Gamma(e^+e^-\gamma)]$$

$$\Gamma_2/(\Gamma_9+\Gamma_{10}+\Gamma_{11})$$

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

1.407±0.020 OUR FIT Error includes scale factor of 1.2.

### 1.1 ±0.4 OUR AVERAGE

$$1.51 ± 0.93 \qquad 75 \qquad \text{KENDALL} \qquad 74 \qquad \text{OSPK}$$

$$0.99 ± 0.48 \qquad \text{CRAWFORD} \qquad 63 \qquad \text{HBC}$$

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

$$\Gamma_{12}/\Gamma$$

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

3.1±0.4 OUR FIT

$$3.1±0.4 \qquad 600 \qquad \text{DZHELYADIN} \qquad 80 \text{ SPEC} \quad \pi^- p \to \eta n$$

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

$$1.5±0.75 \qquad 100 \qquad \text{BUSHNIN} \qquad 78 \qquad \text{SPEC} \quad \text{See DZHELYADIN 80}$$
$\Gamma(e^+ e^-)/\Gamma_{\text{total}}$ \qquad $\Gamma_{13}/\Gamma$

<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;7 × 10<sup>-7</sup></td><td>90</td><td>ACHASOV</td><td>18B</td><td>CNTR<br>Inverse reaction<br>e<sup>+</sup>e<sup>-</sup> → η</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;2.3 × 10<sup>-6</sup></td><td>90</td><td>AGAKISHIEV</td><td>14</td><td>pp → η + X</td></tr><tr><td>&lt;5.6 × 10<sup>-6</sup></td><td>90</td><td>1 AGAKISHIEV</td><td>12A</td><td>pp → η + X</td></tr><tr><td>&lt;2.7 × 10<sup>-5</sup></td><td>90</td><td>BERLOWSKI</td><td>08</td><td>WASA<br>pd → <sup>3</sup>He η</td></tr><tr><td>&lt;0.77 × 10<sup>-4</sup></td><td>90</td><td>BROWDER</td><td>97B</td><td>CLE2<br>e<sup>+</sup>e<sup>-</sup> ≈ 10.5 GeV</td></tr><tr><td>&lt;2 × 10<sup>-4</sup></td><td>90</td><td>WHITE</td><td>96</td><td>SPEC<br>pd → η<sup>3</sup>He</td></tr><tr><td>&lt;3 × 10<sup>-4</sup></td><td>90</td><td>DAVIES</td><td>74</td><td>RVUE<br>Uses ESTEN 67</td></tr></tbody></table>

¹AGAKISHIEV 12A uses a data sample of 3.5 GeV proton beam collisions on liquid hydrogen target collected by the HADES detector.

$\Gamma(\mu^+ \mu^-)/\Gamma_{\text{total}}$ \qquad $\Gamma_{14}/\Gamma$

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="6"><strong>5.8 ± 0.8 OUR AVERAGE</strong></td></tr><tr><td>5.7 ± 0.7 ± 0.5</td><td>114</td><td>ABEGG</td><td>94</td><td>SPEC<br>pd → η<sup>3</sup>He</td><td></td></tr><tr><td>6.5 ± 2.1</td><td>27</td><td>DZHELYADIN</td><td>80B</td><td>SPEC<br>π<sup>-</sup> p → ηn</td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>5.6<sup>+0.6</sup><sub>-0.7</sub> ± 0.5</td><td>100</td><td>KESSLER</td><td>93</td><td>SPEC<br>See ABEGG 94</td></tr><tr><td>&lt; 20</td><td>95</td><td>0</td><td>WEHMANN</td><td>68</td><td>OSPK</td></tr></tbody></table>

$\Gamma(\mu^+ \mu^-)/\Gamma(2\gamma)$ \qquad $\Gamma_{14}/\Gamma_2$

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>5.9 ± 2.2</td><td></td><td>HYAMS</td><td>69</td><td>OSPK</td></tr></tbody></table>

$\Gamma(2e^+ 2e^-)/\Gamma_{\text{total}}$ \qquad $\Gamma_{15}/\Gamma$

<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>COMMENT</th></tr></thead><tbody><tr><td>2.4 ± 0.2 ± 0.1</td><td>362</td><td>1 AMBROSINO</td><td>11B</td><td>KLOE<br>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;9.7</td><td>90</td><td>BERLOWSKI</td><td>08</td><td>WASA<br>pd → <sup>3</sup>He η</td><td></td></tr><tr><td>&lt;6.9</td><td>90</td><td>AKHMETSHIN</td><td>01</td><td>CMD2<br>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td><td></td></tr></tbody></table>

¹This measurement is fully inclusive (includes "2e+ 2e− γ" channel).

$\Gamma(\pi^+ \pi^- e^+ e^-)/\Gamma_{\text{total}}$ \qquad $\Gamma_{16}/\Gamma$

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

<table><tbody><tr><td>2.68 ± 0.11 OUR FIT</td><td></td><td></td><td></td><td></td></tr><tr><td>2.68 ± 0.09 ± 0.07</td><td>1555 ± 52</td><td>1 AMBROSINO</td><td>09B</td><td>KLOE<br>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td></tr></tbody></table>

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

<table><tbody><tr><td>4.3 <sup>+2.0</sup><sub>-1.6</sub> ± 0.4</td><td>16</td><td>BERLOWSKI</td><td>08</td><td>WASA<br>pd → <sup>3</sup>He η</td><td></td></tr><tr><td>4.3 ± 1.3 ± 0.4</td><td>16</td><td>BARGHOLTZ</td><td>07</td><td>CNTR<br>See BERLOWSKI 08</td><td></td></tr><tr><td>3.7 <sup>+2.5</sup><sub>-1.8</sub> ± 0.3</td><td>4</td><td>AKHMETSHIN</td><td>01</td><td>CMD2<br>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td><td></td></tr></tbody></table>

¹This AMBROSINO 09B value includes radiative events.

$\Gamma(e^+ e^- \mu^+ \mu^-)/\Gamma_{\text{total}}$ \qquad $\Gamma_{17}/\Gamma$

<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;1.6 × 10<sup>-4</sup></td><td>90</td><td>BERLOWSKI</td><td>08</td><td>WASA<br>pd → <sup>3</sup>He η</td></tr></tbody></table>

$\Gamma(2\mu^+ 2\mu^-)/\Gamma(\mu^+ \mu^-)$ \qquad $\Gamma_{18}/\Gamma_{14}$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>8.6 ± 1.4 ± 1.2</td><td>49.6</td><td>HAYRAPETY...</td><td>23A</td><td>CMS<br>pp at 13 TeV</td></tr></tbody></table>

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

<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;3.6 × 10<sup>-4</sup></td><td>90</td><td>BERLOWSKI</td><td>08</td><td>WASA<br>pd → <sup>3</sup>He η</td></tr></tbody></table>

$\Gamma(\pi^+ e^- \nu_e + \text{c.c.})/\Gamma(\pi^+ \pi^- \pi^0)$ \qquad $\Gamma_{20}/\Gamma_9$

<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;7.3 × 10<sup>-4</sup></td><td>90</td><td>ABLIKIM</td><td>13G</td><td>BES3<br>J/ψ → φη</td></tr></tbody></table>

$\Gamma(\pi^+ \pi^- 2\gamma)/\Gamma(\pi^+ \pi^- \pi^0)$ \qquad $\Gamma_{21}/\Gamma_9$

<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; 9 × 10<sup>-3</sup></td><td></td><td>PRICE</td><td>67</td><td>HBC</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;16 × 10<sup>-3</sup></td><td>95</td><td>BALTAY</td><td>67B</td><td>DBC</td></tr></tbody></table>

$\Gamma(\pi^+ \pi^- \pi^0 \gamma)/\Gamma(\pi^+ \pi^- \pi^0)$ \qquad $\Gamma_{22}/\Gamma_9$

<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;0.24 × 10<sup>-2</sup></td><td>90</td><td>0</td><td>THALER</td><td>73</td><td>ASPK</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;1.7 × 10<sup>-2</sup></td><td>90</td><td>ARNOLD</td><td>68</td><td>HLBC</td></tr><tr><td>&lt;1.6 × 10<sup>-2</sup></td><td>95</td><td>BALTAY</td><td>67B</td><td>DBC</td></tr><tr><td>&lt;7.0 × 10<sup>-2</sup></td><td></td><td>FLATTE</td><td>67</td><td>HBC</td></tr><tr><td>&lt;0.9 × 10<sup>-2</sup></td><td></td><td>PRICE</td><td>67</td><td>HBC</td></tr></tbody></table>

$\Gamma(\pi^0 \mu^+ \mu^-)/\Gamma_{\text{total}}$ \qquad $\Gamma_{23}/\Gamma$

<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;3 × 10<sup>-6</sup></td><td>90</td><td>DZHELYADIN</td><td>81</td><td>SPEC<br>π<sup>-</sup> p → ηn</td></tr></tbody></table>

Forbidden modes

$\Gamma(\pi^0 \gamma)/\Gamma_{\text{total}}$ \qquad $\Gamma_{24}/\Gamma$

Forbidden by angular momentum 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;9 × 10<sup>-5</sup></td><td>90</td><td>NEFKENS</td><td>05A</td><td>CRYB<br>p(720 MeV/c) π<sup>-</sup> → nη</td></tr></tbody></table>

$\Gamma(\pi^+ \pi^-)/\Gamma_{\text{total}}$ \qquad $\Gamma_{25}/\Gamma$

Forbidden by P and CP invariance.

<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; 4.4 × 10<sup>-6</sup></td><td>90</td><td>83M</td><td>1 BABUSCI</td><td>20A</td><td>KLOE<br>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td></tr><tr><td>&lt;5.3 × 10<sup>-17</sup></td><td></td><td></td><td>2 ZHEVLAKOV</td><td>19</td><td>THEO<br>from nEDM limits</td></tr><tr><td>&lt;1.6 × 10<sup>-5</sup></td><td>90</td><td>25M</td><td>AAIJ</td><td>17D</td><td>LHCB<br>in D → πππ decays</td></tr><tr><td>&lt;3.9 × 10<sup>-4</sup></td><td>90</td><td>225M</td><td>ABLIKIM</td><td>11G</td><td>BES3<br>e<sup>+</sup>e<sup>-</sup> → J/ψ → ηγ</td></tr><tr><td>&lt;1.3 × 10<sup>-5</sup></td><td>90</td><td>16M</td><td>AMBROSINO</td><td>05A</td><td>KLOE<br>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td></tr><tr><td>&lt;3.3 × 10<sup>-4</sup></td><td>90</td><td></td><td>AKHMETSHIN</td><td>99B</td><td>CMD2<br>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td></tr><tr><td>&lt;9 × 10<sup>-4</sup></td><td>90</td><td></td><td>AKHMETSHIN</td><td>97C</td><td>CMD2<br>See AKHMETSHIN 99B</td></tr><tr><td>&lt;15 × 10<sup>-4</sup></td><td>0</td><td></td><td>THALER</td><td>73</td><td>ASPK</td></tr></tbody></table>

¹BABUSCI 20A combines new data with the previous AMBROSINO 05A data, and thus supersedes AMBROSINO 05A.

²ZHEVLAKOV 19 derives the value from the experimental limits of nEDM by a calculation using an effective Lagrangian.

$\Gamma(2\pi^0)/\Gamma_{\text{total}}$ \qquad $\Gamma_{26}/\Gamma$

Forbidden by P and CP invariance.

<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;3.5 × 10<sup>-4</sup></td><td>90</td><td>BLIK</td><td>07</td><td>GAM4<br>π<sup>-</sup> p → ηn</td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;2.7 × 10<sup>-17</sup></td><td></td><td></td><td>1 ZHEVLAKOV</td><td>19</td><td>THEO<br>from nEDM limits</td></tr><tr><td>&lt;6.9 × 10<sup>-4</sup></td><td>90</td><td>225M</td><td>ABLIKIM</td><td>11G</td><td>BES3<br>e<sup>+</sup>e<sup>-</sup> → J/ψ → ηγ</td></tr><tr><td>&lt;4.3 × 10<sup>-4</sup></td><td>90</td><td></td><td>AKHMETSHIN</td><td>99C</td><td>CMD2<br>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td></tr><tr><td>&lt;6 × 10<sup>-4</sup></td><td>90</td><td></td><td>2 ACHASOV</td><td>98</td><td>SND<br>e<sup>+</sup>e<sup>-</sup> → φ → ηγ</td></tr></tbody></table>

¹ZHEVLAKOV 19 derives the value from the experimental limits of nEDM by a calculation using an effective Lagrangian.

²ACHASOV 98 observes one event in a ±3σ region around the η mass, while a Monte Carlo calculation gives 10 ± 5 events. The limit here is the Poisson upper limit for one observed event and no background.

$\Gamma(2\pi^0 \gamma)/\Gamma_{\text{total}}$ \qquad $\Gamma_{27}/\Gamma$

Forbidden by C invariance.

<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 × 10<sup>-4</sup></td><td>90</td><td>NEFKENS</td><td>05</td><td>CRYB</td><td>0<br>p(720 MeV/c) π<sup>-</sup> → nη</td></tr><tr><td>&lt;17 × 10<sup>-4</sup></td><td>90</td><td>BLIK</td><td>07</td><td>GAM4<br>π<sup>-</sup> p → ηn</td><td></td></tr></tbody></table>

$\Gamma(3\pi^0)/\Gamma_{\text{total}}$ \qquad $\Gamma_{28}/\Gamma$

Forbidden by C invariance.

<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; 6 × 10<sup>-5</sup></td><td>90</td><td>NEFKENS</td><td>05</td><td>CRYB</td><td>0<br>p(720 MeV/c) π<sup>-</sup> → nη</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;24 × 10<sup>-5</sup></td><td>90</td><td>BLIK</td><td>07</td><td>GAM4<br>π<sup>-</sup> p → ηn</td><td></td></tr></tbody></table>

$\Gamma(3\gamma)/\Gamma_{\text{total}}$ \qquad $\Gamma_{29}/\Gamma$

Forbidden by C invariance.

<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;16 × 10<sup>-5</sup></td><td>90</td><td>BLIK</td><td>07</td><td>GAM4<br>π<sup>-</sup> p → ηn</td><td></td></tr><tr><td>&lt; 4 × 10<sup>-5</sup></td><td>90</td><td>NEFKENS</td><td>05A</td><td>CRYB<br>p(720 MeV/c) π<sup>-</sup> → nη</td><td></td></tr></tbody></table>

$\Gamma(3\gamma)/\Gamma(2\gamma)$ \qquad $\Gamma_{29}/\Gamma_2$

<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;1.2 × 10<sup>-3</sup></td><td>95</td><td>ALDE</td><td>84</td><td>GAM2</td><td>0</td></tr></tbody></table>

$\Gamma(3\gamma)/\Gamma(3\pi^0)$ \qquad $\Gamma_{29}/\Gamma_3$

<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;4.9 × 10<sup>-5</sup></td><td>90</td><td>ALOISIO</td><td>04</td><td>KLOE<br>φ → ηγ</td></tr></tbody></table>

$\Gamma(4\pi^0)/\Gamma_{\text{total}}$ \qquad $\Gamma_{30}/\Gamma$

Forbidden by P and CP invariance.

<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; 6.9 × 10<sup>-7</sup></td><td>90</td><td>PRAKHOV</td><td>00</td><td>CRYB<br>π<sup>-</sup> p → nη, 720 MeV/c</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;200 × 10<sup>-7</sup></td><td>90</td><td>BLIK</td><td>07</td><td>GAM4<br>π<sup>-</sup> p → ηn</td><td></td></tr></tbody></table>

$\Gamma(\pi^0 e^+ e^-)/\Gamma_{\text{total}}$ \qquad $\Gamma_{31}/\Gamma$

C parity forbids this to occur as a single-photon process.

<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; 7.5 × 10<sup>-6</sup></td><td>90</td><td>ADLARSON</td><td>18C</td><td>WASA<br>pd → η<sup>3</sup>He</td></tr><tr><td>&lt; 1.6 × 10<sup>-4</sup></td><td>90</td><td>MARTYNOV</td><td>76</td><td>HLBC</td></tr><tr><td>&lt; 8.4 × 10<sup>-4</sup></td><td>90</td><td>BAZIN</td><td>68</td><td>DBC</td></tr><tr><td>&lt;70 × 10<sup>-4</sup></td><td></td><td>RITTENBERG</td><td>65</td><td>HBC</td></tr></tbody></table>
## Γ(π⁰e⁺e⁻)/Γ(π⁺π⁻π⁰)

C parity forbids this to occur as a single-photon process.

<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; 3.28 × 10<sup>-5</sup></td><td>90</td><td>ADLARSON</td><td>18c</td><td>WASA p d → η <sup>3</sup>He</td></tr></tbody></table><p>• • • We do not use the following data for averages, fits, limits, etc. • • •</p><table><tbody><tr><td>&lt; 1.9 × 10<sup>-4</sup></td><td>90</td><td>JANE</td><td>75</td><td>OSPK</td></tr><tr><td>&lt; 42 × 10<sup>-4</sup></td><td>90</td><td>BAGLIN</td><td>67</td><td>HLBC</td></tr><tr><td>&lt; 16 × 10<sup>-4</sup></td><td>90</td><td>BILLING</td><td>67</td><td>HLBC</td></tr><tr><td>&lt; 77 × 10<sup>-4</sup></td><td></td><td>FOSTER</td><td>65b</td><td>HBC</td></tr><tr><td>&lt;110 × 10<sup>-4</sup></td><td></td><td>PRICE</td><td>65</td><td>HBC</td></tr></tbody></table>

## Γ₃₁/Γ₉

## Γ(π⁰μ⁺μ⁻)/Γ<sub>total</sub>

C parity forbids this to occur as a single-photon process.

<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; 5 × 10<sup>-6</sup></td><td>90</td><td>DZHELYADIN</td><td>81</td><td>SPEC π⁻p → ηη</td></tr></tbody></table><p>• • • We do not use the following data for averages, fits, limits, etc. • • •</p><table><tbody><tr><td>&lt;500 × 10<sup>-6</sup></td><td></td><td>WEHMANN</td><td>68</td><td>OSPK</td></tr></tbody></table>

## Γ₃₂/Γ₃₂

## Γ(μ⁺e⁻) + Γ(μ⁻e⁺)/Γ<sub>total</sub>

Forbids by lepton family 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;6 × 10<sup>-6</sup></td><td>90</td><td>WHITE</td><td>96</td><td>SPEC p d → η<sup>3</sup>He</td></tr></tbody></table>

## Γ₃₃/Γ₃₃

## η C-NONCONSERVING DECAY PARAMETERS

### π⁺π⁻π⁰ LEFT-RIGHT ASYMMETRY PARAMETER

Measurements with an error > 1.0 × 10⁻² have been omitted.

