the cross section and shape of the Z transverse momentum spectrum, the following 95% C.L. range is reported: $0.61 < \kappa_Z < 1.90$ for a form factor of $\Lambda = 2$ TeV.

11 ABAZOV 11 study the $p_T \to 3\ell\nu$ process arising in WZ production. They observe 34 WZ candidates with an estimated background of 6 events. An analysis of the $p_T$ spectrum of the Z boson leads to a 95% C.L. limit of 0.600 $< \kappa_Z < 1.675$, for a form factor $\Lambda = 2$ TeV.

12 ABAZOV 06h study $p\bar{p} \to WW$ production with a subsequent decay $WW \to e^+\nu_e e^-\bar{\nu}_e, WW \to e^\pm\nu_e\mu^\pm\nu_\mu$ or $WW \to \mu^+\nu_\mu\mu^-\bar{\nu}_\mu$. The 95% C.L. limit for a form factor scale $\Lambda = 2$ TeV is 0.55 $< \kappa_Z < 1.55$, fixing $\lambda_Z=0$. With the assumption that the $WW\gamma$ and $WWZ$ couplings are equal the 95% C.L. one-dimensional limit ($\Lambda = 2$ TeV) is 0.68 $< \kappa < 1.45$.

13 ABAZOV 05s study $p\bar{p} \to WZ$ production with a subsequent trilepton decay to $\ell\nu\ell'\bar{\ell}'$ ($\ell$ and $\ell' = e$ or $\mu$). Three events (estimated background 0.71 $\pm$ 0.08 events) with $WZ$ decay characteristics are observed from which they derive limits on the anomalous $WWZ$ couplings. The 95% CL limit for a form factor scale $\Lambda = 1$ TeV is $-1.0 < \kappa_Z < 3.4$, fixing $\lambda_Z$ and $g_1^Z$ to their Standard Model values.

$\lambda_Z$

This coupling is CP-conserving (C- and P- separately conserving).

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN.</th><th>COMMENT</th></tr></thead><tbody><tr><td>-0.088<sup>+0.060</sup><sub>-0.057</sub> ±0.023</td><td>7171</td><td>1</td><td>ACHARD</td><td>04D L3 E<sup>ee</sup><sub>cm</sub> = 189-209 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>2</td><td>SIRUNYAN</td><td>20BA CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>3</td><td>SIRUNYAN</td><td>19CL CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>4</td><td>SIRUNYAN</td><td>18BZ CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>5</td><td>AABOUD</td><td>17s ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 7+8 TeV</td></tr><tr><td>6</td><td>AABOUD</td><td>17U ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>7</td><td>KHACHATRY...170</td><td>CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>8</td><td>SIRUNYAN</td><td>17x CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>9</td><td>AAD</td><td>16AR ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>10</td><td>AAD</td><td>16p ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>11</td><td>AAD</td><td>14Y ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>12</td><td>AAD</td><td>13AL ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 7 TeV</td></tr><tr><td>13</td><td>CHATRCHYAN13BF</td><td>CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 7 TeV</td></tr><tr><td>14</td><td>AAD</td><td>12CD ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 7 TeV</td></tr><tr><td>15</td><td>AALTONEN</td><td>12AC CDF</td><td>E<sup>pp</sup><sub>cm</sub> = 1.96 TeV</td></tr><tr><td>34</td><td>16 ABAZOV</td><td>11 D0</td><td>E<sup>pp</sup><sub>cm</sub> = 1.96 TeV</td></tr><tr><td>334</td><td>17 AALTONEN</td><td>10k CDF</td><td>E<sup>pp</sup><sub>cm</sub> = 1.96 TeV</td></tr><tr><td>13</td><td>18 ABAZOV</td><td>07z D0</td><td>E<sup>pp</sup><sub>cm</sub> = 1.96 TeV</td></tr><tr><td>17</td><td>19 ABAZOV</td><td>06H D0</td><td>E<sup>pp</sup><sub>cm</sub> = 1.96 TeV</td></tr><tr><td>2.3</td><td>20 ABAZOV</td><td>05s D0</td><td>E<sup>pp</sup><sub>cm</sub> = 1.96 TeV</td></tr></tbody></table>

1 ACHARD 04D study $WW$-pair production, single-$W$ production and single-photon production with missing energy from 189 to 209 GeV. The result quoted here is obtained using the $WW$-pair production sample. Each parameter is determined from a single-parameter fit in which the other parameters assume their Standard Model values.

2 SIRUNYAN 20BA study electroweak production of a W boson in association with two jets, using $W$ decays in the electron or muon channel. The isolated muons (electrons) are required to have a transverse momentum larger than 25 (30) GeV, while the transverse momentum of the two jets has to be larger than 50 and 30 GeV. A total of 2.382 (1.051) million events are selected in the muon (electron) channel, with a Standard Model expectation of 2.39 $\pm$ 0.17 (1.054 $\pm$ 0.058) million events. Analysing the transverse momentum distribution of the charged leptons from $W$ decay, the following 95% C.L. limit is obtained: $-0.0088 < \lambda_Z < 0.0095$. Combining this result with that from the closely-related electroweak Z-jet-jet production SIRUNYAN 18BZ, the limit becomes: $-0.0071 < \lambda_Z < 0.0076$.

3 SIRUNYAN 19CL study $WW$ and $WZ$ production in lepton + jet events, with one W boson decaying leptonically (electron or muon), and another W or Z boson decaying hadronically, reconstructed as a single massive large-radius jet. In the electron channel 2,456 (2,235) events are selected in the $WW(WZ)$ category, while in the muon channel 3,996 (3,572) events are selected in the $WW(WZ)$ category. Analysing the di-boson invariant mass distribution, following this 95% C.L. limit is obtained: $-0.00665 < \lambda_Z < 0.0066$.

4 SIRUNYAN 18BZ study $p\bar{p} \to Z$ jet jet events at 13 TeV where $Z \to e^+e^-/\mu^+\mu^-$. Isolated electrons and muons are selected with $p_T$ of the leading/sub-leading lepton > 30/20 GeV and $|\eta| < 2.4$, with the di-lepton invariant mass within 15 GeV of the Z mass. The two highest $p_T$ jets are selected with $p_T$ of the leading/sub-leading lepton > 50/30 GeV respectively and dijet invariant mass > 200 GeV. Templates in the transverse momentum of the Z are utilized to set limits on the triple gauge couplings in the EFT and the LEP parametrizations. The following 95% C.L. limit is obtained: $-0.010 < \lambda_Z < 0.010$.

5 AABOUD 17s analyze electroweak production of a W boson in association with two jets at high dijet invariant mass, with the W boson decaying to electron or muon plus neutrino. In the signal region of dijet mass larger than 1 TeV and leading-jet transverse momentum larger than 600 GeV, 30 events are observed in the data with 39 $\pm$ 4 events expected in the Standard Model, yielding the following limit at 95% CL for the form factor cut-off scale $\Lambda_{FF} \to \infty$: $-0.053 < \lambda_Z < 0.042$.

6 AABOUD 17U analyze production of $WW$ or $WZ$ boson pairs with one W boson decaying to electron or muon plus neutrino, and the other W or Z boson decaying hadronically. The hadronic decay system is reconstructed as either a resolved two-jet system or as a single large jet. Analysing the transverse momentum distribution of the hadronic system above 100 GeV yields the following limit at 95% CL for the form factor cut-off scale $\Lambda_{FF} \to \infty$: $-0.013 < \lambda_Z < 0.013$.

7 KHACHATRYAN 17o analyse $WZ$ production where each boson decays into electrons or muons. Events are required to have a tri-lepton invariant mass larger than 100 GeV, with one of the lepton pairs having an invariant mass within 20 GeV of the Z boson mass. The Z transverse momentum spectrum is analyzed to set a 95% C.L. limit of: $-0.018 < \lambda_Z < 0.016$.

8 SIRUNYAN 17x study $p\bar{p} \to WW/WZ \to \ell\nu q\bar{\nu}$ production at 8 TeV where $\ell$ is an electron or muon with $p_T > 30$ or 25 GeV respectively. Suitable cuts are put on the $p_T$ of the dijet system and the missing $E_T$ of the event yielding a total of 285 and 204 $WZ$ events observed in the electron and muon channels. The following 95% C.L. limit is obtained: $-0.011 < \lambda_Z < 0.011$.

9 AAD 16AR study $WW$ production in $pp$ collisions and select 6636 $WW$ candidates in decay modes with electrons or muons with an expected background of 1546 $\pm$ 157 events. Assuming the LEP formulation and setting the form-factor $\Lambda$ to infinity, a fit to the transverse momentum distribution of the leading charged lepton, leads to a 95% C.L. range of $-0.019 < \lambda_Z < 0.019$.

10 AAD 16P study $WZ$ production in $pp$ collisions and select 2091 $WZ$ candidates in 4 decay modes with electrons and muons, with an expected background of 1825 $\pm$ 7 events. Analyzing the $WZ$ transverse momentum distribution, the resulting 95% C.L. limit is: $-0.016 < \lambda_Z < 0.016$.

11 AAD 14Y determine the electroweak Z-dijet cross section in 8 TeV $pp$ collisions. $Z \to e\bar{e}$ and $Z \to \mu\mu$ decays are selected with the di-lepton $p_T > 20$ GeV and mass in the 81-101 GeV range. Minimum two jets are required with $p_T > 55$ and 45 GeV and no additional jets with $p_T > 25$ GeV in the rapidity interval between them. The normalized $p_T$ balance between the Z and the two jets is required to be < 0.15. This leads to a selection of 900 events with dijet mass > 1 TeV. The number of signal and background events expected is 261 and 592 respectively. A Poisson likelihood method is used on an event by event basis to obtain the 95% CL limit $-0.15 < \lambda_Z < 0.13$ for a form factor value $\Lambda = \infty$.

12 AAD 13AL study $WW$ production in $pp$ collisions and select 1325 $WW$ candidates in decay modes with electrons or muons with an expected background of 369 $\pm$ 61 events. Assuming the LEP formulation and setting the form-factor $\Lambda = \infty$, a fit to the transverse momentum distribution of the leading charged lepton, leads to a 95% C.L. range of $-0.062 < \lambda_Z < 0.059$. Supersedes AAD 12AC.

13 CHATRCHYAN 13Br determine the $W^+W^-$ production cross section using unlike sign di-lepton ($e$ or $\mu$) events with high $p_T$. The leptons have $p_T > 20$ GeV/c and are isolated. 1134 candidate events are observed with an expected SM background of 247 $\pm$ 34. The $p_T$ distribution of the leading lepton is fitted to obtain 95% C.L. limits of $-0.048 < \lambda_Z < 0.048$.

14 AAD 12CD study $WZ$ production in $pp$ collisions and select 317 $WZ$ candidates in three $\ell\nu$ decay modes with an expected background of 68.0 $\pm$ 10.0 events. The resulting 95% C.L. range is: $-0.046 < \lambda_Z < 0.047$. Supersedes AAD 12v.

15 AALTONEN 12AC study $WZ$ production in $p\bar{p}$ collisions and select 63 $WZ$ candidates in three $\ell\nu$ decay modes with an expected background of 7.9 $\pm$ 1.0 events. Based on the cross section and shape of the Z transverse momentum spectrum, the following 95% C.L. range is reported: $-0.08 < \lambda_Z < 0.10$ for a form factor of $\Lambda = 2$ TeV.

16 ABAZOV 11 study the $p\bar{p} \to 3\ell\nu$ process arising in $WZ$ production. They observe 34 $WZ$ candidates with an estimated background of 6 events. An analysis of the $p_T$ spectrum of the Z boson leads to a 95% C.L. limit of $-0.077 < \lambda_Z < 0.093$, for a form factor $\Lambda = 2$ TeV.

17 AALTONEN 10K study $p\bar{p} \to W^+W^-$ with $W \to e/\mu\nu$. The $p_T$ of the leading (second) lepton is required to be > 20 (10) GeV. The final number of events selected is 654 of which 320 $\pm$ 47 are estimated to be background. The 95% C.L. interval is $-0.16 < \lambda_Z < 0.16$ for $\Lambda = 1.5$ TeV and $-0.14 < \lambda_Z < 0.15$ for $\Lambda = 2$ TeV.

18 ABAZOV 07Z set limits on anomalous TGCs using the measured cross section and $p_T(Z)$ distribution in $WZ$ production with both the W and the Z decaying leptonically into electrons and muons. Setting the other couplings to their standard model values, the 95% C.L. limit for a form factor scale $\Lambda = 2$ TeV is $-0.17 < \lambda_Z < 0.21$.

19 ABAZOV 06h study $p\bar{p} \to WW$ production with a subsequent decay $WW \to e^+\nu_e e^-\bar{\nu}_e, WW \to e^\pm\nu_e\mu^\pm\nu_\mu$ or $WW \to \mu^+\nu_\mu\mu^-\bar{\nu}_\mu$. The 95% C.L. limit for a form factor scale $\Lambda = 2$ TeV is $-0.39 < \lambda_Z < 0.39$, fixing $\kappa_Z=1$. With the assumption that the $WW\gamma$ and $WWZ$ couplings are equal the 95% C.L. one-dimensional limit ($\Lambda = 2$ TeV) is $-0.29 < \lambda < 0.30$.

20 ABAZOV 05s study $p\bar{p} \to WZ$ production with a subsequent trilepton decay to $\ell\nu\ell'\bar{\ell}'$ ($\ell$ and $\ell' = e$ or $\mu$). Three events (estimated background 0.71 $\pm$ 0.08 events) with $WZ$ decay characteristics are observed from which they derive limits on the anomalous $WWZ$ couplings. The 95% CL limit for a form factor scale $\Lambda = 1.5$ TeV is $-0.48 < \lambda_Z < 0.48$, fixing $g_1^Z$ and $\kappa_Z$ to their Standard Model values.

$g_5^Z$

This coupling is CP-conserving but C- and P-violating.

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN.</th><th>COMMENT</th></tr></thead><tbody><tr><td>-0.07±0.09</td><td>OUR AVERAGE</td><td></td><td></td><td>Error includes scale factor of 1.1.</td></tr><tr><td>-0.04+0.13<br>-0.12</td><td>9800</td><td>1</td><td>ABBIENDI</td><td>04D OPAL E<sup>ee</sup><sub>cm</sub> = 183-209 GeV</td></tr><tr><td>0.00±0.13±0.05</td><td>7171</td><td>2</td><td>ACHARD</td><td>04D L3 E<sup>ee</sup><sub>cm</sub> = 189-209 GeV</td></tr><tr><td>-0.44+0.23<br>-0.22</td><td>1154</td><td>3</td><td>ACCIARRI</td><td>99Q L3 E<sup>ee</sup><sub>cm</sub> = 161+172+183 GeV</td></tr></tbody></table>

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

–0.31±0.23 4 EBOLI 00 THEO LEP1, SLC+ Tevatron

1 ABBIENDI 04D combine results from $W^+W^-$ in all decay channels. Only CP-conserving couplings are considered and each parameter is determined from a single-parameter fit in which the other parameters assume their Standard Model values. The 95% confidence interval is $-0.28 < g_5^Z < +0.21$.

2 ACHARD 04D study $WW$-pair production, single-$W$ production and single-photon production with missing energy from 189 to 209 GeV. The result quoted here is obtained using the $WW$-pair production sample. Each parameter is determined from a single-parameter fit in which the other parameters assume their Standard Model values.

3 ACCIARRI 99q study $W$-pair, single-$W$, and single photon events.

4 EBOLI 00 extract this indirect value of the coupling studying the non-universal one-loop contributions to the experimental value of the $Z \to b\bar{b}$ width ($\Lambda=1$ TeV is assumed).
g²

This coupling is CP-violating (C-violating and P-conserving).

<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>-0.30±0.17 OUR AVERAGE</strong></td></tr><tr><td>-0.39<sup>+0.19</sup><sub>-0.20</sub></td><td>1880</td><td>1 ABDALLAH</td><td>08C DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 189-209 GeV</td></tr><tr><td>-0.02<sup>+0.32</sup><sub>-0.33</sub></td><td>1065</td><td>2 ABBIENDI</td><td>01H OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 189 GeV</td></tr></tbody></table>

1 ABDALLAH 08C determine this triple gauge coupling from the measurement of the spin density matrix elements in $e^+e^- \to W^+W^- \to (qq)(\ell\nu)$, where $\ell = e$ or $\mu$. Values of all other couplings are fixed to their standard model values.

2 ABBIENDI 01H study W-pair events, with one leptonicity and one hadronically decaying W. The coupling is extracted using information from the W production angle together with decay angles from the leptonicity decaying W.

ξ̃Z

This coupling is CP-violating (C-conserving and P-violating).

<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>-0.12<sup>+0.06</sup><sub>-0.04</sub> OUR AVERAGE</strong></td></tr><tr><td>-0.09<sup>+0.08</sup><sub>-0.05</sub></td><td>1880</td><td>1 ABDALLAH</td><td>08C DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 189-209 GeV</td></tr><tr><td>-0.20<sup>+0.10</sup><sub>-0.07</sub></td><td>1065</td><td>2 ABBIENDI</td><td>01H OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 189 GeV</td></tr></tbody></table>

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

3 AABOUD 17s ATLS $E_{cm}^{pp} = 7+8$ TeV

4 BLINOV 11 LEP $E_{cm}^{ee} = 183-207$ GeV

1 ABDALLAH 08C determine this triple gauge coupling from the measurement of the spin density matrix elements in $e^+e^- \to W^+W^- \to (qq)(\ell\nu)$, where $\ell = e$ or $\mu$. Values of all other couplings are fixed to their standard model values.

2 ABBIENDI 01H study W-pair events, with one leptonicity and one hadronically decaying W. The coupling is extracted using information from the W production angle together with decay angles from the leptonicity decaying W.

3 AABOUD 17s analyze electroweak production of a W boson in association with two jets at high dijet invariant mass, with the W boson decaying to electron or muon plus neutrino. In the signal region of dijet mass larger than 1 TeV and leading-jet transverse momentum larger than 600 GeV, 30 events are observed in the data with 39 ± 4 events expected in the Standard Model, yielding the following limit at 95% CL for the form factor cut-off scale $\Lambda_{FF} \to \infty$: $-0.56 < \bar{\kappa}_Z < 0.56$.

4 BLINOV 11 use the LEP-average $e^+e^- \to W^+W^-$ cross section data for $\sqrt{s} = 183-207$ GeV to determine an upper limit on the TGC $\bar{\kappa}_Z$. The average values of the cross sections as well as their correlation matrix, and standard model expectations of the cross sections are taken from the LEPEWWG note hep-ex/0612034. At 95% confidence level $|\bar{\kappa}_Z| < 0.13$.

λ̃Z

This coupling is CP-violating (C-conserving and P-violating).

<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>-0.09±0.07 OUR AVERAGE</strong></td></tr><tr><td>-0.08±0.07</td><td>1880</td><td>1 ABDALLAH</td><td>08C DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 189-209 GeV</td></tr><tr><td>-0.18<sup>+0.24</sup><sub>-0.16</sub></td><td>1065</td><td>2 ABBIENDI</td><td>01H OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 189 GeV</td></tr></tbody></table>

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

3 AABOUD 17s ATLS $E_{cm}^{pp} = 7+8$ TeV

4 BLINOV 11 LEP $E_{cm}^{ee} = 183-207$ GeV

1 ABDALLAH 08C determine this triple gauge coupling from the measurement of the spin density matrix elements in $e^+e^- \to W^+W^- \to (qq)(\ell\nu)$, where $\ell = e$ or $\mu$. Values of all other couplings are fixed to their standard model values.

2 ABBIENDI 01H study W-pair events, with one leptonicity and one hadronically decaying W. The coupling is extracted using information from the W production angle together with decay angles from the leptonicity decaying W.

3 AABOUD 17s analyze electroweak production of a W boson in association with two jets at high dijet invariant mass, with the W boson decaying to electron or muon plus neutrino. In the signal region of dijet mass larger than 1 TeV and leading-jet transverse momentum larger than 600 GeV, 30 events are observed in the data with 39 ± 4 events expected in the Standard Model, yielding the following limit at 95% CL for the form factor cut-off scale $\Lambda_{FF} \to \infty$: $-0.047 < \bar{\kappa}_Z < 0.046$.

4 BLINOV 11 use the LEP-average $e^+e^- \to W^+W^-$ cross section data for $\sqrt{s} = 183-207$ GeV to determine an upper limit on the TGC $\bar{\kappa}_Z$. The average values of the cross sections as well as their correlation matrix, and standard model expectations of the cross sections are taken from the LEPEWWG note hep-ex/0612034. At 95% confidence level $|\bar{\kappa}_Z| < 0.31$.

## W ANOMALOUS MAGNETIC MOMENT

The full magnetic moment is given by $\mu_W = e(1+\kappa+\lambda)/2m_W$. In the Standard Model, at tree level, $\kappa=1$ and $\lambda=0$. Some papers have defined $\Delta\kappa=1-\kappa$ and assume that $\lambda=0$. Note that the electric quadrupole moment is given by $-e(\kappa-\lambda)/m_W^2$. A description of the parameterization of these moments and additional references can be found in HAGIWARA 87 and BAUR 88. The parameter $\Lambda$ appearing in the theoretical limits below is a regularization cutoff which roughly corresponds to the energy scale where the structure of the W boson becomes manifest.

<table><thead><tr><th>VALUE (e/2m<sub>W</sub>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2.22<sup>+0.20</sup><sub>-0.19</sub></td><td>2298</td><td>1 ABREU</td><td>01I DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 183+189 GeV</td></tr></tbody></table>

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

2 ABE 95G CDF

3 ALITTI 92C UA2

4 SAMUEL 92 THEO

5 SAMUEL 91 THEO

6 GRIFOLS 88 THEO

7 GROTCH 87 THEO

8 VANDERBIJ 87 THEO

9 GRAU 85 THEO

10 SUZUKI 85 THEO

11 HERZOG 84 THEO

1 ABREU 01I combine results from $e^+e^-$ interactions at 189 GeV leading to $W^+W^-$, $W\bar{e}\nu_e$, and $\nu\tau\gamma$ final states with results from ABREU 99L at 183 GeV to determine $\Delta\gamma e^2$, $\Delta\kappa_\gamma$, and $\lambda_\gamma$. $\Delta\kappa_\gamma$ and $\lambda_\gamma$ are simultaneously floated in the fit to determine $\mu_W$.

2 ABE 95G report $-1.3 < \kappa < 3.2$ for $\lambda=0$ and $-0.7 < \lambda < 0.7$ for $\kappa=1$ in $p\bar{p} \to \nu e\nu e\gamma X$ and $\mu\nu\gamma\mu$ at $\sqrt{s} = 1.8$ TeV.

3 ALITTI 92C measure $\kappa = 1+2.6/2$ and $\lambda = 0+1.7$ in $p\bar{p} \to \nu e\gamma\gamma + X$ at $\sqrt{s} = 630$ GeV. At 95%CL they report $-3.5 < \kappa < 5.9$ and $-3.6 < \lambda < 3.5$.

4 SAMUEL 92 use preliminary CDF and UA2 data and find $-2.4 < \kappa < 3.7$ at 96%CL and $-3.1 < \kappa < 4.2$ at 95%CL respectively. They use data for $W\gamma$ production and radiative W decay.

5 SAMUEL 91 use preliminary CDF data for $p\bar{p} \to W\gamma X$ to obtain $-11.3 \le \Delta\kappa \le 10.9$. Note that their $\kappa = 1-\Delta\kappa$.

6 GRIFOLS 88 uses deviation from $\rho$ parameter to set limit $\Delta\kappa \lesssim 65 (M_W^2/\Lambda^2)$.

7 GROTCH 87 finds the limit $-37 < \Delta\kappa < 73.5$ (90% CL) from the experimental limits on $e^+e^- \to \nu\bar{\nu}\gamma$ assuming three neutrino generations and $-19.5 < \Delta\kappa < 56$ for four generations. Note their $\Delta\kappa$ has the opposite sign as our definition.

8 VANDERBIJ 87 uses existing limits to the photon structure to obtain $|\Delta\kappa| < 33 (m_W/\Lambda)^2$. In addition VANDERBIJ 87 discusses problems with using the $\rho$ parameter of the Standard Model to determine $\Delta\kappa$.

9 GRAU 85 uses the muon anomaly to derive a coupled limit on the anomalous magnetic dipole and electric quadrupole ($\lambda$) moments $1.05 > \Delta\kappa \ln(\Lambda/m_W) + \lambda/2 > -2.77$. In the Standard Model $\lambda=0$.

10 SUZUKI 85 uses partial-wave unitarity at high energies to obtain $|\Delta\kappa| \lesssim 190 (m_W/\Lambda)^2$. From the anomalous magnetic moment of the muon, SUZUKI 85 obtains $|\Delta\kappa| \lesssim 2.2/\ln(\Lambda/m_W)$. Finally SUZUKI 85 uses deviations from the $\rho$ parameter and obtains a very qualitative, order-of-magnitude limit $|\Delta\kappa| \lesssim 150 (m_W/\Lambda)^4$ if $|\Delta\kappa| \ll 1$.

11 HERZOG 84 consider the contribution of W-boson to muon magnetic moment including anomalous coupling of $WW\gamma$. Obtain a limit $-1 < \Delta\kappa < 3$ for $\Lambda \gtrsim 1$ TeV.

### $WW^+/\Lambda^2, W^+/\Lambda^2, C_B/\Lambda^2$

These couplings are used in EFT-based approaches to anomalous couplings. They are linearly related to the couplings discussed above.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>1 TUMASYAN</td><td>22AB CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>2 TUMASYAN</td><td>22E CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>3 AAD</td><td>21AC ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>4 AAD</td><td>21W ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>5 SIRUNYAN</td><td>21G CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>6 SIRUNYAN</td><td>20BA CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>7 SIRUNYAN</td><td>20BF CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>8 AABOUD</td><td>19BA ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>9 SIRUNYAN</td><td>19AD CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>10 SIRUNYAN</td><td>19CL CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>11 AABOUD</td><td>18Q ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>12 SIRUNYAN</td><td>18BZ CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td><td></td></tr><tr><td>13 AABOUD</td><td>17S ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 7+8 TeV</td><td></td></tr><tr><td>14 AABOUD</td><td>17U ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td><td></td></tr><tr><td>15 KHACHATRY...170</td><td>CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td><td></td></tr><tr><td>16 SIRUNYAN</td><td>17X CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td><td></td></tr><tr><td>17 AAD</td><td>16AR ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td><td></td></tr><tr><td>18 AAD</td><td>16P ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td><td></td></tr><tr><td>19 KHACHATRY...16BI</td><td>CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td><td></td></tr></tbody></table>

1 TUMASYAN 22AB study WZ production, measuring cross sections and various distributions. Analysing the WZ invariant mass distribution, the following 95% C.L. limits are derived in units of $TeV^{-2}$: $-2.5 < c_W/\Lambda^2 < 0.3$, $-1.0 < c_WW_W/\Lambda^2 < 1.2$, $-43 < c_B/\Lambda^2 < 113$, $-0.62 < \bar{c}_{WW_W}/\Lambda^2 < 0.53$, $-32 < \bar{c}_W/\Lambda^2 < 32$.

2 TUMASYAN 22E measure $W\gamma$ production where the W boson decays to electrons or muons. Analysing the photon transverse momentum distribution in bins of lepton azimuth, the following 95% C.L. limit is derived in units of $TeV^{-2}$: $-0.062 < c_{31W}/\Lambda^2 < 0.052$. This limit is derived including the non-SM, SM and their interference effects.