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.09<sup>+0.11</sup><sub>-0.12</sub> OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>+0.09 ± 0.10<sup>+0.09</sup><sub>-0.14</sub></td><td>1.34M</td><td>AMBROSINO</td><td>08D KLOE</td></tr><tr><td>0.28 ± 0.26</td><td>165k</td><td>JANE</td><td>74 OSPK</td></tr><tr><td>-0.05 ± 0.22</td><td>220k</td><td>LAYTER</td><td>72 OSPK</td></tr></tbody></table>

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

<table><tr><td>1.5 ± 0.5</td><td>37k</td><td>1 GORMLEY</td><td>68c ASPK</td></tr></table>

¹The GORMLEY 68c asymmetry is probably due to unmeasured (E × B) spark chamber effects. New experiments with (E × B) controls don't observe an asymmetry.

### π⁺π⁻π⁰ SEXTANT ASYMMETRY PARAMETER

Measurements with an error > 2.0 × 10⁻² have been omitted.

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.12<sup>+0.10</sup><sub>-0.11</sub> OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>+0.08 ± 0.10<sup>+0.08</sup><sub>-0.13</sub></td><td>1.34M</td><td>AMBROSINO</td><td>08D KLOE</td></tr><tr><td>0.20 ± 0.25</td><td>165k</td><td>JANE</td><td>74 OSPK</td></tr><tr><td>0.10 ± 0.22</td><td>220k</td><td>LAYTER</td><td>72 ASPK</td></tr><tr><td>0.5 ± 0.5</td><td>37k</td><td>GORMLEY</td><td>68C WIRE</td></tr></tbody></table>

### π⁺π⁻π⁰ QUADRANT ASYMMETRY PARAMETER

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>-0.09<sup>+0.09</sup> OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>-0.05 ± 0.10<sup>+0.03</sup><sub>-0.05</sub></td><td>1.34M</td><td>AMBROSINO</td><td>08D KLOE</td></tr><tr><td>-0.30 ± 0.25</td><td>165k</td><td>JANE</td><td>74 OSPK</td></tr><tr><td>-0.07 ± 0.22</td><td>220k</td><td>LAYTER</td><td>72 ASPK</td></tr></tbody></table>

### π⁺π⁻γ LEFT-RIGHT ASYMMETRY PARAMETER

Measurements with an error > 2.0 × 10⁻² have been omitted.

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>0.9 ± 0.4 OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>1.2 ± 0.6</td><td>35k</td><td>JANE</td><td>74B OSPK</td></tr><tr><td>0.5 ± 0.6</td><td>36k</td><td>THALER</td><td>72 ASPK</td></tr><tr><td>1.22 ± 1.56</td><td>7257</td><td>GORMLEY</td><td>70 ASPK</td></tr></tbody></table>

### π⁺π⁻γ PARAMETER β (D-wave)

Sensitive to a D-wave contribution: $dN/d\cos\theta = \sin^2\theta (1 + \beta \cos^2\theta)$.

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>-0.02 ± 0.07 OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>0.11 ± 0.11</td><td>35k</td><td>JANE</td><td>74B OSPK</td></tr><tr><td>-0.060 ± 0.065</td><td>7250</td><td>GORMLEY</td><td>70 WIRE</td></tr></tbody></table>

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

<table><tr><td>0.12 ± 0.06</td><td>1 THALER</td><td>72 ASPK</td></tr></table>

¹The authors don't believe this indicates D-wave because the dependence of β on the γ energy is inconsistent with the theoretical prediction. A cos²θ dependence can also come from P- and F-wave interference.

## η CP-NONCONSERVING DECAY PARAMETER

### π⁺π⁻e⁺e⁻ DECAY-PLANE ASYMMETRY PARAMETER A<sub>φ</sub>

In the η rest frame, the total momentum of the e⁺e⁻ pair is equal and opposite to that of the π⁺π⁻ pair. Let 2 be the unit vector along the momentum of the e⁺e⁻ pair; let $\hat{n}_{ee}$ and $\hat{n}_{\pi\pi}$ be the unit vectors normal to the e⁺e⁻ and π⁺π⁻ planes; and let $\phi$ be the angle between the two normals. Then

$$ \sin\phi \cos\phi = [(\hat{n}_{ee} \times \hat{n}_{\pi\pi}) \cdot 2] (\hat{n}_{ee} \cdot \hat{n}_{\pi\pi}), $$

and

$$ A_{\phi} \equiv \frac{N_{\sin\phi \cos\phi > 0} - N_{\sin\phi \cos\phi < 0}}{N_{\sin\phi \cos\phi > 0} + N_{\sin\phi \cos\phi < 0}}. $$

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>-0.6 ± 2.5 ± 1.8</td><td>1555 ± 52</td><td>AMBROSINO</td><td>09B</td><td>KLOE e⁺e⁻ → φ → ηγ</td></tr></tbody></table>

## ENERGY DEPENDENCE OF η → 3π DALITZ PLOTS

### PARAMETERS FOR η → π⁺π⁻π⁰

See the "Note on η Decay Parameters," page 1454, in our 1994 edition (Physical Review D50 1173 (1994)). The following experiments fit to one or more of the coefficients $a, b, c, d, e, f$ or $g$ for $|\text{matrix element}|^2 = 1 + ay + by^2 + cx + dx^2 + exy + fy^3 + gx^2y$.

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>631k</td><td>1 ABLIKIM</td><td>23AN BES3</td><td>J/ψ → γη</td><td></td></tr><tr><td>4.7M</td><td>2 ANASTASI</td><td>16A KLOE</td><td>e⁺e⁻ → φ → ηγ</td><td></td></tr><tr><td>79k</td><td>ABLIKIM</td><td>15G BES3</td><td>e⁺e⁻ → J/ψ → γη</td><td></td></tr><tr><td>174k</td><td>ADLARSON</td><td>14A WASA</td><td>p d → η<sup>3</sup>He</td><td></td></tr><tr><td>1.34M</td><td>AMBROSINO</td><td>08D KLOE</td><td></td><td></td></tr><tr><td>3230</td><td>3 ABELE</td><td>98D CBAR</td><td>πp → π<sup>0</sup>π<sup>0</sup>η at rest</td><td></td></tr><tr><td>1077</td><td>4 AMSLER</td><td>95 CBAR</td><td>πp → π<sup>+</sup>π<sup>-</sup>η at rest</td><td></td></tr><tr><td>81k</td><td>LAYTER</td><td>73 ASPK</td><td></td><td></td></tr><tr><td>220k</td><td>LAYTER</td><td>72 ASPK</td><td></td><td></td></tr><tr><td>1138</td><td>CARPENTER</td><td>70 HBC</td><td></td><td></td></tr><tr><td>349</td><td>DANBURG</td><td>70 DBC</td><td></td><td></td></tr><tr><td>7250</td><td>GORMLEY</td><td>70 WIRE</td><td></td><td></td></tr><tr><td>526</td><td>BAGLIN</td><td>69 HLBC</td><td></td><td></td></tr><tr><td>7170</td><td>CNOPS</td><td>68 OSPK</td><td></td><td></td></tr><tr><td>37k</td><td>GORMLEY</td><td>68C WIRE</td><td></td><td></td></tr><tr><td>1300</td><td>CLPWY</td><td>66 HBC</td><td></td><td></td></tr><tr><td>705</td><td>LARRIBE</td><td>66 HBC</td><td></td><td></td></tr></tbody></table>

¹ABLIKIM 23AN fit the Dalitz plot density distribution with two parameter sets (a, b, d, f), and (a, b, d, f, g).

²ANASTASI 16A measure the Dalitz parameters a, b, d, f, and g. This is the first measurement of g.

³ABELE 98D obtains $a = -1.22 \pm 0.07$ and $b = 0.22 \pm 0.11$ when c (or d) is fixed at 0.06.

⁴AMSLER 95 fits to $(1+ay+by^2)$ and obtains $a = -0.94 \pm 0.15$ and $b = 0.11 \pm 0.27$.

### α PARAMETER FOR η → 3π⁰

See the "Note on η Decay Parameters" in our 1994 edition, Phys. Rev. D50, 1 August 1994, Part I, p. 1454. The value here is of α in $|\text{matrix element}|^2 = 1 + 2\alpha z$.

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>-0.0296 ± 0.0016 OUR AVERAGE</td><td></td><td></td><td></td><td>Error includes scale factor of 1.7. See the ideogram below.</td></tr><tr><td>-0.0406 ± 0.0035 ± 0.0008</td><td>272k</td><td>ABLIKIM</td><td>23AN BES3</td><td>J/ψ → γη</td></tr><tr><td>-0.0265 ± 0.0010 ± 0.0009</td><td>7M</td><td>PRAKHOV</td><td>18 CRYB</td><td>γp → pη</td></tr><tr><td>-0.055 ± 0.014 ± 0.004</td><td>33k</td><td>ABLIKIM</td><td>15G BES3</td><td>e⁺e⁻ → J/ψ → γη</td></tr><tr><td>-0.0301 ± 0.0035 ± 0.0022</td><td>512k</td><td>AMBROSINO</td><td>10A KLOE</td><td>e⁺e⁻ → φ → ηγ</td></tr><tr><td>-0.027 ± 0.008 ± 0.005</td><td>120k</td><td>1 ADOLPH</td><td>09 WASA</td><td>pp → ppη</td></tr><tr><td>-0.0322 ± 0.0012 ± 0.0022</td><td>3M</td><td>2 PRAKHOV</td><td>09 CRYB</td><td>γp → pη</td></tr><tr><td>-0.032 ± 0.002 ± 0.002</td><td>1.8M</td><td>2 UNVERZAGT</td><td>09 CRYB</td><td>γp → pη</td></tr><tr><td>-0.026 ± 0.010 ± 0.010</td><td>75k</td><td>BASHKANOV</td><td>07 WASA</td><td>pp → ppη</td></tr><tr><td>-0.010 ± 0.021 ± 0.010</td><td>12k</td><td>ACHASOV</td><td>01C SND</td><td>e⁺e⁻ → φ → ηγ</td></tr><tr><td>-0.031 ± 0.004</td><td>1M</td><td>TIPPENS</td><td>01 CRYB</td><td>π⁻p → nη, 720 MeV</td></tr><tr><td>-0.052 ± 0.017 ± 0.010</td><td>98k</td><td>ABELE</td><td>98C CBAR</td><td>πp → 5π<sup>0</sup></td></tr><tr><td>-0.022 ± 0.023</td><td>50k</td><td>ALDE</td><td>84 GAM2</td><td></td></tr></tbody></table>

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

<table><tr><td>-0.038 ± 0.003</td><td>+0.012</td><td>1.34M</td><td>3 ABLIKIM</td><td>23AN BES3</td></tr><tr><td>-0.032 ± 0.37</td><td>-0.008</td><td>192</td><td>2 PRAKHOV</td><td>09 CRYB</td></tr><tr><td></td><td></td><td></td><td>1 UNVERZAGT</td><td>09 CRYB</td></tr></table>

¹This ADOLPH 09 result is independent of the BASHKANOV 07 result.

²The PRAKHOV 09 and UNVERZAGT 09 results are independent.

³This AMBROSINO 08D value is an indirect result using $η \rightarrow \pi^+\pi^0\pi^-$ events and a rescattering matrix that mixes isospin decay amplitudes.
WEIGHTED AVERAGE
-0.0296±0.0016 (Error scaled by 1.7)

<figure><img src="image_432.png" /></figure>

## PARAMETER $\Lambda$ IN $\eta \to \ell^+\ell^-\gamma$ DECAY

In the pole approximation the electromagnetic transition form factor for a resonance of mass $M$ is given by the expression:

$$|\Lambda^2 = (1 - M^2/\rho^2)^{-2}.$$

where the parameter $\Lambda$ vector dominance predicts $\Lambda \approx 0.770$ GeV.

<table><thead><tr><th>VALUE (GeV/c<sup>2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.716 ±0.011</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>0.712 ±0.020</td><td></td><td>1 ADLARSON</td><td>17B A2MM</td><td>$\gamma p \to \eta p$</td></tr><tr><td>0.7191 ±0.0125 ±0.0093</td><td></td><td>2 ARNALDI</td><td>16 NA60</td><td>400 GeV p-A collisions</td></tr><tr><td>0.716 ±0.031 ±0.009</td><td></td><td>3 ARNALDI</td><td>09 NA60</td><td>158A In-In collisions</td></tr><tr><td>0.72 ±0.09</td><td>600</td><td>DZHELYADIN</td><td>80 SPEC</td><td>$\pi^- p \to \eta n, \eta \to \gamma \mu^+ \mu^-$</td></tr></tbody></table>

¹ ADLARSON 17b reports $\Lambda^2(\eta \to \gamma e^+ e^-) = 1.97 \pm 0.11$ (GeV/c²)⁻² which we converted to the quoted $\Lambda$ value and uncertainty (total=statistical plus systematic).

² ARNALDI 16 reports $\Lambda^2(\eta \to \gamma \mu^+ \mu^-) = 1.934 \pm 0.067$ (GeV/c²)⁻² which we converted to the quoted $\Lambda$ value.

³ ARNALDI 09 reports $\Lambda^2(\eta \to \gamma \mu^+ \mu^-) = 1.95 \pm 0.17$ (GeV/c²)⁻² which we converted to the quoted $\Lambda$ value.

## η REFERENCES

<table><tbody><tr><td>ABLIKIM</td><td>23AN PR D107 920070</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>HAYRAPETY...</td><td>23A PRL 131 091903</td><td>A. Hayrapetyan et al.</td><td>(CMS Collab.)</td></tr><tr><td>ABLIKIM</td><td>21AM PRL D104 20004</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>BABUSCI</td><td>20A JHEP 2010 047</td><td>D. Babusci et al.</td><td>(KLOE-2 Collab.)</td></tr><tr><td>ZHEVLAKOV</td><td>19P PR D99 031703</td><td>A.S. Zhevakov et al.</td><td>(TMSK, MAINZ, TUBIN+)</td></tr><tr><td>ABASOV</td><td>18B PR D99 052000</td><td>M.N. Achasov et al.</td><td>(SND Collab.)</td></tr><tr><td>ADLARSON</td><td>18C PL B784 378</td><td>P. Adlarson et al.</td><td>(WASA-at-COSY Collab.)</td></tr><tr><td>PRAKHOV</td><td>18C PR C97 065203</td><td>S. Prakov et al.</td><td>(A2 Collab. at MAMI)</td></tr><tr><td>AAIJ</td><td>17D PL B764 233</td><td>R. Aaij et al.</td><td>(LHCb Collab.)</td></tr><tr><td>ADLARSON</td><td>17B PR C95 035208</td><td>P. Adlarson et al.</td><td>(A2 Collab. at MAMI)</td></tr><tr><td>ANASTASI</td><td>16A JHEP 1605 019</td><td>A. Anastasi et al.</td><td>(KLOE-2 Collab.)</td></tr><tr><td>ARNALDI</td><td>16 PR B757 437</td><td>R. Arnaldi et al.</td><td>(NA60 Collab.)</td></tr><tr><td>ABLIKIM</td><td>15G PR D92 012014</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ADLARSON</td><td>14A PR C90 045207</td><td>P. Adlarson et al.</td><td>(WASA-at-COSY Collab.)</td></tr><tr><td>AGAKISHEV</td><td>14A PR B731 265</td><td>G. Agakishiev et al.</td><td>(HADES Collab.)</td></tr><tr><td>NEFKENS</td><td>14 PR C90 025206</td><td>B.M.K. Nefkens et al.</td><td>(A2 Collab. at MAMI)</td></tr><tr><td>NIKOLAEV</td><td>14 EPJ A50 58</td><td>N. Nikolaev et al.</td><td>(MAMI-B MAINZ, BONN)</td></tr><tr><td>ABLIKIM</td><td>13G PR D87 012009</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>ABLIKIM</td><td>13G PR D87 032006</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>BABUSCI</td><td>13A PL B718 910</td><td>D. Babusci et al.</td><td>(KLOE/KLOE-2 Collab.)</td></tr><tr><td>BABUSCI</td><td>13A JHEP 1301 119</td><td>D. Babusci et al.</td><td>(KLOE-2 Collab.)</td></tr><tr><td>AGAKISHEV</td><td>12A PR B694 64</td><td>H. AGAKISHEV et al.</td><td>(HADES Collab.)</td></tr><tr><td>OSLAWSKI</td><td>12 PR B85 112011</td><td>P. Goslowski et al.</td><td>(COSY-ANKE Collab.)</td></tr><tr><td>ABLIKIM</td><td>11G PR D84 032006</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>AMBROSINO</td><td>11B PL B702 324</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>BERGAUSER</td><td>11B PL B701 562</td><td>H. Berghauser et al.</td><td>(GIES, UCLA, GUTE Collab.)</td></tr><tr><td>AMBROSINO</td><td>10A PL B694 16</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>ADOLPH</td><td>09 PL B677 24</td><td>C. Adolph et al.</td><td>(WASA-at-COSY Collab.)</td></tr><tr><td>AMBROSINO</td><td>09B PL B675 283</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>ARNALDI</td><td>09B PL B677 260</td><td>R. Arnaldi et al.</td><td>(NA60 Collab.)</td></tr><tr><td>PRAKHOV</td><td>09 PR C79 035204</td><td>S. Prakov et al.</td><td>(MAMI-C Crystal Ball Collab.)</td></tr><tr><td>UNVERZAGT</td><td>09 EPJ A39 169</td><td>M. Unverzagt et al.</td><td>(MAMI-B Crystal Ball Collab.)</td></tr><tr><td>AMBROSINO</td><td>08D JHEP 0805 006</td><td>F. Ambrosino et al.</td><td>(DAPHNE KLOE Collab.)</td></tr><tr><td>BERLOWSKI</td><td>08 PR D77 032004</td><td>M. Berlowski et al.</td><td>(CELSIUS/WASA Collab.)</td></tr><tr><td>PRAKHOV</td><td>08 PR D78 0152004</td><td>S. Prakov et al.</td><td>(BNL Crystal Ball Collab.)</td></tr><tr><td>RODRIGUES</td><td>08 PRL 101 012301</td><td>T.E. Rodrigues et al.</td><td>(USP, FESP, UNESP+)</td></tr><tr><td>AMBROSINO</td><td>07B JHEP 0712 073</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>BARGHOLTZ</td><td>07 B644 299</td><td>Chr. Bargholtz et al.</td><td>(CELSIUS/WASA Collab.)</td></tr><tr><td>BASHKANOV</td><td>07 PR C76 048201</td><td>M. Bashkanov et al.</td><td>(CELSIUS/WASA Collab.)</td></tr><tr><td>BLIK</td><td>07 PAN 70 693</td><td>A.M. Blik et al.</td><td>(GAMS Collab.)</td></tr><tr><td>LOPEZ</td><td>07 PRL 99 122001</td><td>A. Lopez et al.</td><td>(CLEO Collab.)</td></tr><tr><td>MILLER</td><td>07 PRL 99 122002</td><td>D.H. Miller et al.</td><td>(CLEO Collab.)</td></tr><tr><td>ABLIKIM</td><td>06E PR D73 052008</td><td>M. Ablikim et al.</td><td>(BES Collab.)</td></tr><tr><td>ABLIKIM</td><td>06Q PR D97 202002</td><td>M. Ablikim et al.</td><td>(BES Collab.)</td></tr><tr><td>ACHASOV</td><td>06A PR D74 014016</td><td>M.N. Achasov et al.</td><td>(SND Collab.)</td></tr><tr><td>ABDEL-BARY</td><td>05 PL B619 261</td><td>M. Abdel-Bary et al.</td><td>(GEM Collab.)</td></tr><tr><td>AKHMETSHIN</td><td>05 PR B605 26</td><td>R.R. Akhmetshin et al.</td><td>(Novosibirsk CMD-2 Collab.)</td></tr><tr><td>AMBROSINO</td><td>05A PL B606 276</td><td>F. Ambrosino et al.</td><td>(KLOE Collab.)</td></tr><tr><td>NEFKENS</td><td>05A PR C94 041601</td><td>B.M.K. Nefkens et al.</td><td>(BNL Crystal Ball Collab.)</td></tr><tr><td>NEFKENS</td><td>05A PR C72 035212</td><td>B.M.K. Nefkens et al.</td><td>(BNL Crystal Ball Collab.)</td></tr><tr><td>PRAKHOV</td><td>05A PR C72 025201</td><td>S. Prakov et al.</td><td>(BNL Crystal Ball Collab.)</td></tr><tr><td>ALOISIO</td><td>04 PL B591 49</td><td>A. Aloisio et al.</td><td>(KLOE Collab.)</td></tr><tr><td>KNECHT</td><td>04 PL B589 14</td><td>N. Knecht et al.</td><td>(BNL Crystal Ball Collab.)</td></tr><tr><td>LAI</td><td>02 PL B533 196</td><td>A. Lai et al.</td><td>(CERN NA40 Collab.)</td></tr><tr><td>NEFKENS</td><td>02 PS T99 114</td><td>B.M.K. Nefkens, J.W. Price</td><td>(UCLA)</td></tr><tr><td>ACHASOV</td><td>01C PL B504 275</td><td>M.N. Achasov et al.</td><td>(Novosibirsk CMD Collab.)</td></tr><tr><td>ACHASOV</td><td>01C JETP 73 451</td><td>M.N. Achasov et al.</td><td>(Novosibirsk SND Collab.)</td></tr><tr><td></td><td></td><td>Translated from ZETF P 711.</td><td></td></tr></tbody></table>

<table><tbody><tr><td>ACHASOV</td><td>01D NP B600 3</td><td>M.N. Achasov et al.</td><td>(Novosibirsk SND Collab.)</td></tr><tr><td>AKHMETSHIN</td><td>01 PL B501 191</td><td>R.R. Akhmetshin et al.</td><td>(Novosibirsk CMD-2 Collab.)</td></tr><tr><td>AKHMETSHIN</td><td>01B PL B509 217</td><td>R.R. Akhmetshin et al.</td><td>(Novosibirsk CMD-2 Collab.)</td></tr><tr><td>TIPPENS</td><td>01 PRL 87 192001</td><td>W.B. Tippens et al.</td><td>(BNL Crystal Ball Collab.)</td></tr><tr><td>ACHASOV</td><td>00 EPJ C12 25</td><td>M.N. Achasov et al.</td><td>(Novosibirsk SND Collab.)</td></tr><tr><td>ACHASOV</td><td>00B JETP 90 17</td><td>M.N. Achasov et al.</td><td>(Novosibirsk SND Collab.)</td></tr><tr><td>ACHASOV</td><td>00D JETPL 72 282</td><td>M.N. Achasov et al.</td><td>(Novosibirsk SND Collab.)</td></tr><tr><td>PRAKHOV</td><td>00 PRL 84 4802</td><td>5. Prakhov et al.</td><td>(BNL Crystal Ball Collab.)</td></tr><tr><td>AKHMETSHIN</td><td>99B PL B462 371</td><td>R.R. Akhmetshin et al.</td><td>(Novosibirsk CMD-2 Collab.)</td></tr><tr><td>AKHMETSHIN</td><td>99C PL B462 380</td><td>R.R. Akhmetshin et al.</td><td>(Novosibirsk CMD-2 Collab.)</td></tr><tr><td>AKHMETSHIN</td><td>99F PL B460 242</td><td>R.R. Akhmetshin et al.</td><td>(Novosibirsk SND Collab.)</td></tr><tr><td>ABELE</td><td>98C PL B417 193</td><td>A. Abele et al.</td><td>(Crystal Barrel Collab.)</td></tr><tr><td>ABELE</td><td>98D PL B417 197</td><td>A. Abele et al.</td><td>(Crystal Barrel Collab.)</td></tr><tr><td>ACHASOV</td><td>98A PL B405 388</td><td>M.N. Achasov et al.</td><td>(Novosibirsk SND Collab.)</td></tr><tr><td>AKHMETSHIN</td><td>97C PL B415 452</td><td>R.R. Akhmetshin et al.</td><td>(Novosibirsk CMD-2 Collab.)</td></tr><tr><td>BRODER</td><td>97B PR D56 5395</td><td>T.E. Browder et al.</td><td>(CLEO Collab.)</td></tr><tr><td>ABEGG</td><td>96 PR D53 11</td><td>R. Abegg et al.</td><td>(Saturne SPESS2 Collab.)</td></tr><tr><td>WHITE</td><td>96 PR D53 6658</td><td>D.B. White et al.</td><td>(Saturne SPESS2 Collab.)</td></tr><tr><td>AMSLER</td><td>95B PL B46 203</td><td>C. Amsler et al.</td><td>(Crystal Barrel Collab.)</td></tr><tr><td>KRUSCHE</td><td>95D ZPHY A351 237</td><td>B. Krusche et al.</td><td>(STAPS + A2 Collab.)</td></tr><tr><td>ABEGG</td><td>94 PR D50 92</td><td>R. Abegg et al.</td><td>(Saturne SPESS2 Collab.)</td></tr><tr><td>PDG</td><td>94 PR D50 1173</td><td>L. Montanet et al.</td><td>(CERN, LBL, BOST+)</td></tr><tr><td>AMSLER</td><td>94 PR ZPHY C58 175</td><td>C. Amsler et al.</td><td>(Crystal Barrel Collab.)</td></tr><tr><td>KESSLER</td><td>93 PRL 70 892</td><td>R.S. Kessler et al.</td><td>(Saturne SPESS2 Collab.)</td></tr><tr><td>PLAIN</td><td>93 PL P52 526</td><td>F. Ptouin et al.</td><td>(Saturne SPESS4 Collab.)</td></tr><tr><td>BARU</td><td>90 ZPHY C48 581</td><td>S.E. Baru et al.</td><td>(MD-1 Collab.)</td></tr><tr><td>ROE</td><td>90 PR D41 17</td><td>N.A. Roe et al.</td><td>(ASP Collab.)</td></tr><tr><td>WILLIAMS</td><td>88 PRL D38 1365</td><td>D.A. Williams et al.</td><td>(Crystal Ball Collab.)</td></tr><tr><td>AHIARA</td><td>86 PR D33 844</td><td>H. Aihara et al.</td><td>(TPC-2 Collab.)</td></tr><tr><td>BATEL</td><td>86 PL 160B 421</td><td>W. Bartel et al.</td><td>(JADE Collab.)</td></tr><tr><td>LANDSBERG</td><td>85 PRPL 128 401</td><td>L.G. Landsberg</td><td>(SERP)</td></tr><tr><td>ALDE</td><td>84 ZPHY C25 225</td><td>D.M. Alde et al.</td><td>(SERP, BELG, LAPP)</td></tr><tr><td>ALDE</td><td>84 DSNP 40 918</td><td>D.M. Alde et al.</td><td>(SERP, BELG, LAPP)</td></tr><tr><td>Also</td><td>83 Translated from ZETF P 711</td><td>A.YO 40 1447</td><td>(Crystal Ball Collab.)</td></tr><tr><td>WEINSTEIN</td><td>83 PRL D28 2896</td><td>A.J. Weinstein et al.</td><td>(Crystal Ball Collab.)</td></tr><tr><td>BINON</td><td>82 SJPN 36 391</td><td>F.G. Binon et al.</td><td>(SERP, BELG, LAPP+)</td></tr><tr><td>Also</td><td>81 Translated from ZETF P 711</td><td>NC 71A 497</td><td>(SERP, BELG, LAPP+)</td></tr><tr><td>DAVITOV</td><td>81 V.A. Davydov et al.</td><td>V.A. Davydov et al.</td><td>(SERP, BELG, LAPP+)</td></tr><tr><td>Also</td><td>81 V.A. Davydov et al.</td><td>V.A. Davydov et al.</td><td>(SERP, BELG, LAPP+)</td></tr><tr><td>DZHELYADIN</td><td>81 PL 105B 239</td><td>R.I. Dzhelyadin et al.</td><td>(SERP)</td></tr><tr><td>Also</td><td>81 SJPN 33 822</td><td>R.I. Dzhelyadin et al.</td><td>(SERP)</td></tr><tr><td>ABROSIMOV</td><td>80 Translated from ZETF P 711</td><td>A.T. Abrosimov et al.</td><td>(JINR)</td></tr><tr><td>DZHELYADIN</td><td>80 PL 94B 548</td><td>R.I. Dzhelyadin et al.</td><td>(SERP)</td></tr><tr><td>Also</td><td>80 PL B32 516</td><td>R.I. Dzhelyadin et al.</td><td>(SERP)</td></tr><tr><td>DZHELYADIN</td><td>80B PL 97B 471</td><td>R.I. Dzhelyadin et al.</td><td>(SERP)</td></tr><tr><td>Also</td><td>80B PL B32 518</td><td>R.I. Dzhelyadin et al.</td><td>(SERP)</td></tr><tr><td>BUSHIN</td><td>78 PL 79B 147</td><td>Y.B. Bushnин et al.</td><td>(SERP)</td></tr><tr><td>Also</td><td>78 PL 28 775</td><td>Y.B. Bushnин et al.</td><td>(SERP)</td></tr><tr><td>MARTYNOV</td><td>76 Translated from ZETF P 711</td><td>A.S. Martynov et al.</td><td>(JINR)</td></tr><tr><td>JANE</td><td>75 PL 59B 99</td><td>M.R. Jane et al.</td><td>(RHEL, LOWC)</td></tr><tr><td>JANE</td><td>75 PL 59B 103</td><td>M.R. Jane et al.</td><td>(RHEL, LOWC)</td></tr><tr><td>Also</td><td>75 PL 73B 503</td><td>M.R. Jane et al.</td><td>(RHEL, LOWC)</td></tr><tr><td colspan="4">Erratum in private communication.</td></tr><tr><td>BROWMAN</td><td>74B PL 32 1067</td><td>A. Browman et al.</td><td>(CORN, BING)</td></tr><tr><td>DAVIES</td><td>74 NC 24A 324</td><td>J.D. Davies, J.G. Guy, R.K.P. Zia</td><td>(BIRM, RHEL+)</td></tr><tr><td>DUANE</td><td>74 PL 48B 425</td><td>A. Duane et al.</td><td>(LOIC, SHMP)</td></tr><tr><td>JANE</td><td>74 PL 48B 260</td><td>M.R. Jane et al.</td><td>(RHEL, LOWC, SUSS)</td></tr><tr><td>JANE</td><td>74 PL 48B 265</td><td>M.R. Jane et al.</td><td>(RHEL, LOWC, SUSS)</td></tr><tr><td>KENDALL</td><td>74C NCI 21A 387</td><td>B.N. Kendall et al.</td><td>(BROW, BARI, MIT)</td></tr><tr><td>LAYER</td><td>73 PR D7 2565</td><td>J.G. Layer et al.</td><td>(COLU)</td></tr><tr><td>THALER</td><td>73 PR D7 2569</td><td>J.J. Thaler et al.</td><td>(COLU)</td></tr><tr><td>AGUILAR...</td><td>72B PR D6 29</td><td>M. Aguilar-Benitez et al.</td><td>(BNL)</td></tr><tr><td>BLOODWOQ...</td><td>72B NP B39 525</td><td>I.J. Bloodworth et al.</td><td>(TNT0)</td></tr><tr><td>LAYER</td><td>72 PR 29 316</td><td>J.G. Layer et al.</td><td>(COLU)</td></tr><tr><td>THALER</td><td>72 PR 29 313</td><td>J.J. Thaler et al.</td><td>(COLU)</td></tr><tr><td>BASILE</td><td>71 NC 3A 796</td><td>M. Basile et al.</td><td>(CERN, BGNA, STRB)</td></tr><tr><td>STRUGALSKI</td><td>71 NP B27 429</td><td>Z.S. Strugalski et al.</td><td>(JINR)</td></tr><tr><td>BAGLIN</td><td>70 PL 24 66</td><td>C. Baglin et al.</td><td>(EPOL, MADR, STRB)</td></tr><tr><td>BUTTRAM</td><td>70 PL 25 1358</td><td>M.T. Buttram, M.N. Kreister, R.E. Mischke</td><td>(PRIN)</td></tr><tr><td>CARPENTER</td><td>70 PR D1 1303</td><td>D.W. Carpenter et al.</td><td>(DUKE)</td></tr><tr><td>COX</td><td>70 PL 24 534</td><td>B. Cox, L. Fortney, J.P. Golson</td><td>(DUKE)</td></tr><tr><td>DANBURG</td><td>70 PR D2 2564</td><td>J.S. Danburg et al.</td><td>(LRL)</td></tr><tr><td>DEVONS</td><td>70 PR D1 1936</td><td>S. Devons et al.</td><td>(COLU, SYRA)</td></tr><tr><td>GORMLEY</td><td>70 PR D2 501</td><td>M. Gormley et al.</td><td>(COLU, BNL)</td></tr><tr><td>Also</td><td>70</td><td>Thesis Nevis 181</td><td>(COLU)</td></tr><tr><td>BAGLIN</td><td>69 PL 29B 445</td><td>C. Baglin et al.</td><td>(EPOL, UCB, MADR, STRB)</td></tr><tr><td>Also</td><td>69 NP B22 66</td><td>C. Baglin et al.</td><td>(EPOL, MADR, STRB)</td></tr><tr><td>HYAMS</td><td>69 PL 29B 128</td><td>B.D. Hyams et al.</td><td>(CERN, MPIM)</td></tr><tr><td>ARNOLD</td><td>69 PL 27B 466</td><td>R.G. Arnold et al.</td><td>(STRB, MADR, EPOL+)</td></tr><tr><td>BAZIN</td><td>68 PL 20 895</td><td>M.J. Bazin et al.</td><td>(PRIN, QUKI)</td></tr><tr><td>BULLOCK</td><td>68 PL 27B 402</td><td>F.W. Bullock et al.</td><td>(LOUC)</td></tr><tr><td>CNOPS</td><td>68 PL 21 1609</td><td>A.M. Cnops et al.</td><td>(BNL, ORNL, UCND+)</td></tr><tr><td>GORMLEY</td><td>68C PL 21 402</td><td>M. Gormley et al.</td><td>(COLU, BNL)</td></tr><tr><td>WEHMANN</td><td>68 PL 20 748</td><td>A.W. Wehmann et al.</td><td>(HARV, CASE, SLC+)</td></tr><tr><td>BAGLIN</td><td>67 PL 24B 637</td><td>C. Baglin et al.</td><td>(EPOL, UCB)</td></tr><tr><td>BAGLIN</td><td>67B BAPS 12 567</td><td>C. Baglin et al.</td><td>(EPOL, UCB)</td></tr><tr><td>BALTAY</td><td>67D PL 19 1498</td><td>C. Baltay et al.</td><td>(COLU, STON)</td></tr><tr><td>BALTAY</td><td>67B PL 19 1495</td><td>C. Baltay et al.</td><td>(COLU, BRAN)</td></tr><tr><td>BEMPORAD</td><td>67 PL 25B 380</td><td>C. Bemporad et al.</td><td>(PISA, BONN)</td></tr><tr><td>Also</td><td>67</td><td>I. Ion</td><td>(COLU)</td></tr><tr><td>BILLING</td><td>67 PL 25B 435</td><td>K.D. Billling et al.</td><td>(LOUC, OXF)</td></tr><tr><td>BUNIATOV</td><td>67 PL 25B 560</td><td>S.A. Bunyatov et al.</td><td>(CERN, KARL)</td></tr><tr><td>CENCE</td><td>67 PL 19 1393</td><td>R.J. Cence et al.</td><td>(HAWA, LRL)</td></tr><tr><td>ESTEN</td><td>67 PL 24B 115</td><td>M.J. Esten et al.</td><td>(LOUC, OXF)</td></tr><tr><td>FELDMAN</td><td>67 PL 18 868</td><td>M. Feldman et al.</td><td>(PENN)</td></tr><tr><td>FLATTE</td><td>67 PL 18 976</td><td>S.M. Flatte et al.</td><td>(LRL)</td></tr><tr><td>FLATTE</td><td>67B PL 163 1441</td><td>S.M. Flatte, C. G. Wohl</td><td>(LRL)</td></tr><tr><td>LITCHFIELD</td><td>67B PL 24B 486</td><td>P.J. Litchfield et al.</td><td>(RHEL, SACL)</td></tr><tr><td>PRICE</td><td>67 PL 18 1207</td><td>L.R. Price, F.S. Crawford</td><td>(LRL)</td></tr><tr><td>ALFEE...</td><td>67 PL 145 1072</td><td>A. Alff-Steinberger et al.</td><td>(COLU, RUTG)</td></tr><tr><td>CLPARG...</td><td>67 PL 149 1044</td><td>C. Baltay et al.</td><td>(SCUC, LRL, PURD, WISC, YALE)</td></tr><tr><td>CRAWFORD</td><td>66 PL 16 333</td><td>F.S. Crawford, L.R. Price</td><td>(LRL)</td></tr><tr><td>DIGLIUGNO</td><td>66 PL 16 767</td><td>G. di Giugno et al.</td><td>(NAPL, TRST, FRAS)</td></tr><tr><td>GRUNHAUS</td><td>66 Thesis</td><td>J. Grunhaus</td><td>(COLU)</td></tr><tr><td>JAMES</td><td>66 PL 142 896</td><td>F.E. James, H.L. Kraybill</td><td>(YALE, BNL)</td></tr><tr><td>JONES</td><td>66 PL 23 597</td><td>W.G. Jones et al.</td><td>(LOIC, RHEL)</td></tr><tr><td>LARRIBE</td><td>66 PL 23 600</td><td>A. Laribe et al.</td><td>(SACL, RHEL)</td></tr><tr><td>FOSTER</td><td>65 PL 138 8652</td><td>M. Foster et al.</td><td>(WISC, PURD)</td></tr><tr><td>FOSTER</td><td>65B Athens Conf.</td><td>M. Foster, M. Good, M. Meer</td><td>(WISC)</td></tr><tr><td>FOSTER</td><td>65C Thesis</td><td>M. Foster</td><td>(WISC)</td></tr><tr><td>PRICE</td><td>65 PL 15 123</td><td>L.R. Price, F.S. Crawford</td><td>(LRL)</td></tr><tr><td>RITTENBERG</td><td>65 PL 15 556</td><td>A. Rittenberg, G.R. Kalbfleisch</td><td>(LRL, BNL)</td></tr><tr><td>FOELSCHE</td><td>64 PL 134 1138</td><td>H.W.J. Foetsche, H.L. Kraybill</td><td>(YALE)</td></tr></tbody></table>
# Meson Particle Listings