3 AAD 21AC study the differential cross-section for the electroweak production of dijets in association with a Z boson, where the Z boson decays to electrons or muons. The number of events selected in the data is 10,870 (12,125) in the electron (muon) channel. Analyzing the distribution of the azimuthal separation of the two jets, the following 95% C.L. limits are derived in units of $TeV^{-2}$: $-2.7 < c_{WW_W}/\Lambda^2 < 5.8$, $-1.6 < \bar{c}_{WW_W}/\Lambda^2 < 2.0$, $-0.19 < c_W/\Lambda^2 < 0.41$, $-0.11 < \bar{c}_W/\Lambda^2 < 0.14$, $-6.31 < c_HW_B/\Lambda^2 < 1.01$, $0.23 < \bar{c}_{HW_B}/\Lambda^2 < 2.35$.
⁴AAD 21W analyze $W^{+}W^{-}$ production in association with at least one jet. Events with exactly one oppositely-charged electron-muon pair and at least one hadronic jet of transverse momentum larger than 30 GeV (120 GeV) are selected. In the data, 89,239 (5,825) events are found, with a total Standard-Model expectation of 91600 ± 2500 (5980 ± 150). Analyzing the electron-muon invariant mass distribution, the following limit at 95% C.L. is obtained: $-0.33 < c_W/\Lambda^2 < 0.33$ ($-0.60 < c_W/\Lambda^2 < 0.58$), for a fixed choice of $\Lambda = 1$ TeV.

⁵SIRUNYAN 216 measure $W^{+}$ production where the $W$ decays into electrons or muons. In the data, 385,224 (395,818) events are selected in the electron (muon) channel, with a total Standard-Model expectation of 396913 ± 54686 (396257 ± 22837) events. Analysing the photon transverse momentum distribution, the following 95% C.L. limits are derived in units of $\text{TeV}^{-2}$: $-0.90 < c_{WWW}/\Lambda^2 < 0.91$, $-40 < c_{B}/\Lambda^2 < 41$, $-0.45 < c_{\overline{WWW}}/\Lambda^2 < 0.45$, $-20 < c_{\overline{W}/\Lambda^2} < 20$.

⁶SIRUNYAN 208A study electroweak production of a W boson in association with two jets, using $W$ decays in the electron or muon channel. The isolated muons (electrons) are required to have a transverse momentum larger than 25 (30) GeV, while the transverse momentum of the two jets has to be larger than 50 and 30 GeV. A total of 2,382 (1,051) million events are selected in the muon (electron) channel, with a Standard Model expectation of 2.39 ± 0.17 (1.054 ± 0.058) million events. Analysing the transverse momentum distribution of the charged leptons from $W$ decay, the following 95% C.L. limits are obtained in units of $\text{TeV}^{-2}$: $-2.3 < c_{WWW}/\Lambda^2 < 2.5$, $-8.8 < c_W/\Lambda^2 < 16$, $-45 < c_B/\Lambda^2 < 46$. Combining these results with those from the closely-related electroweak Z-jet production SIRUNYAN 18bz, the limits become: $-1.8 < c_{WWW}/\Lambda^2 < 2.0$, $-5.8 < c_W/\Lambda^2 < 10$, $-43 < c_B/\Lambda^2 < 45$.

⁷SIRUNYAN 208F study $W^{+}W^{-}$ production with the $W$ bosons decaying to electrons or muons. The leading (subleading) lepton is required to have a transverse momentum larger than 25 (20) GeV. Events with a same-flavor di-lepton invariant mass within 15 GeV of the $Z$ mass are rejected, as are event with a third lepton of transverse momentum larger than 10 GeV. In the same- (different-) flavor category a total of 9,604 (20,270) events are selected while the number of expected events is 9640 ± 490 (20280 ± 430). Analyzing the different-flavor di-lepton invariant mass distribution, the following 95% C.L. limits are obtained in units of $\text{TeV}^{-2}$: $-1.8 < c_{WWW}/\Lambda^2 < 1.8$, $-3.6 < c_W/\Lambda^2 < 2.8$, $-9.4 < c_B/\Lambda^2 < 8.5$.

⁸AABOUD 198A study $WW$ production in decay modes with an electron and a muon. The charged leptons are each required to have a transverse momentum larger than 27 GeV and rapidity less than 2.5. The electron-muon system is required to have a mass larger than 55 GeV and a transverse momentum larger than 30 GeV. The missing transverse energy must be larger than 20 GeV. Events containing a jet with transverse momentum exceeding 35 GeV and rapidity smaller than 4.5 are rejected. A total of 12,659 events are selected in the data, with an expected background of 4240 ± 477 events. Analysing the transverse momentum spectrum of the leading charged lepton, the following 95% C.L. limits are derived in units of $\text{TeV}^{-2}$: $-3.4 < c_{WWW}/\Lambda^2 < 3.3$, $-7.4 < c_W/\Lambda^2 < 4.1$, $-21 < c_B/\Lambda^2 < 18$, $-1.6 < c_{\overline{WWW}}/\Lambda^2 < 1.6$, $-76 < c_{\overline{W}}/\Lambda^2 < 76$.

⁹SIRUNYAN 19AD study inclusive $WZ$ production, with $W$ and $Z$ decaying to electrons or muons. The leading (subleading) charged lepton candidate from the $Z$ boson decay is required to have a transverse momentum larger than 25 GeV (10 GeV). The charged lepton candidate from the $W$ boson decay is required to have a transverse momentum larger than 25 GeV. The invariant mass of the two leptons from $Z$ decay is required to be within 15 GeV of the $Z$ mass, while the invariant mass of the tri-lepton system is required to exceed 100 GeV. A total of 3,831 tri-lepton events are observed, with a fitted SM $WZ$ signal of 3166 ± 62 events and a fitted background of 666 ± 45 events. The approximated $WZ$ invariant mass distribution is analyzed to set 95% C.L. limits as follows: $-4.1 < c_W/\Lambda^2 < 1.1$, $-2.0 < c_{WWW}/\Lambda^2 < 2.1$, $-100 < c_B/\Lambda^2 < 160$, in units of $\text{TeV}^{-2}$.

¹⁰SIRUNYAN 19CL study $WW$ and $WZ$ production in lepton + jet events, with one $W$ boson decaying leptonicly (electron or muon), and another $W$ or $Z$ boson decaying hadronically, reconstructed as a single massive large-radius jet. In the electron channel 2,456 (2,235) events are selected in the $WW(WZ)$ category, while in the muon channel 3,996 (3572) events are selected in the $WW(WZ)$ category. Analysing the di-boson invariant mass distribution, the following 95% C.L. limits are obtained in units of $\text{TeV}^{-2}$: $-1.58 < c_{WWW}/\Lambda^2 < 1.59$, $-2.00 < c_W/\Lambda^2 < 2.65$, $-8.78 < c_B/\Lambda^2 < 8.54$.

¹¹AABOUD 180 study $pp \to ZZ$ events at $\sqrt{s} = 13$ TeV with $Z \to e^{+}e^{-}$ or $Z \to \mu^{+}\mu^{-}$. The number of events observed in the $e4$, $e2\mu2$, and $4\mu$ channels is 249, 465, and 303 respectively. Analysing the $p_T$ spectrum of the leading $Z$ boson, the following the following 95% C.L. limits are derived in units of $\text{TeV}^{-4}$: $-5.9 < c_{\overline{BW}}/\Lambda^2 < 5.9$, $-3.0 < c_{WW}/\Lambda^4 < 3.0$, $-3.3 < c_{BW}/\Lambda^4 < 3.3$, $-2.7 < c_{BB}/\Lambda^4 < 2.8$.

¹²SIRUNYAN 18BZ study $pp \to Z$ jet $Z$ event at 13 TeV where $Z \to e^{+}e^{-}/\mu^{+}\mu^{-}$. Isolated electrons and muons are selected with $p_T$ of the leading/sub-leading lepton > 30/20 GeV and $|\eta| < 2.4$, with the di-lepton invariant mass within 15 GeV of the $Z$ mass. The two highest $p_T$ jets are selected with $p_T$ of the leading/sub-leading jet > 50/30 GeV respectively and dijet invariant mass > 200 GeV. Templates in the transverse momentum of the $Z$ are utilized to set limits on the triple gauge couplings in the EFT and the LEP parametrizations. The following 95% C.L. limits are obtained in units of $\text{TeV}^{-2}$: $-2.6 < c_{WWW}/\Lambda^2 < 2.6$ and $-8.4 < c_W/\Lambda^2 < 10.1$.

¹³AABOUD 17S analyze electroweak production of a W boson in association with two jets at high dijet invariant mass, with the W boson decaying to electron or muon plus neutrino. In the signal region of dijet mass larger than 1 TeV and leading-jet transverse momentum larger than 600 GeV, 30 events are observed in the data with 39 ± 4 events expected in the Standard Model, yielding the following limits at 95% CL for the form factor cut-off scale $\Lambda_{FF} \to \infty$: $-33 < c_W/\Lambda^2 < 30$, $-170 < c_B/\Lambda^2 < 160$, $-13 < c_{WWW}/\Lambda^2 < 9$, $-580 < c_{\overline{W}}/\Lambda^2 < 580$, $-11 < c_{\overline{WWW}}/\Lambda^2 < 11$, in units of $\text{TeV}^{-2}$.

¹⁴AABOUD 17U analyze production of $WW$ or $WZ$ boson pairs with one $W$ boson decaying to electron or muon plus neutrino, and the other $W$ or $Z$ boson decaying hadronically. The hadronic decay system is reconstructed as either a resolved two-jet system or as a single large jet. Analysing the transverse momentum distribution of the hadronic system above 100 GeV yields the following limits at 95% CL for the form factor cut-off scale $\Lambda_{FF} \to \infty$: $-3.1 < c_{WWW}/\Lambda^2 < 3.1$, $-19 < c_B/\Lambda^2 < 20$, $-5.1 < c_W/\Lambda^2 < 5.8$, in units of $\text{TeV}^{-2}$.

¹⁵KHACHATRYAN 17O analyse $WZ$ production where each boson decays into electrons or muons. Events are required to have a tri-lepton invariant mass larger than 100 GeV, with one of the lepton pairs having an invariant mass within 20 GeV of the $Z$ boson mass. The $Z$ transverse momentum spectrum is analyzed to set 95% C.L. limits of: $-260 < c_B/\Lambda^2 < 210$, $-4.2 < c_W/\Lambda^2 < 8.0$, $-4.6 < c_{WWW}/\Lambda^2 < 4.2$, in units of $\text{TeV}^{-2}$.

¹⁶SIRUNYAN 17X study $pp \to WW/WZ \to \ell\nu q\bar{q}$ production at 8 TeV where $\ell$ is an electron or muon with $p_T > 30$ or 25 GeV respectively. Suitable cuts are put on the $p_T$ of the dijet system and the missing $E_T$ of the event yielding a total of 285 and 204 $WW$ events observed in the electron and muon channels. The following 95% C.L. limits in units of $\text{TeV}^{-2}$ are obtained: $-2.7 < c_{WWW}/\Lambda^2 < 2.7$, $-14 < c_B/\Lambda^2 < 17$, $-2.0 < c_W/\Lambda^2 < 5.7$.

¹⁷AAD 16AR study $WW$ production in $pp$ collisions and select 6636 $WW$ candidates in decay modes with electrons or muons with an expected background of 1546 ± 157 events. Assuming an EFT formulation, a fit to the transverse momentum distribution of the leading charged lepton, leads to 95% C.L. ranges of: $-4.61 < c_{WWW}/\Lambda^2 < 4.60$, $-5.87 < c_W/\Lambda^2 < 10.54$ and $-20.9 < c_B/\Lambda^2 < 26.3$, in units of $\text{TeV}^{-2}$.

¹⁸AAD 16P study $WZ$ production in $pp$ collisions and select 2091 $WZ$ candidates in 4 decay modes with electrons and muons, with an expected background of 1825 ± 7 events. Analyzing the $WZ$ transverse momentum distribution, the resulting 95% C.L. limits are: $-3.9 < c_{WWW}/\Lambda^2 < 4.0$, $-4.3 < c_W/\Lambda^2 < 6.8$, and $-320 < c_B/\Lambda^2 < 210$, in units of $\text{TeV}^{-2}$.

¹⁹KHACHATRYAN 16BI determine the $W^{+}W^{-}$ production cross section using unlike sign di-lepton ($e$ or $\mu$) events with high $p_T$. The leptons have $p_T > 20$ GeV/c and are isolated. Events are required to have no jets above $p_T$ of 30 GeV/c. 4847 (2233) events are selected with different (same) flavor leptons, with an expected total background of 1179 ± 123 (643 ± 73) events. Analysing the di-lepton invariant mass spectrum, the following values are obtained: $c_{WWW}/\Lambda^2 = 0.1 \pm 3.2$, $c_W/\Lambda^2 = -3.6^{+5.0}_{-4.5}$ and $c_B/\Lambda^2 = -3.2^{+15.0}_{-14.5}$ in units of $\text{TeV}^{-2}$. The limits at 95% C.L. are: $-5.7 < c_{WWW}/\Lambda^2 < 5.9$, $-11.4 < c_W/\Lambda^2 < 5.4$ and $-29.2 < c_B/\Lambda^2 < 23.9$, in units of $\text{TeV}^{-2}$.

## ANOMALOUS W/Z QUARTIC COUPLINGS

Revised March 2024 by M.W. Grünewald (U. College Dublin) and A. Gurtu (CERN; TIFR Mumbai).

Quartic couplings, $WWZZ$, $WWZ\gamma$, $WW\gamma\gamma$, and $ZZ\gamma\gamma$, were studied at LEP and Tevatron at energies at which the Standard Model predicts negligible contributions to multiboson production. Thus, to parametrize limits on these couplings, an effective theory approach is adopted which supplements the Standard Model Lagrangian with higher dimensional operators which include quartic couplings. The LEP collaborations chose the lowest dimensional representation of operators (dimension 6) which presumes the $SU(2) \times U(1)$ gauge symmetry is broken by means other than the conventional Higgs scalar doublet [1–3]. In this representation possible quartic couplings, $a_0$, $a_c$, $a_n$, are expressed in terms of the following dimension-6 operators [1,2];

$$L_6^0 = -\frac{e^2}{16\Lambda^2} a_0 F^{\mu\nu} F_{\mu\nu} \vec{W}^\alpha \cdot \vec{W}_\alpha$$

$$L_6^c = -\frac{e^2}{16\Lambda^2} a_c F^{\mu\alpha} F_{\mu\beta} \vec{W}^\beta \cdot \vec{W}_\alpha$$

$$L_6^n = -i \frac{e^2}{16\Lambda^2} a_n \epsilon_{ijk} W_{\mu\alpha}^{(i)} W_{\nu}^{(j)} W^{(k)\alpha} F^{\mu\nu}$$

$$\tilde{L}_6^0 = -\frac{e^2}{16\Lambda^2} \tilde{a}_0 F^{\mu\nu} \tilde{F}_{\mu\nu} \cdot \tilde{W}^\alpha \cdot \tilde{W}_\alpha$$

$$\tilde{L}_6^n = -i \frac{e^2}{16\Lambda^2} \tilde{a}_n \epsilon_{ijk} W_{\mu\alpha}^{(i)} W_{\nu}^{(j)} W^{(k)\alpha} \tilde{F}_{\mu\nu}$$

where $F, W$ are photon and $W$ fields, $L_6^0$ and $L_6^n$ conserve $C$, $P$ separately ($\tilde{L}_6^0$ conserves only $C$) and generate anomalous $W^{+}W^{-}\gamma\gamma$ and $ZZ\gamma\gamma$ couplings, $L_6^n$ violates $CP$ ($\tilde{L}_6^n$ violates both $C$ and $P$) and generates an anomalous $W^{+}W^{-}Z\gamma$ coupling, and $\Lambda$ is an energy scale for new physics. For the $ZZ\gamma\gamma$ coupling the $CP$-violating term represented by $L_6^n$ does not contribute. These couplings are assumed to be real and to vanish at tree level in the Standard Model.

Within the same framework as above, a more recent description of the quartic couplings [3] treats the anomalous parts of the $WW\gamma\gamma$ and $ZZ\gamma\gamma$ couplings separately, leading to two sets parametrized as $a_0^V/\Lambda^2$ and $a_c^V/\Lambda^2$, where $V = W$ or $Z$.

With the discovery of a Higgs at the LHC in 2012, it is then useful to go to the next higher dimensional representation (dimension 8 operators) in which the gauge symmetry is
broken by the conventional Higgs scalar doublet [3,4]. There are 14 operators which can contribute to the anomalous quartic coupling signal. Some of the operators have analogues in the dimension 6 scheme. The CMS collaboration, [5], have used this parametrization, in which the connections between the two schemes are also summarized:

$$ \mathcal{L}_{AQGC} = -\frac{e^2 a_0^W}{8 \Lambda^2} F_{\mu\nu} F^{\mu\nu} W^{+a} W_a^- \\ -\frac{e^2 a_c^W}{16 \Lambda^2} F_{\mu\nu} F^{\mu a} (W^{+\nu} W_a^- + W^{-\nu} W_a^+) \\ -e^2 g^2 \frac{\kappa_0^W}{\Lambda^2} F_{\mu\nu} Z^{\mu\nu} W^{+a} W_a^- \\ -\frac{e^2 g^2 \kappa_c^W}{2 \Lambda^2} F_{\mu\nu} Z^{\mu a} (W^{+\nu} W_a^- + W^{-\nu} W_a^+) \\ + \frac{f_{T,0}}{\Lambda^4} \mathrm{Tr}[\widehat{W}_{\mu\nu} \widehat{W}^{\mu\nu}] \times \mathrm{Tr}[\widehat{W}_{\alpha\beta} \widehat{W}^{\alpha\beta}] $$

The energy scale of possible new physics is $\Lambda$, and $g = e/\sin(\theta_W)$, $e$ being the unit electric charge and $\theta_W$ the Weinberg angle. The field tensors are described in [3,4].

The two dimension 6 operators $a_0^W/\Lambda^2$ and $a_c^W/\Lambda^2$ are associated with the $WW\gamma\gamma$ vertex. Among dimension 8 operators, $\kappa_0^W/\Lambda^2$ and $\kappa_c^W/\Lambda^2$ are associated with the $WWZ\gamma$ vertex, whereas the parameter $f_{T,0}/\Lambda^4$ contributes to both vertices. There is a relationship between these two dimension 6 parameters and the dimension 8 parameters $f_{M,i}/\Lambda^4$ as follows [3]:

$$ \frac{a_0^W}{\Lambda^2} = -\frac{4M_W^2 f_{M,0}}{g^2 \Lambda^4} - \frac{8M_W^2 f_{M,2}}{g'^2 \Lambda^4} $$

$$ \frac{a_c^W}{\Lambda^2} = -\frac{4M_W^2 f_{M,1}}{g^2 \Lambda^4} - \frac{8M_W^2 f_{M,3}}{g'^2 \Lambda^4} $$

where $g' = e/\cos(\theta_W)$ and $M_W$ is the invariant mass of the W boson. This relation provides a translation between limits on dimension 6 operators $a_{0,c}^W$ and $f_{M,j}/\Lambda^4$. It is further required [4] that $f_{M,0} = 2f_{M,2}$ and $f_{M,1} = 2f_{M,3}$ which suppresses contributions to the $WWZ\gamma$ vertex. The complete set of Lagrangian contributions as presented in [4] corresponds to 19 anomalous couplings in total – $f_{S,i}$, $i = 1,2$, $f_{M,i}$, $i = 0, \dots, 8$ and $f_{T,i}$, $i = 0, \dots, 9$ – each scaled by $1/\Lambda^4$.

Another approach to couplings is the so called K-matrix framework [7], in which the anomalous couplings can be expressed in terms of two parameters $\alpha_4$ and $\alpha_5$, which account for all BSM effects.

The LHC collaborations have published couplings results based on various theoretical frameworks. It is hoped that the collaborations will agree to use at least one common set of parameters to express these limits to enable the reader to make a comparison, and to allow for a possible LHC combination.

References

1. G. Belanger and F. Boudjema, Phys. Lett. B288, 201 (1992).

2. J.W. Stirling and A. Werthenbach, Eur. Phys. J. C14, 103 (2000);

J.W. Stirling and A. Werthenbach, Phys. Lett. B466, 369 (1999);

A. Denner et al., Eur. Phys. J. C20, 201 (2001);

G. Montagna et al., Phys. Lett. B515, 197 (2001).

3. G. Belanger et al., Eur. Phys. J. C13, 283 (2000).

4. O.J.P. Éboli, M.C. Gonzalez-Garcia, and S.M. Lietti, Phys. Rev. D69, 095005 (2004);

O.J.P. Éboli, M.C. Gonzalez-Garcia, and J.K. Mizukoshi, Phys. Rev. D77, 073005 (2008).

5. S. Chatrchyan et al., Phys. Rev. D90, 032008 (2014); S. Chatrchyan et al., Phys. Rev. Lett. 114, 051801 (2015).

6. G. Aad et al., Phys. Rev. Lett. 113, 141803 (2014).

7. A. Albateanu, W. Killian, and J. Reuter, JHEP 0811, 010 (2008).

$a_0/\Lambda^2$, $a_c/\Lambda^2$, $a_n/\Lambda^2$, $\kappa_0^W/\Lambda^2$, $\kappa_c^W/\Lambda^2$, $f_{T,0}/\Lambda^4$, $f_{M,i}/\Lambda^4$, $\alpha_4$, $\alpha_5$, $f_{S,i}/\Lambda^4$, $F_{M,i}/\Lambda^4$, $F_{T,i}/\Lambda^4$

Anomalous W quartic couplings are measured by the experiments at LEP, the Tevatron, and the LHC. Some of the recent results from the Tevatron and LHC experiments individually surpass the combined LEP-2 results in precision (see below). As discussed in the review on the “Anomalous W/Z quartic couplings (QGC5),” the measurements are typically done using different operator expansions which then do not allow the results to be compared and averaged. At least one common framework should be agreed upon for the use in the future publications by the experiments.

Some publications from LHC experiments derive limits for various assumed values of the form-factor cutoff $\Lambda_{FF} \to \infty$.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>• • •</td><td>We do not use the following data for averages, fits, limits, etc.</td><td></td><td>• • •</td></tr><tr><td>1</td><td>AAD</td><td>24C ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>2</td><td>AAD</td><td>23BH ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>3</td><td>AAD</td><td>23K ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>4</td><td>TUMASYAN</td><td>23AK CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>5</td><td>TUMASYAN</td><td>23AM CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>6</td><td>SIRUNYAN</td><td>21 CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>7</td><td>TUMASYAN</td><td>21A CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>8</td><td>TUMASYAN</td><td>21B CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>9</td><td>SIRUNYAN</td><td>20 CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>10</td><td>SIRUNYAN</td><td>20AL CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>11</td><td>SIRUNYAN</td><td>20BD CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>12</td><td>SIRUNYAN</td><td>19BM CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>13</td><td>SIRUNYAN</td><td>19BP CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>14</td><td>SIRUNYAN</td><td>19CQ CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>15</td><td>SIRUNYAN</td><td>18CC CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>16</td><td>AABOUD</td><td>17AA ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>17</td><td>AABOUD</td><td>17AG ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>18</td><td>AABOUD</td><td>17D ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>19</td><td>AABOUD</td><td>17J ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>20</td><td>AABOUD</td><td>17M ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>21</td><td>KHACHATRY...</td><td>17AA CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>22</td><td>KHACHATRY...</td><td>17M CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>23</td><td>SIRUNYAN</td><td>17AD CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>24</td><td>SIRUNYAN</td><td>17AR CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>25</td><td>AABOUD</td><td>16E ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>26</td><td>AAD</td><td>16Q ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>27</td><td>KHACHATRY...</td><td>16AX CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>28</td><td>AAD</td><td>15N ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>29</td><td>KHACHATRY...</td><td>15D CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>30</td><td>AAD</td><td>14AM ATLS</td><td></td></tr><tr><td>31</td><td>CHATRCHYAN...</td><td>14Q CMS</td><td></td></tr><tr><td>32</td><td>ABAZOV</td><td>13D D0</td><td></td></tr><tr><td>33</td><td>CHATRCHYAN...</td><td>13AA CMS</td><td></td></tr><tr><td>34</td><td>ABBIENDI</td><td>04B OPAL</td><td></td></tr><tr><td>35</td><td>ABBIENDI</td><td>04L OPAL</td><td></td></tr><tr><td>36</td><td>HEISTER</td><td>04A ALEP</td><td></td></tr><tr><td>37</td><td>ABDALLAH</td><td>03I DLPH</td><td></td></tr><tr><td>38</td><td>ACHARD</td><td>02F L3</td><td></td></tr></tbody></table>

<footnote n="1">¹AAD 24C study the production of four charged leptons (electrons or muons) in association with two jets. Analysing the 4-lepton invariant mass distribution and the di-jet invarian mass distribution leads to the following 95% C.L. limits: -0.98 < $f_{T,0}/\Lambda^4$ < 0.93, -1.2 < $f_{T,1}/\Lambda^4$ < 1.2, -2.5 < $f_{T,2}/\Lambda^4$ < 2.4, -2.5 < $f_{T,5}/\Lambda^4$ < 2.4, -3.9 < $f_{T,6}/\Lambda^4$ < 3.9, -8.5 < $f_{T,7}/\Lambda^4$ < 8.1, -2.1 < $f_{T,8}/\Lambda^4$ < 2.1, -4.5 < $f_{T,9}/\Lambda^4$ < 4.5, in units of TeV⁻⁴. The article also reports limits on these couplings by cutting the EFT expansion at various values of the cut-off scale.</footnote>
²AAD 238H study pp → Zγγ events with the Z boson decaying to electron or muon pairs. The number of observed data events is 148 for the electron mode and 171 for the muon mode. The respective number of (data-background) events is 105.5 ± 12.2(stat) ± 8.1(syst) and 120.4 ± 13.1(stat) ± 9.4(syst). The corresponding number of predicted signal events is 91.5 ± 0.9 and 119.5 ± 1.0 using SHERPA (NLO), and 91.0 ± 1.0 and 118.1 ± 1.2 using MADGRAPH 5 AMC (NLO), where the error is statistical only. Analysing the transverse momentum distribution of the dilepton system, the following 95% C.L. limits are derived: -9.87 < $f_{T,0}$/A^4 < 9.33, -9.88 < $f_{T,1}$/A^4 < 9.34, -20.31 < $f_{T,2}$/A^4 < 18.68, -4.64 < $f_{T,5}$/A^4 < 4.54, -7.04 < $f_{T,6}$/A^4 < 6.94, -15.55 < $f_{T,7}$/A^4 < 15.04, -1.64 < $f_{T,8}$/A^4 < 1.61, -3.26 < $f_{T,9}$/A^4 < 3.26, in units of TeV⁻⁴.

³AAD 23k measure Z production in association with a photon and two jets in proton-proton collisions at 13 TeV CM energy, where the Z boson decays into neutrinos. Within a sensitive fiducial phase-space region, 356 signal events are selected, with an expectation of 357 ± 30. Analysing the photon transverse energy distribution, the following 95% C.L. limits are derived in units of TeV⁻⁴: -0.094 < $f_{T,0}$/A^4 < 0.084, -0.088 < $f_{T,5}$/A^4 < 0.099, -0.059 < $f_{T,8}$/A^4 < 0.059, -0.13 < $f_{T,9}$/A^4 < 0.13, -4.6 < $f_{M,0}$/A^4 < 4.6, -7.7 < $f_{M,1}$/A^4 < 7.7, -1.9 < $f_{M,2}$/A^4 < 1.9.