η, f₀(500)

<table><tr><td>KRAEMER</td><td>64</td><td>PR 136 B496</td></tr><tr><td>PAULI</td><td>64</td><td>PL 13 351</td></tr><tr><td>BACCI</td><td>63</td><td>PRL 11 37</td></tr><tr><td>CRAWFORD</td><td>63</td><td>PRL 10 546</td></tr><tr><td>Also</td><td></td><td>PRL 16 907</td></tr><tr><td>ALFF...</td><td>62</td><td>PRL 9 322</td></tr><tr><td>BASTIEN</td><td>62</td><td>PRL 8 114</td></tr><tr><td>PICKUP</td><td>62</td><td>PRL 8 329</td></tr></table>

<table><tr><td>R.W. Kraemer et al.</td><td>(JHU, NWES, WOOD)</td></tr><tr><td>E. Pauli, A. Müller</td><td>(SACL)</td></tr><tr><td>C. Bacci et al.</td><td>(ROMA, FRAS)</td></tr><tr><td>F.S.Jr. Crawford, L.J. Lloyd, E.C. Fowler</td><td>(LRL+)</td></tr><tr><td>F.S. Crawford, L.J. Lloyd, E.C. Fowler</td><td>(LRL+)</td></tr><tr><td>C. Aßf. Steinberger et al.</td><td>(COLU, RUTG)</td></tr><tr><td>P.L. Bastien et al.</td><td>(LRL)</td></tr><tr><td>E. Pickup, D.K. Robinson, E.O. Salant</td><td>(CNRC+)</td></tr></table>

$f_0(500)$

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

also known as σ; was f₀(600), f₀(400–1200)

See the related review(s):

Scalar Mesons below 1 GeV

$f_0(500) \text{ T-MATRIX POLE } \sqrt{s}$

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

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4">(400-550)-i(200-300) OUR ESTIMATE (see Fig. 64.3 in the review)</td></tr><tr><td>(458 ± 7<sup>+4</sup><sub>-10</sub>)-i(245 ± 6<sup>+7</sup><sub>-10</sub>)</td><td>1 DANILKIN</td><td>21</td><td>RVUE Compilation</td></tr><tr><td>(410 ± 20)-i(240 ± 15)</td><td>SARANTSEV</td><td>21</td><td>RVUE J/ψ(1S) → γ (ππ, K<sup>π</sup>, ηη, ωϕ)</td></tr><tr><td>(512 ± 15)-i(188 ± 12)</td><td>2 ABLIKIM</td><td>17</td><td>BES3 J/ψ → γ3π</td></tr><tr><td>(440 ± 10)-i(238 ± 10)</td><td>3 BONALADEJO 12</td><td>17</td><td>RVUE Compilation</td></tr><tr><td>(445 ± 25)-i(278<sup>+22</sup><sub>-18</sub>)</td><td>4,5 GARCIA-MAR..11</td><td>17</td><td>RVUE Compilation</td></tr><tr><td>(457<sup>+14</sup><sub>-13</sub>)-i(279<sup>+11</sup><sub>-7</sub>)</td><td>4,6 GARCIA-MAR..11</td><td>17</td><td>RVUE Compilation</td></tr><tr><td>(442<sup>+8</sup><sub>-8</sub>)-i(274<sup>+6</sup><sub>-5</sub>)</td><td>7 MOUSSALLAM11</td><td>17</td><td>RVUE Compilation</td></tr><tr><td>(452 ± 13)-i(259 ± 16)</td><td>8 MENNESSIER 10</td><td>17</td><td>RVUE Compilation</td></tr><tr><td>(448 ± 43)-i(266 ± 43)</td><td>9 MENNESSIER 10</td><td>17</td><td>RVUE Compilation</td></tr><tr><td>(455 ± 6<sup>+31</sup><sub>-13</sub>)-i(278 ± 6<sup>+34</sup><sub>-43</sub>)</td><td>10 CAPRINI</td><td>08</td><td>RVUE Compilation</td></tr><tr><td>(463 ± 6<sup>+31</sup><sub>-17</sub>)-i(259 ± 6<sup>+33</sup><sub>-34</sub>)</td><td>11 CAPRINI</td><td>08</td><td>RVUE Compilation</td></tr><tr><td>(552<sup>+84</sup><sub>-106</sub>)-i(232<sup>+81</sup><sub>-72</sub>)</td><td>12 ABLIKIM</td><td>07A</td><td>BES2 ψ(2S) → π<sup>+</sup>π<sup>-</sup> J/ψ</td></tr><tr><td>(466 ± 18)-i(223 ± 28)</td><td>13 BONVICINI</td><td>07</td><td>CLEO D<sup>+</sup> → π<sup>-</sup>π<sup>+</sup>π<sup>+</sup></td></tr><tr><td>(472 ± 30)-i(271 ± 30)</td><td>14 BUGG</td><td>07A</td><td>RVUE Compilation</td></tr><tr><td>(484 ± 17)-i(255 ± 10)</td><td>GARCIA-MAR..07</td><td>07A</td><td>RVUE Compilation</td></tr><tr><td>(430)-i(325)</td><td>15 ANISOVICH</td><td>06</td><td>RVUE Compilation</td></tr><tr><td>(441<sup>+16</sup><sub>-8</sub>)-i(272<sup>+9</sup><sub>-12.5</sub>)</td><td>16 CAPRINI</td><td>06</td><td>RVUE ππ → ππ</td></tr><tr><td>(470 ± 50)-i(285 ± 25)</td><td>17 ZHOU</td><td>05</td><td>RVUE</td></tr><tr><td>(541 ± 39)-i(252 ± 42)</td><td>18 ABLIKIM</td><td>04A</td><td>BES2 J/ψ → ωπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>(528 ± 32)-i(207 ± 23)</td><td>19 GALLEGOS</td><td>04</td><td>RVUE Compilation</td></tr><tr><td>(533 ± 25)-i(249 ± 25)</td><td>20 BUGG</td><td>03</td><td>RVUE</td></tr><tr><td>(517 - i240)</td><td>BLACK</td><td>01</td><td>RVUE ππ → ππ</td></tr><tr><td>(470 ± 30)-i(295 ± 20)</td><td>16 COLANGELO</td><td>01</td><td>RVUE ππ → ππ</td></tr><tr><td>(535<sup>+36</sup><sub>-36</sub>)-i(155<sup>+76</sup><sub>-53</sub>)</td><td>21 ISHIDA</td><td>01</td><td>Υ(3S) → Υππ</td></tr><tr><td>610 ± 14 - i(310 ± 13)</td><td>22 SUROVTSnev</td><td>01</td><td>RVUE ππ → ππ, K<sup>π</sup></td></tr><tr><td>(540<sup>+36</sup><sub>-29</sub>)-i(193<sup>+32</sup><sub>-40</sub>)</td><td>ISHIDA</td><td>00B</td><td>p p&#773; → π<sup>0</sup>π<sup>0</sup>π<sup>0</sup></td></tr><tr><td>445 - i235</td><td>HANNAH</td><td>99</td><td>RVUE π scalar form factor</td></tr><tr><td>(523 ± 12)-i(259 ± 7)</td><td>KAMINSKI</td><td>99</td><td>RVUE ππ → ππ, K<sup>π</sup>, σσ</td></tr><tr><td>442 - i 227</td><td>OLLER</td><td>99</td><td>RVUE ππ → ππ, K<sup>π</sup></td></tr><tr><td>469 - i203</td><td>OLLER</td><td>99B</td><td>RVUE ππ → ππ, K<sup>π</sup></td></tr><tr><td>445 - i221</td><td>OLLER</td><td>99C</td><td>RVUE ππ → ππ, K<sup>π</sup>, ηη</td></tr><tr><td>420 - i 212</td><td>LOCHER</td><td>98</td><td>RVUE ππ → ππ, K<sup>π</sup></td></tr><tr><td>440 - i245</td><td>23 DOBADO</td><td>97</td><td>RVUE Compilation</td></tr><tr><td>(602 ± 26)-i(196 ± 27)</td><td>24 ISHIDA</td><td>97</td><td>ππ → ππ</td></tr><tr><td>(537 ± 20)-i(250 ± 17)</td><td>25 KAMINSKI</td><td>97B</td><td>RVUE ππ → ππ, K<sup>π</sup>, 4π</td></tr><tr><td>470 - i250</td><td>26,27 TORNQVIST</td><td>96</td><td>RVUE ππ → ππ, K<sup>π</sup>, K<sup>π</sup>, ηη</td></tr><tr><td>387 - i305</td><td>27,28 JANSSEN</td><td>95</td><td>RVUE ππ → ππ, K<sup>π</sup></td></tr><tr><td>420 - i370</td><td>29 ACHASOV</td><td>94</td><td>RVUE ππ → ππ</td></tr><tr><td>(506 ± 10)-i(247 ± 3)</td><td>KAMINSKI</td><td>94</td><td>RVUE ππ → ππ, K<sup>π</sup></td></tr><tr><td>370 - i356</td><td>30 ZOU</td><td>94B</td><td>RVUE ππ → ππ, K<sup>π</sup></td></tr><tr><td>408 - i342</td><td>27,30 ZOU</td><td>93</td><td>RVUE ππ → ππ, K<sup>π</sup></td></tr><tr><td>470 - i208</td><td>31 VANBEVEREN 86</td><td>86</td><td>RVUE ππ → ππ, K<sup>π</sup>, ηη</td></tr><tr><td>(750 ± 50)-i(450 ± 50)</td><td>32 ESTABROOKS 79</td><td>RVUE</td><td>ππ → ππ, K<sup>π</sup></td></tr><tr><td>(660 ± 100)-i(320 ± 70)</td><td>PROTOPOP... 73</td><td>HBC</td><td>ππ → ππ, K<sup>π</sup></td></tr><tr><td>650 - i370</td><td>33 BASDEVANT</td><td>72</td><td>RVUE ππ → ππ</td></tr></tbody></table>

1. Data driven analysis using partial-wave dispersion relations.

2. S-matrix pole; 8595 events.

3. Applying the chiral unitary approach at NLO to the $K_{\pi}$ data of BATLEY 10 and $πN → ππN$ data of HYAMS 73, GRAYER 74, and PROTOPOPESCU 73.

4. Uses the $K_{\pi}$ data of BATLEY 10C and the $πN → ππN$ data of HYAMS 73, GRAYER 74, and PROTOPOPESCU 73.

5. Analytic continuation using Roy equations.

6. Analytic continuation using GKPY equations.

7. Using Roy equations.

8. Average of three variants of the analytic K-matrix model. Uses the $K_{\pi}$ data of BAT-LEY 08A and the $πN → ππN$ data of HYAMS 73 and GRAYER 74.

9. Average of the analyses of three data sets in the K-matrix model. Uses the data of BATLEY 08A, HYAMS 73, and GRAYER 74, partially of COHEN 80 or ETKIN 82b.

10. From the $K_{\pi}$ data of BATLEY 08A and $πN → ππN$ data of HYAMS 73.

11. From the $K_{\pi}$ data of BATLEY 08A and $πN → ππN$ data of PROTOPOPESCU 73, GRAYER 74, and ESTABROOKS 74.

12. From a mean of three different $f_0(500)$ parametrizations. Uses 40k events.

13. From an isobar model using 2.6k events.

14. Reanalysis of ABLIKIM 04A, PISLAK 01, and HYAMS 73 data.

15. Using the N/D method.

16. From the solution of the Roy equation (ROY 71) for the isoscalar S-wave and using a phase-shift analysis of HYAMS 73 and PROTOPOPESCU 73 data.

17. Reanalysis of the data from PROTOPOPESCU 73, ESTABROOKS 74, GRAYER 74, ROSSELET 77, PISLAK 03, and AKHMETSHIN 04.

18. From a mean of six different analyses and $f_0(500)$ parameterizations.

19. Using data on $ψ(2S) → J/ψππ$ from BAI 00E and on $Υ(nS) → Υ(mS)ππ$ from BUTLER 94b and ALEXANDER 98.

20. From a combined analysis of HYAMS 73, AUGUSTIN 89, AITALA 01B, and PISLAK 01.

21. A similar analysis (KOMADA 01) finds $(580^{+79}_{-30})-i(190^{+107}_{-49})$ MeV.

22. Coupled channel reanalysis of BATON 70, BENSINGER 71, BAILLON 72, HYAMS 73, HYAMS 75, ROSSELET 77, COHEN 80, and ETKIN 82b using the uniformizing variable.

23. Using the inverse amplitude method and data of ESTABROOKS 73, GRAYER 74, and PROTOPOPESCU 73.

24. Reanalysis of data from HYAMS 73, GRAYER 74, SRINIVASAN 75, and ROSSELET 77 using the interfering amplitude method.

25. Average and spread of 4 variants ("up" and "down") of KAMINSKI 97B 3-channel model.

26. Uses data from BEIER 72B, OCHS 73, HYAMS 73, GRAYER 74, ROSSELET 77, CA-SON 83, ASTON 88, and ARMSTRONG 91B. Coupled channel analysis with flavor symmetry and all light two-pseudoscalars systems.

27. Demonstrates explicitly that $f_0(500)$ and $f_0(1370)$ are two different poles.

28. Analysis of data from FALVARD 88.

29. Analysis of data from OCHS 73, ESTABROOKS 75, ROSSELET 77, and MUKHIN 80.

30. Analysis of data from OCHS 73, GRAYER 74, and ROSSELET 77.

31. Coupled-channel analysis using data from PROTOPOPESCU 73, HYAMS 73, HYAMS 75, GRAYER 74, ESTABROOKS 74, ESTABROOKS 75, FROGGATT 77, COR-DEN 79, BISWAS 81.

32. Analysis of data from APEL 72C, GRAYER 74, CASON 76, PAWLICKI 77. Includes spread and errors of 4 solutions.

33. Analysis of data from BATON 70, BENSINGER 71, COLTON 71, BAILLON 72, PRO-TOPOPESCU 73, and WALKER 67.

$f_0(500) \text{ BREIT-WIGNER MASS}$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4">400 to 800 OUR ESTIMATE</td></tr><tr><td>513 ± 32</td><td>34 MURAMATSU 02</td><td>CLEO</td><td>e<sup>+</sup> e<sup>-</sup> ≈ 10 GeV</td></tr><tr><td>478<sup>+24</sup><sub>-23</sub> ± 17</td><td>AITALA</td><td>01B</td><td>E791 D<sup>+</sup> → π<sup>-</sup>π<sup>+</sup>π<sup>+</sup></td></tr><tr><td>563<sup>+58</sup><sub>-29</sub></td><td>35 ISHIDA</td><td>01</td><td>Υ(3S) → Υππ</td></tr><tr><td>555</td><td>36 ASNER</td><td>00</td><td>CLE2 τ<sup>-</sup> → π<sup>-</sup>π<sup>0</sup>π<sup>0</sup>ν<sub>T</sub></td></tr><tr><td>540 ± 36</td><td>ISHIDA</td><td>00B</td><td>p p&#773; → π<sup>0</sup>π<sup>0</sup>π<sup>0</sup></td></tr><tr><td>750 ± 4</td><td>Alekseev</td><td>99</td><td>SPEC 1.78 π<sup>-</sup> p<sub>polar</sub> → π<sup>-</sup>π<sup>+</sup>π<sup>+</sup></td></tr><tr><td>744 ± 5</td><td>Alekseev</td><td>98</td><td>SPEC 1.78 π<sup>-</sup> p<sub>polar</sub> → π<sup>-</sup>π<sup>+</sup>π<sup>+</sup></td></tr><tr><td>759 ± 5</td><td>37 TROYAN</td><td>98</td><td>5.2 n p → n pπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>780 ± 30</td><td>ALDE</td><td>97</td><td>GAM2 450 p p → p pπ<sup>0</sup>π<sup>0</sup></td></tr><tr><td>585 ± 20</td><td>38 ISHIDA</td><td>97</td><td>ππ → ππ</td></tr><tr><td>761 ± 12</td><td>39 SVEC</td><td>96</td><td>RVUE 6-17 πN polar → π<sup>+</sup>π<sup>-</sup> N</td></tr><tr><td>~ 860</td><td>40,41 TORNQVIST</td><td>96</td><td>RVUE ππ → ππ, K<sup>π</sup>, K<sup>π</sup>, ηη</td></tr><tr><td>1165 ± 50</td><td>42,43 ANISOVICH</td><td>95</td><td>RVUE π<sup>-</sup> p → π<sup>0</sup>π<sup>0</sup>η<sub>T</sub>, p p&#773; → π<sup>0</sup>π<sup>0</sup>π<sup>0</sup>, π<sup>0</sup>π<sup>0</sup>η<sub>T</sub>, π<sup>0</sup>ηη</td></tr><tr><td>414 ± 20</td><td>39 AUGUSTIN</td><td>89</td><td>DM2</td></tr></tbody></table>

34. Statistical uncertainty only.

35. A similar analysis (KOMADA 01) finds $526^{+48}_{-37}$ MeV.

36. From the best fit of the Dalitz plot.

37. $\sigma$ effect, no PWA.

38. Reanalysis of data from HYAMS 73, GRAYER 74, SRINIVASAN 75, and ROSSELET 77 using the interfering amplitude method.

39. Breit-Wigner fit to S-wave intensity measured in $πN → π^-π^+N$ on polarized targets. The fit does not include $f_0(980)$.

40. Uses data from ASTON 88, OCHS 73, HYAMS 73, ARMSTRONG 91B, GRAYER 74, CASON 83, ROSSELET 77, and BEIER 72B. Coupled channel analysis with flavor symmetry and all light two-pseudoscalars systems.

41. Also observed by ASNER 00 in $τ^- → π^-π^0π^0ν_T$ decays.

42. Uses $π^0π^0$ data from ANISOVICH 94, AMSLER 94D, and ALDE 95B, $π^+π^-$ data from OCHS 73, GRAYER 74 and ROSSELET 77, and $ηη$ data from ANISOVICH 94.

43. The pole is on Sheet III. Demonstrates explicitly that $f_0(500)$ and $f_0(1370)$ are two different poles.

$f_0(500) \text{ BREIT-WIGNER WIDTH}$

<table><thead><tr><th>VALUE (MeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4">100 to 800 OUR ESTIMATE</td></tr><tr><td>335 ± 67</td><td>44 MURAMATSU 02</td><td>CLEO</td><td>e<sup>+</sup> e<sup>-</sup> ≈ 10 GeV</td></tr><tr><td>324<sup>+42</sup><sub>-40</sub> ± 21</td><td>AITALA</td><td>01B</td><td>E791 D<sup>+</sup> → π<sup>-</sup>π<sup>+</sup>π<sup>+</sup></td></tr><tr><td>372<sup>+229</sup><sub>-95</sub></td><td>45 ISHIDA</td><td>01</td><td>Υ(3S) → Υππ</td></tr><tr><td>540</td><td>46 ASNER</td><td>00</td><td>CLE2 τ<sup>-</sup> → π<sup>-</sup>π<sup>0</sup>π<sup>0</sup>ν<sub>T</sub></td></tr><tr><td>372 ± 80</td><td>ISHIDA</td><td>00B</td><td>p p&#773; → π<sup>0</sup>π<sup>0</sup>π<sup>0</sup></td></tr><tr><td>119 ± 13</td><td>Alekseev</td><td>99</td><td>SPEC 1.78 π<sup>-</sup> p<sub>polar</sub> → π<sup>-</sup>π<sup>+</sup>π<sup>+</sup></td></tr><tr><td>77 ± 22</td><td>Alekseev</td><td>98</td><td>SPEC 1.78 π<sup>-</sup> p<sub>polar</sub> → π<sup>-</sup>π<sup>+</sup>π<sup>+</sup></td></tr></tbody></table>
<table><tbody><tr><td>35 ± 12</td><td>47 TROYAN</td><td>98</td><td>5.2 np → npπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>780 ± 60</td><td>ALDE</td><td>97</td><td>GAM2 450 pp → ppπ<sup>0</sup>π<sup>0</sup></td></tr><tr><td>385 ± 70</td><td>48 ISHIDA</td><td>97</td><td>ππ → ππ</td></tr><tr><td>290 ± 54</td><td>49 SVEC</td><td>96</td><td>RVUE 6-17 πN polar → π<sup>+</sup>π<sup>-</sup> N</td></tr><tr><td>~ 880</td><td>50,51 TORNQVIST</td><td>96</td><td>RVUE ππ → ππ, K<sup>π</sup>, Kπ, ηπ</td></tr><tr><td>460 ± 40</td><td>52,53 ANISOVICH</td><td>95</td><td>RVUE π<sup>-</sup> → π<sup>0</sup>π<sup>0</sup>π<sup>0</sup>, p<sup>0</sup>p → π<sup>0</sup>π<sup>0</sup>π<sup>0</sup>, π<sup>0</sup>π<sup>0</sup>η</td></tr><tr><td>494 ± 58</td><td>49 AUGUSTIN</td><td>89</td><td>DM2</td></tr></tbody></table>

44 Statistical uncertainty only.

45 A similar analysis (KOMADA 01) finds $301_{-100}^{+145}$ MeV.

46 From the best fit of the Dalitz plot.

47 $\sigma$ effect, no PWA.

48 Reanalysis of data from HYAMS 73, GRAYER 74, SRINIVASAN 75, and ROSSELET 77 using the interfering amplitude method.

49 Breit-Wigner fit to S-wave intensity measured in $\pi N \to \pi^-\pi^+ N$ on polarized targets. The fit does not include $f_0(980)$.

50 Uses data from ASTON 88, OCHS 73, HYAMS 73, ARMSTRONG 91B, GRAYER 74, CASON 83, ROSSELET 77, and BEIER 72b. Coupled channel analysis with flavor symmetry and all light two-pseudoscalars systems.

51 Also observed by ASNER 00 in $\tau^- \to \pi^-\pi^0\pi^0\nu_\tau$ decays.

52 Uses $\pi^0\pi^0$ data from ANISOVICH 94, AMSLER 94D, and ALDE 95b, $\pi^+\pi^-$ data from OCHS 73, GRAYER 74 and ROSSELET 77, and $\eta\eta$ data from ANISOVICH 94.

53 The pole is on Sheet III. Demonstrates explicitly that $f_0(500)$ and $f_0(1370)$ are two different poles.

## $f_0(500)$ DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction ($\Gamma_f/\Gamma$)</th></tr></thead><tbody><tr><td>$\Gamma_1 \quad \pi\pi$</td><td>seen</td></tr><tr><td>$\Gamma_2 \quad \gamma\gamma$</td><td>seen</td></tr></tbody></table>

## $f_0(500)$ PARTIAL WIDTHS

<table><thead><tr><th>Γ(γγ)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>• • • We do not use the following data for averages, fits, limits, etc. • • •</td><td></td><td></td><td></td></tr><tr><td>1.37 ± 13 <sup>+0.09</sup><sub>-0.06</sub></td><td>54 DANILKIN</td><td>21</td><td>RVUE Compilation</td></tr><tr><td>2.05 ± 0.21</td><td>55 DAI</td><td>14A</td><td>RVUE Compilation</td></tr><tr><td>1.7 ± 0.4</td><td>56 HOFERICHT... 11</td><td>11</td><td>RVUE Compilation</td></tr><tr><td>3.08 ± 0.82</td><td>57 MENNESSIER 11</td><td>11</td><td>RVUE Compilation</td></tr><tr><td>2.08 ± 0.2 <sup>+0.07</sup><sub>-0.04</sub></td><td>58 MOUSSALLAM 11</td><td>11</td><td>RVUE Compilation</td></tr><tr><td>2.08</td><td>59 MAO</td><td>09</td><td>RVUE Compilation</td></tr><tr><td>1.2 ± 0.4</td><td>60 BERNABEU 09</td><td>08</td><td>RVUE</td></tr><tr><td>3.9 ± 0.6</td><td>57 MENNESSIER 08</td><td>08</td><td>RVUE γγ → π<sup>+</sup>π<sup>-</sup>, π<sup>0</sup>π<sup>0</sup></td></tr><tr><td>1.8 ± 0.4</td><td>61 OLLER</td><td>08</td><td>RVUE Compilation</td></tr><tr><td>1.68 ± 0.15</td><td>61.62 OLLER</td><td>08A</td><td>RVUE Compilation</td></tr><tr><td>3.1 ± 0.5</td><td>63.64 PENNINGTON 08</td><td>08</td><td>RVUE Compilation</td></tr><tr><td>2.4 ± 0.4</td><td>64.65 PENNINGTON 08</td><td>08</td><td>RVUE Compilation</td></tr><tr><td>4.1 ± 0.3</td><td>66 PENNINGTON 08</td><td>08</td><td>RVUE γγ → π<sup>0</sup>π<sup>0</sup></td></tr><tr><td>3.8 ± 1.5</td><td>67.68 BOGLIONE 99</td><td>99</td><td>RVUE γγ → π<sup>+</sup>π<sup>-</sup>, π<sup>0</sup>π<sup>0</sup></td></tr><tr><td>5.4 ± 2.3</td><td>67 MORGAN 90</td><td>90</td><td>RVUE γγ → π<sup>+</sup>π<sup>-</sup>, π<sup>0</sup>π<sup>0</sup></td></tr><tr><td>10 ± 6</td><td>COURAU 86</td><td>86</td><td>DM1 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>e<sup>+</sup>e<sup>-</sup></td></tr></tbody></table>

54 Using the value of the coupled channel analysis.

55 Using dispersive analysis with phases from GARCIA-MARTIN 11A and BUETTIKER 04 as input.

56 Using Roy-Steiner equations with $\pi\pi$ phase shifts from an update of COLANGELO 01 and from GARCIA-MARTIN 11A.

57 Using an analytic K-matrix model.

58 Using dispersion integral with phase input from Roy equations and data from MARSISKE 90, BOYER 90, BEHREND 92, UEHARA 08A, and MORI 07.

59 Used dispersion theory. The value quoted used the $f_0(500)$ pole position of $457 - i276$ MeV.

60 Using $p, n$ polarizabilities from PDG 06 and fitting to $\pi\pi$ phase motion from GARCIA-MARTIN 07 and $\sigma$-poles from GARCIA-MARTIN 07 and CAPRINI 06.

61 Using twice-subtracted dispersion integrals.

62 Supersedes OLLER 08.

63 Solution A (preferred solution based on $\chi^2$-analysis).

64 Dispersion theory based amplitude analysis of BOYER 90, MARSISKE 90, BEHREND 92, and MORI 07.

65 Solution B (worse than solution A; still acceptable when systematic uncertainties are included).

66 Using unitarity and the $\sigma$ pole position from CAPRINI 06.

67 This width could equally well be assigned to the $f_0(1370)$. The authors analyse data from BOYER 90 and MARSISKE 90 and report strong correlation with $\gamma\gamma$ width of $f_2(1270)$.

68 Supersedes MORGAN 90.

<table><tbody><tr><td>L.Y. Dai, M.R. Pennington</td><td>(CEBAF)</td></tr><tr><td>M. Albaladejo, J.A. Oller</td><td>(MURC)</td></tr><tr><td>R. Garcia-Martin et al.</td><td>(MADR, CRAC)</td></tr><tr><td>R. Garcia-Martin, D.R. Phillips, C. Schat</td><td>(BONN+)</td></tr><tr><td>G. Mennessier, S. Narison, X.-G. Wang</td><td></td></tr><tr><td>B. Moussallam</td><td></td></tr><tr><td>J.R. Batley et al.</td><td>(CERN NA48/2 Collab.)</td></tr><tr><td>J.R. Batley et al.</td><td>(CERN NA48/2 Collab.)</td></tr><tr><td>G. Mennessier, S. Narison, X.-G. Wang</td><td></td></tr><tr><td>Y. Mao et al.</td><td>(CERN NA48/2 Collab.)</td></tr><tr><td>J.R. Batley et al.</td><td>(IFIC, GRAN)</td></tr><tr><td>J. Bernabeu, J. Prades</td><td></td></tr><tr><td>I. Caprini</td><td></td></tr><tr><td>G. Mennessier, S. Narison, W. Ochs</td><td></td></tr><tr><td>J.A. Oller, L. Roca, C. Schat</td><td>(MURC, UBA)</td></tr><tr><td>J.A. Oller, L. Roca</td><td>(MURC)</td></tr><tr><td>M.R. Pennington et al.</td><td></td></tr><tr><td>S. Uehara et al.</td><td>(BELLE Collab.)</td></tr><tr><td>M. Ablikim et al.</td><td>(BES Collab.)</td></tr><tr><td>G. Bonvicini et al.</td><td>(CLEO Collab.)</td></tr><tr><td>D.V. Bugg et al.</td><td></td></tr><tr><td>R. Garcia-Martin, J.R. Pelaez, F.J. Yndurain</td><td></td></tr><tr><td>T. Mori et al.</td><td>(BELLE Collab.)</td></tr><tr><td>V.V. Anisovich</td><td></td></tr><tr><td>I. Caprini, G. Colangelo, H. Leutwyler</td><td>(BCIP+)</td></tr><tr><td>W.-M. Yao et al.</td><td>(PDG Collab.)</td></tr><tr><td>M.R. Pennington</td><td></td></tr><tr><td>Z.Y. Zhou et al.</td><td></td></tr><tr><td>M. Ablikim et al.</td><td>(BES Collab.)</td></tr><tr><td>R.R. Akhmetshin et al.</td><td>(Novosibirsk, CMD-2 Collab.)</td></tr><tr><td>P. Buettiker, S. Descotes-Genon, B. Moussallam</td><td></td></tr><tr><td>A. Gallegos et al.</td><td></td></tr><tr><td>D.V. Bugg</td><td></td></tr><tr><td>S. Pislak et al.</td><td>(BNL E865 Collab.)</td></tr><tr><td>S. Pislak et al.</td><td>(BNL E865 Collab.)</td></tr><tr><td>H. Muramatsu et al.</td><td>(CLEO Collab.)</td></tr><tr><td>H. Muramatsu et al.</td><td>(CLEO Collab.)</td></tr><tr><td>E.M. Aitala et al.</td><td>(FNAL E791 Collab.)</td></tr><tr><td>D. Black et al.</td><td></td></tr><tr><td>G. Colangelo, J. Gasser, H. Leytwyler</td><td></td></tr><tr><td>M. Ishida et al.</td><td></td></tr><tr><td>T. Komada et al.</td><td></td></tr><tr><td>S. Pislak et al.</td><td>(BNL E865 Collab.)</td></tr><tr><td>S. Pislak et al.</td><td>(BNL E865 Collab.)</td></tr><tr><td>S. Pislak et al.</td><td>(BNL E865 Collab.)</td></tr><tr><td>S. Pislak et al.</td><td>(BNL E865 Collab.)</td></tr><tr><td>Y.S. Surovtsev, D. Krupa, M. Nagy</td><td></td></tr><tr><td>D.M. Asner et al.</td><td>(CLEO Collab.)</td></tr><tr><td>J. Bai et al.</td><td></td></tr><tr><td>M. Ishida et al.</td><td>(BES Collab.)</td></tr><tr><td>I.G. Alekseev et al.</td><td></td></tr><tr><td>M. Boglione, M.R. Pennington</td><td></td></tr><tr><td>T. Hannah</td><td></td></tr><tr><td>R. Kaminski, L. Lesniak, B. Loiseau</td><td>(CRAC, PARIN)</td></tr><tr><td>J.A. Oller et al.</td><td></td></tr><tr><td>J.A. Oller, E. Oset</td><td></td></tr><tr><td>J.A. Oller, E. Oset</td><td></td></tr><tr><td>I.G. Alekseev et al.</td><td></td></tr><tr><td>J.P. Alexander et al.</td><td>(CLEO Collab.)</td></tr><tr><td>M.P. Locher et al.</td><td>(PSI)</td></tr><tr><td>Yu. Troyan et al.</td><td></td></tr><tr><td>D.M. Alde et al.</td><td>(GAMS Collab.)</td></tr><tr><td>A. Dobado, J.R. Pelaez</td><td></td></tr><tr><td>S. Ishida et al.</td><td>(TOKY, MIYA, KEK)</td></tr><tr><td>R. Kaminski, L. Lesniak, B. Loiseau</td><td>(CRAC, IPN)</td></tr><tr><td>S. Ishida et al.</td><td>(TOKY, MIYA, KEK)</td></tr><tr><td>M. Svec</td><td>(MCGI)</td></tr><tr><td>N.A. Tornqvist, M. Roos</td><td>(HELS)</td></tr><tr><td>D.M. Alde et al.</td><td>(GAMS Collab.)</td></tr><tr><td>V.V. Anisovich et al.</td><td>(PNPI, SERP)</td></tr><tr><td>G. Janssen et al.</td><td>(STON, ADLD, JULI)</td></tr><tr><td>N.N. Achasov, G.N. Shestakov</td><td>(NOVYM)</td></tr><tr><td>C. Amsler et al.</td><td>(Crystal Barrel Collab.)</td></tr><tr><td>V.V. Anisovich et al.</td><td>(Crystal Barrel Collab.)</td></tr><tr><td>F. Butler et al.</td><td>(CLEO Collab.)</td></tr><tr><td>R. Kaminski, L. Lesniak, J.P. Maillet</td><td>(CRAC+)</td></tr><tr><td>B.S. Zou, D.V. Bugg</td><td>(LOQM)</td></tr><tr><td>B.S. Zou, D.V. Bugg</td><td>(LOQM)</td></tr><tr><td>H.V. Behrend</td><td>(CELLO Collab.)</td></tr><tr><td>T.A. Armstrong et al.</td><td>(ATHU, BARI, BIRM+)</td></tr><tr><td>J. Boyer et al.</td><td>(Mark II Collab.)</td></tr><tr><td>H. Marsiske et al.</td><td>(Crystal Ball Collab.)</td></tr><tr><td>D. Morgan, M.R. Pennington</td><td>(RAL, DURH)</td></tr><tr><td>J.E. Augustin, G. Cosme</td><td>(DM2 Collab.)</td></tr><tr><td>D. Aston et al.</td><td>(SLAC, NAGO, CINC, INUS)</td></tr><tr><td>A. Falvard et al.</td><td>(CLER, FRAS, LALO+)</td></tr><tr><td>A. Courau et al.</td><td>(CLER, LALO)</td></tr><tr><td>E. van Beveren et al.</td><td>(NIMJ, BIEL)</td></tr><tr><td>N.M. Cason et al.</td><td>(NDAM, ANL)</td></tr><tr><td>A. Etkin et al.</td><td>(BNL, CUNY, TUFTS, VAND)</td></tr><tr><td>N.N. Biswas et al.</td><td>(NDAM, ANL)</td></tr><tr><td>D. Cohen et al.</td><td>(ANL)JP</td></tr><tr><td>K.N. Mukhin et al.</td><td>(KIAE)</td></tr><tr><td>Translated from ZETF 32 616</td><td></td></tr><tr><td>M.J. Corden et al.</td><td>(BIRM, RHEL, TELA+)</td></tr><tr><td>P. Estabrooks</td><td>(CARL)</td></tr><tr><td>C.D. Froggatt, J.L. Petersen</td><td>(GLAS, NORD)</td></tr><tr><td>A.J. Pawlicki</td><td>(ANL)JP</td></tr><tr><td>Rosselet et al.</td><td></td></tr><tr><td>L. Rosselet et al.</td><td>(GEVA, SACL)</td></tr><tr><td>N.M. Cason et al.</td><td>(NDAM, ANL)JP</td></tr><tr><td>P.G. Estabrooks, A.D. Martin</td><td>(DURH)</td></tr><tr><td>B.D. Hyams et al.</td><td>(CERN, MPIM)</td></tr><tr><td>V. Srinivasan et al.</td><td>(NDAM, ANL)</td></tr><tr><td>P.G. Estabrooks, A.D. Martin</td><td>(DURH)</td></tr><tr><td>G. Grayer et al.</td><td>(CERN, MPIM)</td></tr><tr><td>P.G. Estabrooks, A.D. Martin</td><td>(CERN, MPIM)</td></tr><tr><td>B.D. Hyams et al.</td><td>(CERN, MPIM)</td></tr><tr><td>W. Ochs</td><td>(MIMI)</td></tr><tr><td>S.D. Protopopescu et al.</td><td>(LBL)</td></tr><tr><td>W.D. Apel et al.</td><td>(KARLK, KARLE, PISA)</td></tr><tr><td>P.H. Baillon et al.</td><td>(SLAC)</td></tr><tr><td>J.L. Basdevant, C.D. Froggatt, J.L. Petersen</td><td>(CERN)</td></tr><tr><td>E.W. Beier et al.</td><td>(PENN)</td></tr><tr><td>J.R. Bensinger et al.</td><td>(WISC)</td></tr><tr><td>E. Colton et al.</td><td>(LBL, FNAL, UCLA+)</td></tr><tr><td>S.M. Roy</td><td></td></tr><tr><td>J.P. Baton, G. Laurens, J. Reignier</td><td>(SACL)</td></tr><tr><td>W.D. Walker</td><td>(WISC)</td></tr></tbody></table>