⁴TUMASYAN 23AK study electroweak Wγ production in association with 2 jets. The events selected for the couplings analysis are required to have a dijet invariant mass in excess of 800 GeV, jet-part separation of at least 2.5 in rapidity, invariant mass of the Wγ system larger than 150 GeV and transverse photon momentum larger than 100 GeV. Analysing the Wγ invariant mass distribution, varying one coupling at a time while fixing the others to their Standard Model value, leads to the following 95% C.L. limits: -5.6 < $f_{M,0}$/A^4 < 5.5, -7.8 < $f_{M,1}$/A^4 < 8.1, -1.9 < $f_{M,2}$/A^4 < 1.9, -2.7 < $f_{M,3}$/A^4 < 2.7, -3.7 < $f_{M,4}$/A^4 < 3.6, -3.9 < $f_{M,5}$/A^4 < 3.9, -14 < $f_{M,7}$/A^4 < 14, -0.47 < $f_{T,0}$/A^4 < 0.51, -0.31 < $f_{T,1}$/A^4 < 0.34, -0.85 < $f_{T,2}$/A^4 < 1.0, -0.31 < $f_{T,5}$/A^4 < 0.33, -0.25 < $f_{T,6}$/A^4 < 0.27, -0.67 < $f_{T,7}$/A^4 < 0.73, in units of TeV⁻⁴.

⁵TUMASYAN 23AM use the combined CMS-TOTEM detector system study exclusive γγ → WW and γγ → ZZ production in pp collisions at 13 TeV. The W and Z are identified through their hadronic decay with the added requirements of the invariant mass of the di-boson pair to be larger than 1 TeV, and the relative beam proton momentum loss between 0.04 and 0.20. The following limits are derived at 95% C.L.: (i) on the dimension-6 (LEP) couplings, in units of GeV⁻²: $|a_0^W/A^2| < 4.0 \times 10^{-6}$, $|a_C^W/A^2| < 1.6 \times 10^{-5}$, $|a_0^Z/A^2| < 0.9 \times 10^{-5}$, $|a_C^Z/A^2| < 4.0 \times 10^{-5}$. (ii) on the dimension-8 operators, in units of TeV⁻⁴: $|f_{M,0}|^4 < 66.0$, $|f_{M,1}|^4 < 245.5$, $|f_{M,2}|^4 < 9.8$, $|f_{M,3}|^4 < 73.0$, $|f_{M,4}|^4 < 36.0$, $|f_{M,5}|^4 < 67.0$, $|f_{M,7}|^4 < 490.9$.

⁶SIRUNYAN 21 study electroweak Z-pair production in association with two jets, with the Z bosons decaying to oppositely-charged electron or muon pairs. Leptons with high transverse momentum are selected, with the di-lepton invariant mass of the Z boson candidates between 60 GeV and 120 GeV and the four-lepton invariant mass larger than 180 GeV. A total of 365 events are selected in the data, while the number of expected events is 370 ± 48. Analysing the di-lepton invariant mass distribution, the following 95% C.L. limits are derived: -0.24 < $f_{T,0}$/A^4 < 0.22, -0.31 < $f_{T,1}$/A^4 < 0.31, -0.63 < $f_{T,2}$/A^4 < 0.59, -0.43 < $f_{T,8}$/A^4 < 0.43, -0.92 < $f_{T,9}$/A^4 < 0.92, in units of TeV⁻⁴.

⁷TUMASYAN 21A study electroweak Zγ production in association with two jets, where the Z boson decays to electron or muon pairs and the pair of two jets has high invariant mass, superseding SIRUNYAN 20AL. The number of observed (expected) electron events in the barrel and endcap regions are 375 (349 ± 9) and 174 (166 ± 6) events, respectively, while for muon events the respective numbers are 584 (612 ± 13) and 320 (303 ± 8). Analysing the Zγ invariant mass distribution, the following 95% C.L. limits are derived: -15.8 < $f_{M,0}$/A^4 < 16.0, -35.0 < $f_{M,1}$/A^4 < 34.7, -6.55 < $f_{M,2}$/A^4 < 6.49, -13.0 < $f_{M,3}$/A^4 < 13.0, -13.0 < $f_{M,4}$/A^4 < 12.7, -22.2 < $f_{M,5}$/A^4 < 21.3, -56.6 < $f_{M,7}$/A^4 < 55.9, -0.64 < $f_{T,0}$/A^4 < 0.57, -0.81 < $f_{T,1}$/A^4 < 0.90, -1.68 < $f_{T,2}$/A^4 < 1.54, -0.58 < $f_{T,5}$/A^4 < 0.64, -1.30 < $f_{T,6}$/A^4 < 1.33, -2.15 < $f_{T,7}$/A^4 < 2.43, -0.47 < $f_{T,8}$/A^4 < 0.47, -0.91 < $f_{T,9}$/A^4 < 0.91, in units of TeV⁻⁴.

⁸SIRUNAYN 21B measure W or Z boson production in association with two photons, using the leptonic decays modes of the W and Z with electrons or muons. The number of $W \to e(\mu)\nu$ events is 1987 (2384) and the number of selected Z → e(µ)ν events is 110 (272) respectively. Analysing the transverse momentum of the di-photon system, the following 95% C.L. limits are derived in units of TeV⁻⁴: In the W production channel, the observed limits are: -39.9 < $f_{M,2}$/A^4 < 39.5, -63.8 < $f_{M,3}$/A^4 < 65.0, -1.30 < $f_{T,0}$/A^4 < 1.30, -1.70 < $f_{T,1}$/A^4 < 1.66, -3.64 < $f_{T,2}$/A^4 < 3.64, -0.52 < $f_{T,5}$/A^4 < 0.60, -0.60 < $f_{T,6}$/A^4 < 0.68, -1.16 < $f_{T,7}$/A^4 < 1.16. In the Z production channel, the observed limits are: -5.70 < $f_{T,0}$/A^4 < 5.46, -5.70 < $f_{T,1}$/A^4 < 5.46, -11.4 < $f_{T,2}$/A^4 < 10.9, -2.92 < $f_{T,5}$/A^4 < 2.92, -3.80 < $f_{T,6}$/A^4 < 3.88, -7.88 < $f_{T,7}$/A^4 < 7.72, -1.06 < $f_{T,8}$/A^4 < 1.10, -1.82 < $f_{T,9}$/A^4 < 1.82, in units of TeV⁻⁴.

⁹SIRUNAYN 20 study WZ and same-sign WW production in association with two jets, using the leptonic decays modes of the W and Z bosons with electrons or muons. Overall, 524 WW events and 229 WZ events are selected, with a Standard Model expectation of 535 ± 52 and 216 ± 21 events, respectively. Analysing the transverse mass spectrum of the di-boson system and the di-lepton invariant mass, the following 95% C.L. limits are derived, not using any unitarization procedure: -0.25 < $f_{T,0}$/A^4 < 0.28, -0.12 < $f_{T,1}$/A^4 < 0.14, -0.35 < $f_{T,2}$/A^4 < 0.48, -2.7 < $f_{M,0}$/A^4 < 2.9, -4.1 < $f_{M,1}$/A^4 < 4.2, -5.4 < $f_{M,6}$/A^4 < 5.8, -5.7 < $f_{M,7}$/A^4 < 6.0, -5.7 < $f_{S,0}$/A^4 < 6.1, -16 < $f_{S,1}$/A^4 < 17, in units of TeV⁻⁴. The article also reports limits on these couplings by cutting the EFT expansion at the unitarity limit.

¹⁰SIRUNYAN 20AL study electroweak production of a Z boson and a photon in association with two jets in the electron and muon decay modes of the Z. A signal with a significance of 3.9 standard deviations is observed, compared to a Standard Model expectation of 5.2 standard deviations. Combining with KHACHATRYAN 17AA data at 8 TeV the final observed and expected signal significance is 4.7 and 5.5 standard deviations. Analysing the Z-photon invariant mass distribution, the following 95% C.L. limits are derived: -19.5 < $f_{M,0}$/A^4 < 20.3, -40.5 < $f_{M,1}$/A^4 < 39.5, -8.22 < $f_{M,2}$/A^4 < 8.10, -17.7 < $f_{M,3}$/A^4 < 17.9, -15.3 < $f_{M,4}$/A^4 < 15.8, -25.1 < $f_{M,5}$/A^4 < 24.5, -38.9 < $f_{M,6}$/A^4 < 40.6, -60.3 < $f_{M,7}$/A^4 < 62.5, -0.74 < $f_{T,0}$/A^4 < 0.69, -0.98 < $f_{T,1}$/A^4 < 0.96, -1.97 < $f_{T,2}$/A^4 < 1.86, -0.70 < $f_{T,5}$/A^4 < 0.75, -1.64 < $f_{T,6}$/A^4 < 1.68, -2.59 < $f_{T,7}$/A^4 < 2.82, -0.47 < $f_{T,8}$/A^4 < 0.47, -1.27 < $f_{T,9}$/A^4 < 1.27, in units of TeV⁻⁴.

¹¹SIRUNYAN 20BD study electroweak Wγ production in association with two jets, where the W boson decays to electron or muon and the two jets have high invariant mass. The number of observed (expected) electron events with the photon in the barrel and endcap regions are 393 (397.1 ± 18.5) and 159 (145.2 ± 10.0) respectively, while for muon events the respective numbers are 565 (537.9 ± 21.4) and 201 (188.2 ± 10.5). Analysing the Wγ invariant mass distribution, the following 95% C.L. limits are derived: -8.1 < $f_{M,0}$/A^4 < 8.0, -12 < $f_{M,1}$/A^4 < 12, -2.8 < $f_{M,2}$/A^4 < 2.8, -4.4 < $f_{M,3}$/A^4 < 4.4, -5.0 < $f_{M,4}$/A^4 < 5.0, -8.3 < $f_{M,5}$/A^4 < 8.3, -16 < $f_{M,6}$/A^4 < 16, -21 < $f_{M,7}$/A^4 < 20, -0.6 < $f_{T,0}$/A^4 < 0.6, -0.4 < $f_{T,1}$/A^4 < 0.4, -1.0 < $f_{T,2}$/A^4 < 1.2, -0.5 < $f_{T,5}$/A^4 < 0.5, -0.4 < $f_{T,6}$/A^4 < 0.4, -0.9 < $f_{T,7}$/A^4 < 0.9, in units of TeV⁻⁴.

¹²SIRUNYAN 19BM search for the final state W⁺W⁻W⁺W⁻ using W decays to electrons or muons. Two event samples are considered, events with three leptons, or events with two oppositely charged leptons accompanied by two jets. In a kinematic region selected to enhance the effect of anomalous couplings, no events are selected in the data, and 95% C.L. upper limits are obtained as follows: -1.2 < $f_{T,0}$/A^4 < 1.2, -3.3 < $f_{T,1}$/A^4 < 3.3, -2.7 < $f_{T,2}$/A^4 < 2.6, in units of TeV⁻⁴ and without application of a form factor.

¹³SIRUNYAN 19BP study WZ plus 2 jets production, using W and Z decay channels with electrons or muons. In the data, 75 events are selected, with a fitted SM signal of 15.1 ± 1.6 events and a fitted background of 62.4 ± 2.8 events. The transverse mass distribution of the WZ system is analyzed to set the following limits at 95% C.L., in units of TeV⁻⁴: -9.15 < $f_{M,0}$/A^4 < 9.15, -9.15 < $f_{M,1}$/A^4 < 9.45, -26.5 < $f_{S,0}$/A^4 < 27.5, -41.2 < $f_{S,1}$/A^4 < 42.8, -0.75 < $f_{T,0}$/A^4 < 0.81, -0.49 < $f_{T,1}$/A^4 < 0.55, -1.49 < $f_{T,2}$/A^4 < 1.85.

¹⁴SIRUNYAN 19CQ search for anomalous electroweak production of vector boson pairs in association with two jets. Events are selected by requiring two jets with a large invariant mass and rapidity separation, one or two leptons (electrons or muons), and a W or Z boson decaying hadronically. In the WV (ZV) channel, 347 (47) events are selected in the data, with a total expected background of 352 ± 19 (50.3 ± 5.8) events. Analysing the mass distribution of the WV or ZV system, the following 95% C.L. limits are obtained: -2.7 < $f_{S,0}$/A^4 < 2.7, -3.4 < $f_{S,1}$/A^4 < 3.4, -0.69 < $f_{M,0}$/A^4 < 0.70, -2.0 < $f_{M,1}$/A^4 < 2.1, -1.3 < $f_{M,6}$/A^4 < 1.3, -3.4 < $f_{M,7}$/A^4 < 3.4, -0.12 < $f_{T,0}$/A^4 < 0.11, -0.12 < $f_{T,1}$/A^4 < 0.13, -0.28 < $f_{T,2}$/A^4 < 0.28, in units of TeV⁻⁴.

¹⁵SIRUNYAN 18CC study pp collisions at $\sqrt{s} = 13$ TeV leading to a pair of same-sign W pairs decaying leptonically (e or µ) associated with a pair of jets. Isolated leptons with $\rho_T > 25$ (20) GeV for the leading (trailing) lepton, with $|\eta| < 2.5$ (2.4) for e (µ) and jets with $\rho_T > 30$ GeV, $|\eta| < 5.0$, $|\Delta\eta_{jj}| > 2.5$ and $m_{jj} > 500$ GeV is required. Further cuts are applied to minimize Z → ee events, non-prompt leptons and hadronically decaying taus. The number of selected events is 201, with an expected SM signal of 66.9 ± 2.4 and background of 138 ± 13 events. Analysing the dilepton invariant mass spectrum the following 95% C.L. limits are derived: -7.7 < $f_{S,0}$/A^4 < 7.7, -21.6 < $f_{S,1}$/A^4 < 21.8, -6.0 < $f_{M,0}$/A^4 < 5.9, -8.7 < $f_{M,1}$/A^4 < 9.1, -11.9 < $f_{M,6}$/A^4 < 11.8, -13.3 < $f_{M,7}$/A^4 < 12.9, -0.62 < $f_{T,0}$/A^4 < 0.65, -0.28 < $f_{T,1}$/A^4 < 0.31, -0.89 < $f_{T,2}$/A^4 < 1.02.

¹⁶AABOUD 17AA analyze W∓W∓ production in association with two jets and W decay modes with electrons or muons. In the kinematic region of VBS effect of anomalous QGCs is enhanced by requiring the transverse mass of the W system to be larger than 400 GeV. In the data, 8 events are selected with a total background expected from SM processes of 3.8 ± 0.6 events. Assuming the other QGC coupling to have the SM value of zero, the observed event yield is used to determine 95% CL limits on the QGCs: -0.14 < $\alpha_4 < 0.15$ and -0.22 < $\alpha_5 < 0.22$. Supersedes AAD 14AM.

¹⁷AABOUD 17AG determine the WWγ and WZγ cross sections in 8 TeV pp interactions by studying the final states eνµνγ and eνjjγ or µνjjγ. Upper limits on the production cross sections are derived in a fiducial region optimized for BSM physics. These are used to derive the following 95% C.L. upper limits for quark couplings assuming the form scale factor, $\Lambda_{FF} = \infty$ (all in units of $10^3$ TeV⁻⁴): -0.3 < $f_{M,0}$/A^4 < 0.3, -0.5 < $f_{M,1}$/A^4 < 0.5, -1.8 < $f_{M,2}$/A^4 < 1.8, -1.1 < $f_{M,4}$/A^4 < 1.1, -1.7 < $f_{M,5}$/A^4 < 1.7, -0.6 < $f_{M,6}$/A^4 < 0.6, -1.1 < $f_{M,7}$/A^4 < 1.1, -0.1 < $f_{T,0}$/A^4 < 0.1, -0.2 < $f_{T,1}$/A^4 < 0.2, -0.4 < $f_{T,4}$/A^4 < 0.4, -1.5 < $f_{T,5}$/A^4 < 1.6, -1.9 < $f_{T,6}$/A^4 < 1.9, -4.3 < $f_{T,7}$/A^4 < 4.3.

¹⁸AABOUD 17D analyze electroweak diboson (WV, V = W, Z) production in association with a high-mass dijet system. In the data, 32 events are selected with an expected total background of 32 ± 12 events. Analysing the transverse mass distribution of the WV system, the following limits are set at 95% C.L.: -0.024 < $\alpha_4 < 0.030$ and -0.028 < $\alpha_5 < 0.033$.

¹⁹AABOUD 17J analyze the Zγ production in association with a high-mass dijet system, with the Z boson decaying into a pair of electrons, muons, or neutrinos. In the charged lepton (neutrino) channel, events are selected with a dijet mass larger than 500 (600) GeV and a transverse photon energy larger than 250 (150) GeV, with 2 (4) events selected in the data and 0.30 ± 0.08 (1.6 ± 0.5) expected background events. The observed event yield is used to determine 95% CL limits as follows: -4.1 × $10^3$ <
$f_{T,9}/\Lambda^4 < 4.2 \times 10^3$, $-1.9 \times 10^3 < f_{T,8}/\Lambda^4 < 2.1 \times 10^3$, $-1.9 \times 10^1 < f_{T,0}/\Lambda^4 < 1.6 \times 10^4$, $-1.6 \times 10^2 < f_{M,0}/\Lambda^4 < 1.8 \times 10^2$, $-3.5 \times 10^2 < f_{M,1}/\Lambda^4 < 3.4 \times 10^2$, $-8.9 \times 10^2 < f_{M,2}/\Lambda^4 < 8.9 \times 10^2$, $-1.7 \times 10^3 < f_{M,3}/\Lambda^4 < 1.7 \times 10^3$, in units of TeV$^{-4}$ and without application of a form factor.

20 AABOUD 17m analyse tri-boson $W^\pm W^\pm W^\mp W^\mp$ production in decay channels with three charged leptons or two like-sign charged leptons with two jets, where the lepton can be an electron or muon. In the data, 24 tri-lepton events and 21 di-lepton plus jets events are selected, compared to a total event yield expected in the SM of 30.8±3.0 and 21.9±2.0, respectively. Analysing the tri-lepton transverse mass or the transverse momentum sum of the two leptons, two jets and the missing transverse energy, the following limits at 95% CL are derived for the form factor cut-off scale $\Lambda_{FF} \to \infty$: $-0.13 < f_{S,0}/\Lambda^4 < 0.18$, $-0.21 < f_{S,1}/\Lambda^4 < 0.27$, in units of $10^4$ TeV$^{-4}$, which are converted into the following limits: $-0.49 < \alpha_4 < 0.75$ and $-0.48 < \alpha_5 < 0.62$.

21 KHACHATRYAN 17AA analyse electroweak production of $Z\gamma$ in association with two hadronic jets, with the Z boson decaying to electron or muon pairs. Events with photon transverse momentum larger than 60 GeV and di-jet invariant mass larger than 400 GeV are selected. The $Z\gamma$ invariant mass spectrum is analysed to set 95% C.L. limits as follows: $-71 < f_{M,0}/\Lambda^4 < 75$, $-190 < f_{M,1}/\Lambda^4 < 182$, $-32 < f_{M,2}/\Lambda^4 < 31$, $-58 < f_{M,3}/\Lambda^4 < 59$, $-3.8 < f_{T,0}/\Lambda^4 < 3.4$, $-4.4 < f_{T,1}/\Lambda^4 < 4.4$, $-9.9 < f_{T,2}/\Lambda^4 < 9.0$, $-1.8 < f_{T,8}/\Lambda^4 < 1.8$, $-4.0 < f_{T,9}/\Lambda^4 < 4.0$, in units of TeV$^{-4}$ and without application of a form factor.

22 KHACHATRYAN 17m analyse electroweak production of $W\gamma$ in association with two hadronic jets, with the W boson decaying to electron or muons. Events with photon transverse momentum larger than 200 GeV and di-jet invariant mass larger than 200 GeV are selected. The W transverse momentum spectrum is analysed to set 95% C.L. limits as follows: $-77 < f_{M,0}/\Lambda^4 < 74$, $-125 < f_{M,1}/\Lambda^4 < 129$, $-26 < f_{M,2}/\Lambda^4 < 26$, $-43 < f_{M,3}/\Lambda^4 < 44$, $-40 < f_{M,4}/\Lambda^4 < 40$, $-65 < f_{M,5}/\Lambda^4 < 65$, $-129 < f_{M,6}/\Lambda^4 < 129$, $-164 < f_{M,7}/\Lambda^4 < 162$, $-5.4 < f_{T,0}/\Lambda^4 < 5.6$, $-3.7 < f_{T,1}/\Lambda^4 < 4.0$, $-11 < f_{T,2}/\Lambda^4 < 12$, $-3.8 < f_{T,5}/\Lambda^4 < 3.8$, $-2.8 < f_{T,6}/\Lambda^4 < 3.0$, $-7.3 < f_{T,7}/\Lambda^4 < 7.7$, in units of TeV$^{-4}$ and without application of a form factor.

23 SIRUNYAN 17A\d study pp collisions at $\sqrt{s} = 13$ TeV to determine the cross section of $ZZjj$ with the $Z$ decaying to $e e$ or $\mu \mu$. The $ZZ$ mass distribution is used to set upper limits on the anomalous quartic couplings. The 95% upper limits for the relevant quartic couplings in units of TeV$^{-4}$ are: $-0.46 < f_{T,0}/\Lambda^4 < 0.44$, $-0.61 < f_{T,1}/\Lambda^4 < 0.61$, $-1.2 < f_{T,2}/\Lambda^4 < 1.2$, $-0.84 < f_{T,8}/\Lambda^4 < 0.84$, $-1.8 < f_{T,9}/\Lambda^4 < 1.8$.

24 SIRUNYAN 17AR study pp collisions at $\sqrt{s} = 8$ TeV to determine the cross section of $pp \to W\gamma\gamma$ and $pp \to Z\gamma\gamma$ where $W \to \ell\nu$ and $Z \to \ell^+\ell^-$, $\ell$ being an electron or a muon. The number of W events in the $e$ and $\mu$ channels is 63 and 108 respectively, and the number of Z events in the $e$ and $\mu$ channels is 117 and 141. To increase sensitivity, the transverse momentum of the leading photon is required to be larger than 70 GeV. The 95% C.L. upper limits in units of TeV$^{-4}$ are $-701 < f_{M,2}/\Lambda^4 < 683$, $-1170 < f_{M,3}/\Lambda^4 < 1220$, $-335 < f_{T,0}/\Lambda^4 < 340$, $-44.3 < f_{T,1}/\Lambda^4 < 44.8$, $-93.8 < f_{T,2}/\Lambda^4 < 93.2$.

25 AABOUD 16E study WW production in two-photon mediated pp collisions at 8 TeV where the W boson decays into an electron or muon, probing the $\gamma\gamma$ WW vertex for anomalous quartic gauge couplings. The lepton $p_T$ is required to be larger than 30 GeV. Limits on anomalous couplings are determined from events with $p_T$ larger than 120 GeV where the aQGC effect is enhanced and the SM background reduced; in the data corresponding to an integrated luminosity of 20.2fb$^{-1}$, 1 event is selected with an expected SM background of 0.37 ± 0.13 events. The 95% C.L. limits without a form-factor cutoff ($\Lambda_{Cutoff} \to \infty$) are as follows: $-1.7 < a_0^W/\Lambda^2 < 1.7$ and $-6.4 < a_0^W/\Lambda^2 < 6.3$ in units of $10^{-6}$ GeV$^{-2}$. In terms of another set of variables: $-6.6 < f_{M,0}/\Lambda^4 < 6.6$ and $-24 < f_{M,1}/\Lambda^4 < 25$ in units of $10^{-11}$ GeV$^{-4}$.

26 AAD 16q study $Z\gamma\gamma$ production in pp collisions. In events with no additional jets, 29 (22) Z decays to electron (muon) pairs are selected, with an expected background of 3.3 ± 1.1 (6.5 ± 2.0) events, as well as 19 Z decays to neutrino pairs with an expected background of 8.3 ± 4.4 events. Analysing the photon transverse momentum distribution for $m_{\gamma\gamma}$ above 200 GeV (300 GeV) for lepton (neutrino) events, yields the 95% C.L. limits: $-1.6 \times 10^4 < f_{M,2}/\Lambda^4 < 1.6 \times 10^4$, $-2.9 \times 10^4 < f_{M,3}/\Lambda^4 < 2.7 \times 10^4$, $-0.86 \times 10^2 < f_{T,0}/\Lambda^4 < 1.03 \times 10^2$, $-0.9 \times 10^3 < f_{T,5}/\Lambda^4 < 0.68 \times 10^3$, $-0.74 \times 10^4 < f_{T,9}/\Lambda^4 < 0.74 \times 10^4$ in units of TeV$^{-4}$ and without application of a form factor $\Lambda_{FF}$.

27 KHACHATRYAN 16AX searches for anomalous $W^+W^-$ quartic gauge couplings in the two-photon-mediated process $pp \to ppWW$, assuming the $W^+W^-$ triple gauge boson couplings to be at their Standard Model values. 13 events containing an $e^\pm\mu^\pm$ pair with $p_T(e, \mu) > 30$ GeV are selected in a total luminosity of 19.7 fb$^{-1}$, with an expected $\gamma\gamma \to WW$ signal of 5.3 ± 0.1 events and an expected background of 3.9 ± 0.5 events. When combining with the data collected at 7 TeV (CHATRCHYAN 13AA), and not assuming a form factor, the following 1-parameter limits at 95% C.L. are obtained from the $p_T(e, \mu)$ spectrum: $|a_0^W/\Lambda^2| < 1.1 \times 10^{-6}$ GeV$^{-2}$ ($a_0^W = 0$), and $|a_0^W/\Lambda^2| < 4.1 \times 10^{-6}$ GeV$^{-2}$ ($a_0^W = 0$). In terms of another set of variables: $|f_{M,0}/\Lambda^4| < 4.2 \times 10^{-12}$ GeV$^{-4}$, $|f_{M,1}/\Lambda^4| < 16 \times 10^{-12}$ GeV$^{-4}$, $|f_{M,2}/\Lambda^4| < 2.1 \times 10^{-12}$ GeV$^{-4}$, $|f_{M,3}/\Lambda^4| < 7.8 \times 10^{-12}$ GeV$^{-4}$.

28 AAD 15n study $W\gamma\gamma$ events in 8 TeV pp interactions, where the W decays into an electron or a muon. The events are characterized by an isolated lepton, a missing transverse energy due to the decay neutrino, and two isolated photons, with the $p_T$ of the lepton and the photons being > 20 GeV. The number of candidate events observed in the electron channel for Njet) $\ge$ 0 and N(jet) = 0 is 47 and 15, the corresponding numbers for the muon channel being 110 and 53. The backgrounds expected are 30.2 ± 7.4, 8.7 ± 3.0, 52.1 ± 12.2, and 24.4 ± 8.3 respectively. The 95% C.L. limits on the values of the parameters $f_{T,0}/\Lambda^4$, $f_{M,2}/\Lambda^4$ and $f_{M,3}/\Lambda^4$ are $-0.9 \times 10^2$, $-0.8 \times 10^4$, and $-1.5 \times 1.4 \times 10^4$ respectively, without application of a form factor $\Lambda_{FF}$.

29 KHACHATRYAN 15D study vector-boson-scattering tagged by two jets, two same-sign charged leptons arising from $W^\pm W^\pm$ production and decay. The two jets must have a transverse momentum larger than 30 GeV, while the leptons, electrons or muons must have a transverse momentum > 20 GeV. The dijet mass is required to be > 500 GeV, the dilepton mass > 50 GeV, with additional requirement of differing from the $Z$ mass by > 15 GeV. In the two categories $W^+W^+$ and $W^+W^-$, 10 and 2 data events are observed in a data sample corresponding to an integrated luminosity of 19.4 fb$^{-1}$, with an expected background of 3.1 ± 0.6 and 2.6 ± 0.5 events. Analysing the distribution of the dilepton invariant mass, the following limits at 95% C.L. are obtained, in units of TeV$^{-4}$: $-38 < f_{S,0}/\Lambda^4 < 40$, $-118 < f_{S,1}/\Lambda^4 < 120$, $-33 < f_{M,0}/\Lambda^4 < 32$, $-44 < f_{M,1}/\Lambda^4 < 47$, $-65 < f_{M,6}/\Lambda^4 < 63$, $-70 < f_{M,7}/\Lambda^4 < 66$, $-4.2 < f_{T,0}/\Lambda^4 < 4.6$, $-1.9 < f_{T,1}/\Lambda^4 < 2.2$, $-5.2 < f_{T,2}/\Lambda^4 < 6.4$.

30 AAD 14AM analyse electroweak production of WW jet jet same-charge diboson plus two jets production, with the W bosons decaying to electron or muon, to study the quarky $WWWW$ coupling. In a kinematic region enhancing the electroweak production over the strong production, 34 events are observed in the data while 29.8 ± 2.4 events are expected with a background of 15.9 ± 1.9 events. Assuming the other QGC coupling to have the SM value of zero, the observed event yield is used to determine 95% CL limits on the quarky gauge couplings: $-0.14 < \alpha_4 < 0.16$ and $-0.23 < \alpha_5 < 0.24$.

31 CHATRCHYAN 14Q study $W^+\gamma$ production in 8 TeV pp collisions, in the single lepton final state, with $W \to \ell\nu$, $Z \to$ dijet or $W \to \ell\nu$, $W \to$ dijet, the dijet mass resolution precluding differentiation between the $W$ and $Z$. $p_T$ and pseudo-rapidity cuts are put on the lepton, the photon and the two jets to minimize backgrounds. The dijet mass is required to be between 70-100 GeV and $|\alpha_{jj}| < 1.4$. The selected number of muon (electron) events are 183 (139), with SM expectation being 194.2 ± 11.5 (147.9 ± 10.7) including signal and background. The photon $E_\gamma$ distribution is used to set limits on the anomalous quartic couplings. The following 95% CL limits are deduced (all in units of TeV$^{-2}$ or TeV$^{-4}$): $-21 < a_0^W/\Lambda^2 < 20$, $-34 < a_0^W/\Lambda^2 < 32$, $-12 < \kappa_0^W/\Lambda^2 < 10$ and $-18 < \kappa_0^W/\Lambda^2 < 17$; and $-25 < f_{T,0}/\Lambda^4 < 24$ TeV$^{-4}$.

32 ABAZOV 13D searches for anomalous $WW^{\gamma\gamma}$ quartic gauge couplings in the two-photon-mediated process $pp \to ppWW$, assuming the $W^+\gamma$ triple gauge boson couplings to be at their Standard Model values. 946 events containing an $e^+e^-$ pair with missing energy are selected in a total luminosity of 9.7 fb$^{-1}$, with an expectation of 983 ± 108 events from Standard-Model processes. The following 1-parameter limits at 95% CL are obtained: $|a_0^W/\Lambda^2| < 4.3 \times 10^{-4}$ GeV$^{-2}$ ($a_0^W = 0$), $|a_0^W/\Lambda^2| < 1.5 \times 10^{-3}$ GeV$^{-2}$ ($a_0^W = 0$).

33 CHATRCHYAN 13AA searches for anomalous $WW^{\gamma\gamma}$ quartic gauge couplings in the two-photon-mediated process $pp \to ppWW$, assuming the $W^+\gamma$ triple gauge boson couplings to be at their Standard Model values. 2 events containing an $e^\pm\mu^\pm$ pair with $p_T(e, \mu) > 30$ GeV are selected in a total luminosity of 5.05 fb$^{-1}$, with an expected $ppWW$ signal of 2.2 ± 0.4 events and an expected background of 0.84 ± 0.15 events. The following 1-parameter limits at 95% CL are obtained from the $p_T(e, \mu)$ spectrum: $|a_0^W/\Lambda^2| < 4.0 \times 10^{-6}$ GeV$^{-2}$ ($a_0^W = 0$), $|a_0^W/\Lambda^2| < 1.5 \times 10^{-5}$ GeV$^{-2}$ ($a_0^W = 0$).

34 ABBIENDI 04b select 187 $e^+e^- \to W^+W^-$ events in the C.M. energy range 180-209 GeV, where $E_\gamma > 2.5$ GeV, the photon has a polar angle $|\cos\theta_\gamma| < 0.975$ and is well isolated from the nearest jet and charged lepton, and the effective masses of both fermion-antifermion systems agree with the $W$ mass within 3 $\Gamma_W$. The measured differential cross section as a function of the photon energy and photon polar angle is used to extract the 95% CL limits: $-0.020 \text{ GeV}^{-2} < a_0^W/\Lambda^2 < 0.020 \text{ GeV}^{-2}$, $-0.053 \text{ GeV}^{-2} < a_0^W/\Lambda^2 < 0.037 \text{ GeV}^{-2}$ and $-0.16 \text{ GeV}^{-2} < a_0^W/\Lambda^2 < 0.15 \text{ GeV}^{-2}$.

35 ABBIENDI 04l select $20 e^+e^- \to \nu\bar{\nu}\gamma\gamma$ events in the energy range 180-209 GeV and 176 $e^+e^- \to q\bar{q}\gamma\gamma$ events in the energy range 130-209 GeV. These samples are used to constrain possible anomalous $W^+W^-$ and $Z\gamma\gamma$ quartic couplings. Further combining with the $W^+W^-$ sample of ABBIENDI 04b the following one-parameter 95% CL limits are obtained: $-0.007 < a_0^Z/\Lambda^2 < 0.023 \text{ GeV}^{-2}$, $-0.029 < a_0^Z/\Lambda^2 < 0.029 \text{ GeV}^{-2}$, $-0.041 < a_0^Z/\Lambda^2 < 0.044 \text{ GeV}^{-2}$, $-0.060 < a_0^W/\Lambda^2 < 0.055 \text{ GeV}^{-2}$, $-0.099 < a_0^W/\Lambda^2 < 0.093 \text{ GeV}^{-2}$.

36 In the CM energy range 183 to 209 GeV HEISTER 04a select $30 e^+e^- \to \nu\bar{\nu}\gamma\gamma$ events with two acoplanar, high energy and high transverse momentum photons. The photon-photon acoplanarity is required to be > 5°, $E_\gamma/\sqrt{s} > 0.025$ (the more energetic photon having energy > 0.2 $\sqrt{s}$), $p_T(e, \mu)/E_{\text{beam}} > 0.05$ and $|\cos\theta_\gamma| < 0.94$. A likelihood fit to the photon energy and recoil missing mass yields the following one-parameter 95% CL limits: $-0.012 < a_0^Z/\Lambda^2 < 0.019 \text{ GeV}^{-2}$, $-0.041 < a_0^Z/\Lambda^2 < 0.044 \text{ GeV}^{-2}$, $-0.060 < a_0^W/\Lambda^2 < 0.055 \text{ GeV}^{-2}$, $-0.099 < a_0^W/\Lambda^2 < 0.093 \text{ GeV}^{-2}$.

37 ABDALLAH 03i select 122 $e^+e^- \to W^+W^-$ events in the C.M. energy range 189-209 GeV, where $E_\gamma > 5$ GeV, the photon has a polar angle $|\cos\theta_\gamma| < 0.95$ and is well isolated from the nearest charged fermion. A fit to the photon energy spectra yields $a_c/\Lambda^2 = 0.000 \pm 0.019 \text{ GeV}^{-2}$, $a_0/\Lambda^2 = -0.004 \pm 0.018 \text{ GeV}^{-2}$, $a_0/\Lambda^2 = -0.007 \pm 0.019 \text{ GeV}^{-2}$, $a_n/\Lambda^2 = -0.09 \pm 0.16 \text{ GeV}^{-2}$, and $\bar{a}_n/\Lambda^2 = +0.05 \pm 0.07 \text{ GeV}^{-2}$, keeping the other parameters fixed to their Standard Model values (0). The 95% CL limits are: $-0.063 \text{ GeV}^{-2} < a_c/\Lambda^2 < +0.032 \text{ GeV}^{-2}$, $-0.020 \text{ GeV}^{-2} < a_0/\Lambda^2 < +0.020 \text{ GeV}^{-2}$, $-0.020 \text{ GeV}^{-2} < a_0/\Lambda^2 < +0.020 \text{ GeV}^{-2}$, $-0.18 \text{ GeV}^{-2} < a_n/\Lambda^2 < +0.14 \text{ GeV}^{-2}$, $-0.16 \text{ GeV}^{-2} < \bar{a}_n/\Lambda^2 < +0.17 \text{ GeV}^{-2}$.

38 ACHARD 02f select 86 $e^+e^- \to W^+W^-$ events at 192-207 GeV, where $E_\gamma > 5$ GeV and the photon is well isolated. They also select 43 acoplanar $e^+e^- \to \nu\bar{\nu}\gamma\gamma$ events in this energy range, where the photon energies are > 5 GeV and > 1 GeV and the photon polar angles are between 14° and 166°. All these 43 events are in the recoil mass region corresponding to the $Z$ (75-110 GeV). Using the shape and normalization of the photon spectra in the $W^+W^-$ events, and combining with the 42 event sample from 189 GeV data (ACCIARRI 00T), they obtain: $a_0^W/\Lambda^2 = 0.000 \pm 0.010 \text{ GeV}^{-2}$, $a_c/\Lambda^2 = -0.013 \pm 0.023 \text{ GeV}^{-2}$, and $a_n/\Lambda^2 = -0.002 \pm 0.076 \text{ GeV}^{-2}$. Further combining the analyses of $W^+W^-$ events with the low recoil mass region of $\nu\bar{\nu}\gamma\gamma$ events (including samples collected at 183 + 189 GeV), they obtain the following one-parameter 95% CL
limits: $-0.015 \text{ GeV}^{-2} < a_0/\Lambda^2 < 0.015 \text{ GeV}^{-2}$, $-0.048 \text{ GeV}^{-2} < a_c/\Lambda^2 < 0.026 \text{ GeV}^{-2}$, and $-0.14 \text{ GeV}^{-2} < a_p/\Lambda^2 < 0.13 \text{ GeV}^{-2}$.

W REFERENCES

<table><thead><tr><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>AAD</td><td>24</td><td>JHEP 2401 004</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AMOROSO</td><td>24</td><td>EPJ C84 451</td><td>S. Amoroso et al. (DESY, SACL, EDIN+)</td></tr><tr><td>PDG</td><td>24</td><td>PR D110 00001</td><td>(PDG Collab.)</td></tr><tr><td>AAD</td><td>23BH</td><td>EPJ C83 539</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>23K</td><td>PR D105 082</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAIJ</td><td>23AM</td><td>CP C47 093002</td><td>R. Aaij et al. (LHCb Collab.)</td></tr><tr><td>TUMASYAN</td><td>23AK</td><td>PR D108 032017</td><td>A. Tumasyan et al. (CMS Collab.)</td></tr><tr><td>TUMASYAN</td><td>23AM</td><td>JHEP 2307 229</td><td>A. Tumasyan et al. (CMS Collab.)</td></tr><tr><td>AAIJ</td><td>22C</td><td>JHEP 2201 036</td><td>R. Aaij et al. (LHCb Collab.)</td></tr><tr><td>AALTONEN</td><td>22</td><td>PTEP 2027 083C01</td><td>T. Aaltonen et al. (R.L. Workman et al.)</td></tr><tr><td>PDG</td><td>22</td><td>PTEP 2022 083C01</td><td></td></tr><tr><td>TUMASYAN</td><td>22AB</td><td>JHEP 2207 032</td><td>A. Tumasyan et al. (CMS Collab.)</td></tr><tr><td>TUMASYAN</td><td>22E</td><td>PR D105 052003</td><td>A. Tumasyan et al. (CMS Collab.)</td></tr><tr><td>TUMASYAN</td><td>22F</td><td>PR D105 072008</td><td>A. Tumasyan et al. (CMS Collab.)</td></tr><tr><td>AAD</td><td>21AC</td><td>EPJ C81 163</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>21BC</td><td>PR D105 072001</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>21W</td><td>JHEP 2106 003</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>21R</td><td>PL B812 135992</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>21G</td><td>PRL 126 25002</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>21I</td><td>PL B819 136409</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>21J</td><td>PL B811 13598</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>20BF</td><td>PR D105 029001</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>AABOUD</td><td>19BA</td><td>EPJ C79 884</td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>19AD</td><td>JHEP 1904 122</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>19B6</td><td>PRL 122 151802</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>19BM</td><td>PR D100 012004</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>19C</td><td>PR D100 012004</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>19CL</td><td>JHEP 1912 062</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>19CQ</td><td>PL B798 134985</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>AABOUD</td><td>18J</td><td>EPJ C78 110</td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>Also</td><td></td><td></td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>AABOUD</td><td>18Q</td><td>PR D105 032005</td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>ANDREEV</td><td>18A</td><td>EPJ C78 777</td><td>V. Andreev et al. (H1 Collab.)</td></tr><tr><td>SIRUNYAN</td><td>18BZ</td><td>EPJ C78 589</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>18CC</td><td>PRL 120 081801</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>AABOUD</td><td>17AA</td><td>PR D96 012007</td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>AABOUD</td><td>17AG</td><td>EPJ C77 646</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AABOUD</td><td>17AD</td><td>PR D105 032001</td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>AABOUD</td><td>17J</td><td>JHEP 1707 107</td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>AABOUD</td><td>17M</td><td>EPJ C77 141</td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>AABOUD</td><td>17Q</td><td>EPJ C77 367</td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>AABOUD</td><td>17S</td><td>EPJ C77 474</td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>AABOUD</td><td>17T</td><td>EPJ C77 563</td><td>M. Aaboud et al. (LHCb Collab.)</td></tr><tr><td>KHACHATRY...</td><td>17AA</td><td>PL B770 380</td><td>V. Khachatryan et al. (CMS Collab.)</td></tr><tr><td>KHACHATRY...</td><td>17M</td><td>JHEP 1706 106</td><td>V. Khachatryan et al. (CMS Collab.)</td></tr><tr><td>KHACHATRY...</td><td>17O</td><td>EPJ C77 236</td><td>V. Khachatryan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>17AD</td><td>PL B774 682</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>17A</td><td>JHEP 1710 072</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>SIRUNYAN</td><td>17X</td><td>PL B772 21</td><td>A. M. Sirunyan et al. (CMS Collab.)</td></tr><tr><td>AABOUD</td><td>16E</td><td>PR D94 032011</td><td>M. Aaboud et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>16AR</td><td>JHEP 1609 029</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>16P</td><td>PR D93 092004</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>16Q</td><td>PR D93 112002</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>16A</td><td>PL B71 030</td><td>R. Aad et al. (LHCb Collab.)</td></tr><tr><td>KHACHATRY...</td><td>16AX</td><td>JHEP 1608 119</td><td>V. Khachatryan et al. (CMS Collab.)</td></tr><tr><td>KHACHATRY...</td><td>16BI</td><td>EPJ C76 401</td><td>V. Khachatryan et al. (CMS Collab.)</td></tr><tr><td>AAD</td><td>15N</td><td>PR L15 031802</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>KHACHATRY...</td><td>15D</td><td>PRL 114 051801</td><td>V. Khachatryan et al. (CMS Collab.)</td></tr><tr><td>AAD</td><td>14AM</td><td>PL P13 141803</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>14Y</td><td>JHEP 1404 031</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AALTONEN</td><td>14D</td><td>PR D89 072003</td><td>T. Aaltonen et al. (CDF Collab.)</td></tr><tr><td>CHATRCHYAN</td><td>14AB</td><td>PR D89 092005</td><td>S. Chatrchyan et al. (CMS Collab.)</td></tr><tr><td>CHATRCHYAN</td><td>14Q</td><td>PR D90 032008</td><td>S. Chatrchyan et al. (CMS Collab.)</td></tr><tr><td>AAD</td><td>13AL</td><td>PR D87 112001</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>Also</td><td></td><td></td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>13AN</td><td>PR D87 112003</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>Also</td><td></td><td></td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>ABAZOV</td><td>13D</td><td>PR D88 012005</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>CHATRCHYAN</td><td>13AA</td><td>EPJ C137 116</td><td>S. Chatrchyan et al. (CMS Collab.)</td></tr><tr><td>CHATRCHYAN</td><td>13B</td><td>PR D105 032001</td><td>S. Chatrchyan et al. (CMS Collab.)</td></tr><tr><td>AAD</td><td>13A</td><td>PL B712 119</td><td>S. Schael et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>13C</td><td>PRL B712 289</td><td>G. Aad et al. (CMS Collab.)</td></tr><tr><td>AAD</td><td>12BX</td><td>PL B717 49</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>12CD</td><td>PRL B72 2173</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AAD</td><td>12D</td><td>PL B71 345</td><td>G. Aad et al. (ATLAS Collab.)</td></tr><tr><td>AALTONEN</td><td>12AC</td><td>PR D86 031104</td><td>T. Aaltonen et al. (CDF Collab.)</td></tr><tr><td>AALTONEN</td><td>12E</td><td>PRL 108 151803</td><td>T. Aaltonen et al. (CDF Collab.)</td></tr><tr><td>AALTONEN</td><td>12W</td><td>PR D85 032001</td><td>T. Aaltonen et al. (CDF Collab.)</td></tr><tr><td>ABAZOV</td><td>12AG</td><td>PL B718 451</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ABAZOV</td><td>12F</td><td>PRL D108 151804</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>Also</td><td></td><td></td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ABAZOV</td><td>11</td><td>PL B695 67</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ABAZOV</td><td>11AC</td><td>PRL 107 241803</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>BLINOV</td><td>11</td><td>PL B69 287</td><td>A.E. Blinov, A.S. Rudenko (NOVO)</td></tr><tr><td>CHATRCHYAN</td><td>11M</td><td>PL B701 535</td><td>S. Chatrchyan et al. (CMS Collab.)</td></tr><tr><td>AALTONEN</td><td>10K</td><td>PR D104 201801</td><td>T. Aaltonen et al. (CDF Collab.)</td></tr><tr><td>Also</td><td></td><td></td><td>T. Aaltonen et al. (CDF Collab.)</td></tr><tr><td>ABDALLAH</td><td>10</td><td>EPJ C66 35</td><td>J. Abdallah et al. (H1 Collab.)</td></tr><tr><td>AARON</td><td>09B</td><td>EPJ C64 251</td><td>F.D. Aaron et al. (D0 Collab.)</td></tr><tr><td>ABAZOV</td><td>09AB</td><td>PRL 103 141801</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ABAZOV</td><td>09AD</td><td>PR D80 053012</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ABAZOV</td><td>09AJ</td><td>PR 103 191801</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ABAZOV</td><td>09AK</td><td>PRL 103 231802</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>AALTONEN</td><td>08B</td><td>PRL 100 071801</td><td>T. Aaltonen et al. (CDF Collab.)</td></tr><tr><td>ABAZOV</td><td>08R</td><td>PRL 100 241805</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ABDALLAH</td><td>08A</td><td>EPJ C55 1</td><td>J. Abdallah et al. (DELPHI Collab.)</td></tr><tr><td>ABDALLAH</td><td>08D</td><td>EPJ C54 345</td><td>J. Abdallah et al. (DELPHI Collab.)</td></tr><tr><td>AALTONEN</td><td>07F</td><td>PR 99 151801</td><td>T. Aaltonen et al. (CDF Collab.)</td></tr><tr><td>Also</td><td></td><td></td><td>T. Aaltonen et al. (CDF Collab.)</td></tr><tr><td>AALTONEN</td><td>07L</td><td>PR D76 111103</td><td>T. Aaltonen et al. (CDF Collab.)</td></tr><tr><td>ABAZOV</td><td>07Z</td><td>PR D76 111104</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ABBIENDI</td><td>07A</td><td>PR D75 767</td><td>G. Abbiendi et al. (D0 Collab.)</td></tr><tr><td>ABAZOV</td><td>06H</td><td>PR D74 057101</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>Also</td><td></td><td></td><td>PR D74 059904(errat.) (D0 Collab.)</td></tr><tr><td>ABBIENDI</td><td>06</td><td>EPJ C45 307</td><td>G. Abbiendi et al. (OPAL Collab.)</td></tr><tr><td>ABBIENDI</td><td>06A</td><td>EPJ C45 291</td><td>G. Abbiendi et al. (OPAL Collab.)</td></tr><tr><td>ACHARD</td><td>06</td><td>EPJ C45 569</td><td>P. Achard et al. (L3 Collab.)</td></tr><tr><td>AKTAS</td><td>06</td><td>EPJ C632 35</td><td>A. Aktas et al. (H1 Collab.)</td></tr><tr><td>SCHAEL</td><td>06</td><td>EPJ C47 309</td><td>S. Schael et al. (ALEPH Collab.)</td></tr><tr><td>ABAZOV</td><td>05J</td><td>PR D71 091108</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr></tbody></table>

<table><tbody><tr><td>ABAZOV</td><td>055</td><td>PRL 95 141802</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>SCHAEL</td><td>05A</td><td>PL B614 7</td><td>S. Schael et al. (ALEPH Collab.)</td></tr><tr><td>ABOUD</td><td>04A</td><td>PR D70 09200</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ABBIENDI</td><td>04B</td><td>PL B580 17</td><td>G. Abbiendi et al. (OPAL Collab.)</td></tr><tr><td>ABBIENDI</td><td>04D</td><td>EPJ C33 463</td><td>G. Abbiendi et al. (OPAL Collab.)</td></tr><tr><td>ABBIENDI</td><td>04L</td><td>PR D70 032005</td><td>G. Abbiendi et al. (OPAL Collab.)</td></tr><tr><td>ABDALLAH</td><td>04G</td><td>EPJ C34 127</td><td>J. Abdallah et al. (DELPHI Collab.)</td></tr><tr><td>ACHARD</td><td>04H</td><td>PL B586 151</td><td>P. Achard et al. (L3 Collab.)</td></tr><tr><td>ACHARD</td><td>04J</td><td>PL B600 22</td><td>P. Achard et al. (L3 Collab.)</td></tr><tr><td>ACHARD</td><td>04A</td><td>PL B602 31</td><td>A. Heister et al. (ALEPH Collab.)</td></tr><tr><td>SCHAEL</td><td>04A</td><td>EPJ C38 147</td><td>S. Schael et al. (ALEPH Collab.)</td></tr><tr><td>ABBIENDI</td><td>03C</td><td>EPJ C26 321</td><td>G. Abbiendi et al. (OPAL Collab.)</td></tr><tr><td>ABBIENDI</td><td>03I</td><td>EPJ C31 139</td><td>J. Abdallah et al. (DELPHI Collab.)</td></tr><tr><td>ABAZOV</td><td>02D</td><td>PR D66 012001</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ABAZOV</td><td>02E</td><td>PR D66 032008</td><td>V.M. Abazov et al. (D0 Collab.)</td></tr><tr><td>ACHARD</td><td>02F</td><td>PL B527 29</td><td>P. Achard et al. (L3 Collab.)</td></tr><tr><td>CHEKANOV</td><td>02G</td><td>PL B539 197</td><td>S. Chekanov et al. (ZEUS Collab.)</td></tr><tr><td>ABBIENDI</td><td>01H</td><td>EPJ C19 229</td><td>G. Abbiendi et al. (OPAL Collab.)</td></tr><tr><td>ABREU</td><td>01I</td><td>PL B502 9</td><td>P. Abreu et al. (DELPHI Collab.)</td></tr><tr><td>AFFOLDER</td><td>01E</td><td>PR D64 052001</td><td>T. Affolder et al. (CDF Collab.)</td></tr><tr><td>ABBIENDI</td><td>00V</td><td>PL B490 71</td><td>G. Abbiendi et al. (OPAL Collab.)</td></tr><tr><td>ABBOTT</td><td>00B</td><td>PR D61 072001</td><td>B. Abbott et al. (D0 Collab.)</td></tr><tr><td>ABBOTT</td><td>00D</td><td>PL B48 9710</td><td>B. Abbott et al. (D0 Collab.)</td></tr><tr><td>ABBREU,P</td><td>00F</td><td>EPJ C18 203</td><td>P. Abreu et al. (DELPHI Collab.)</td></tr><tr><td>Also</td><td></td><td>EPJ C25 493 (errat.)</td><td>P. Abreu et al. (DELPHI Collab.)</td></tr><tr><td>ACCIARRI</td><td>00T</td><td>PL B490 187</td><td>M. Acciarri et al. (L3 Collab.)</td></tr><tr><td>AFFOLDER</td><td>00M</td><td>PL 85 3347</td><td>T. Affolder et al. (CDF Collab.)</td></tr><tr><td>BREITWEG</td><td>00L</td><td>PL B41 141</td><td>J. Breitweg et al. (DELPHI Collab.)</td></tr><tr><td>BREITWEG</td><td>00D</td><td>EPJ C12 411</td><td>J. Breitweg et al. (DELPHI Collab.)</td></tr><tr><td>EBOLI</td><td>00</td><td>MPL A15 1</td><td>O. Eboïl, M. Gonzalez-Garcia, S. Novaes</td></tr><tr><td>ABBIENDI</td><td>99N</td><td>PL B453 153</td><td>G. Abbiendi et al. (OPAL Collab.)</td></tr><tr><td>ABBOTT</td><td>99H</td><td>PR D60 052003</td><td>B. Abbott et al. (D0 Collab.)</td></tr><tr><td>ABBOTT</td><td>99C</td><td>PR D60 072002</td><td>B. Abbott et al. (D0 Collab.)</td></tr><tr><td>ABREU</td><td>99L</td><td>PL B459 382</td><td>P. Achard et al. (DELPHI Collab.)</td></tr><tr><td>ACCIARRI</td><td>99P</td><td>PL B454 386</td><td>M. Acciarri et al. (L3 Collab.)</td></tr><tr><td>ACCIARRI</td><td>99Q</td><td>PL B467 171</td><td>M. Acciarri et al. (L3 Collab.)</td></tr><tr><td>BARATE</td><td>99I</td><td>PL B453 107</td><td>R. Barate et al. (ALEPH Collab.)</td></tr><tr><td>BARATE</td><td>99L</td><td>PL B462 389</td><td>R. Barate et al. (ALEPH Collab.)</td></tr><tr><td>BARATE</td><td>99C</td><td>PL B465 349</td><td>R. Barate et al. (ALEPH Collab.)</td></tr><tr><td>BARATE</td><td>98N</td><td>PL D58 092003</td><td>P. Abreu et al. (D0 Collab.)</td></tr><tr><td>ABBOTT</td><td>98P</td><td>PR D58 012002</td><td>B. Abbott et al. (D0 Collab.)</td></tr><tr><td>ABE</td><td>98H</td><td>PR D58 031101</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ABE</td><td>98P</td><td>PR D58 091101</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ABREU</td><td>98Q</td><td>PL B416 233</td><td>P. Abreu et al. (DELPHI Collab.)</td></tr><tr><td>ABREU</td><td>98N</td><td>PL B439 209</td><td>P. Abreu et al. (DELPHI Collab.)</td></tr><tr><td>BARATE</td><td>97</td><td>PL B401 347</td><td>R. Barate et al. (ALEPH Collab.)</td></tr><tr><td>BARATE</td><td>97S</td><td>PL B415 435</td><td>R. Barate et al. (ALEPH Collab.)</td></tr><tr><td>ABACHI</td><td>95D</td><td>PRL 75 1456</td><td>S. Abachi et al. (D0 Collab.)</td></tr><tr><td>ABE</td><td>95C</td><td>PL B74 341</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ABE</td><td>95F</td><td>PL B73 936</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ABE</td><td>95P</td><td>PL R75 11</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>Also</td><td></td><td>PL D52 4784</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ABE</td><td>95W</td><td>PR D52 2624</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>Also</td><td></td><td>PL R73 220</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ABE</td><td>92E</td><td>PL D68 3398</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ABE</td><td>92I</td><td>PL 69 28</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ALITTI</td><td>92L</td><td>PL B276 365</td><td>J. Alititi et al. (UA2 Collab.)</td></tr><tr><td>ALITTI</td><td>92B</td><td>PL B276 354</td><td>J. Alititi et al. (UA2 Collab.)</td></tr><tr><td>ALITTI</td><td>92C</td><td>PL B277 194</td><td>J. Alititi et al. (UA2 Collab.)</td></tr><tr><td>ALITTI</td><td>92D</td><td>PL B277 203</td><td>J. Alititi et al. (UA2 Collab.)</td></tr><tr><td>ALITTI</td><td>92F</td><td>PL B280 137</td><td>J. Alititi et al. (UA2 Collab.)</td></tr><tr><td>SAMUEL</td><td>92P</td><td>PL B280 124</td><td>M.A. Samuel et al. (OKSU, CARL)</td></tr><tr><td>ABE</td><td>91C</td><td>PR D44 29</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ALBAJAR</td><td>91</td><td>PL B253 503</td><td>C. Albajar et al. (UA1 Collab.)</td></tr><tr><td>ALITTI</td><td>91C</td><td>ZPHY C52 209</td><td>J. Alititi et al. (UA2 Collab.)</td></tr><tr><td>SAMUEL</td><td>91P</td><td>M.A. Samuel et al. (OKSU, CARL)</td><td>M.A. Samuel et al. (OKSU, CARL)</td></tr><tr><td>Also</td><td></td><td>PL 67 2920 (errat.)</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ABE</td><td>90G</td><td>PL D5 2243</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>Also</td><td></td><td>PR D43 2070</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ALBAJAR</td><td>90B</td><td>PL B241 283</td><td>C. Albajar et al. (UA1 Collab.)</td></tr><tr><td>ALITTI</td><td>90D</td><td>PL B241 150</td><td>J. Alititi et al. (UA2 Collab.)</td></tr><tr><td>ABE</td><td>89I</td><td>PL B62 1005</td><td>F. Abe et al. (CDF Collab.)</td></tr><tr><td>ALBAJAR</td><td>89</td><td>ZPHY C44 15</td><td>C. Albajar et al. (UA1 Collab.)</td></tr><tr><td>BAUR</td><td>88</td><td>NP B308 127</td><td>U. Baur, D. Zeppenfeld (FSU, WISC)</td></tr><tr><td>GRIFOLS</td><td>88</td><td>IMP A3 225</td><td>J.A. Grifols, S. Peris, J. Sola (BARC, DESY)</td></tr><tr><td>Also</td><td></td><td>NP B197 437</td><td>J.A. Grifols, S. Peris, J. Sola (BARC, DESY)</td></tr><tr><td>ALBAJAR</td><td>87</td><td>PL P185 233</td><td>C. Albajar et al. (UA1 Collab.)</td></tr><tr><td>ANSARI</td><td>87</td><td>PL P186 440</td><td>R. Ansari et al. (UA2 Collab.)</td></tr><tr><td>GROTCH</td><td>87</td><td>PR D36 2153</td><td>H. Grotch, R.W. Robinett (PSU)</td></tr><tr><td>HAGIWARA</td><td>87</td><td>NP B282 253</td><td>K. Hagiwara et al. (KEK, UCLA, FSU)</td></tr><tr><td>VANDERBIJ</td><td>87</td><td>PL D35 1088</td><td>J.J. van der Bij (FNAL)</td></tr><tr><td>GRAS</td><td>85</td><td>PL 154B 283</td><td>A. Grau, J.A. Grifols (BARC)</td></tr><tr><td>SUZUKI</td><td>85</td><td>PL 153B 289</td><td>M. Suzuki (LBL)</td></tr><tr><td>ARNISON</td><td>84D</td><td>PL 134B 469</td><td>G.T.J. Arnison et al. (UA1 Collab.)</td></tr><tr><td>HERZOG</td><td>84</td><td>PL 148B 355</td><td>F. Herzog (WISC)</td></tr><tr><td>ARNISON</td><td>83</td><td>PL 122B 103</td><td>F. Herzog (WISC)</td></tr><tr><td>BANNER</td><td>83B</td><td>PL 122B 476</td><td>G.T.J. Arnison et al. (UA1 Collab.)</td></tr><tr><td></td><td></td><td></td><td>M. Banner et al. (UA2 Collab.)</td></tr></tbody></table>