## $f_0(500)$ REFERENCES

DANILKIN 21 PR D103 114023 J. Danilkin, O. Deineka, M. Vanderhaeghen (MAINZ)

SARANTSEV 21 PR B816 136227 A.V. Sarantsev et al. (BONN, PNPI)

ABLIKIM 17 PRL 118 012001 M. Ablikim et al. (BESIII Collab.)
$\rho(770)$

$I^G(JPC) = 1^+(1^-)$

## ρ(770) T-MATRIX POLE $\sqrt{s}$

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

<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>(761-765) - i (71-74) OUR ESTIMATE</strong></td></tr><tr><td>(763.7<sup>+1.7</sup><sub>-1.5</sub>) - i (73.2<sup>+1.0</sup><sub>-1.1</sub>)</td><td>1</td><td>GARCIA-MAR...</td><td>11</td><td>RVUE Compilation</td></tr><tr><td>(754 ± 18) - i (74 ± 10)</td><td>2</td><td>PELAEZ</td><td>04A</td><td>RVUE ππ → ππ</td></tr><tr><td>(762.4 ± 1.8) - i (72.6 ± 1.4)</td><td>3</td><td>COLANGELO</td><td>01</td><td>RVUE ππ → ππ</td></tr></tbody></table>

¹Reanalysis of the $K_{ρ0}$ data of BATLEY 10C and the $πN → ππN$ data of HYAMS 73, GRAYÉR 74, and PROTOPOPESCU 73 using GKPY equations.

²Reanalysis of data from PROTOPOPESCU 73, ESTABROOKS 74, GRAYER 74, and COHEN 80 in the unitarized ChPT model.

## ρ(770) MASS

We no longer list S-wave Breit-Wigner fits, or data with high combinatorial background.

### NEUTRAL ONLY, $e^+e^-$

<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>775.26 ± 0.23 OUR AVERAGE</strong></td></tr><tr><td>775.3 ± 0.5 ± 0.6</td><td>1</td><td>ACHASOV</td><td>21</td><td>SND e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>775.02 ± 0.35</td><td>2</td><td>LEES</td><td>126</td><td>BABR e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>775.97 ± 0.46 ± 0.70</td><td>3</td><td>3 AKHMETSHIN 07</td><td></td><td>e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>774.6 ± 0.4 ± 0.5</td><td>4,5</td><td>ACHASOV</td><td>06</td><td>SND e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>775.65 ± 0.64 ± 0.50</td><td>6,7</td><td>AKHMETSHIN 04</td><td>04</td><td>CMD2 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>775.9 ± 0.5 ± 0.5</td><td>8</td><td>ALOISIO</td><td>03</td><td>KLOE 1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>775.8 ± 0.9 ± 2.0</td><td>9</td><td>ACHASOV</td><td>02</td><td>SND 1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>775.9 ± 1.1</td><td>9</td><td>BARKOV</td><td>85</td><td>OLYA e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

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

<table><tbody><tr><td>763.49 ± 0.53</td><td>10</td><td>BARTOS</td><td>17</td><td>RVUE e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>758.23 ± 0.46</td><td>11</td><td>BARTOS</td><td>17A</td><td>RVUE e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>775.8 ± 0.5 ± 0.3</td><td>12</td><td>ALOISIO</td><td>03</td><td>KLOE 1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>775.9 ± 0.6 ± 0.5</td><td>13</td><td>ALOISIO</td><td>03</td><td>KLOE 1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>775.0 ± 0.6 ± 1.1</td><td>14</td><td>ACHASOV</td><td>02</td><td>SND 1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>775.1 ± 0.7 ± 5.3</td><td>15</td><td>BENAYOUN</td><td>98</td><td>RVUE e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>, μ<sup>+</sup>μ<sup>-</sup></td></tr><tr><td>770.5 ± 1.9 ± 5.1</td><td>16</td><td>GARDNER</td><td>98</td><td>RVUE 0.28-0.92 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>764.1 ± 0.7</td><td>17</td><td>O'CONNELL</td><td>97</td><td>RVUE e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>757.5 ± 1.5</td><td>18</td><td>BERNICHA</td><td>94</td><td>RVUE e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>768 ± 1</td><td>19</td><td>GESHKEN...</td><td>89</td><td>RVUE e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

¹From a fit of the cross section in the energy range $0.525 < \sqrt{s} < 0.883$ GeV parameterized by the sum of the Breit-Wigner amplitudes for the $\rho(770)$, $\omega$ and $\rho(1450)$ resonances.

²Using the GOUNARIS 68 parametrization with the complex phase of the $\rho-\omega$ interference and leaving the masses and widths of the $\rho(1450)$, $\rho(1700)$, and $\rho(2150)$ resonances as free parameters of the fit.

³A combined fit of AKHMETSHIN 07, AULCHENKO 06, and AULCHENKO 05.

⁴Supersedes ACHASOV 05A.

⁵A fit of the SND data from 400 to 1000 MeV using parameters of the $\rho(1450)$ and $\rho(1700)$ from a fit of the data of BARKOV 85, BISELLO 89 and ANDERSON 00A.

⁶Using the GOUNARIS 68 parametrization with the complex phase of the $\rho-\omega$ interference.

⁷Update of AKHMETSHIN 02.

⁸Assuming $m_{\rho^+} = m_{\rho^-}$, $\Gamma_{\rho^+} = \Gamma_{\rho^-}$.

⁹From the GOUNARIS 68 parametrization of the pion form factor.

¹⁰Applies the Unitary & Analytic Model of the pion electromagnetic form factor of DUB-NICKA 10 to analyze the data of LEES 12G and ABLIKIM 16c.

¹¹Applies the Unitary & Analytic Model of the pion electromagnetic form factor of DUB-NICKA 10 to analyze the data of ACHASOV 06, AKHMETSHIN 07, AUBERT 09AS, and AMBROSINO 11A.

¹²Assuming $m_{\rho^+} = m_{\rho^-} = m_{\rho^0}$, $\Gamma_{\rho^+} = \Gamma_{\rho^-} = \Gamma_{\rho^0}$.

¹³Without limitations on masses and widths.

¹⁴Assuming $m_{\rho^0} = m_{\rho^+} = \beta_{\rho^0} \pi \pi = \beta_{\rho^+} \pi \pi$.

¹⁵Using the data of BARKOV 85 in the hidden local symmetry model.

¹⁶From the fit to $e^+e^- \to \pi^+\pi^-$ data from the compilations of HEYN 81 and BARKOV 85, including the GOUNARIS 68 parametrization of the pion form factor.

¹⁷A fit of BARKOV 85 data assuming the direct $\omega\pi\pi$ coupling.

¹⁸Applying the S-matrix formalism to the BARKOV 85 data.

¹⁹Includes BARKOV 85 data. Model-dependent width definition.

### CHARGED ONLY, $\tau$ DECAYS AND $e^+e^-$

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="6"><strong>775.11 ± 0.34 OUR AVERAGE</strong></td></tr><tr><td>774.6 ± 0.2 ± 0.5</td><td>5.4M</td><td>1,2 FUJIKAWA</td><td>08</td><td>BELL ±</td><td>$\tau^- \to \pi^- \pi^0 \nu_\tau$</td></tr><tr><td>775.5 ± 0.7</td><td>2,3 SCHAEL</td><td>05C</td><td>ALEP</td><td></td><td>$\tau^- \to \pi^- \pi^0 \nu_\tau$</td></tr><tr><td>775.5 ± 0.5 ± 0.4</td><td>1.98M</td><td>4 ALOISIO</td><td>03</td><td>KLOE</td><td>$1.02 e^+ e^- \to \pi^+ \pi^- \pi^0 \to \pi^- \pi^0 \nu_\tau$</td></tr><tr><td>775.1 ± 1.1 ± 0.5</td><td>87k</td><td>5,6 ANDERSON</td><td>00A</td><td>CLE2</td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>761.60 ± 0.95</td><td>7</td><td>BARTOS</td><td>17A</td><td>RVUE</td><td>$\tau^- \to \pi^- \pi^0 \nu_\tau$</td></tr><tr><td>774.8 ± 0.6 ± 0.4</td><td>1.98M</td><td>8</td><td>ALOISIO</td><td>03</td><td>KLOE -</td></tr><tr><td>776.3 ± 0.6 ± 0.7</td><td>1.98M</td><td>8</td><td>ALOISIO</td><td>03</td><td>KLOE +</td></tr><tr><td>773.9 ± 2.0 ± 0.3</td><td>10</td><td>SANZ-CILLERO</td><td>03</td><td>RVUE</td><td>$\tau^- \to \pi^- \pi^0 \nu_\tau$</td></tr><tr><td>774.5 ± 0.7 ± 1.5</td><td>500k</td><td>4</td><td>ACHASOV</td><td>02</td><td>SND ±</td></tr><tr><td>775.1 ± 0.5</td><td>10</td><td>PICH</td><td>01</td><td>RVUE</td><td>$\tau^- \to \pi^- \pi^0 \nu_\tau$</td></tr></tbody></table>

¹$|\Gamma_\pi(0)|^2$ fixed to 1.

²From the GOUNARIS 68 parametrization of the pion form factor.

³The error combines statistical and systematic uncertainties. Supersedes BARATE 97M.

⁴Assuming $m_{\rho^+} = m_{\rho^-}$, $\Gamma_{\rho^+} = \Gamma_{\rho^-}$.

⁵$\rho(1700)$ mass and width fixed at 1700 MeV and 235 MeV respectively.

⁶From the GOUNARIS 68 parametrization of the pion form factor. The second error is a model error taking into account different parametrizations of the pion form factor.

⁷Applies the Unitary & Analytic Model of the pion electromagnetic form factor of DUB-NICKA 10 to analyze the data of FUJIKAWA 08.

⁸Without limitations on masses and widths.

⁹Using the data of BARATE 97M and the effective chiral Lagrangian.

¹⁰From a fit of the model-independent parameterization of the pion form factor to the data of BARATE 97M.

### MIXED CHARGES, OTHER REACTIONS

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>763.0 ± 0.3 ± 1.2</strong></td><td><strong>600k</strong></td><td><strong>1 ABELE</strong></td><td><strong>99E</strong></td><td><strong>CBAR</strong></td><td><strong>0 ±</strong></td></tr></tbody></table>

¹Assuming the equality of $\rho^+$ and $\rho^-$ masses and widths.

### CHARGED ONLY, HADROPRODUCED

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="6"><strong>766.5 ± 1.1 OUR AVERAGE</strong></td></tr><tr><td>763.7 ± 3.2</td><td></td><td>ABELE</td><td>97</td><td>CBAR</td><td>$\bar{p}n \to \pi^- \pi^0 \pi^0$</td></tr><tr><td>768 ± 9</td><td></td><td>AGUILAR...</td><td>91</td><td>EHS</td><td>400 pp</td></tr><tr><td>767 ± 3</td><td>2935</td><td>1 CAPRARO</td><td>87</td><td>SPEC -</td><td>200 $\pi^- \text{Cu} \to \pi^- \pi^0 \text{Cu}$</td></tr><tr><td>761 ± 5</td><td>967</td><td>1 CAPRARO</td><td>87</td><td>SPEC -</td><td>200 $\pi^- \text{Pb} \to \pi^- \pi^0 \text{Pb}$</td></tr><tr><td>771 ± 4</td><td></td><td>HUSTON</td><td>86</td><td>SPEC +</td><td>202 $\pi^+ A \to \pi^+ \pi^0 A$</td></tr><tr><td>766 ± 7</td><td>6500</td><td>2 BYERLY</td><td>73</td><td>OSPK</td><td>5 $\pi^- p$</td></tr><tr><td>766.8 ± 1.5</td><td>9650</td><td>3 PISUT</td><td>68</td><td>RVUE -</td><td>1.7-3.2 $\pi^- p$, t < 10</td></tr><tr><td>767 ± 6</td><td>900</td><td>1 EISNER</td><td>67</td><td>HBC -</td><td>4.2 $\pi^- p$, t < 10</td></tr></tbody></table>

¹Mass errors enlarged by us to $\Gamma/\sqrt{n}$; see the note with the $K^*(892)$ mass.

²Phase shift analysis. Systematic errors added corresponding to spread of different fits.

³From fit of 3-parameter relativistic P-wave Breit-Wigner to total mass distribution. Includes BATON 68, MILLER 67b, ALFF-STEINBERGER 66, HAGOPIAN 66, HAGO-PIAN 66b, JACOBS 66b, JAMES 66, WEST 66, BLIEDEN 65 and CARMONY 64.

### NEUTRAL ONLY, PHOTOPRODUCED

<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>769.2 ± 0.9 OUR AVERAGE</strong></td></tr><tr><td>770.8 ± 1.3 ± 2.3</td><td>2.4</td><td>900k</td><td>ANDREEV</td><td>H1</td><td>$ep \to e^+ \pi^+ p$</td></tr><tr><td>771 ± 2 ± 1</td><td>63.5k</td><td>1 ABRAMOWICZ</td><td>12</td><td>ZEUS</td><td>$ep \to e^+ \pi^+ p$</td></tr><tr><td>770 ± 2 ± 1</td><td>79k</td><td>2 BREITWEG</td><td>98b</td><td>ZEUS</td><td>50-100 $\gamma p$</td></tr><tr><td>767.6 ± 2.7</td><td></td><td>BARTALUCCI</td><td>78</td><td>CNTR</td><td>$\gamma p \to e^+ e^- p$</td></tr><tr><td>775 ± 5</td><td></td><td>GLADDING</td><td>73</td><td>CNTR</td><td>2.9-4.7 $\gamma p$</td></tr><tr><td>767 ± 4</td><td>1930</td><td>BALLAM</td><td>72</td><td>HBC</td><td>2.8 $\gamma p$</td></tr><tr><td>770 ± 4</td><td>2430</td><td>BALLAM</td><td>72</td><td>HBC</td><td>4.7 $\gamma p$</td></tr><tr><td>765 ± 10</td><td></td><td>ALVENSLEB...</td><td>70</td><td>CNTR</td><td>$\gamma A, t < 0.01$</td></tr><tr><td>767.7 ± 1.9</td><td>140k</td><td>BIGGS</td><td>70</td><td>CNTR</td><td>$<4.1 \gamma C \to \pi^+ \pi^- C$</td></tr><tr><td>765 ± 5</td><td>4000</td><td>ASBURY</td><td>67b</td><td>HBC</td><td>$\gamma + Pb$</td></tr></tbody></table>

771 ± 2 79k 3 BREITWEG 98b ZEUS 50-100 $\gamma p$

¹Using the KUHN 90 parametrization of the pion form factor, neglecting $\rho-\omega$ interference.

²From the parametrization according to SOEDING 66.

³From the parametrization according to ROSS 66.