Z

J = 1

See the related review(s):

Z Boson

Z MASS

OUR AVERAGE is given by the weighted average of the combined CDF result and the combined LEP result, assuming no correlations between CDF and LEP. The combined LEP result, 91.876 ± 0.0021 GeV, is obtained using the fit procedure and correlations as determined by the LEP Electroweak Working Group (see the note "The Z boson" and ref. LEP-SLC 06). The LEP fit is performed using the Z mass and width, the Z hadronic pole cross section, the ratios of hadronic to leptonic partial widths, and the Z pole forward-backward lepton asymmetries. This set is believed to be most free of correlations.

The Z-boson mass listed here corresponds to the mass parameter in a Breit-Wigner distribution with mass dependent width. The value is 34 MeV greater than the real part of the position of the pole (in the energy-squared plane) in the Z-boson propagator. Also the LEP experiments have generally assumed a fixed value of the $\gamma-Z$ interferences term based on the
standard model. Keeping this term as free parameter leads to a somewhat larger error on the fitted Z mass. See ACCIARRI 00q and ABBIENDI 04g for a detailed investigation of both these issues.

<table><thead><tr><th>VALUE (GeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>91.1880±0.0020 OUR AVERAGE</strong></td></tr><tr><td>91.1923±0.0071</td><td>1</td><td>AALTONEN</td><td>22</td><td>CDF E<sup>ee</sup><sub>cm</sub> = 1.8 TeV</td></tr><tr><td>91.1876±0.0021</td><td>2</td><td>LEP-SLC</td><td>06</td><td>LEP E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>91.084 ±0.107</td><td>3</td><td>ANDREEV</td><td>18A</td><td>H1 e<sup>±</sup> p</td></tr><tr><td>91.1872±0.0033</td><td>4</td><td>ABBIENDI</td><td>04G</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = LEP1 +<br>130-209 GeV</td></tr><tr><td>91.272 ±0.032 ±0.033</td><td>5</td><td>ACHARD</td><td>04C</td><td>L3 E<sup>ee</sup><sub>cm</sub> = 183-209 GeV</td></tr><tr><td>91.1852±0.0030</td><td>6</td><td>ABBIENDI</td><td>01A</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>91.1863±0.0028</td><td>7</td><td>ABREU</td><td>00F</td><td>DLPH E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>91.1898±0.0031</td><td>8</td><td>ACCIARRI</td><td>00C</td><td>L3 E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>91.1875±0.0039</td><td>9</td><td>ACCIARRI</td><td>00Q</td><td>L3 E<sup>ee</sup><sub>cm</sub> = LEP1 +<br>130-189 GeV</td></tr><tr><td>91.1885±0.0031</td><td>10</td><td>BARATE</td><td>00C</td><td>ALEP E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>91.151 ±0.008</td><td>11</td><td>MIYABAYASHI</td><td>95</td><td>TOPZ E<sup>ee</sup><sub>cm</sub> = 57.8 GeV</td></tr><tr><td>91.74 ±0.28 ±0.93</td><td>12</td><td>ALITTI</td><td>92B</td><td>UA2 E<sup>pp</sup><sub>cm</sub> = 630 GeV</td></tr><tr><td>90.9 ±0.3 ±0.2</td><td>13</td><td>ABE</td><td>89C</td><td>CDF E<sup>pp</sup><sub>cm</sub> = 1.8 TeV</td></tr><tr><td>91.14 ±0.12</td><td>14</td><td>ABRAMS</td><td>89B</td><td>MRK2 E<sup>ee</sup><sub>cm</sub> = 89-93 GeV</td></tr><tr><td>93.1 ±1.0 ±3.0</td><td>15</td><td>ALBAJAR</td><td>89</td><td>UA1 E<sup>pp</sup><sub>cm</sub> = 546,630 GeV</td></tr></tbody></table>

1 AALTONEN 22 analyse Z decays in the di-muon and di-electron channels using their full Run-II data set. They obtain Z mass values of 91192.0 ± 6.4(stat.) ± 4.0(syst.) GeV and 91194.3 ± 13.8(stat.) ± 7.6(syst.) MeV, respectively. Combining these results using the systematic uncertainty contributions and their correlations as given in AALTONEN 22, we obtain an average of 91192.3 ± 5.8(stat.) ± 4.1(syst.) MeV.

2 This result combines ABBIENDI 01A, ABREU 00F, ACCIARRI 00C, BARATE 00C, taking correlated uncertainties into account.

3 ANDREEV 18A obtain this result in a combined electroweak and QCD analysis using all deep-inelastic e⁺p and e⁻p neutral current and charged current scattering cross sections published by the H1 Collaboration, including data with longitudinally polarized lepton beams.

4 ABBIENDI 04G obtain this result using the S-matrix formalism for a combined fit to their cross section and asymmetry data at the Z peak and their data at 130-209 GeV. The authors have corrected the measurement for the 34 MeV shift with respect to the Breit-Wigner fits.

5 ACHARD 04C select e⁺e⁻ → Zγ events with hard initial-state radiation. Z decays to q ¯ q and muon pairs are considered. The fit results obtained in the two samples are found consistent to each other and combined considering the uncertainty due to ISR modelling as fully correlated.

6 ABBIENDI 01A error includes approximately 2.3 MeV due to statistics and 1.8 MeV due to LEP energy uncertainty. This result is included in the LEP average LEP-SLC 06.

7 The error includes 1.6 MeV due to LEP energy uncertainty. This result is included in the LEP average LEP-SLC 06.

8 The error includes 1.8 MeV due to LEP energy uncertainty. This result is included in the LEP average LEP-SLC 06.

9 ACCIARRI 00Q interpret the s-dependence of the cross sections and lepton forward-backward asymmetries in the framework of the S-matrix formalism. They fit to their cross section and asymmetry data at high energies, using the results of S-matrix fits to Z-ppeak data (ACCIARRI 00C) as constraints. The 130-189 GeV data constrains the γ/Z interference term. The authors have corrected the measurement for the 34.1 MeV shift with respect to the Breit-Wigner fits. The error contains a contribution of ±2.3 MeV due to the uncertainty on the γ/Z interference.

10 BARATE 00C error includes approximately 2.4 MeV due to statistics, 0.2 MeV due to experimental systematics, and 1.7 MeV due to LEP energy uncertainty. This result is included in the LEP average LEP-SLC 06.

11 MIYABAYASHI 95 combine their low energy total hadronic cross-section measurement with the ACTON 93d data and perform a fit using an S-matrix formalism. As expected, this result is below the mass values obtained with the standard Breit-Wigner parametrization.

12 Enters fit through W/Z mass ratio given in the W Particle Listings. The ALITTI 92B systematic error (±0.93) has two contributions: one (±0.92) cancels in m<sub>W</sub>/m<sub>Z</sub> and one (±0.12) is noncancelling. These were added in quadrature.

13 First error of ABE 89 is combination of statistical and systematic contributions; second is mass scale uncertainty.

14 ABRAMS 89b uncertainty includes 35 MeV due to the absolute energy measurement.

15 ALBAJAR 89 result is from a total sample of 33 Z → e⁺e⁻ events.

Z WIDTH

OUR EVALUATION is obtained using the fit procedure and correlations as determined by the LEP Electroweak Working Group (see the note "The Z boson" and ref. LEP-SLC 06). Corrections as discussed in VOUTSINAS 20 and JANOT 20 are also included.

<table><thead><tr><th>VALUE (GeV)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>2.4955±0.0023 OUR EVALUATION</strong></td></tr><tr><td>2.4955±0.0023</td><td>1</td><td>JANOT</td><td>20</td><td></td></tr><tr><td>2.4952±0.0023</td><td>2</td><td>VOUTSINAS</td><td>20</td><td></td></tr><tr><td>2.4943±0.0041</td><td>3</td><td>ABBIENDI</td><td>06</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>2.4948±0.0041</td><td>4</td><td>ABBIENDI</td><td>01A</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>2.4876±0.0041</td><td>5</td><td>ABREU</td><td>00F</td><td>DLPH E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

<table><tbody><tr><td>2.5024±0.0042</td><td>3.96M</td><td>6</td><td>ACCIARRI</td><td>00C L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>2.5025±0.0041</td><td>3.97M</td><td>7</td><td>ACCIARRI</td><td>00Q L3</td><td>E<sup>ee</sup><sub>cm</sub> = LEP1 +<br>130-189 GeV</td></tr><tr><td>2.4951±0.0043</td><td>4.57M</td><td>8</td><td>BARATE</td><td>00C ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>2.50 ±0.21 ±0.06</td><td></td><td>9</td><td>ABREU</td><td>96R DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 91.2 GeV</td></tr><tr><td>3.8 ±0.8 ±1.0</td><td>188</td><td>ABE</td><td>89C CDF</td><td>E<sup>pp</sup><sub>cm</sub> = 1.8 TeV</td></tr><tr><td>2.42 ±0.45<br>-0.35</td><td>480</td><td>10</td><td>ABRAMS</td><td>89B MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 89-93 GeV</td></tr><tr><td>2.7 ±1.2<br>-1.0</td><td>24</td><td>11</td><td>ALBAJAR</td><td>89 UA1</td><td>E<sup>pp</sup><sub>cm</sub> = 546,630 GeV</td></tr><tr><td>2.7 ±2.0 ±1.0</td><td>25</td><td>12</td><td>ANSARI</td><td>87 UA2</td><td>E<sup>pp</sup><sub>cm</sub> = 546,630 GeV</td></tr></tbody></table>

1 JANOT 20 applies a correction to LEP-SLC 06 using an updated Bhabha cross section calculation. This result also includes a correction to account for correlated luminosity bias as presented in VOUTSINAS 20.

2 VOUTSINAS 20 applies a correction to LEP-SLC 06 to account for correlated luminosity bias.

3 ABBIENDI 04G obtain this result using the S-matrix formalism for a combined fit to their cross section and asymmetry data at the Z peak and their data at 130-209 GeV. The authors have corrected the measurement for the 1 MeV shift with respect to the Breit-Wigner fits.

4 ABBIENDI 01A error includes approximately 3.6 MeV due to statistics, 1 MeV due to event selection systematics, and 1.3 MeV due to LEP energy uncertainty.

5 The error includes 1.2 MeV due to LEP energy uncertainty.

6 The error includes 1.3 MeV due to LEP energy uncertainty.

7 ACCIARRI 00q interpret the s-dependence of the cross sections and lepton forward-backward asymmetries in the framework of the S-matrix formalism. They fit to their cross section and asymmetry data at high energies, using the results of S-matrix fits to Z-ppeak data (ACCIARRI 00C) as constraints. The 130-189 GeV data constrains the γ/Z interference term. The authors have corrected the measurement for the 0.9 MeV shift with respect to the Breit-Wigner fits.

8 BARATE 00C error includes approximately 3.8 MeV due to statistics, 0.9 MeV due to experimental systematics, and 1.3 MeV due to LEP energy uncertainty.

9 ABREU 96R obtain this value from a study of the interference between initial and final state radiation in the process e⁺e⁻ → Z → µ⁺µ⁻.

10 ABRAMS 89b uncertainty includes 50 MeV due to the miniSAM background subtraction error.

11 ALBAJAR 89 result is from a total sample of 33 Z → e⁺e⁻ events.

12 Quoted values of ANSARI 87 are from direct fit. Ratio of Z and W production gives either Γ( Z ) < (1.09 ± 0.07) × Γ( W ), CL = 90% or Γ( Z ) = (0.82 +0.19 -0.11 ± 0.06) × Γ( W ). Assuming Standard-Model value Γ( W ) = 2.65 GeV then gives Γ( Z ) < 2.89 ± 0.19 or = 2.17 +0.50 -0.37 ± 0.16.

Z DECAY MODES

<table><thead><tr><th>Mode</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th></tr></thead><tbody><tr><td>Γ<sub>1</sub></td><td>e<sup>+</sup>e<sup>-</sup></td><td>( 3.3632±0.0042 ) %</td></tr><tr><td>Γ<sub>2</sub></td><td>μ<sup>+</sup>μ<sup>-</sup></td><td>( 3.3662±0.0066 ) %</td></tr><tr><td>Γ<sub>3</sub></td><td>τ<sup>+</sup>τ<sup>-</sup></td><td>( 3.3696±0.0083 ) %</td></tr><tr><td>Γ<sub>4</sub></td><td>ℓ<sup>+</sup>ℓ<sup>-</sup></td><td>[a] ( 3.3658±0.0023 ) %</td></tr><tr><td>Γ<sub>5</sub></td><td>μ<sup>+</sup>μ<sup>-</sup> μ<sup>+</sup>μ<sup>-</sup></td><td></td></tr><tr><td>Γ<sub>6</sub></td><td>ℓ<sup>+</sup>ℓ<sup>-</sup> ℓ<sup>+</sup>ℓ<sup>-</sup></td><td>[b] ( 4.55 ±0.17 ) × 10<sup>-6</sup></td></tr><tr><td>Γ<sub>7</sub></td><td>invisible</td><td>( 20.000 ±0.055 ) %</td></tr><tr><td>Γ<sub>8</sub></td><td>hadrons</td><td>( 69.911 ±0.056 ) %</td></tr><tr><td>Γ<sub>9</sub></td><td>(uū + cτ̄)/2</td><td>( 11.6 ±0.6 ) %</td></tr><tr><td>Γ<sub>10</sub></td><td>(dū + sū + bū)/3</td><td>( 15.6 ±0.4 ) %</td></tr><tr><td>Γ<sub>11</sub></td><td>cτ̄</td><td>( 12.03 ±0.21 ) %</td></tr><tr><td>Γ<sub>12</sub></td><td>bū</td><td>( 15.12 ±0.05 ) %</td></tr><tr><td>Γ<sub>13</sub></td><td>būbū</td><td>( 3.6 ±1.3 ) × 10<sup>-4</sup></td></tr><tr><td>Γ<sub>14</sub></td><td>ḡḡḡ</td><td>&lt; 1.1 %</td></tr><tr><td>Γ<sub>15</sub></td><td>π<sup>0</sup>γ</td><td>&lt; 2.01 × 10<sup>-5</sup></td></tr><tr><td>Γ<sub>16</sub></td><td>ηγ</td><td>&lt; 5.1 × 10<sup>-5</sup></td></tr><tr><td>Γ<sub>17</sub></td><td>ρ<sup>0</sup>γ</td><td>&lt; 4.0 × 10<sup>-6</sup></td></tr><tr><td>Γ<sub>18</sub></td><td>ωγ</td><td>&lt; 3.9 × 10<sup>-6</sup></td></tr><tr><td>Γ<sub>19</sub></td><td>η'(958)γ</td><td>&lt; 4.2 × 10<sup>-5</sup></td></tr><tr><td>Γ<sub>20</sub></td><td>φγ</td><td>&lt; 7 × 10<sup>-7</sup></td></tr><tr><td>Γ<sub>21</sub></td><td>γγ</td><td>&lt; 1.46 × 10<sup>-5</sup></td></tr><tr><td>Γ<sub>22</sub></td><td>π<sup>0</sup>π<sup>0</sup></td><td>&lt; 1.52 × 10<sup>-5</sup></td></tr><tr><td>Γ<sub>23</sub></td><td>γγγ</td><td>&lt; 2.2 × 10<sup>-6</sup></td></tr><tr><td>Γ<sub>24</sub></td><td>π<sup>±</sup>W<sup>∓</sup></td><td>[c] &lt; 7 × 10<sup>-5</sup></td></tr><tr><td>Γ<sub>25</sub></td><td>ρ<sup>±</sup>W<sup>∓</sup></td><td>[c] &lt; 8.3 × 10<sup>-5</sup></td></tr><tr><td>Γ<sub>26</sub></td><td>J/ψ(1S)X</td><td>( 3.51 +0.23 -0.25 ) × 10<sup>-3</sup> S=1.1</td></tr><tr><td>Γ<sub>27</sub></td><td>J/ψ(1S)γ</td><td>&lt; 1.2 × 10<sup>-6</sup></td></tr><tr><td>Γ<sub>28</sub></td><td>ψ(2S)X</td><td>( 1.60 ±0.29 ) × 10<sup>-3</sup></td></tr><tr><td>Γ<sub>29</sub></td><td>ψ(2S)γ</td><td>&lt; 2.4 × 10<sup>-6</sup></td></tr><tr><td>Γ<sub>30</sub></td><td>J/ψ(1S)ℓ<sup>+</sup>ℓ<sup>-</sup></td><td></td></tr><tr><td>Γ<sub>31</sub></td><td>J/ψ(1S)J/ψ(1S)</td><td>&lt; 2.2 × 10<sup>-6</sup></td></tr><tr><td>Γ<sub>32</sub></td><td>χ<sub>1</sub>(1P)X</td><td>( 2.9 ±0.7 ) × 10<sup>-3</sup></td></tr><tr><td>Γ<sub>33</sub></td><td>χ<sub>2</sub>(1P)X</td><td>&lt; 3.2 × 10<sup>-3</sup></td></tr><tr><td>Γ<sub>34</sub></td><td>Γ(1S) X + Γ(2S) X<br>+ Γ(3S) X</td><td>( 1.0 ±0.5 ) × 10<sup>-4</sup></td></tr><tr><td>Γ<sub>35</sub></td><td>Γ(1S) X</td><td>&lt; 4.4 × 10<sup>-5</sup></td></tr></tbody></table>
<table><tbody><tr><td>Γ<sub>36</sub></td><td>Υ(1S)γ</td><td>&lt; 1.1</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>37</sub></td><td>Υ(2S)X</td><td>&lt; 1.39</td><td>× 10<sup>-4</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>38</sub></td><td>Υ(2S)γ</td><td>&lt; 1.3</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>39</sub></td><td>Υ(3S)X</td><td>&lt; 9.4</td><td>× 10<sup>-5</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>40</sub></td><td>Υ(3S)γ</td><td>&lt; 2.4</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>41</sub></td><td>Υ(1,2,3S) Υ(1,2,3S)</td><td>&lt; 1.5</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>42</sub></td><td>D<sup>0</sup>γ</td><td>&lt; 2.2</td><td>× 10<sup>-3</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>43</sub></td><td>(D<sup>0</sup>/D̄<sup>0</sup>) X</td><td>(20.7 ±2.0)</td><td>%</td><td></td></tr><tr><td>Γ<sub>44</sub></td><td>D<sup>±</sup>X</td><td>(12.2 ±1.7)</td><td>%</td><td></td></tr><tr><td>Γ<sub>45</sub></td><td>D<sup>*</sup>(2010)<sup>±</sup>X</td><td>[c] (11.4 ±1.3)</td><td>%</td><td></td></tr><tr><td>Γ<sub>46</sub></td><td>D<sub>S1</sub>(2536)<sup>±</sup>X</td><td>(3.6 ±0.8)</td><td>× 10<sup>-3</sup></td><td></td></tr><tr><td>Γ<sub>47</sub></td><td>D<sub>S,J</sub>(2573)<sup>±</sup>X</td><td>(5.8 ±2.2)</td><td>× 10<sup>-3</sup></td><td></td></tr><tr><td>Γ<sub>48</sub></td><td>D<sup>*f</sup>(2629)<sup>±</sup>X</td><td>searched for</td><td></td><td></td></tr><tr><td>Γ<sub>49</sub></td><td>BX</td><td></td><td></td><td></td></tr><tr><td>Γ<sub>50</sub></td><td>B<sup>±</sup>X</td><td></td><td></td><td></td></tr><tr><td>Γ<sub>51</sub></td><td>B<sup>+</sup>X</td><td>[d] (6.08 ±0.13)</td><td>%</td><td></td></tr><tr><td>Γ<sub>52</sub></td><td>B<sup>0</sup><sub>S</sub>X</td><td>[d] (1.59 ±0.13)</td><td>%</td><td></td></tr><tr><td>Γ<sub>53</sub></td><td>B<sup>±</sup><sub>C</sub>X</td><td>searched for</td><td></td><td></td></tr><tr><td>Γ<sub>54</sub></td><td>Λ<sup>±</sup><sub>C</sub>X</td><td>(1.54 ±0.33)</td><td>%</td><td></td></tr><tr><td>Γ<sub>55</sub></td><td>Ξ<sup>0</sup><sub>X</sub>X</td><td>seen</td><td></td><td></td></tr><tr><td>Γ<sub>56</sub></td><td>Ξ<sub>b</sub>X</td><td>seen</td><td></td><td></td></tr><tr><td>Γ<sub>57</sub></td><td>b-baryon X</td><td>[d] (1.38 ±0.22)</td><td>%</td><td></td></tr><tr><td>Γ<sub>58</sub></td><td>anomalous γ + hadrons</td><td>[e] &lt; 3.2</td><td>× 10<sup>-3</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>59</sub></td><td>e<sup>+</sup> e<sup>-</sup>γ</td><td>[e] &lt; 5.2</td><td>× 10<sup>-4</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>60</sub></td><td>μ<sup>+</sup> μ<sup>-</sup>γ</td><td>[e] &lt; 5.6</td><td>× 10<sup>-4</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>61</sub></td><td>τ<sup>+</sup> τ<sup>-</sup>γ</td><td>[e] &lt; 7.3</td><td>× 10<sup>-4</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>62</sub></td><td>ℓ<sup>+</sup> ℓ<sup>-</sup>γγ</td><td>[f] &lt; 6.8</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>63</sub></td><td>q̄qγγ</td><td>[f] &lt; 5.5</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>64</sub></td><td>ν̄νγγ</td><td>[f] &lt; 3.1</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>65</sub></td><td>e<sup>±</sup> μ<sup>∓</sup></td><td>LF [c] &lt; 2.62</td><td>× 10<sup>-7</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>66</sub></td><td>e<sup>±</sup> τ<sup>∓</sup></td><td>LF [c] &lt; 5.0</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>67</sub></td><td>μ<sup>±</sup> τ<sup>∓</sup></td><td>LF [c] &lt; 6.5</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>68</sub></td><td>pe</td><td>L,B &lt; 1.8</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Γ<sub>69</sub></td><td>pμ</td><td>L,B &lt; 1.8</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr></tbody></table>

[a] $ℓ$ indicates each type of lepton ($e, μ$, and $τ$), not sum over them.

[b] Here $ℓ$ indicates $e$ or $μ$.

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

[d] This value is updated using the product of (i) the $Z \to b\bar{b}$ fraction from this listing and (ii) the b-hadron fraction in an unbiased sample of weakly decaying b-hadrons produced in Z-decays provided by the Heavy Flavor Averaging Group (HFLAV, http://www.slac.stanford.edu/xorg/hflav/osc/PDG_2009/#FRACZ).

[e] See the Particle Listings below for the $γ$ energy range used in this measurement.

[f] For $m_{γγ} = (60 \pm 5)$ GeV.

## Z PARTIAL WIDTHS

Γ(e⁺e⁻) Γ₁
For the LEP experiments, this parameter is not directly used in the overall fit but is derived using the fit results; see the note "The Z boson" and ref. LEP-SLC 06.

<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>83.91 ± 0.12 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>83.66 ± 0.20</td><td>137.0k</td><td>ABBIENDI</td><td>01A</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>83.54 ± 0.27</td><td>117.8k</td><td>ABREU</td><td>00F</td><td>DLPH E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>84.16 ± 0.22</td><td>124.4k</td><td>ACCIARRI</td><td>00C</td><td>L3 E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>83.88 ± 0.19</td><td></td><td>BARATE</td><td>00C</td><td>ALEP E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>82.89 ± 1.20 ± 0.89</td><td></td><td>1 ABE</td><td>95J</td><td>SLD E<sup>ee</sup><sub>cm</sub> = 91.31 GeV</td></tr></tbody></table>

¹ ABE 95J obtain this measurement from Bhabha events in a restricted fiducial region to improve systematics. They use the values 91.187 and 2.489 GeV for the Z mass and total decay width to extract this partial width.

Γ(μ⁺μ⁻) Γ₂
This parameter is not directly used in the overall fit but is derived using the fit results; see the note "The Z boson" and ref. LEP-SLC 06.

<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>83.99 ± 0.18 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>84.03 ± 0.30</td><td>182.8k</td><td>ABBIENDI</td><td>01A</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>84.48 ± 0.40</td><td>157.6k</td><td>ABREU</td><td>00F</td><td>DLPH E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>83.95 ± 0.44</td><td>113.4k</td><td>ACCIARRI</td><td>00C</td><td>L3 E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>84.02 ± 0.28</td><td></td><td>BARATE</td><td>00C</td><td>ALEP E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

Γ(τ⁺τ⁻) Γ₃
This parameter is not directly used in the overall fit but is derived using the fit results; see the note "The Z boson" and ref. LEP-SLC 06.

<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>84.08 ± 0.22 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>83.94 ± 0.41</td><td>151.5k</td><td>ABBIENDI</td><td>01A</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>83.71 ± 0.58</td><td>104.0k</td><td>ABREU</td><td>00F</td><td>DLPH E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>84.23 ± 0.58</td><td>103.0k</td><td>ACCIARRI</td><td>00C</td><td>L3 E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>84.38 ± 0.31</td><td></td><td>BARATE</td><td>00C</td><td>ALEP E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

Γ(ℓ⁺ℓ⁻) Γ₄
$ℓ$ indicates each type of lepton ($e, μ$, and $τ$), not sum over them.

In our fit Γ(ℓ⁺ℓ⁻) is defined as the partial Z width for the decay into a pair of massless charged leptons. This parameter is not directly used in the 5-parameter fit assuming lepton universality but is derived using the fit results. See the note "The Z boson" and ref. LEP-SLC 06.

<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>83.984 ± 0.086 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>83.82 ± 0.15</td><td>471.3k</td><td>ABBIENDI</td><td>01A</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>83.85 ± 0.17</td><td>379.4k</td><td>ABREU</td><td>00F</td><td>DLPH E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>84.14 ± 0.17</td><td>340.8k</td><td>ACCIARRI</td><td>00C</td><td>L3 E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>84.02 ± 0.15</td><td>500k</td><td>BARATE</td><td>00C</td><td>ALEP E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

Γ(invisible) Γ₇
The Z boson also decays to final states invisible in any detector, for example, the decay to a neutrino pair as predicted in the Standard Model. Measurements of Γ(invisible) fall into two categories: direct or indirect. Direct measurements look for final states with missing energy, missing momentum, or missing mass, corresponding to the invisible decay of a produced Z boson, including single-photon final states which arise from initial-state radiation. The indirect determination is based on Z lineshape analyses performed at the LEP collider, where the invisible decay width is calculated by subtracting all visible partial decay widths from the total decay width of the Z boson. Within the framework of the Standard Model these two determinations should be identical, but not in non-SM scenarios.

<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>499.2 ± 1.5 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>523 ± 3 ± 16</td><td></td><td>1 TUMASYAN</td><td>23E</td><td>CMS E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>499.0 ± 1.5</td><td></td><td>2 LEP-SLC</td><td>06</td><td>LEP E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>498 ± 12 ± 12</td><td>1791</td><td>3 ACCIARRI</td><td>98G</td><td>L3 E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>539 ± 26 ± 17</td><td>410</td><td>3 AKERS</td><td>95C</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>450 ± 34 ± 34</td><td>258</td><td>3 BUSKULIC</td><td>93L</td><td>ALEP E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>540 ± 80 ± 40</td><td>52</td><td>3 ADEVA</td><td>92</td><td>L3 E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>498.1 ± 2.6</td><td></td><td>4 ABBIENDI</td><td>01A</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>498.1 ± 3.2</td><td></td><td>4 ABREU</td><td>00F</td><td>DLPH E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>499.1 ± 2.9</td><td></td><td>4 ACCIARRI</td><td>00C</td><td>L3 E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>499.1 ± 2.5</td><td></td><td>4 BARATE</td><td>00C</td><td>ALEP E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ TUMASYAN 23E analyses leptonic Z decay modes, with the invisible Z decay identified by missing momentum.

² The LEP Collaborations perform a combined fit to their line-shape results and determine this quantity as a difference between the total width and the sum of all the visible widths, assuming lepton universality. This result combines ABBIENDI 01A, ABREU 00F, ACCIARRI 00C, BARATE 00C, taking correlated uncertainties into account.

³ This analysis selects single-photon events arising from initial state radiation.

⁴ This is an indirect determination of Γ(invisible) from a fit to the visible Z decay modes. It is included in the determination of the LEP average LEP-SLC 06 reported above.

Γ(hadrons) Γ₈
This parameter is not directly used in the 5-parameter fit assuming lepton universality, but is derived using the fit results. See the note "The Z boson" and ref. LEP-SLC 06.

<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>1744.4 ± 2.0 OUR FIT</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>1745.4 ± 3.5</td><td>4.10M</td><td>ABBIENDI</td><td>01A</td><td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>1738.1 ± 4.0</td><td>3.70M</td><td>ABREU</td><td>00F</td><td>DLPH E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>1751.1 ± 3.8</td><td>3.54M</td><td>ACCIARRI</td><td>00C</td><td>L3 E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>1744.0 ± 3.4</td><td>4.07M</td><td>BARATE</td><td>00C</td><td>ALEP E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

## Z BRANCHING RATIOS

OUR FIT is obtained using the fit procedure and correlations as determined by the LEP Electroweak Working Group (see the note "The Z boson" and ref. LEP-SLC 06).

Γ(μ⁺μ⁻)/Γ(e⁺e⁻) Γ₂/Γ₁

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>1.0001 ± 0.0024 OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>0.9974 ± 0.0050</td><td>1 AABOUD</td><td>17Q</td><td>ATLS E<sup>pp</sup><sub>cm</sub> = 7 TeV</td></tr><tr><td>1.0009 ± 0.0028</td><td>2 LEP-SLC</td><td>06</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ AABOUD 17Q make a precise determination of $Z \to ee$ and $Z \to μμ$ production in the lepton pseudo-rapidity range $|η| < 2.5$ and determine the ratio of the Z branching fractions $B(Z \to ee)/B(Z \to μμ) = 1.0026 \pm 0.0013 \pm 0.0048 = 1.0026 \pm 0.0050$.

² This parameter is not directly used in the overall fit but is derived using the fit results; see the note "The Z boson" and ref. LEP-SLC 06.
$$ \Gamma(\tau^{+} \tau^{-})/\Gamma(e^{+} e^{-}) \qquad \Gamma_3/\Gamma_1 $$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4"><strong>1.0020 ± 0.0032 OUR AVERAGE</strong></td></tr></tbody></table>

<table><tr><td>1.02 ± 0.06</td><td>1 AAIJ</td><td>18AR LHCB</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>1.0019 ± 0.0032</td><td>2 LEP-SLC</td><td>06</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr></table>

¹AAIJ 18AR obtain the result from the ratio of the measured $pp \to Z + X$ cross sections in the corresponding Z decay channels.

²This parameter is not directly used in the overall fit but is derived using the fit results; see the note “The Z boson” and ref. LEP-SLC 06.

$$ \Gamma(\tau^{+} \tau^{-})/\Gamma(\mu^{+} \mu^{-}) \qquad \Gamma_3/\Gamma_2 $$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4"><strong>1.0010 ± 0.0026 OUR AVERAGE</strong></td></tr></tbody></table>

<table><tr><td>1.01 ± 0.05</td><td>1 AAIJ</td><td>18AR LHCB</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>1.0010 ± 0.0026</td><td>2 LEP-SLC</td><td>06</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr></table>

¹AAIJ 18AR obtain the result from the ratio of the measured $pp \to Z + X$ cross sections in the corresponding Z decay channels.

²This parameter is not directly used in the overall fit but is derived using the fit results; see the note “The Z boson” and ref. LEP-SLC 06.

$$ \Gamma(\ell^{+} \ell^{-} \ell^{+} \ell^{-})/\Gamma_{\text{total}} \qquad \Gamma_6/\Gamma $$

Here $\ell$ indicates either $e$ or $\mu$. The branching fractions in this node are given within the phase-space defined by the requirements that (i) the 4-lepton invariant mass is between 80 GeV and 100 GeV, and (ii) any opposite-sign same-flavor lepton pair has a di-lepton invariant mass larger than 4 GeV.

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>4.55 ± 0.17 OUR AVERAGE</strong></td></tr></tbody></table>

<table><tbody><tr><td>4.41 ± 0.13 ± 0.27</td><td>1 AAD</td><td>21AQ ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>4.70 ± 0.32 ± 0.25</td><td>2 AABOUD</td><td>19N ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>4.83<sup>+0.23</sup><sub>-0.22</sub> ± 0.35</td><td>509</td><td>3 SIRUNYAN</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>4.9<sup>+0.8</sup><sub>-0.7</sub> ± 0.4</td><td>39</td><td>4 KHACHATRY...</td><td>16CC CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>4.31 ± 0.34 ± 0.17</td><td>172</td><td>AAD</td><td>14N ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 7, 8 TeV</td></tr><tr><td>4.6<sup>+1.0</sup><sub>-0.9</sub> ± 0.2</td><td>28</td><td>5 CHATRCHYAN</td><td>12BN CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 7 TeV</td></tr></tbody></table>

¹AAD 21AQ analyze differential cross-sections in four-lepton events. Based on the measured cross section in the $Z \to 4\ell$ channel, a branching fraction of $B(Z \to 4\ell) = (4.41 \pm 0.13 \pm 0.23 \pm 0.09 \pm 0.12) \times 10^{-6}$ is obtained, where the uncertainties are statistical, systematic, theory and luminosity, respectively.

²AABOUD 19n reports $(4.70 \pm 0.32 \pm 0.21 \pm 0.14) \times 10^{-6}$, where the uncertainties are statistical, systematic, and luminosity. We have combined the latter two in quadrature.

³SIRUNYAN 18BT report the $Z \to 4\ell$ branching fraction = $(4.83 \pm 0.29 \pm 0.32 \pm 0.08 \pm 0.12) \times 10^{-6}$, where the uncertainties are statistical, systematic, due to theory, and luminosity. The last three have been added in quadrature to obtain the total systematic error.

⁴KHACHATRYAN 16CC reports $(4.9 \pm 0.8 \pm 0.3 \pm 0.2 \pm 0.1) \pm 0.7 \pm 0.2 \pm 0.1 \pm 0.1) \times 10^{-6}$ value, where the uncertainties are statistical, systematic, theory, and due to luminosity. We have combined uncertainties in quadrature.

⁵CHATRCHYAN 12BN reports $(4.2 \pm 0.9 \pm 0.8 \pm 0.2) \times 10^{-6}$ value. Their result (both central value and uncertainties) is scaled up by 10% to account for the different phase-space definition used here (see RAINBOLT 19).

$$ \Gamma(\text{hadrons})/\Gamma(e^{+} e^{-}) \qquad \Gamma_8/\Gamma_1 $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>20.804 ± 0.050 OUR FIT</strong></td></tr></tbody></table>

<table><tr><td>20.902 ± 0.084</td><td>137.0k</td><td>1 ABBIENDI</td><td>01A OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.88 ± 0.12</td><td>117.8k</td><td>ABREU</td><td>00F DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.816 ± 0.089</td><td>124.4k</td><td>ACCIARRI</td><td>00C L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.677 ± 0.075</td><td></td><td>2 BARATE</td><td>00C ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr></table>

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

<table><tr><td>27.0<sup>+11.7</sup><sub>-8.8</sub></td><td>12</td><td>3 ABRAMS</td><td>89D MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 89–93 GeV</td></tr></table>

¹ABBIENDI 01A error includes approximately 0.067 due to statistics, 0.040 due to event selection systematics, 0.027 due to the theoretical uncertainty in t-channel prediction, and 0.014 due to LEP energy uncertainty.

²BARATE 00C error includes approximately 0.062 due to statistics, 0.033 due to experimental systematics, and 0.026 due to the theoretical uncertainty in t-channel prediction.

³ABRAMS 89D have included both statistical and systematic uncertainties in their quoted errors.

$$ \Gamma(\text{hadrons})/\Gamma(\mu^{+} \mu^{-}) \qquad \Gamma_8/\Gamma_2 $$

OUR FIT is obtained using the fit procedure and correlations as determined by the LEP Electroweak Working Group (see the note “The Z boson” and ref. LEP-SLC 06).

<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>20.785 ± 0.033 OUR FIT</strong></td></tr></tbody></table>

<table><tr><td>20.811 ± 0.058</td><td>182.8k</td><td>1 ABBIENDI</td><td>01A OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.65 ± 0.08</td><td>157.6k</td><td>ABREU</td><td>00F DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.861 ± 0.097</td><td>113.4k</td><td>ACCIARRI</td><td>00C L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.799 ± 0.056</td><td></td><td>2 BARATE</td><td>00C ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr></table>

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

<table><tr><td>18.9<sup>+7.1</sup><sub>-5.3</sub></td><td>13</td><td>3 ABRAMS</td><td>89D MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 89–93 GeV</td></tr></table>

¹ABBIENDI 01A error includes approximately 0.050 due to statistics and 0.027 due to event selection systematics.

²BARATE 00C error includes approximately 0.053 due to statistics and 0.021 due to experimental systematics.

³ABRAMS 89D have included both statistical and systematic uncertainties in their quoted errors.

$$ \Gamma(\text{hadrons})/\Gamma(\tau^{+} \tau^{-}) \qquad \Gamma_8/\Gamma_3 $$

OUR FIT is obtained using the fit procedure and correlations as determined by the LEP Electroweak Working Group (see the note “The Z boson” and ref. LEP-SLC 06).

<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>20.764 ± 0.045 OUR FIT</strong></td></tr></tbody></table>

<table><tr><td>20.832 ± 0.091</td><td>151.5k</td><td>1 ABBIENDI</td><td>01A OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.84 ± 0.13</td><td>104.0k</td><td>ABREU</td><td>00F DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.792 ± 0.133</td><td>103.0k</td><td>ACCIARRI</td><td>00C L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.707 ± 0.062</td><td></td><td>2 BARATE</td><td>00C ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr></table>

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

<table><tr><td>15.2<sup>+4.8</sup><sub>-3.9</sub></td><td>21</td><td>3 ABRAMS</td><td>89D MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 89–93 GeV</td></tr></table>

¹ABBIENDI 01A error includes approximately 0.055 due to statistics and 0.071 due to event selection systematics.

²BARATE 00C error includes approximately 0.054 due to statistics and 0.033 due to experimental systematics.

³ABRAMS 89D have included both statistical and systematic uncertainties in their quoted errors.

$$ \Gamma(\text{hadrons})/\Gamma(\ell^{+} \ell^{-}) \qquad \Gamma_8/\Gamma_4 $$

$\ell$ indicates each type of lepton ($e, \mu$, and $\tau$), not sum over them.

Our fit result is obtained requiring lepton universality.

<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>20.767 ± 0.025 OUR FIT</strong></td></tr></tbody></table>

<table><tr><td>20.823 ± 0.044</td><td>471.3k</td><td>1 ABBIENDI</td><td>01A OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.730 ± 0.060</td><td>379.4k</td><td>ABREU</td><td>00F DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.810 ± 0.060</td><td>340.8k</td><td>ACCIARRI</td><td>00C L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>20.725 ± 0.039</td><td>500k</td><td>2 BARATE</td><td>00C ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr></table>

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

<table><tr><td>18.9<sup>+3.6</sup><sub>-3.2</sub></td><td>46</td><td>ABRAMS</td><td>89B MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 89–93 GeV</td></tr></table>

¹ABBIENDI 01A error includes approximately 0.034 due to statistics and 0.027 due to event selection systematics.

²BARATE 00C error includes approximately 0.033 due to statistics, 0.020 due to experimental systematics, and 0.005 due to the theoretical uncertainty in t-channel prediction.

$$ \Gamma((u\bar{u}+c\bar{c})/2)/\Gamma(\text{hadrons}) \qquad \Gamma_9/\Gamma_8 $$

This quantity is the branching ratio of $Z \to \text{up-type}$ quarks to $Z \to \text{hadrons}$. Except ACKERSTAFF 97T the values of $Z \to \text{up-type}$ and $Z \to \text{down-type}$ branchings are extracted from measurements of $\Gamma(\text{hadrons})$, and $\Gamma(Z \to \gamma + \text{jets})$ where $\gamma$ is a high-energy ($>5$ or $7$ GeV) isolated photon. As the experiments use different procedures and slightly different values of $M_Z$, $\Gamma(\text{hadrons})$ and $\alpha_S$ in their extraction procedures, our average has to be taken with caution.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4"><strong>0.166 ± 0.009 OUR AVERAGE</strong></td></tr></tbody></table>

<table><tr><td>0.172<sup>+0.111</sup><sub>-0.010</sub></td><td>1 ABBIENDI</td><td>04E OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 91.2 GeV</td></tr><tr><td>0.160 ± 0.019 ± 0.019</td><td>2 ACKERSTAFF</td><td>97T OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>0.137<sup>+0.038</sup><sub>-0.054</sub></td><td>3 ABREU</td><td>95X DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>0.137 ± 0.033</td><td>4 ADRIANI</td><td>93 L3</td><td>E<sup>ee</sup><sub>cm</sub> = 91.2 GeV</td></tr></table>

¹ABBIENDI 04E select photons with energy > 7 GeV and use $\Gamma(\text{hadrons}) = 1744.4 \pm 2.0$ MeV and $\alpha_S = 0.1172 \pm 0.002$ to obtain $\Gamma_u = 300 \pm 19$ MeV.

²ACKERSTAFF 97T measure $\Gamma_u u\bar{u}/(\Gamma_d d\bar{d} + \Gamma_u u\bar{u} + \Gamma_s s\bar{s}) = 0.258 \pm 0.031 \pm 0.032$. To obtain this branching ratio authors use $R_C + R_B = 0.380 \pm 0.010$. This measurement is fully negatively correlated with the measurement of $\Gamma_d d\bar{d}/(\Gamma_d d\bar{d} + \Gamma_u u\bar{u} + \Gamma_s s\bar{s})$ given in the next data block.

³ABREU 95X use $M_Z = 91.187 \pm 0.009$ GeV, $\Gamma(\text{hadrons}) = 1725 \pm 12$ MeV and $\alpha_S = 0.123 \pm 0.005$. To obtain this branching ratio we divide their value of $C_{2/3} = 0.91 \pm 0.25$ by their value of $(3C_{1/3} + 2C_{2/3}) = 6.66 \pm 0.05$.

⁴ADRIANI 93 use $M_Z = 91.181 \pm 0.022$ GeV, $\Gamma(\text{hadrons}) = 1742 \pm 19$ MeV and $\alpha_S = 0.125 \pm 0.009$. To obtain this branching ratio we divide their value of $C_{2/3} = 0.92 \pm 0.22$ by their value of $(3C_{1/3} + 2C_{2/3}) = 6.720 \pm 0.076$.

$$ \Gamma((d\bar{d}+s\bar{s}+b\bar{b})/3)/\Gamma(\text{hadrons}) \qquad \Gamma_{10}/\Gamma_8 $$

This quantity is the branching ratio of $Z \to \text{down-type}$ quarks to $Z \to \text{hadrons}$. Except ACKERSTAFF 97T the values of $Z \to \text{up-type}$ and $Z \to \text{down-type}$ branchings are extracted from measurements of $\Gamma(\text{hadrons})$, and $\Gamma(Z \to \gamma + \text{jets})$ where $\gamma$ is a high-energy ($>5$ or $7$ GeV) isolated photon. As the experiments use different procedures and slightly different values of $M_Z$, $\Gamma(\text{hadrons})$ and $\alpha_S$ in their extraction procedures, our average has to be taken with caution.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4"><strong>0.223 ± 0.006 OUR AVERAGE</strong></td></tr></tbody></table>

<table><tr><td>0.218 ± 0.007</td><td>1 ABBIENDI</td><td>04E OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 91.2 GeV</td></tr><tr><td>0.230 ± 0.010 ± 0.010</td><td>2 ACKERSTAFF</td><td>97T OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>0.243<sup>+0.036</sup><sub>-0.026</sub></td><td>3 ABREU</td><td>95X DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88–94 GeV</td></tr><tr><td>0.243 ± 0.022</td><td>4 ADRIANI</td><td>93 L3</td><td>E<sup>ee</sup><sub>cm</sub> = 91.2 GeV</td></tr></table>

¹ABBIENDI 04E select photons with energy > 7 GeV and use $\Gamma(\text{hadrons}) = 1744.4 \pm 2.0$ MeV and $\alpha_S = 0.1172 \pm 0.002$ to obtain $\Gamma_d = 381 \pm 12$ MeV.

²ACKERSTAFF 97T measure $\Gamma_d d\bar{d}/(\Gamma_d d\bar{d} + \Gamma_u u\bar{u} + \Gamma_s s\bar{s}) = 0.371 \pm 0.016 \pm 0.016$. To obtain this branching ratio authors use $R_C + R_B = 0.380 \pm 0.010$. This measurement is fully negatively correlated with the measurement of $\Gamma_u u\bar{u}/(\Gamma_d d\bar{d} + \Gamma_u u\bar{u} + \Gamma_s s\bar{s})$ presented in the previous data block.
³ABREU 95x use $M_Z = 91.187 \pm 0.009$ GeV, $\Gamma(\text{hadrons}) = 1725 \pm 12$ MeV and $\alpha_s = 0.123 \pm 0.005$. To obtain this branching ratio we divide their value of $C_{1/3} = 1.62_{-0.17}^{+0.24}$ by their value of $(3C_{1/3} + 2C_{2/3}) = 6.66 \pm 0.05$.

⁴ADRIANI 93 use $M_Z = 91.181 \pm 0.022$ GeV, $\Gamma(\text{hadrons}) = 1742 \pm 19$ MeV and $\alpha_s = 0.125 \pm 0.009$. To obtain this branching ratio we divide their value of $C_{1/3} = 1.63_{-0.15}^{+0.15}$ by their value of $(3C_{1/3} + 2C_{2/3}) = 6.720 \pm 0.076$.

$$R_c = \Gamma(c\bar{c})/\Gamma(\text{hadrons}) \qquad \Gamma_{11}/\Gamma_8$$

OUR FIT is obtained by a simultaneous fit to several c- and b-quark measurements as explained in the note "The Z boson" and ref. LEP-SLC 06.

The Standard Model predicts $R_c = 0.1723$ for $m_t = 174.3$ GeV and $M_H = 150$ GeV.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.1721 &pm; 0.0030 OUR FIT</strong></td><td></td><td></td><td></td></tr><tr><td>0.1744 &pm; 0.0031 &pm; 0.0021</td><td>1 ABE</td><td>05F</td><td>SLD E<sup>ee</sup><sub>cm</sub>=91.28 GeV</td></tr><tr><td>0.1665 &pm; 0.0051 &pm; 0.0081</td><td>2 ABREU</td><td>00</td><td>DLPH E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>0.1698 &pm; 0.0069</td><td>3 BARATE</td><td>00B</td><td>ALEP E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>0.180 &pm; 0.011 &pm; 0.013</td><td>4 ACKERSTAFF</td><td>98E</td><td>OPAL E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>0.167 &pm; 0.011 &pm; 0.012</td><td>5 ALEXANDER</td><td>96R</td><td>OPAL E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td colspan="4">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.1623 &pm; 0.0085 &pm; 0.0209</td><td>6 ABREU</td><td>95D</td><td>DLPH E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr></tbody></table>

¹ABE 05f use hadronic Z decays collected during 1996-98 to obtain an enriched sample of cτ events using a double tag method. The single c-tag is obtained with a neural network trained to perform flavor discrimination using as input several signatures (cor- rected secondary vertex mass, vertex decay length, multiplicity and total momentum of the hemisphere). A multitag approach is used, defining 4 regions of the output value of the neural network and $R_c$ is extracted from a simultaneous fit to the count rates of the 4 different tags. The quoted systematic error includes an uncertainty of ±0.0006 due to the uncertainty on $R_b$.

²ABREU 00 obtain this result properly combining the measurement from the $D^+\pi^-$ production rate ($R_c = 0.1610 \pm 0.0104 \pm 0.0077 \pm 0.0043$ (BR)) with that from the overall charm counting ($R_c = 0.1692 \pm 0.0047 \pm 0.0063 \pm 0.0074$ (BR)) in cτ events. The sys- tematic error includes an uncertainty of ±0.0054 due to the uncertainty on the charmed hadron branching fractions.

³BARATE 00b use exclusive decay modes to independently determine the quantities $R_c \times f(c \to X)$, $X=D^0, D^+, D_s^+$, and $\Lambda_c$. Estimating $R_c \times f(c \to \Xi_c/\Omega_c) = 0.0034$, they simply sum over all the charm decays to obtain $R_c = 0.1738 \pm 0.0047 \pm 0.0088 \pm 0.0075$(BR). This is combined with all previous ALEPH measurements (BARATE 98T and BUSKULIC 94g, $R_c = 0.1681 \pm 0.0054 \pm 0.0062$) to obtain the quoted value.

⁴ACKERSTAFF 98e use an inclusive/exclusive double tag. In one jet $D^\pm$ mesons are exclusively reconstructed in several decay channels and in the opposite jet a slow pion (opposite charge inclusive $D^\pm$) tag is used. The b content of this sample is measured by the simultaneous detection of a lepton in one jet and an inclusively reconstructed $D^\pm$ meson in the opposite jet. The systematic error includes an uncertainty of ±0.006 due to the external branching ratios.

⁵ALEXANDER 96r obtain this value via direct charm counting, summing the partial contributions from $D^0, D^+, D_s^+$, and $\Lambda_c^+$, and assuming that strange-charmed baryons account for the 15% of the $\Lambda_c^+$ production. An uncertainty of ±0.005 due to the uncertainties in the charm hadron branching ratios is included in the overall systematics.

⁶ABREU 95d perform a maximum likelihood fit to the combined p and $p_T$ distributions of single and dilepton samples. The second error includes an uncertainty of ±0.0124 due to models and branching ratios.

$$R_b = \Gamma(b\bar{b})/\Gamma(\text{hadrons}) \qquad \Gamma_{12}/\Gamma_8$$

OUR FIT is obtained by a simultaneous fit to several c- and b-quark measurements as explained in the note "The Z boson" and ref. LEP-SLC 06.