### NEUTRAL ONLY, OTHER REACTIONS

<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>765 ± 6</td><td></td><td>BERTIN</td><td>97c</td><td>OBLX</td><td>$0.0 \bar{p}p \to \pi^+ \pi^- \pi^0$</td></tr><tr><td>773 ± 1.6</td><td></td><td>WEIDENAUER</td><td>93</td><td>ASTE</td><td>$\bar{p}p \to \pi^+ \pi^- \omega$</td></tr><tr><td>762.6 ± 2.6</td><td></td><td>AGUILAR...</td><td>91</td><td>EHS</td><td>400 pp</td></tr><tr><td>770 ± 2</td><td></td><td>1 HEYN</td><td>81</td><td>RVUE</td><td>Pion form factor</td></tr><tr><td>768 ± 4</td><td></td><td>2,3 BOHACIK</td><td>80</td><td>RVUE</td><td></td></tr><tr><td>769 ± 3</td><td></td><td>4 WICKLUND</td><td>78</td><td>ASPK</td><td>3,4,6 $\pi^+ N$</td></tr><tr><td>768 ± 1</td><td>76k</td><td>DEUTSCH...</td><td>76</td><td>HBC</td><td>16 $\pi^+ p$</td></tr><tr><td>767 ± 4</td><td>4100</td><td>ENGLER</td><td>74</td><td>DBC</td><td>$6 \pi^+ n \to \pi^+ \pi^- \pi^-$</td></tr><tr><td>775 ± 4</td><td>32k</td><td>2 PROTOPOP...</td><td>73</td><td>HBC</td><td>7.1 $\pi^+ p$, t < 0.4</td></tr><tr><td>764 ± 3</td><td>6.8k</td><td>5 RATCLIFF</td><td>72</td><td>ASPK</td><td>15 $\pi^- p$, t < 0.3</td></tr><tr><td>774 ± 3</td><td>1.7k</td><td>REYNOLDS</td><td>69</td><td>HBC</td><td>2.26 $\pi^- p$</td></tr><tr><td>769.2 ± 1.5</td><td>13.3k</td><td>6 PISUT</td><td>68</td><td>RVUE</td><td>1.7-3.2 $\pi^- p$, t < 10</td></tr></tbody></table>
• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>774.34 ± 0.18 ± 0.35</td><td>970k</td><td>7 ABLIKIM</td><td>18c BES3</td><td>η'(958) → γπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>772.93 ± 0.18 ± 0.34</td><td>970k</td><td>8 ABLIKIM</td><td>18c BES3</td><td>η'(958) → γπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>773.5 ± 2.5</td><td></td><td>9 COLANGELO</td><td>01 RVUE</td><td>ππ → ππ</td></tr><tr><td>762.3 ± 0.5 ± 1.2</td><td>600k</td><td>10 ABELE</td><td>99e CBAR</td><td>0.0 p̄p → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>777 ± 2</td><td>4.9k</td><td>11 ADAMS</td><td>97 E665</td><td>470 μp → μXB</td></tr><tr><td>770 ± 2</td><td></td><td>12 BOGOLYUB...</td><td>97 MIRA</td><td>32 p̄p → π<sup>+</sup>π<sup>-</sup>X</td></tr><tr><td>768 ± 8</td><td></td><td>12 BOGOLYUB...</td><td>97 MIRA</td><td>32 p̄p → π<sup>+</sup>π<sup>-</sup>X</td></tr><tr><td>761.1 ± 2.9</td><td></td><td>DUBNICKA</td><td>89 RVUE</td><td>π form factor</td></tr><tr><td>777.4 ± 2.0</td><td></td><td>13 CHABAUD</td><td>83 ASPK</td><td>17 π<sup>-</sup> p polarized</td></tr><tr><td>769.5 ± 0.7</td><td></td><td>2.3 LANG</td><td>79 RVUE</td><td></td></tr><tr><td>770 ± 9</td><td></td><td>3 ESTABROOKS</td><td>74 RVUE</td><td>17 π<sup>-</sup> p → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>773.5 ± 1.7</td><td>11.2k</td><td>14 JACOBS</td><td>72 HBC</td><td>2.8 π<sup>-</sup> p</td></tr><tr><td>775 ± 3</td><td>2.2k</td><td>15 HYAMS</td><td>68 OSPK</td><td>11.2 π<sup>-</sup> p</td></tr></tbody></table>

¹HEYN 81 includes all spacelike and timelike $F_π$ values until 1978.

²From pole extrapolation.

³From phase shift analysis of GRAYER 74 data.

⁴Phase shift analysis. Systematic errors added corresponding to spread of different fits.

⁵Published values contain misprints. Corrected by private communication RATCLIFF 74.

⁶Includes MALAMUD 69, ARMENISE 68, BACON 67, HUWE 67, MILLER 67B, ALFF-STEINBERGER 66, HAGOPIAN 66, HAGOPIAN 66B, JACOBS 66B, JAMES 66, WEST 66, GOLDHABER 64, ABOLINS 63.

⁷From a fit to $π^+π^-$ mass using $ρ(770)$ (parametrized with the Gounaris-Sakurai approach), $ω(782)$, and box anomaly components.

⁸From a fit to $π^+π^-$ mass using $ρ(770)$ (parametrized with the Gounaris-Sakurai approach), $ω(782)$, and $ρ(1450)$ components.

⁹Breit-Wigner mass from a phase-shift analysis of HYAMS 73 and PROTOPOPESCU 73 data.

¹⁰Using relativistic Breit-Wigner and taking into account $ρ-ω$ interference.

¹¹Systematic errors not evaluated.

¹²Systematic effects not studied.

¹³From fit of 3-parameter relativistic Breit-Wigner to helicity-zero part of P-wave intensity. CHABAUD 83 includes data of GRAYER 74.

¹⁴Mass errors enlarged by us to $Γ/\sqrt{N}$; see the note with the $K^*(892)$ mass.

¹⁵Of HYAMS 68 six parametrizations, this is theoretically soundest. MR

<figure><img src="image_433.png" /><figcaption>WEIGHTED AVERAGE
769.0±0.9 (Error scaled by 1.4)</figcaption></figure>

$$m_{\rho(770)}^{0} - m_{\rho(770)}^{\pm}$$

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>-0.7 ± 0.8</strong></td><td><strong>OUR AVERAGE</strong></td><td colspan="4">Error includes scale factor of 1.5. See the ideogram below.</td></tr><tr><td>-2.4 ± 0.8</td><td>1 SCHAEEL</td><td>05c</td><td>ALEP</td><td></td><td>τ<sup>-</sup> → π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td></tr><tr><td>0.4 ± 0.7 ± 0.6 1.98M</td><td>2 ALOISIO</td><td>03</td><td>KLOE</td><td></td><td>1.02 e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>1.3 ± 1.1 ± 2.0 500k</td><td>2 ACHASOV</td><td>02</td><td>SND</td><td></td><td>1.02 e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>1.6 ± 0.6 ± 1.7 600k</td><td>ABELE</td><td>99c</td><td>CBAR</td><td>±0</td><td>0.0 p̄p → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>-4 ± 4</td><td>3 REYNOLDS</td><td>69</td><td>HBC</td><td>±0</td><td>2.26 π<sup>-</sup> p</td></tr><tr><td>-5 ± 5</td><td>3 FOSTER</td><td>68</td><td>HBC</td><td>±0</td><td>0.0 p̄p</td></tr><tr><td>2.4 ± 2.1</td><td>4 PISUT</td><td>68</td><td>RVUE</td><td></td><td>πN → ρN</td></tr></tbody></table>

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

<table><tbody><tr><td>-3.37 ± 1.06</td><td>5 BARTOS</td><td>17A</td><td>RVUE</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>,<br/>τ<sup>-</sup> → π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td></tr></tbody></table>

¹From the combined fit of the $τ^-$ data from ANDERSON 00A and SCHAEL 05C and $e^+e^-$ data from the compilation of BARKOV 85, AKHMETSHIN 04, and ALOISIO 05. Supersedes BARATE 97M.

²Assuming $m_{ρ^+} = m_{ρ^-}, Γ_{ρ^+} = Γ_{ρ^-}$.

³From quoted masses of charged and neutral modes.

⁴Includes MALAMUD 69, ARMENISE 68, BATON 68, BACON 67, HUWE 67, MILLER 67B, ALFF-STEINBERGER 66, HAGOPIAN 66, HAGOPIAN 66B, JACOBS 66B, JAMES 66, WEST 66, BLIEDEN 65, CARMONY 64, GOLDHABER 64, ABOLINS 63.

⁵Applies the Unitary & Analytic Model of the pion electromagnetic form factor of DUB-NICKA 10 to analyze the data of ACHASOV 06, AKHMETSHIN 07, AUBERT 09AS, AMBROSINO 11A, and FUJIKAWA 08.

<figure><img src="image_434.png" /><figcaption>WEIGHTED AVERAGE
-0.7±0.8 (Error scaled by 1.5)</figcaption></figure>

$$m_{\rho(770)}^{+} - m_{\rho(770)}^{-}$$

<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></table>

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

<table><tbody><tr><td>1.5±0.8±0.7</td><td>1.98M</td><td>1 ALOISIO</td><td>03</td><td>KLOE</td><td>1.02 e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr></tbody></table>

¹Without limitations on masses and widths.

## $\rho(770)$ RANGE PARAMETER

The range parameter $R$ enters an energy-dependent correction to the width, of the form $(1 + q_T^2 R^2) / (1 + q_T^2 R^2)$, where $q$ is the momentum of one of the pions in the $ππ$ rest system. At resonance, $q = q_T$.

<table><thead><tr><th>VALUE (GeV<sup>-1</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>5.3<sup>+0.9</sup><sub>-0.7</sub></strong></td><td>1 CHABAUD</td><td>83</td><td>ASPK</td><td>0 17 π<sup>-</sup> p polarized</td></tr></tbody></table>

¹The old PISUT 68 value, properly corrected, was $3.2 \pm 0.6$.

## $\rho(770)$ WIDTH

We no longer list S-wave Breit-Wigner fits, or data with high combinatorial background.

### NEUTRAL ONLY, $e^+e^-$

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>147.4 ± 0.8</strong></td><td><strong>OUR AVERAGE</strong></td><td colspan="3">Error includes scale factor of 2.0.</td></tr><tr><td>145.6 ± 0.6 ± 0.8</td><td></td><td>1 ACHASOV</td><td>21</td><td>SND</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>149.59 ± 0.67</td><td></td><td>2 LEES</td><td>12G</td><td>BABR</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>γ</td></tr><tr><td>145.98 ± 0.75 ± 0.50</td><td>900k</td><td>3 AKHMETSHIN 07</td><td></td><td></td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>146.1 ± 0.8 ± 1.5</td><td>800k</td><td>4,5 ACHASOV</td><td>06</td><td>SND</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>143.85 ± 1.33 ± 0.80</td><td>114k</td><td>6,7 AKHMETSHIN 04</td><td>CMD2</td><td></td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>147.3 ± 1.5 ± 0.7</td><td>1.98M</td><td>8 ALOISIO</td><td>03</td><td>KLOE</td><td>1.02 e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>151.1 ± 2.6 ± 3.0</td><td>500k</td><td>8 ACHASOV</td><td>02</td><td>SND</td><td>1.02 e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>150.5 ± 3.0</td><td></td><td>9 BARKOV</td><td>85</td><td>OLYA</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

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

<table><tbody><tr><td>144.06 ± 0.85</td><td>10 BARTOS</td><td>17</td><td>RVUE</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>144.56 ± 0.80</td><td>11 BARTOS</td><td>17A</td><td>RVUE</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>143.9 ± 1.3 ± 1.1</td><td>1.98M</td><td>12 ALOISIO</td><td>03</td><td>KLOE</td><td>1.02 e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>147.4 ± 1.5 ± 0.7</td><td>1.98M</td><td>13 ALOISIO</td><td>03</td><td>KLOE</td><td>1.02 e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>149.8 ± 2.2 ± 2.0</td><td>500k</td><td>14 ACHASOV</td><td>02</td><td>SND</td><td>1.02 e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>147.9 ± 1.5 ± 7.5</td><td></td><td>15 BENAYOUN</td><td>98</td><td>RVUE</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>,<br/>μ<sup>+</sup> μ<sup>-</sup></td></tr><tr><td>153.5 ± 1.3 ± 4.6</td><td></td><td>16 GARDNER</td><td>98</td><td>RVUE</td><td>0.28-0.92 e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>145.0 ± 1.7</td><td></td><td>17 O'CONNELL</td><td>97</td><td>RVUE</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>142.5 ± 3.5</td><td></td><td>18 BERNICHA</td><td>94</td><td>RVUE</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr><tr><td>138 ± 1</td><td></td><td>19 GESHKEN...</td><td>89</td><td>RVUE</td><td>e<sup>+</sup> e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup></td></tr></tbody></table>

¹From a fit of the cross section in the energy range $0.525 < \sqrt{s} < 0.883$ GeV parameterized by the sum of the Breit-Wigner amplitudes for the $ρ(770)$, $ω$ and $ρ(1450)$ resonances.

²Using the GOUNARIS 68 parametrization with the complex phase of the $ρ-ω$ interference and leaving the masses and widths of the $ρ(1450)$, $ρ(1700)$, and $ρ(2150)$ resonances as free parameters of the fit.

³A combined fit of AKHMETSHIN 07, AULCHENKO 06, and AULCHENKO 05.

⁴Supersedes ACHASOV 05A.

⁵A fit of the SND data from 400 to 1000 MeV using parameters of the $ρ(1450)$ and $ρ(1700)$ from a fit of the data of BARKOV 85, BISELLO 89 and ANDERSON 00A.

⁶Using the GOUNARIS 68 parametrization with the complex phase of the $ρ-ω$ interference.
# Meson Particle Listings

## $\rho(770)$

7 From a fit in the energy range 0.61 to 0.96 GeV. Update of AKHMETSHIN 02.

8 Assuming $m_{\rho^+} = m_{\rho^-}, \Gamma_{\rho^+} = \Gamma_{\rho^-}$.

9 From the GOUNARIS 68 parametrization of the pion form factor.

10 Applies the Unitary & Analytic Model of the pion electromagnetic form factor of DUB-NICKA 10 to analyze the data of LEES 12G and ABLIKIM 16C.

11 Applies the Unitary & Analytic Model of the pion electromagnetic form factor of DUB-NICKA 10 to analyze the data of ACHASOV 06, AKHMETSHIN 07, AUBERT 09AS, and AMBROSINO 11A.

12 Assuming $m_{\rho^+} = m_{\rho^-} = m_{\rho^0}, \Gamma_{\rho^+} = \Gamma_{\rho^-} = \Gamma_{\rho^0}$.

13 Without limitations on masses and widths.

14 Assuming $m_{\rho^0} = m_{\rho^+}, g_{\rho^0\pi\pi} = g_{\rho^+\pi\pi}$.

15 Using the data of BARKOV 85 in the hidden local symmetry model.

16 From the fit to $e^+e^- \to \pi^+\pi^-$ data from the compilations of HEYN 81 and BARKOV 85, including the GOUNARIS 68 parametrization of the pion form factor.

17 A fit of BARKOV 85 data assuming the direct $\pi\omega\pi\pi$ coupling.

18 Applying the S-matrix formalism to the BARKOV 85 data.

19 Includes BARKOV 85 data. Model-dependent width definition.

WEIGHTED AVERAGE
147.4±0.8 (Error scaled by 2.0)

<figure><img src="image_435.png" /></figure>

## CHARGED ONLY, $\tau$ DECAYS and $e^+e^-$

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>149.1 ±0.8</strong></td><td><strong>OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td><strong>149.1 ±0.8</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>148.1 ±0.4</td><td>±1.7 5.4M</td><td>1,2 FUJIKAWA</td><td>08</td><td>BELL</td><td>± τ<sup>-</sup> → π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td></tr><tr><td>149.0 ±1.2</td><td></td><td>2,3 SCHAEL</td><td>05C</td><td>Alep</td><td>τ<sup>-</sup> → π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td></tr><tr><td>149.9 ±2.3</td><td>±2.0 500k</td><td>4 ACHASOV</td><td>02</td><td>SND</td><td>1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>150.4 ±1.4</td><td>±1.4 87k</td><td>5,6 ANDERSON</td><td>00A</td><td>CLE2</td><td>τ<sup>-</sup> → π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td></tr></tbody></table>

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

<table><tbody><tr><td>139.90 ±0.46</td><td>7 BARTOS</td><td>17A</td><td>RVUE</td><td>τ<sup>-</sup> → π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td></tr><tr><td>143.7 ±1.3</td><td>±1.2 1.98M</td><td>4 ALOISIO</td><td>03</td><td>KLOE</td><td>± 1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>142.9 ±1.3</td><td>±1.4 1.98M</td><td>8 ALOISIO</td><td>03</td><td>KLOE</td><td>± 1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>144.7 ±1.4</td><td>±1.2 1.98M</td><td>8 ALOISIO</td><td>03</td><td>KLOE</td><td>± 1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>150.2 ±2.0</td><td>±0.7<br>1.6</td><td>9 SANZ-CILLERO3</td><td>RVUE</td><td>τ<sup>-</sup> → π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td></tr><tr><td>150.9 ±2.2</td><td>±2.0 500k</td><td>10 ACHASOV</td><td>02</td><td>SND</td><td>± 1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr></tbody></table>

1 $|F_\pi(0)|^2$ fixed to 1.

2 From the GOUNARIS 68 parametrization of the pion form factor.

3 The error combines statistical and systematic uncertainties. Supersedes BARATE 97M.

4 Assuming $m_{\rho^+} = m_{\rho^-}, \Gamma_{\rho^+} = \Gamma_{\rho^-}$.

5 $\rho(1700)$ mass and width fixed at 1700 MeV and 235 MeV respectively.

6 From the GOUNARIS 68 parametrization of the pion form factor. The second error is a model error taking into account different parametrizations of the pion form factor.

7 Applies the Unitary & Analytic Model of the pion electromagnetic form factor of DUB-NICKA 10 to analyze the data of FUJIKAWA 08.

8 Without limitations on masses and widths.

9 Using the data of BARATE 97M and the effective chiral Lagrangian.

10 Assuming $m_{\rho^0} = m_{\rho^+}, g_{\rho^0\pi\pi} = g_{\rho^+\pi\pi}$.

## MIXED CHARGES, OTHER REACTIONS

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>149.5 ±1.3</strong></td><td><strong>600k</strong></td><td>1 ABELE</td><td>99E</td><td>CBAR</td><td>0± 0.0 p̄p → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr></tbody></table>

1 Assuming the equality of $\rho^+$ and $\rho^-$ masses and widths.

## CHARGED ONLY, HADROPRODUCED

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>CHG</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>150.2 ±2.4</strong></td><td><strong>OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td><strong>150.2 ±2.4</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>152.8 ±4.3</td><td>ABELE</td><td>97</td><td>CBAR</td><td>p̄n → π<sup>-</sup>π<sup>0</sup>π<sup>0</sup></td><td></td></tr><tr><td>155 ±11</td><td>2.9k</td><td>1 CAPRARO</td><td>87</td><td>SPEC</td><td>200 π<sup>-</sup> Cu → π<sup>-</sup>π<sup>0</sup> Cu</td></tr></tbody></table>

<table><tbody><tr><td>154 ±20</td><td>967</td><td>1 CAPRARO</td><td>87</td><td>SPEC</td><td>200 π<sup>-</sup> Pb → π<sup>-</sup>π<sup>0</sup>Pb</td></tr><tr><td>150 ±5</td><td></td><td>HUSTON</td><td>86</td><td>SPEC</td><td>202 π<sup>+</sup> A → π<sup>+</sup>π<sup>0</sup>A</td></tr><tr><td>146 ±12</td><td>6.5k</td><td>2 BYERLY</td><td>73</td><td>OSPK</td><td>5 π<sup>-</sup> p</td></tr><tr><td>148.2 ±4.1</td><td>9.6k</td><td>3 PISUT</td><td>68</td><td>RVUE</td><td>1.7-3.2 π<sup>-</sup> p, t <10</td></tr><tr><td>146 ±13</td><td>900</td><td>EISNER</td><td>67</td><td>HBC</td><td>4.2 π<sup>-</sup> p, t <10</td></tr></tbody></table>

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

<table><tr><td>137.0 ±0.4</td><td>4 ABLIKIM</td><td>17</td><td>BES3</td><td>J/ψ → γ3π</td></tr></table>

1 Width errors enlarged by us to $4\Gamma/\sqrt{N}$; see the note with the K*(892) mass.

2 Phase shift analysis. Systematic errors added corresponding to spread of different fits.

3 From fit of 3-parameter relativistic P-wave Breit-Wigner to total mass distribution. Includes BATON 68, MILLER 67B, ALFF-STEINBERGER 66, HAGOPIAN 66B, JACOBS 66B, JAMES 66, WEST 66, BLIEDEN 65 and CARMONY 64.