The Standard Model predicts $R_b=0.21581$ for $m_t=174.3$ GeV and $M_H=150$ GeV.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.21629 &pm; 0.00066 OUR FIT</strong></td><td></td><td></td><td></td></tr><tr><td>0.21594 &pm; 0.00094 &pm; 0.00075</td><td>1 ABE</td><td>05F</td><td>SLD E<sup>ee</sup><sub>cm</sub>=91.28 GeV</td></tr><tr><td>0.2174 &pm; 0.0015 &pm; 0.0028</td><td>2 ACCIARRI</td><td>00</td><td>L3 E<sup>ee</sup><sub>cm</sub>=89-93 GeV</td></tr><tr><td>0.2178 &pm; 0.0011 &pm; 0.0013</td><td>3 ABBIENDI</td><td>99B</td><td>OPAL E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>0.21634 &pm; 0.00067 &pm; 0.00060</td><td>4 ABREU</td><td>99B</td><td>DLPH E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>0.2159 &pm; 0.0009 &pm; 0.0011</td><td>5 BARATE</td><td>97F</td><td>ALEP E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td colspan="4">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>0.2145 &pm; 0.0089 &pm; 0.0067</td><td>6 ABREU</td><td>95D</td><td>DLPH E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>0.219 &pm; 0.006 &pm; 0.005</td><td>7 BUSKULIC</td><td>94G</td><td>ALEP E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>0.251 &pm; 0.049 &pm; 0.030</td><td>8 JACOBSEN</td><td>91</td><td>MRK2 E<sup>ee</sup><sub>cm</sub>=91 GeV</td></tr></tbody></table>

¹ABE 05f use hadronic Z decays collected during 1996-98 to obtain an enriched sample of b\bar{b} events using a double tag method. The single b-tag is obtained with a neural network trained to perform flavor discrimination using as input several signatures (cor- rected secondary vertex mass, vertex decay length, multiplicity and total momentum of the hemisphere; the key tag is obtained requiring the secondary vertex corrected mass to be above the D-meson mass). ABE 05f obtain $R_b = 0.21604 \pm 0.00098 \pm 0.00074$ where the systematic error includes an uncertainty of ±0.00012 due to the uncertainty on $R_c$. The value reported here is obtained properly combining with ABE 98d. The quoted systematic error includes an uncertainty of ±0.00012 due to the uncertainty on $R_c$.

²ACCIARRI 00 obtain this result using a double-tagging technique, with a high $p_T$ lepton tag and an impact parameter tag in opposite hemispheres.

³ABBIENDI 99b tag $Z \to b\bar{b}$ decays using leptons and/or separated decay vertices. The b-tagging efficiency is measured directly from the data using a double-tagging technique.

⁴ABREU 99b obtain this result combining in a multivariate analysis several tagging meth- ods (impact parameter and secondary vertex reconstruction, complemented by event

shape variables). For $R_c$ different from its Standard Model value of 0.172, $R_b$ varies as $-0.024 \times (R_c - 0.172)$.

⁵BARATE 97f combine the lifetime-mass hemisphere tag (BARATE 97e) with event shape information and lepton tag to identify $Z \to b\bar{b}$ candidates. They further use c- and uds-selection tags to identify the background. For $R_c$ different from its Standard Model value of 0.172, $R_b$ varies as $-0.019 \times (R_c - 0.172)$.

⁶ABREU 95d perform a maximum likelihood fit to the combined p and $p_T$ distributions of single and dilepton samples. The second error includes an uncertainty of ±0.0023 due to models and branching ratios.

⁷BUSKULIC 94g perform a simultaneous fit to the p and $p_T$ spectra of both single and dilepton events.

⁸JACOBSEN 91 tagged $b\bar{b}$ events by requiring coincidence of ≥ 3 tracks with significant impact parameters using vertex detector. Systematic error includes lifetime and decay uncertainties (±0.014).

$$\Gamma(b\bar{b}b\bar{b})/\Gamma(\text{hadrons}) \qquad \Gamma_{13}/\Gamma_8$$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>5.2 &pm; 1.9 OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>3.6 &pm; 1.7 &pm; 2.7</td><td>1 ABBIENDI</td><td>01G</td><td>OPAL E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>6.0 &pm; 1.9 &pm; 1.4</td><td>2 ABREU</td><td>99U</td><td>DLPH E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr></tbody></table>

¹ABBIENDI 01g use a sample of four-jet events from hadronic Z decays. To enhance the $b\bar{b}b\bar{b}$ signal, at least three of the four jets are required to have a significantly detached secondary vertex.

²ABREU 99u force hadronic Z decays into 3 jets to use all the available phase space and require a b tag for every jet. This decay mode includes primary and secondary 4b production, e.g. from gluon splitting to $b\bar{b}$.

$$\Gamma(gg)/\Gamma(\text{hadrons}) \qquad \Gamma_{14}/\Gamma_8$$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;1.6 &times; 10<sup>-2</sup></strong></td><td>95</td><td>1 ABREU</td><td>96s</td><td>DLPH E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr></tbody></table>

¹This branching ratio is slightly dependent on the jet-finder algorithm. The value we quote is obtained using the JADE algorithm, while using the DURHAM algorithm ABREU 96s obtain an upper limit of $1.5 \times 10^{-2}$.

$$\Gamma(\pi^0\gamma)/\Gamma_{\text{total}} \qquad \Gamma_{15}/\Gamma$$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;2.01 &times; 10<sup>-5</sup></strong></td><td>95</td><td>AALTONEN</td><td>14E</td><td>CDF E<sup>pp</sup><sub>cm</sub>=1.96 TeV</td></tr><tr><td>&lt;5.2 &times; 10<sup>-5</sup></td><td>95</td><td>1 ACCIARRI</td><td>95G</td><td>L3 E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>&lt;5.5 &times; 10<sup>-5</sup></td><td>95</td><td>ABREU</td><td>94B</td><td>DLPH E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>&lt;2.1 &times; 10<sup>-4</sup></td><td>95</td><td>DECAMP</td><td>92</td><td>ALEP E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>&lt;1.4 &times; 10<sup>-4</sup></td><td>95</td><td>AKRAWY</td><td>91F</td><td>OPAL E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr></tbody></table>

¹This limit is for both decay modes $Z \to \pi^0\gamma/\gamma\gamma$ which are indistinguishable in ACCIA- RRI 95c.

$$\Gamma(\eta\gamma)/\Gamma_{\text{total}} \qquad \Gamma_{16}/\Gamma$$

<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;7.6 &times; 10<sup>-5</sup></td><td>95</td><td>ACCIARRI</td><td>95G</td><td>L3 E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>&lt;8.0 &times; 10<sup>-5</sup></td><td>95</td><td>ABREU</td><td>94B</td><td>DLPH E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>&lt;5.1 &times; 10<sup>-5</sup></td><td>95</td><td>DECAMP</td><td>92</td><td>ALEP E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr><tr><td>&lt;2.0 &times; 10<sup>-4</sup></td><td>95</td><td>AKRAWY</td><td>91F</td><td>OPAL E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr></tbody></table>

$$\Gamma(\rho^0\gamma)/\Gamma_{\text{total}} \qquad \Gamma_{17}/\Gamma$$

<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><strong>&lt;4.0 &times; 10<sup>-6</sup></strong></td><td>95</td><td>12.5k</td><td>1 AABOUD</td><td>18AU</td><td>ATLS E<sup>pp</sup><sub>cm</sub>=13 TeV</td></tr></tbody></table>

¹AABOUD 18AU search for the $Z \to \rho\gamma$ decay mode where the $\rho$ is identified through its decay $\rho \to \pi^+\pi^-$. In the data corresponding to 32.3 fb$^{-1}$, 12,583 events are selected for 635 < m($\pi^+\pi^-$) < 915 MeV. See erratum AABOUD 23A.

$$\Gamma(\omega\gamma)/\Gamma_{\text{total}} \qquad \Gamma_{18}/\Gamma$$

<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;3.9 &times; 10<sup>-6</sup></td><td>95</td><td>AAD</td><td>23BS</td><td>ATLS E<sup>pp</sup><sub>cm</sub>=13 TeV</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •
&lt;6.5 &times; 10<sup>-4</sup> 95 ABREU 94B DLPH E<sup>ee</sup><sub>cm</sub>=88-94 GeV

$$\Gamma(\eta'(958)\gamma)/\Gamma_{\text{total}} \qquad \Gamma_{19}/\Gamma$$

<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;4.2 &times; 10<sup>-5</sup></td><td>95</td><td>DECAMP</td><td>92</td><td>ALEP E<sup>ee</sup><sub>cm</sub>=88-94 GeV</td></tr></tbody></table>

$$\Gamma(\phi\gamma)/\Gamma_{\text{total}} \qquad \Gamma_{20}/\Gamma$$

<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;7 &times; 10<sup>-7</sup></td><td>95</td><td>3.3k</td><td>1 AABOUD</td><td>18AU</td><td>ATLS E<sup>pp</sup><sub>cm</sub>=13 TeV</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •
&lt;8.3 &times; 10<sup>-6</sup> 95 1.0k 2 AABOUD 16K ATLS E<sup>ee</sup><sub>cm</sub>=13 TeV

¹AABOUD 18AU search for the $Z \to \phi\gamma$ decay mode where the $\phi$ is identified through its decay $\phi \to K^+K^-$. In the data corresponding to 32.3 fb$^{-1}$, 3,364 events are selected for 1012 < m($K^+K^-$) < 1028 MeV. See erratum AABOUD 23A.

²AABOUD 16K search for the $Z \to \phi\gamma$ decay mode where the $\phi$ is identified through its decay into $K^+K^-$. In the data corresponding to a total luminosity of 2.7 fb$^{-1}$, 1065 events are selected and their $K^+K^-\gamma$ invariant mass spectrum is analyzed.
$$\Gamma(\gamma\gamma)/\Gamma_{\text{total}}$$

This decay would violate the Landau-Yang theorem.

<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;1.46 &times; 10<sup>-5</sup></td><td>95</td><td>AALTONEN</td><td>14E CDF</td><td>E<sup>pp</sup><sub>cm</sub> = 1.96 TeV</td></tr><tr><td>&lt;5.2 &times; 10<sup>-5</sup></td><td>95</td><td>1 ACCIARRI</td><td>95G L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>&lt;5.5 &times; 10<sup>-5</sup></td><td>95</td><td>ABREU</td><td>94B DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>&lt;1.4 &times; 10<sup>-4</sup></td><td>95</td><td>AKRAWY</td><td>91F OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ This limit is for both decay modes $Z \to \pi^0\gamma/\gamma\gamma$ which are indistinguishable in ACCIA-RRI 95G.

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

<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;1.52 &times; 10<sup>-5</sup></td><td>95</td><td>AALTONEN</td><td>14E CDF</td><td>E<sup>pp</sup><sub>cm</sub> = 1.96 TeV</td></tr></tbody></table>

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

<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;2.2 &times; 10<sup>-6</sup></td><td>95</td><td>AAD</td><td>16L ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr><tr><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>95</td><td>1 ACCIARRI</td><td>95C L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>&lt;1.7 &times; 10<sup>-5</sup></td><td>95</td><td>1 ABREU</td><td>94B DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>&lt;6.6 &times; 10<sup>-5</sup></td><td>95</td><td>AKRAWY</td><td>91F OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ Limit derived in the context of composite Z model.

$$\Gamma(\pi^{+}W^{\mp})/\Gamma_{\text{total}}$$

The value is for the sum of the charge states indicated.

<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 &times; 10<sup>-5</sup></td><td>95</td><td>DECAMP</td><td>92</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

$$\Gamma(\rho^{+}W^{\mp})/\Gamma_{\text{total}}$$

The value is for the sum of the charge states indicated.

<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;8.3 &times; 10<sup>-5</sup></td><td>95</td><td>DECAMP</td><td>92</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

$$\Gamma(J/\psi(1S)X)/\Gamma_{\text{total}}$$

<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>

³.51 $\pm 0.23_{-0.25}^+ $ OUR AVERAGE Error includes scale factor of 1.1.

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>3.21 $\pm 0.21_{-0.28}^+ $</td><td>553</td><td>1 ACCIARRI</td><td>99F L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>3.9 $\pm 0.2$ $\pm 0.3$</td><td>511</td><td>2 ALEXANDER</td><td>96B OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>3.73 $\pm 0.39 \pm 0.36$</td><td>153</td><td>3 ABREU</td><td>94P DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ACCIARRI 99F combine $\mu^+\mu^-$ and $e^+e^-$ $J/\psi(1S)$ decay channels. The branching ratio for prompt $J/\psi(1S)$ production is measured to be $(2.1 \pm 0.6) \pm 0.4_{-0.2}^{+0.4}(\text{theor.}) \times 10^{-4}$.

² ALEXANDER 96B identify $J/\psi(1S)$ from the decays into lepton pairs. $(4.8 \pm 2.4)\%$ of this branching ratio is due to prompt $J/\psi(1S)$ production (ALEXANDER 96N).

³ Combining $\mu^+\mu^-$ and $e^+e^-$ channels and taking into account the common systematic errors. $(7.7 \pm 6.3_{-5.4}^{+5.4})\%$ of this branching ratio is due to prompt $J/\psi(1S)$ production.

$$\Gamma(J/\psi(1S)\gamma)/\Gamma_{\text{total}}$$

<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 &times; 10<sup>-6</sup></td><td>95</td><td>AAD</td><td>23CD ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>&lt;1.4 &times; 10<sup>-6</sup></td><td>95</td><td>1 SIRUNYAN</td><td>19AJ CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>&lt;2.3 &times; 10<sup>-6</sup></td><td>95</td><td>2 AABOUD</td><td>18BL ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>&lt;2.6 &times; 10<sup>-6</sup></td><td>95</td><td>3 AAD</td><td>15I ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr></tbody></table>

¹ SIRUNYAN 19AJ study $Z \to J/\psi\gamma$ with $J/\psi \to \mu^+\mu^-$. Candidate events are selected by requiring a pair of oppositely charged muons and a well isolated photon. The leading (subleading) muon is required to have a transverse momentum larger than 20 GeV (4 GeV), while the photon must have a transverse energy larger than 33 GeV. Requiring the invariant mass of the $\mu\mu$ ($\mu\mu\gamma$) system in the range $3.0 \sim 3.2$ (81 to 101) GeV, selects 183 data events which is consistent with the expected background. The 95% C.L. limit on the Z branching fraction is obtained assuming the $J/\psi$ to be unpolarized.

² AABOUD 18BL study $Z \to J/\psi\gamma$ in 13 TeV pp interactions. Two triggers were used: isolated photon of $p_T > 35(25)$ GeV and a muon with $p_T > 18(24)$ GeV. The $J/\psi$ is detected via its dimuon decay and it is required that the azimuthal angle between the photon and the $J/\psi$ in the plane transverse to the beam direction is $> \pi/2$. The number of observed/expected background events is 92/89 $\pm 6$ in the dimuon mass range 2.9-3.3 GeV leading to the quoted 95% C.L. limit.

³ AAD 15I use events with the highest $p_T$ muon in the pair required to have $p_T > 20$ GeV, the dimuon mass required to be within 0.2 GeV of the $J/\psi(1S)$ mass and it's transverse momentum required to be > 36 GeV. The photon is also required to have its $p_T > 36$ GeV.

$$\Gamma(\psi(2S)X)/\Gamma_{\text{total}}$$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.60 $\pm 0.29 $ OUR AVERAGE</td><td>39</td><td>1 ACCIARRI</td><td>97J L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>1.6 $\pm 0.3$ $\pm 0.2$</td><td>46.9</td><td>2 ALEXANDER</td><td>96B OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>1.60 $\pm 0.73 \pm 0.33$</td><td>5.4</td><td>3 ABREU</td><td>94P DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ACCIARRI 97J measure this branching ratio via the decay channel $\psi(2S) \to \ell^+\ell^- (\ell = \mu, e)$.

² ALEXANDER 96B measure this branching ratio via the decay channel $\psi(2S) \to J/\psi\pi^+\pi^-$, with $J/\psi \to \ell^+\ell^-\ell^+\ell^-$.

³ ABREU 94P measure this branching ratio via decay channel $\psi(2S) \to J/\psi\pi^+\pi^-$, with $J/\psi \to \mu^+\mu^-\mu^+\mu^-\mu^-$.

$$\Gamma(\psi(2S)\gamma)/\Gamma_{\text{total}}$$

<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;2.4 &times; 10<sup>-6</sup></td><td>95</td><td>AAD</td><td>23CD ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr></tbody></table>

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

<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;4.5 &times; 10<sup>-6</sup></td><td>95</td><td>1 AABOUD</td><td>18BL ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr></tbody></table>

¹ AABOUD 18BL study $Z \to \psi(2S)\gamma$ in 13 TeV pp interactions. Two triggers were used: isolated photon of $p_T > 35(25)$ GeV and a muon with $p_T > 18(24)$ GeV. The $\psi(2S)$ is detected via its dimuon decay and it is required that the azimuthal angle between the photon and the $\psi(2S)$ in the plane transverse to the beam direction is $> \pi/2$. The number of observed/expected background events is 43/42 $\pm 5$ in the dimuon mass range 3.5-3.9 GeV leading to the quoted 95% C.L. limit.

$$\Gamma(J/\psi(1S)\ell^+\ell^-)/\Gamma(\mu^+\mu^-\mu^+\mu^-)$$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.67 $\pm 0.18 \pm 0.05$</td><td>1 SIRUNYAN</td><td>18DZ CMS</td><td>pp at 13 TeV</td><td></td></tr></tbody></table>

¹ SIRUNYAN 18DZ observe the decay $Z \to \psi\ell^+\ell^-$ in pp collisions at $\sqrt{s} = 13$ TeV, where $\psi$ includes $J/\psi$ as well as $\psi(2S) \to J/\psi X$, and $\ell^+\ell^-$ represents an electron or muon pair while the $J/\psi$ is detected via its $\mu^+\mu^-$ decay channel. To reduce systematic errors they determine the ratio of the branching fraction of this decay to that of $Z \to \mu^+\mu^-\mu^+\mu^-$ within phase-space cuts imposed on lepton transverse momentum and pseudo rapidity, dilepton invariant mass, and $J/\psi$ transverse momentum. The number of selected $\psi\mu^+\mu^-$ ($\psi e^+e^-$) candidate events is 29 (18). Analyzing the $\mu^+\mu^-$ and $\mu^+\mu^-\ell^+\ell^-$ invariant mass distributions, a yield of 13.0 $\pm 3.9$ (11.2 $\pm 3.4$) events is obtained. The ratio of the branching fractions is determined as $0.67 \pm 0.18 \pm 0.05$ within the selected phase-space cuts. Assuming extrapolation to full phase space cancels in the ratio, and using their measured value of $B(Z \to \mu^+\mu^-\mu^+\mu^-) = (1.20 \pm 0.08) \times 10^{-6}$, they estimate $B(Z \to J/\psi\ell^+\ell^-) = 8 \times 10^{-7}$.

$$\Gamma(J/\psi(1S)J/\psi(1S))/\Gamma_{\text{total}}$$

<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;2.2 &times; 10<sup>-6</sup></td><td>95</td><td>189</td><td>1 SIRUNYAN</td><td>19BR CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr></tbody></table>

¹ SIRUNYAN 19BR search for $Z$ decays to a pair of $J/\psi$ mesons in the channel $J/\psi \to \mu^+\mu^-$. The invariant masses of the higher/lower-$p_T$ $J/\psi$ candidates have to be within 0.1/0.15 GeV of the nominal $J/\psi$ mass. A total of 189 events are selected in the 40-140 GeV 4-muon muon mass range. An un-binned extended maximum likelihood fit leads to the 95% C.L. upper limit, obtained assuming the $J/\psi$ mesons to be unpolarized.

$$\Gamma(\chi_{c1}(1P)X)/\Gamma_{\text{total}}$$

<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>

².9 $\pm 0.7$ OUR AVERAGE

<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>2.7 $\pm 0.6 \pm 0.5$</td><td>33</td><td>1 ACCIARRI</td><td>97J L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>5.0 $\pm 2.1_{-0.9}^{+1.5}$</td><td>6.4</td><td>2 AABREU</td><td>94P DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ACCIARRI 97J measure this branching ratio via the decay channel $\chi_{c1} \to J/\psi + \gamma$, with $J/\psi \to \ell^+\ell^- (\ell = \mu, e)$. The $M(\ell^+\ell^-\gamma) - M(\ell^+\ell^-)$ mass difference spectrum is fitted with two gaussian shapes for $\chi_{c1}$ and $\chi_{c2}$.

² This branching ratio is measured via the decay channel $\chi_{c1} \to J/\psi + \gamma$, with $J/\psi \to \mu^+\mu^-\mu^+\mu^-\mu^-$.

$$\Gamma(\chi_{c2}(1P)X)/\Gamma_{\text{total}}$$

<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;3.2 &times; 10<sup>-3</sup></td><td>90</td><td>1 ACCIARRI</td><td>97J L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ACCIARRI 97J derive this limit via the decay channel $\chi_{c2} \to J/\psi + \gamma$, with $J/\psi \to \ell^+\ell^- (\ell = \mu, e)$. The $M(\ell^+\ell^-\gamma) - M(\ell^+\ell^-)$ mass difference spectrum is fitted with two gaussian shapes for $\chi_{c1}$ and $\chi_{c2}$.

$$\Gamma(\gamma(1S)X + \gamma(2S)X + \gamma(3S)X)/\Gamma_{\text{total}}$$

<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><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>1.0 $\pm 0.4 \pm 0.22$</td><td>6.4</td><td>1 ALEXANDER</td><td>96F L3</td><td>OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ALEXANDER 96F identify the $\gamma$ (which refers to any of the three lowest bound states) through its decay into $e^+e^-$ and $\mu^+\mu^-$. The systematic error includes an uncertainty of $\pm 0.2$ due to the production mechanism.

$$\Gamma(\gamma(1S)X)/\Gamma_{\text{total}}$$

<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 &times; 10<sup>-5</sup></td><td>95</td><td>1 ACCIARRI</td><td>99F L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ACCIARRI 99F search for $\gamma(1S)$ through its decay into $\ell^+\ell^- (\ell = e \text{ or } \mu)$.

$$\Gamma(\gamma(1S)\gamma)/\Gamma_{\text{total}}$$

<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;1.1 &times; 10<sup>-6</sup></td><td>95</td><td>AAD</td><td>23CD ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr></tbody></table>

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

<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 &times; 10<sup>-6</sup></td><td>95</td><td>1 AABOUD</td><td>18BL ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>&lt;3.4 &times; 10<sup>-6</sup></td><td>95</td><td>2 AAD</td><td>15I ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr></tbody></table>

¹ AABOUD 18BL study $Z \to \gamma(1S)\gamma$ in 13 TeV pp interactions. Two triggers were used: isolated photon of $p_T > 35(25)$ GeV and a muon with $p_T > 18(24)$ GeV. The $\gamma(1S)$ is detected via its dimuon decay and it is required that the azimuthal angle between the photon and the $\gamma(1S)$ in the plane transverse to the beam direction is $> \pi/2$. The number of observed/expected background events is 115/126 $\pm 8$ in the dimuon mass range 9.0-10.0 GeV leading to the quoted 95% C.L. limit.

² AAD 15I use events with the highest $p_T$ muon in the pair required to have $p_T > 20$ GeV, the dimuon mass required to be in the range 8-12 GeV and it's transverse momentum required to be > 36 GeV. The photon is also required to have its $p_T > 36$ GeV.
$$ \Gamma(\mathcal{T}(2S)X)/\Gamma_{\text{total}} \quad \Gamma_{37/\Gamma} $$

<table><thead><tr><th>VALUE</th><th>CL%</th></tr></thead><tbody><tr><td>&lt;13.9 × 10<sup>-5</sup></td><td>95</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 ACCIARRI</td><td>97R</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ACCIARRI 97R search for $\mathcal{T}(2S)$ through its decay into $\ell^+\ell^-$ ($\ell = e$ or $\mu$).

$$ \Gamma(\mathcal{T}(2S)\gamma)/\Gamma_{\text{total}} \quad \Gamma_{38/\Gamma} $$

<table><thead><tr><th>VALUE</th><th>CL%</th></tr></thead><tbody><tr><td>&lt;1.3 × 10<sup>-6</sup></td><td>95</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>AAD</td><td>23CD ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr></tbody></table>

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

<table><thead><tr><th>&lt;1.7 × 10<sup>-6</sup></th><th>95</th></tr></thead><tbody><tr><td>1 AABOUD</td><td>18BL ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>&lt;6.5 × 10<sup>-6</sup></td><td>95</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 AABOUD</td><td>18BL ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>2 AAD</td><td>15I ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr></tbody></table>

¹ AABOUD 18BL study $Z \to \mathcal{T}(2S)\gamma$ in 13 TeV $pp$ interactions. Two triggers were used: isolated photon of $p_T > 35(25)$ GeV and a muon with $p_T > 18(24)$ GeV. The $\mathcal{T}(2S)$ is detected via its dimuon decay and it is required that the azimuthal angle between the photon and the $\mathcal{T}(2S)$ in the plane transverse to the beam direction is $> \pi/2$. The number of observed/expected background events is 106/121 ± 8 in the dimuon mass range 9.5–10.5 GeV leading to the quoted 95% C.L. limit.

² AAD 15i use events with the highest $p_T$ muon in the pair required to have $p_T > 20$ GeV, the dimuon mass required to be in the range 8–12 GeV and it's transverse momentum required to be > 36 GeV. The photon is also required to have its $p_T > 36$ GeV.

$$ \Gamma(\mathcal{T}(3S)X)/\Gamma_{\text{total}} \quad \Gamma_{39/\Gamma} $$

<table><thead><tr><th>VALUE</th><th>CL%</th></tr></thead><tbody><tr><td>&lt;9.4 × 10<sup>-5</sup></td><td>95</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 ACCIARRI</td><td>97R</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ACCIARRI 97R search for $\mathcal{T}(3S)$ through its decay into $\ell^+\ell^-$ ($\ell = e$ or $\mu$).

$$ \Gamma(\mathcal{T}(3S)\gamma)/\Gamma_{\text{total}} \quad \Gamma_{40/\Gamma} $$

<table><thead><tr><th>VALUE</th><th>CL%</th></tr></thead><tbody><tr><td>&lt;2.4 × 10<sup>-6</sup></td><td>95</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>AAD</td><td>23CD ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr></tbody></table>

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

<table><thead><tr><th>&lt;4.8 × 10<sup>-6</sup></th><th>95</th></tr></thead><tbody><tr><td>1 AABOUD</td><td>18BL ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr><tr><td>&lt;5.4 × 10<sup>-6</sup></td><td>95</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2 AAD</td><td>15I ATLS</td><td>E<sup>pp</sup><sub>cm</sub> = 8 TeV</td></tr></tbody></table>

¹ AABOUD 18BL study $Z \to \mathcal{T}(3S)\gamma$ in 13 TeV $pp$ interactions. Two triggers were used: isolated photon of $p_T > 35(25)$ GeV and a muon with $p_T > 18(24)$ GeV. The $\mathcal{T}(3S)$ is detected via its dimuon decay and it is required that the azimuthal angle between the photon and the $\mathcal{T}(3S)$ in the plane transverse to the beam direction is $> \pi/2$. The number of observed/expected background events is 112/113 ± 8 in the dimuon mass range 10.0–11.0 GeV leading to the quoted 95% C.L. limit.

² AAD 15i use events with the highest $p_T$ muon in the pair required to have $p_T > 20$ GeV, the dimuon mass required to be in the range 8–12 GeV and it's transverse momentum required to be > 36 GeV. The photon is also required to have its $p_T > 36$ GeV.

$$ \Gamma(\mathcal{T}(1,2,3S)\mathcal{T}(1,2,3S))/\Gamma_{\text{total}} \quad \Gamma_{41/\Gamma} $$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>EVTS</th></tr></thead><tbody><tr><td>&lt;1.5 × 10<sup>-6</sup></td><td>95</td><td>106</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 SIRUNYAN</td><td>19BR CMS</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr></tbody></table>

¹ SIRUNYAN 19BR search for $Z$ decays to a pair of $\mathcal{T}$ mesons in the channel $\mathcal{T} \to \mu^+\mu^-$. The invariant mass of the $\mathcal{T}$ candidates has to be in the range of 8.5 to 11 GeV. A total of 106 events are selected in the 20–140 GeV 4-muon invariant mass range. An un-binned extended maximum likelihood fit leads to the 95% C.L. upper limit, obtained assuming the $\mathcal{T}$ mesons to be unpolarised.

$$ \Gamma(D^0\gamma)/\Gamma(\mu^+\mu^-) \quad \Gamma_{42/\Gamma} $$

<table><thead><tr><th>VALUE</th><th>CL%</th></tr></thead><tbody><tr><td>&lt;6.4 × 10<sup>-2</sup></td><td>95</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 AAJ</td><td>23AM LHCB</td><td>E<sup>pp</sup><sub>cm</sub> = 13 TeV</td></tr></tbody></table>

¹ AAJ 23AM also quotes the branching fraction limit $B(Z \to D^0\gamma) < 2.1 \times 10^{-3}$, using the known $Z \to \mu\mu$ branching fraction.

$$ \Gamma((D^0/D^0)X)/\Gamma(\text{hadrons}) \quad \Gamma_{43/\Gamma} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th></tr></thead><tbody><tr><td>0.296 ± 0.019 ± 0.021</td><td>369</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 ABREU</td><td>93I</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ The $(D^0/D^0)$ states in ABREU 93I are detected by the $K\pi$ decay mode. This is a corrected result (see the erratum of ABREU 93I).

$$ \Gamma(D^{\pm}X)/\Gamma(\text{hadrons}) \quad \Gamma_{44/\Gamma} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th></tr></thead><tbody><tr><td>0.174 ± 0.016 ± 0.018</td><td>539</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 ABREU</td><td>93I</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ The $D^{\pm}$ states in ABREU 93I are detected by the $K\pi\pi$ decay mode. This is a corrected result (see the erratum of ABREU 93I).

$$ \Gamma(D^{*}(2010)\pm X)/\Gamma(\text{hadrons}) \quad \Gamma_{45/\Gamma} $$

The value is for the sum of the charge states indicated.

<table><thead><tr><th>VALUE</th><th>EVTS</th></tr></thead><tbody><tr><td>0.163 ± 0.019</td><td>OUR AVERAGE</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>Error includes scale factor of 1.3.</td><td></td><td></td></tr></tbody></table>

<table><thead><tr><th>0.155 ± 0.010 ± 0.013</th><th>358</th></tr></thead><tbody><tr><td>1 ABREU</td><td>93I</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>0.21 ± 0.04</td><td>362</td></tr></tbody></table>

<table><thead><tr><th>0.155 ± 0.010 ± 0.013</th><th>358</th></tr></thead><tbody><tr><td>1 ABREU</td><td>93I</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>0.21 ± 0.04</td><td>362</td></tr></tbody></table>

¹ $D^{*}(2010)\pm$ in ABREU 93I are reconstructed from $D^0\pi^+$, with $D^0 \to K^-\pi^+$. The new CLEO II measurement of $B(D^*\to D^0\pi^+) = (68.1 \pm 1.6)\%$ is used. This is a corrected result (see the erratum of ABREU 93I).

² DECAMP 91J report $B(D^{*}(2010)\to D^0\pi^+)B(D^0 \to K^-\pi^+) \Gamma(D^{*}(2010)\pm X) / \Gamma(\text{hadrons}) = (5.11 \pm 0.34) \times 10^{-3}$. They obtained the above number assuming $B(D^0 \to K^-\pi^+) = (3.62 \pm 0.34 \pm 0.44)\%$ and $B(D^{*}(2010)\to D^0\pi^+) = (55 \pm 4)\%$. We have rescaled their original result of 0.26 ± 0.05 taking into account the new CLEO II branching ratio $B(D^{*}(2010)\to D^0\pi^+) = (68.1 \pm 1.6)\%$.

$$ \Gamma(D_{S1}(2536)\pm X)/\Gamma(\text{hadrons}) \quad \Gamma_{46/\Gamma} $$

$D_{S1}(2536)\pm$ is an expected orbitally-excited state of the $D_S$ meson.

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th></tr></thead><tbody><tr><td>0.52 ± 0.09 ± 0.06</td><td>92</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 HEISTER</td><td>02B ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ HEISTER 02B reconstruct this meson in the decay modes $D_{S1}(2536)\pm \to D^*\pm K^0$ and $D_{S1}(2536)\pm \to D^*\pm K^+$. The quoted branching ratio assumes that the decay width of the $D_{S1}(2536)$ is saturated by the two measured decay modes.

$$ \Gamma(D_{sJ}(2573)\pm X)/\Gamma(\text{hadrons}) \quad \Gamma_{47/\Gamma} $$

$D_{sJ}(2573)\pm$ is an expected orbitally-excited state of the $D_S$ meson.

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th></tr></thead><tbody><tr><td>0.83 ± 0.29 + 0.07 - 0.13</td><td>64</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 HEISTER</td><td>02B ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ HEISTER 02B reconstruct this meson in the decay mode $D_{S2}^{*}(2573)\pm \to D^0 K^\pm$. The quoted branching ratio assumes that the detected decay mode represents 45% of the full decay width.

$$ \Gamma(D^{*}(2629)\pm X)/\Gamma(\text{hadrons}) \quad \Gamma_{48/\Gamma} $$

$D^{*}(2629)\pm$ is a predicted radial excitation of the $D^*(2010)\pm$ meson.

<table><thead><tr><th>VALUE</th><th>EVTS</th></tr></thead><tbody><tr><td>searched for</td><td>1 ABBIENDI</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>01N OPAL</td><td>88-94 GeV</td></tr></tbody></table>

¹ ABBIENDI 01N searched for the decay mode $D^{*}(2629)\pm \to D^*\pm\pi^+\pi^-$ with $D^+ \to D^0\pi^+$, and $D^0 \to K^-\pi^+$. They quote a 95% CL limit for $Z \to D^{*}(2629)\pm B(D^{*}(2629)\to D^+\pi^+\pi^-) < 3.1 \times 10^{-3}$.

$$ \Gamma(B^*(X)/\Gamma(B^X) + \Gamma(B^*X)) \quad \Gamma_{50/\Gamma}(\Gamma_{49} + \Gamma_{50}) $$

As the experiments assume different values of the b-hadron contribution, our average should be taken with caution.

<table><thead><tr><th>VALUE</th><th>EVTS</th></tr></thead><tbody><tr><td>0.75 ± 0.04</td><td>OUR AVERAGE</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 ACKERSTAFF</td><td>97M OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>0.771 ± 0.026 ± 0.070</td><td>2 BUSKULIC</td><td>96D ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>0.72 ± 0.03 ± 0.06</td><td>3 ABREU</td><td>95R DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>0.76 ± 0.08 ± 0.06</td><td>4 ACCIARRI</td><td>95B L3</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ACKERSTAFF 97M use an inclusive B reconstruction method and assume a (13.2 ± 4.1)% b-hadron contribution. The value refers to a b-flavored meson mixture of $B_u, B_d$, and $B_s$.

² BUSKULIC 96D use an inclusive reconstruction of B hadrons and assume a (12.2 ± 4.3)% b-hadron contribution. The value refers to a b-flavored mixture of $B_u, B_d$, and $B_s$.

³ ABREU 95R use an inclusive B-reconstruction method and assume a (10 ± 4)% b-hadron contribution. The value refers to a b-flavored meson mixture of $B_u, B_d$, and $B_s$.

⁴ ACCIARRI 95B assume a 9.4% b-hadron contribution. The value refers to a b-flavored mixture of $B_u, B_d$, and $B_s$.

$$ \Gamma(B^+X)/\Gamma(\text{hadrons}) \quad \Gamma_{51/\Gamma} $$

"OUR EVALUATION" is obtained using our current values for $f(\bar{b} \to B^+) + R_b = \Gamma(\bar{b}b)/\Gamma(\text{hadrons})$. We calculate $\Gamma(B^+X)/\Gamma(\text{hadrons}) = R_b \times f(\bar{b} \to B^+) + R_b$.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.0869 ± 0.0019</td><td>OUR EVALUATION</td><td>(Produced by HFLAV)</td><td></td></tr><tr><td>0.0887 ± 0.0030</td><td>1 ABDALLAH</td><td>03k DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 ABDALLAH</td><td>03k DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ABDALLAH 03k measure the production fraction of $B^+$ mesons in hadronic Z decays $f(B^+) = (40.99 \pm 0.82 \pm 1.11)\%$. The value quoted here is obtained multiplying this production fraction by our value of $R_b = \Gamma(\bar{b}b)/\Gamma(\text{hadrons})$.

$$ \Gamma(B_s^0 X)/\Gamma(\text{hadrons}) \quad \Gamma_{52/\Gamma} $$

"OUR EVALUATION" is obtained using our current values for $f(\bar{b} \to B_s^0) + R_b = \Gamma(\bar{b}b)/\Gamma(\text{hadrons})$. We calculate $\Gamma(B_s^0)/\Gamma(\text{hadrons}) = R_b \times f(\bar{b} \to B_s^0) + R_b$.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.0227 ± 0.0019</td><td>OUR EVALUATION</td><td>(Produced by HFLAV)</td><td></td></tr></tbody></table>

<table><thead><tr><th>seen</th><th>1 ABREU</th><th>92M DLPH</th><th>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</th></tr></thead><tbody><tr><td>seen</td><td>2 ACTON</td><td>92N OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>seen</td><td>3 BUSKULIC</td><td>92E ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 ABREU</td><td>92M DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>2 ACTON</td><td>92N OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>3 BUSKULIC</td><td>92E ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ABREU 92M reported value is $\Gamma(B_s^0 X) \times B(D_s^0 \to D_S \mu^+\mu^-) \times B(D_S \to \phi\pi^-)/\Gamma(\text{hadrons}) = (18 \pm 8) \times 10^{-5}$.

² ACTON 92N find evidence for $B_s^0$ production using $D_S^-$-$\ell$ correlations, with $D_S^+ \to \phi\pi^+$ and $K^*(892) K^+$. Assuming $R_b$ from the Standard Model and averaging over the $e$ and $\mu$ channels, authors measure the product branching fraction to be $f(\bar{b} \to B_s^0) \times B(D_s^0 \to D_S^+ \ell^+\nu_\ell X) \times B(D_s^0 \to \phi\pi^-) = (3.9 \pm 1.1 \pm 0.8) \times 10^{-4}$.

³ BUSKULIC 92e find evidence for $B_s^0$ production using $D_S^-$-$\ell$ correlations, with $D_S^+ \to \phi\pi^+$ and $K^*(892) K^+$. Using $B(D_S^+ \to \phi\pi^-) = (2.7 \pm 0.7)\%$ and summing up the $e$ and $\mu$ channels, the weighted average product branching fraction is measured to be $B(\bar{b} \to B_s^0) \times B(D_s^0 \to D_S^+ \ell^+\nu_\ell X) = 0.040 \pm 0.011 \pm 0.010 \pm 0.012\%$.

$$ \Gamma(B_c^+ X)/\Gamma(\text{hadrons}) \quad \Gamma_{53/\Gamma} $$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>searched for</td><td>1 ACKERSTAFF</td><td>980 OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>searched for</td><td>2 ABREU</td><td>97E DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>searched for</td><td>3 BARATE</td><td>97H ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 ACKERSTAFF</td><td>980 OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>2 ABREU</td><td>97E DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>3 BARATE</td><td>97H ALEP</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr></tbody></table>

¹ ACKERSTAFF 980 searched for the decay modes $B_c \to J/\psi\pi^+$, $J/\psi a_1^+$, and $J/\psi\ell^+\nu_\ell$, with $J/\psi \to \ell^+\ell^-$, $\ell = e,\mu$. The number of candidates (background) for
the three decay modes is 2 (0.63 ± 0.2), 0 (1.10 ± 0.22), and 1 (0.82 ± 0.19) respectively. Interpreting the $2B_c \to J/\psi\pi^+$ candidates as signal, they report $\Gamma(B_c^+X) \times B(B_c \to J/\psi\pi^+) / \Gamma(\text{hadrons}) = (3.8^{+5.0}_{-2.4} \pm 0.5) \times 10^{-5}$. Interpreted as background, the 90% CL bounds are $\Gamma(B_c^+X) \times B(B_c \to J/\psi\pi^+) / \Gamma(\text{hadrons}) < 1.06 \times 10^{-4}$, $\Gamma(B_c^+X) \times B(B_c \to J/\psi a_1^+) / \Gamma(\text{hadrons}) < 5.29 \times 10^{-4}$, $\Gamma(B_c^+X) \times B(B_c \to J/\psi\ell\ell) / \Gamma(\text{hadrons}) < 6.96 \times 10^{-5}$.

²ABREU 97E searched for the decay modes $B_c \to J/\psi\pi^+$, $J/\psi\ell^+\ell^-$, and $J/\psi(3\pi)^+$, with $J/\psi \to \ell^+\ell^-$, $\ell = e, \mu$. The number of candidates (background) for the three decay modes is 1 (1.7), 0 (0.3), and 1 (2.3) respectively. They report the following 90% CL limits: $\Gamma(B_c^+) \times B(B_c \to J/\psi\pi^+) / \Gamma(\text{hadrons}) < (1.05-0.84) \times 10^{-4}$, $\Gamma(B_c^+) \times B(B_c \to J/\psi\ell\ell) / \Gamma(\text{hadrons}) < (5.8-5.0) \times 10^{-5}$, $\Gamma(B_c^+) \times B(B_c \to J/\psi(3\pi)^+) / \Gamma(\text{hadrons}) < 1.75 \times 10^{-4}$, where the ranges are due to the predicted $B_c$ lifetime (0.4-1.4) ps.

³BARATE 97H searched for the decay modes $B_c \to J/\psi\pi^+$ and $J/\psi\ell^+\ell^-$ with $J/\psi \to \ell^+\ell^-$, $\ell = e, \mu$. The number of candidates (background) for the two decay modes is 0 (0.44) and 2 (0.81) respectively. They report the following 90% CL limits: $\Gamma(B_c^+) \times B(B_c \to J/\psi\pi^+) / \Gamma(\text{hadrons}) < 3.6 \times 10^{-5}$ and $\Gamma(B_c^+) \times B(B_c \to J/\psi\ell\ell) / \Gamma(\text{hadrons}) < 5.2 \times 10^{-5}$.

$$ \Gamma(\Lambda^+ X) / \Gamma(\text{hadrons}) \qquad \Gamma_{54/\Gamma} $$

VALUE DOCUMENT ID TECN COMMENT

$0.024 \pm 0.005 \pm 0.006$

¹ ALEXANDER 96R OPAL $E_{cm}^{ee} = 88-94$ GeV

$0.021 \pm 0.003 \pm 0.005$

² BUSKULIC 96Y ALEP $E_{cm}^{ee} = 88-94$ GeV

¹ ALEXANDER 96R measure $R_b \times f(b \to \Lambda_c^+ X) \times B(\Lambda_c^+ \to pK^-\pi^+) = (0.122 \pm 0.023 \pm 0.010)\%$ in hadronic Z decays; the value quoted here is obtained using our best value $B(\Lambda_c^+ \to pK^-\pi^+) = (5.0 \pm 1.3)\%$. The first error is the total experiment's error and the second error is the systematic error due to the branching fraction uncertainty.

² BUSKULIC 96Y obtain the production fraction of $\Lambda_c^+$ baryons in hadronic Z decays $f(b \to \Lambda_c^+ X) = 0.110 \pm 0.014 \pm 0.006$ using $B(\Lambda_c^+ \to pK^-\pi^+) = (4.4 \pm 0.6)\%$; we have rescaled using our best value $B(\Lambda_c^+ \to pK^-\pi^+) = (5.0 \pm 1.3)\%$ obtaining $f(b \to \Lambda_c^+ X) = 0.097 \pm 0.013 \pm 0.025$ where the first error is their total experiment's error and the second error is the systematic error due to the branching fraction uncertainty. The value quoted here is obtained multiplying this production fraction by our value of $R_b = \Gamma(b\bar{b}) / \Gamma(\text{hadrons})$.

$$ \Gamma(\Xi_0^0 X) / \Gamma(\text{hadrons}) \qquad \Gamma_{55/\Gamma} $$

VALUE DOCUMENT ID TECN COMMENT

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

seen

¹ ABDALLAH 05C DLPH $E_{cm}^{ee} = 88-94$ GeV

¹ ABDALLAH 05C searched for the charmed strange baryon $\Xi_0^0$ in the decay channel $\Xi_0^0 \to \Xi^- \pi^+ (\Xi^- \to \Lambda^- \pi^-)$. The production rate is measured to be $f_{\Xi_0^0} \times B(\Xi_0^0 \to \Xi^- \pi^+) = (4.7 \pm 1.4 \pm 1.1) \times 10^{-4}$ per hadronic Z decay.

$$ \Gamma(\Xi_b X) / \Gamma(\text{hadrons}) \qquad \Gamma_{56/\Gamma} $$

Here $\Xi_b$ is used as a notation for the strange b-baryon states $\Xi_b^0$ and $\Xi_b^0$.

VALUE DOCUMENT ID TECN COMMENT

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

seen

¹ ABDALLAH 05C DLPH $E_{cm}^{ee} = 88-94$ GeV

seen

² BUSKULIC 96T ALEP $E_{cm}^{ee} = 88-94$ GeV

seen

³ ABREU 95V DLPH $E_{cm}^{ee} = 88-94$ GeV

¹ ABDALLAH 05C searched for the beauty strange baryon $\Xi_b$ in the inclusive semileptonic decay channel $\Xi_b \to \Xi^- \ell^- \nu_\ell X$. Evidence for the $\Xi_b$ production is seen from the observation of $\Xi^\mp$ production accompanied by a lepton of the same sign. From the excess of "right-sign" pairs $\Xi^\mp \ell^\mp$ compared to "wrong-sign" pairs $\Xi^\mp \ell^\pm$ the production rate is measured to be $B(b \to \Xi_b) \times B(\Xi_b \to \Xi^- \ell^- X) = (3.0 \pm 1.0 \pm 0.3) \times 10^{-4}$ per lepton species, averaged over electrons and muons.

² BUSKULIC 96T investigate $\Xi$-lepton correlations and find a significant excess of "right-sign" pairs $\Xi^\mp \ell^\mp$ compared to "wrong-sign" pairs $\Xi^\mp \ell^\pm$. This excess is interpreted as evidence for $\Xi_b$ semileptonic decay. The measured product branching ratio is $B(b \to \Xi_b) \times B(\Xi_b \to \chi_c X \ell^- \nu_\ell) \times B(\chi_c \to \Xi^- X') = (5.4 \pm 1.1 \pm 0.8) \times 10^{-4}$ per lepton species, averaged over electrons and muons, with $\chi_c$ a charmed baryon.

³ ABREU 95V observe an excess of "right-sign" pairs $\Xi^\mp \ell^\mp$ compared to "wrong-sign" pairs $\Xi^\mp \ell^\pm$ in jets; this excess is interpreted as evidence for the beauty strange baryon $\Xi_b$ production, with $\Xi_b \to \Xi^- \ell^- \nu_\ell X$. They find that the probability for this signal to come from non b-baryon decays is less than $5 \times 10^{-4}$ and that $\Lambda_b$ decays can account for less than 10% of these events. The $\Xi_b$ production rate is then measured to be $B(b \to \Xi_b) \times B(\Xi_b \to \Xi^- \ell^- X) = (5.9 \pm 2.1 \pm 1.0) \times 10^{-4}$ per lepton species, averaged over electrons and muons.

$$ \Gamma(b\bar{b}\text{-baryon}) / \Gamma(\text{hadrons}) \qquad \Gamma_{57/\Gamma} $$

"OUR EVALUATION" is obtained using our current values for $f(b \to b\bar{b}\text{-baryon})$ and $R_b = \Gamma(b\bar{b}) / \Gamma(\text{hadrons})$. We calculate $\Gamma(b\bar{b}\text{-baryon}) X / \Gamma(\text{hadrons}) = R_b \times f(b \to b\bar{b}\text{-baryon})$.

VALUE DOCUMENT ID TECN COMMENT

$0.0197 \pm 0.0032 \pm 0.0008 \text{ OUR EVALUATION}$

(Produced by HFLAV)

$0.0221 \pm 0.0015 \pm 0.0008$

¹ BARATE 98V ALEP $E_{cm}^{ee} = 88-94$ GeV

¹ BARATE 98V use the overall number of identified protons in b-hadron decays to measure $f(b \to b\bar{b}\text{-baryon}) = 0.102 \pm 0.007 \pm 0.027$. They assume $BR(b\bar{b}\text{-baryon} \to pX) = (58 \pm 6)\%$ and $BR(B_0^0 \to pX) = (8.0 \pm 4.0)\%$. The value quoted here is obtained multiplying this production fraction by our value of $R_b = \Gamma(b\bar{b}) / \Gamma(\text{hadrons})$.

$$ \Gamma(\gamma^+ \text{ hadrons}) / \Gamma_{\text{total}} \qquad \Gamma_{58/\Gamma} $$

Limits on additional sources of prompt photons beyond expectations for final-state bremsstrahlung.

VALUE CL% DOCUMENT ID TECN COMMENT

$<3.2 \times 10^{-3}$

95 1 AKRAWY 90J OPAL $E_{cm}^{ee} = 88-94$ GeV

¹ AKRAWY 90J report $\Gamma(\gamma X) < 8.2$ MeV at 95% CL. They assume a three-body $\gamma q\bar{q}$ distribution and use $E(\gamma) > 10$ GeV.

$$ \Gamma(e^+ e^-) / \Gamma_{\text{total}} \qquad \Gamma_{59/\Gamma} $$

VALUE CL% DOCUMENT ID TECN COMMENT

$<5.2 \times 10^{-4}$

95 1 ACTON 91B OPAL $E_{cm}^{ee} = 91.2$ GeV

¹ ACTON 91B looked for isolated photons with $E > 2\%$ of beam energy ($> 0.9$ GeV).

$$ \Gamma(\mu^+ \mu^-) / \Gamma_{\text{total}} \qquad \Gamma_{60/\Gamma} $$

VALUE CL% DOCUMENT ID TECN COMMENT

$<5.6 \times 10^{-4}$

95 1 ACTON 91B OPAL $E_{cm}^{ee} = 91.2$ GeV

¹ ACTON 91B looked for isolated photons with $E > 2\%$ of beam energy ($> 0.9$ GeV).

$$ \Gamma(\tau^+ \tau^-) / \Gamma_{\text{total}} \qquad \Gamma_{61/\Gamma} $$

VALUE CL% DOCUMENT ID TECN COMMENT

$<7.3 \times 10^{-4}$

95 1 ACTON 91B OPAL $E_{cm}^{ee} = 91.2$ GeV

¹ ACTON 91B looked for isolated photons with $E > 2\%$ of beam energy ($> 0.9$ GeV).

$$ \Gamma(\ell^+ \ell^- \gamma) / \Gamma_{\text{total}} \qquad \Gamma_{62/\Gamma} $$

The value is the sum over $\ell = e, \mu, \tau$.

VALUE CL% DOCUMENT ID TECN COMMENT

$<6.8 \times 10^{-6}$

95 1 ACTON 93E OPAL $E_{cm}^{ee} = 88-94$ GeV

¹ For $m_{\gamma\gamma} = 60 \pm 5$ GeV.

$$ \Gamma(q\bar{q}\gamma\gamma) / \Gamma_{\text{total}} \qquad \Gamma_{63/\Gamma} $$

VALUE CL% DOCUMENT ID TECN COMMENT

$<5.5 \times 10^{-6}$

95 1 ACTON 93E OPAL $E_{cm}^{ee} = 88-94$ GeV

¹ For $m_{\gamma\gamma} = 60 \pm 5$ GeV.

$$ \Gamma(\nu\bar{\nu}\gamma\gamma) / \Gamma_{\text{total}} \qquad \Gamma_{64/\Gamma} $$

VALUE CL% DOCUMENT ID TECN COMMENT

$<3.1 \times 10^{-6}$

95 1 ACTON 93E OPAL $E_{cm}^{ee} = 88-94$ GeV

¹ For $m_{\gamma\gamma} = 60 \pm 5$ GeV.

$$ \Gamma(\pm \mu^\mp) / \Gamma_{\text{total}} \qquad \Gamma_{65/\Gamma} $$

Test of lepton family number conservation. The value is for the sum of the charge states indicated.

VALUE CL% DOCUMENT ID TECN COMMENT

$<2.62 \times 10^{-7}$

95 AAD 23AQ ATLS $E_{cm}^{pp} = 13$ TeV

$<7.5 \times 10^{-7}$

95 AAD 14AU ATLS $E_{cm}^{pp} = 8$ TeV

$<2.5 \times 10^{-6}$

95 97C DLPH $E_{cm}^{ee} = 88-94$ GeV

$<1.7 \times 10^{-6}$

95 AKERS 95W OPAL $E_{cm}^{ee} = 88-94$ GeV

$<0.6 \times 10^{-5}$

95 ADRIANI 93I L3 $E_{cm}^{ee} = 88-94$ GeV

$<2.6 \times 10^{-5}$

95 DECAMP 92 ALEP $E_{cm}^{ee} = 88-94$ GeV

$$ \Gamma(\pm e^+ \mu^-) / \Gamma(e^+ e^-) \qquad \Gamma_{65/\Gamma} $$

Test of lepton family number conservation. The value is for the sum of the charge states indicated.

VALUE CL% DOCUMENT ID TECN COMMENT

$<0.07$

90 ALBAJAR 89 UA1 $E_{cm}^{pp} = 546,630$ GeV

$$ \Gamma(\pm e^+ \tau^-) / \Gamma_{\text{total}} \qquad \Gamma_{66/\Gamma} $$

Test of lepton family number conservation. The value is for the sum of the charge states indicated.

VALUE CL% DOCUMENT ID TECN COMMENT

$<5.0 \times 10^{-6}$

95 AAD 21AQ ATLS $E_{cm}^{pp} = 13$ TeV

$<8.1 \times 10^{-6}$

95 AAD 21AQ ATLS $E_{cm}^{pp} = 13$ TeV

$<5.8 \times 10^{-5}$

95 AABOUD 18CN ATLS $E_{cm}^{pp} = 13$ TeV

$<2.2 \times 10^{-5}$

95 97C DLPH $E_{cm}^{ee} = 88-94$ GeV

$<9.8 \times 10^{-6}$

95 AKERS 95W OPAL $E_{cm}^{ee} = 88-94$ GeV

$<1.3 \times 10^{-5}$

95 ADRIANI 93I L3 $E_{cm}^{ee} = 88-94$ GeV

$<1.2 \times 10^{-4}$

95 DECAMP 92 ALEP $E_{cm}^{ee} = 88-94$ GeV

$$ \Gamma(\mu^+ \tau^-) / \Gamma_{\text{total}} \qquad \Gamma_{67/\Gamma} $$

Test of lepton family number conservation. The value is for the sum of the charge states indicated.

VALUE CL% DOCUMENT ID TECN COMMENT

$<6.5 \times 10^{-6}$

95 AAD 21AQ ATLS $E_{cm}^{pp} = 13$ TeV

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

$<9.5 \times 10^{-6}$

95 AAD 21AQ ATLS $E_{cm}^{pp} = 13$ TeV

$<1.3 \times 10^{-5}$

95 AABOUD 18CN ATLS $E_{cm}^{pp} = 8, 13$ TeV

$<1.2 \times 10^{-5}$

95 97C DLPH $E_{cm}^{ee} = 88-94$ GeV

$<1.7 \times 10^{-5}$

95 AKERS 95W OPAL $E_{cm}^{ee} = 88-94$ GeV

$<1.9 \times 10^{-5}$

95 ADRIANI 93I L3 $E_{cm}^{ee} = 88-94$ GeV

$<1.0 \times 10^{-4}$

95 DECAMP 92 ALEP $E_{cm}^{ee} = 88-94$ GeV