4 S-matrix pole at a fixed $\rho$ meson mass of 775.49 MeV.

## NEUTRAL ONLY, PHOTOPRODUCED

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>151.5 ±1.9</strong></td><td><strong>2.1</strong> OUR AVERAGE</td><td></td><td></td><td></td></tr><tr><td>151.3 ±2.2<sup>+</sup><sub>1.6</sub></td><td>900k</td><td>ANDREEV</td><td>20</td><td>H1 ep → eπ<sup>+</sup>π<sup>-</sup> p</td></tr><tr><td>155 ±5</td><td>±2 63.5k</td><td>1 ABRAMOWICZ12</td><td>ZEUS</td><td>ep → eπ<sup>+</sup>π<sup>-</sup> p</td></tr><tr><td>146 ±3</td><td>±13 79k</td><td>2 BREITWEG</td><td>98B</td><td>ZEUS 50-100 γp</td></tr><tr><td>150.9 ±3.0</td><td></td><td>BARTALUCCI</td><td>78</td><td>CNTR γp → eπ<sup>+</sup> e<sup>-</sup> p</td></tr><tr><td>138 ±3</td><td>79k</td><td>3 BREITWEG</td><td>98B</td><td>ZEUS 50-100 γp</td></tr><tr><td>147 ±11</td><td></td><td>GLADDING</td><td>73</td><td>CNTR 2.9-4.7 γp</td></tr><tr><td>155 ±12</td><td>2430</td><td>BALLAM</td><td>72</td><td>HBC 4.7 γp</td></tr><tr><td>145 ±13</td><td>1930</td><td>BALLAM</td><td>72</td><td>γp</td></tr><tr><td>140 ±5</td><td></td><td>ALVENSLEB...</td><td>70</td><td>CNTR γA, t <0.01</td></tr><tr><td>146.1 ±2.9</td><td>140k</td><td>BIGGS</td><td>70</td><td>CNTR <4.1 γC → π<sup>+</sup>π<sup>-</sup> C</td></tr><tr><td>160 ±10</td><td></td><td>LANZEROTTI</td><td>68</td><td>CNTR γp</td></tr><tr><td>130 ±5</td><td>4000</td><td>ASBURY</td><td>67B</td><td>CNTR γ + Pb</td></tr></tbody></table>

1 Using the KUHN 90 parametrization of the pion form factor, neglecting $\rho-\omega$ interference.

2 From the parametrization according to SOEDING 66.

3 From the parametrization according to ROSS 66.

## NEUTRAL ONLY, OTHER REACTIONS

<table><thead><tr><th>VALUE (MeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>150.9 ±1.7</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>122 ±20</td><td></td><td>BERTIN</td><td>97C</td><td>OBLX 0.0 p̄p → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>145.7 ±5.3</td><td></td><td>WEIDENAUER</td><td>93</td><td>ASTE p̄p → π<sup>+</sup>π<sup>-</sup>ω</td></tr><tr><td>144.9 ±3.7</td><td></td><td>DUBNICKA</td><td>89</td><td>RVUE π form factor</td></tr><tr><td>148 ±6</td><td></td><td>1,2 BOHAKIC</td><td>80</td><td>RVUE</td></tr><tr><td>152 ±9</td><td></td><td>3 WICKLUND</td><td>78</td><td>ASPK 3,4,6 π<sup>+</sup> pN</td></tr><tr><td>154 ±2</td><td>76k</td><td>DEUTSCH...</td><td>76</td><td>HBC 16 π<sup>+</sup> p</td></tr><tr><td>157 ±8</td><td>6.8k</td><td>4 RATCLIFF</td><td>72</td><td>ASPK 15 π<sup>-</sup> p, t <0.3</td></tr><tr><td>143 ±8</td><td>1.7k</td><td>REYNOLDS</td><td>69</td><td>HB 2.26 π<sup>-</sup> p</td></tr><tr><td>150.85 ±0.55</td><td>±0.67</td><td>5 ABLIKIM</td><td>18C</td><td>BES3 η'(958) → γπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>150.18 ±0.55</td><td>±0.65</td><td>6 ABLIKIM</td><td>18C</td><td>BES3 η'(958) → γπ<sup>+</sup>π<sup>-</sup></td></tr><tr><td>147.0 ±2.5</td><td></td><td>7 ABELE</td><td>99E</td><td>CBAR 0.0 p̄p → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>146 ±3</td><td>4.9k</td><td>8 ADAMS</td><td>97</td><td>E665 470 μp → μXB</td></tr><tr><td>160.0 ±4.1</td><td>±4.0</td><td>9 CHABAUD</td><td>83</td><td>ASPK 17 π<sup>-</sup> p polarized</td></tr><tr><td>155 ±1</td><td></td><td>10 HEYN</td><td>81</td><td>RVUE π form factor</td></tr><tr><td>148.0 ±1.3</td><td></td><td>1,2 LANG</td><td>79</td><td>RVUE</td></tr><tr><td>146 ±14</td><td>4.1k</td><td>ENGLER</td><td>74</td><td>DBC 6 π<sup>+</sup> n → π<sup>+</sup>π<sup>-</sup> p</td></tr><tr><td>143 ±13</td><td></td><td>2 ESTABROOKS</td><td>74</td><td>RVUE 17 π<sup>-</sup> p → π<sup>+</sup>π<sup>-</sup> n</td></tr><tr><td>160 ±10</td><td>32k</td><td>1 PROTOPOP...</td><td>73</td><td>HBC 7.1 π<sup>+</sup> p, t <0.4</td></tr><tr><td>145 ±12</td><td>2.2k</td><td>3,11 HYAMS</td><td>68</td><td>OSPK 11.2 π<sup>-</sup> p</td></tr><tr><td>163 ±15</td><td>13.3k</td><td>12 PISUT</td><td>68</td><td>RVUE 1.7-3.2 π<sup>-</sup> p, t <10</td></tr></tbody></table>

1 From pole extrapolation.

2 From phase shift analysis of GRAYER 74 data.

3 Width errors enlarged by us to $4\Gamma/\sqrt{N}$; see the note with the K*(892) mass.

4 Published values contain misprints. Corrected by private communication RATCLIFF 74.

5 From a fit to $\pi^+\pi^-$ mass using $\rho(770)$ (parametrized with the Gounaris-Sakurai approach), $\omega(782)$, and box anomaly components.

6 From a fit to $\pi^+\pi^-$ mass using $\rho(770)$ (parametrized with the Gounaris-Sakurai approach), $\omega(782)$, and $\rho(1450)$ components.

7 Using relativistic Breit-Wigner and taking into account $\rho-\omega$ interference.

8 Systematic errors not evaluated.

9 From fit of 3-parameter relativistic Breit-Wigner to helicity-zero part of P-wave intensity. CHABAUD 83 includes data of GRAYER 74.

10 HEYN 81 includes all spacelike and timelike $F_\pi$ values until 1978.

11 Of HYAMS 68 six parametrizations this is theoretically soundest. MR

12 Includes MALAMUD 69, ARMENISE 68, BACON 67, HUWE 67, MILLER 67B, ALFF-STEINBERGER 66, HAGOPIAN 66B, JACOBS 66B, JAMES 66, WEST 66, GOLDHABER 64, ABOLINS 63.

$$ \Gamma(770)^0 - \Gamma(770)^\pm \qquad \text{0.3} \pm \text{1.3} \quad \text{OUR AVERAGE} $$

<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>-0.2 ±1.0</td><td></td><td>1 SCHAEI</td><td>05C</td><td>ALEP τ<sup>-</sup> → π<sup>-</sup>π<sup>0</sup>τ<sup>-</sup></td></tr><tr><td>3.6 ±1.8 ±1.7</td><td>1.98M</td><td>2 ALOISIO</td><td>03</td><td>KLOE 1.02 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr></tbody></table>
• • • We do not use the following data for averages, fits, limits, etc. • • •

4.66±0.85

³BARTOS

17A RVUE

$e^+e^- \to \pi^+\pi^-$, $\tau^- \to \pi^-\pi^0\nu_\tau$

¹From the combined fit of the $\tau^-$ data from ANDERSON 00A and SCHAEHL 05C and $e^+e^-$ data from the compilation of BARKOV 85, AKHMETSHIN 04, and ALOISIO 05. Supersedes BARATE 97M.

²Assuming $m_{\rho^+} = m_{\rho^-}, \Gamma_{\rho^+} = \Gamma_{\rho^-}$.

³Applies the Unitary & Analytic Model of the pion electromagnetic form factor of DUB-NICKA 10 to analyze the data of ACHASOV 06, AKHMETSHIN 07, AUBERT 09A5, AMBROSINO 11A, and FUJIKAWA 08.

$\Gamma(\rho(770)^+ - \Gamma(\rho(770)^-)$

<table><thead><tr><th>VALUE</th><th>EVTS</th></tr></thead><tbody><tr><td>1.8±2.0±0.5</td><td>1.98M</td></tr></tbody></table>

¹ALOISIO

03

KLOE

$1.02 e^+e^- \to \pi^+\pi^-\pi^0$

¹Without limitations on masses and widths.

## $\rho(770)$ DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction (Γ<sub>i</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th></tr></thead><tbody><tr><td>Γ<sub>1</sub> ππ</td><td>~ 100</td><td>%</td></tr><tr><td colspan="3"><strong>ρ(770)± decays</strong></td></tr><tr><td>Γ<sub>2</sub> π<sup>±</sup>π<sup>0</sup></td><td>~ 100</td><td>%</td></tr><tr><td>Γ<sub>3</sub> π<sup>±</sup>γ</td><td>( 4.5 ± 0.5)</td><td>× 10<sup>-4</sup> S=2.2</td></tr><tr><td>Γ<sub>4</sub> π<sup>±</sup>η</td><td>&lt; 6</td><td>× 10<sup>-3</sup> CL=84%</td></tr><tr><td>Γ<sub>5</sub> π<sup>±</sup>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>&lt; 2.0</td><td>× 10<sup>-3</sup> CL=84%</td></tr><tr><td colspan="3"><strong>ρ(770)<sup>0</sup> decays</strong></td></tr><tr><td>Γ<sub>6</sub> π<sup>+</sup>π<sup>-</sup></td><td>~ 100</td><td>%</td></tr><tr><td>Γ<sub>7</sub> π<sup>+</sup>π<sup>-</sup>γ</td><td>( 9.9 ± 1.6)</td><td>× 10<sup>-3</sup></td></tr><tr><td>Γ<sub>8</sub> π<sup>0</sup>γ</td><td>( 4.7 ± 0.8)</td><td>× 10<sup>-4</sup></td></tr><tr><td>Γ<sub>9</sub> ηγ</td><td>( 3.00 ± 0.21)</td><td>× 10<sup>-4</sup></td></tr><tr><td>Γ<sub>10</sub> π<sup>0</sup>π<sup>0</sup>γ</td><td>( 4.5 ± 0.8)</td><td>× 10<sup>-5</sup></td></tr><tr><td>Γ<sub>11</sub> μ<sup>+</sup>μ<sup>-</sup></td><td>[a] ( 4.55 ± 0.28)</td><td>× 10<sup>-5</sup></td></tr><tr><td>Γ<sub>12</sub> e<sup>+</sup>e<sup>-</sup></td><td>[a] ( 4.72 ± 0.05)</td><td>× 10<sup>-5</sup></td></tr><tr><td>Γ<sub>13</sub> π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>( 1.01<sup>+0.54</sup><sub>-0.36</sub>±0.34)</td><td>× 10<sup>-4</sup></td></tr><tr><td>Γ<sub>14</sub> π<sup>+</sup>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td><td>( 1.8 ± 0.9)</td><td>× 10<sup>-5</sup></td></tr><tr><td>Γ<sub>15</sub> π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>π<sup>0</sup></td><td>( 1.6 ± 0.8)</td><td>× 10<sup>-5</sup></td></tr><tr><td>Γ<sub>16</sub> π<sup>0</sup>e<sup>+</sup>e<sup>-</sup></td><td>&lt; 1.2</td><td>× 10<sup>-5</sup> CL=90%</td></tr><tr><td>Γ<sub>17</sub> ηe<sup>+</sup>e<sup>-</sup></td><td></td><td></td></tr></tbody></table>

[a] The $\omega\rho$ interference is then due to $\omega\rho$ mixing only, and is expected to be small. If $e\mu$ universality holds, $\Gamma(\rho^0 \to \mu^+\mu^-) = \Gamma(\rho^0 \to e^+e^-) \times 0.99785$.

## CONSTRAINED FIT INFORMATION

An overall fit to the total width and a partial width uses 10 measurements and one constraint to determine 3 parameters. The overall fit has a $\chi^2 = 10.7$ for 8 degrees of freedom.

The following off-diagonal array elements are the correlation coefficients $\langle\delta\rho_i\delta\rho_j\rangle/(\delta\rho_i\delta\rho_j)$, in percent, from the fit to parameters $\rho_i$, 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.

<figure><img src="image_436.png" /></figure>

<table><thead><tr><th>Mode</th><th>Rate (MeV)</th><th>Scale factor</th></tr></thead><tbody><tr><td>Γ<sub>2</sub> π<sup>±</sup>π<sup>0</sup></td><td>150.2 ± 2.4</td><td></td></tr><tr><td>Γ<sub>3</sub> π<sup>±</sup>γ</td><td>0.068 ± 0.007</td><td>2.3</td></tr></tbody></table>

## CONSTRAINED FIT INFORMATION

An overall fit to the total width, a partial width, and 7 branching ratios uses 21 measurements and one constraint to determine 9 parameters. The overall fit has a $\chi^2 = 9.5$ for 13 degrees of freedom.

The following off-diagonal array elements are the correlation coefficients $\langle\delta\rho_i\delta\rho_j\rangle/(\delta\rho_i\delta\rho_j)$, in percent, from the fit to parameters $\rho_i$, 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.

<figure><img src="image_437.png" /></figure>

<table><thead><tr><th>Mode</th><th>Rate (MeV)</th><th>Scale factor</th></tr></thead><tbody><tr><td>Γ<sub>6</sub> π<sup>+</sup>π<sup>-</sup></td><td>147.5 ± 0.9</td><td></td></tr><tr><td>Γ<sub>7</sub> π<sup>+</sup>π<sup>-</sup>γ</td><td>1.48 ± 0.24</td><td></td></tr><tr><td>Γ<sub>8</sub> π<sup>0</sup>γ</td><td>0.070 ± 0.012</td><td rowspan="2">1.7</td></tr><tr><td>Γ<sub>9</sub> ηγ</td><td>0.0447 ± 0.0032</td></tr><tr><td>Γ<sub>10</sub> π<sup>0</sup>π<sup>0</sup>γ</td><td>0.0066 ± 0.0012</td><td></td></tr><tr><td>Γ<sub>11</sub> μ<sup>+</sup>μ<sup>-</sup></td><td>[a] 0.0068 ± 0.0004</td><td></td></tr><tr><td>Γ<sub>12</sub> e<sup>+</sup>e<sup>-</sup></td><td>[a] 0.00704 ± 0.00006</td><td></td></tr><tr><td>Γ<sub>14</sub> π<sup>+</sup>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td><td>0.0027 ± 0.0014</td><td></td></tr></tbody></table>

## $\rho(770)$ PARTIAL WIDTHS

$\Gamma(\pi^{\pm}\gamma)$

VALUE (keV)

DOCUMENT ID

TECN

CHG

COMMENT

Γ<sub>3</sub>

68 ± 7 OUR FIT Error includes scale factor of 2.3.

68 ± 7 OUR AVERAGE Error includes scale factor of 2.2. See the ideogram below.

81 ± 4

± 4

CAPRARO

87

SPEC

–

200 π<sup>-</sup> A → π<sup>-</sup>π<sup>0</sup> A

59.8 ± 4.0

HUSTON

86

SPEC

–

202 π<sup>+</sup> A → π<sup>+</sup>π<sup>0</sup> A

71 ± 7

JENSEN

83

SPEC

–

156–260 π<sup>-</sup> A → π<sup>-</sup>π<sup>0</sup> A

WEIGHTED AVERAGE
68±7 (Error scaled by 2.2)

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.

<figure><img src="image_438.png" /></figure>

$\Gamma(\pi^0\gamma)$

VALUE (keV)

EVTS

DOCUMENT ID

TECN

COMMENT

Γ<sub>8</sub>

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

77±17±11

36500

1

ACHASOV

SND

0.60–0.97 e<sup>+</sup>e<sup>-</sup> → π<sup>0</sup>γ

121±31

DOLINSKY

89

ND

SPEC

e<sup>+</sup>e<sup>-</sup> → π<sup>0</sup>γ

¹Using $\Gamma_{\text{total}} = 147.9 \pm 1.3$ MeV and $B(\rho \to \pi^0\gamma)$ from ACHASOV 03.

$\Gamma(\eta\gamma)$

VALUE (keV)

EVTS

DOCUMENT ID

TECN

COMMENT

Γ<sub>9</sub>

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

62±17

1

DOLINSKY

89

ND

e<sup>+</sup>e<sup>-</sup>

→ ηγ

¹Solution corresponding to constructive $\omega-\rho$ interference.

$\Gamma(e^+e^-)$

VALUE (keV)

EVTS

DOCUMENT ID

TECN

COMMENT

Γ<sub>12</sub>

7.04 ±0.06 OUR FIT

7.04 ±0.06 OUR AVERAGE

7.048 ±0.057 ±0.050

900k

1

AKHMETSHIN

07

e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>

7.06 ±0.11 ±0.05

114k

2,3

AKHMETSHIN

04

CMD2 e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>

6.77 ±0.10 ±0.30

BARKOV

85

OLYA

e<sup>+</sup>e<sup>-</sup>

→ π<sup>+</sup>π<sup>-</sup>

7.12 ±0.02 ±0.11

800k

4

ACHASOV

06

SND e<sup>+</sup>e<sup>-</sup> → π<sup>+</sup>π<sup>-</sup>

6.3 ±0.1

5

BENAYOUN

98

RVUE

e<sup>+</sup>e<sup>-</sup>

→ π<sup>+</sup>π<sup>-</sup>