$$ \Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) / \Gamma_{\text{total}} \quad \Gamma_4 / \Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVENTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>0.367 ± 0.008 OUR AVERAGE</strong></td></tr><tr><td>0.363 ± 0.002 ± 0.015</td><td>22k</td><td>1</td><td>SHIMIZU</td><td>18A BELL 711 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>0.369 ± 0.003 ± 0.010</td><td>16k</td><td>2</td><td>LEES</td><td>15G BABR 431 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>0.361 ± 0.016 ± 0.035</td><td></td><td>3</td><td>BERGFELD</td><td>00 CLEO E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

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

<table><tr><td>0.30 ± 0.04 ± 0.05</td><td>116</td><td>4</td><td>ALEXANDER</td><td>96s OPAL 1991–1994 LEP runs</td></tr><tr><td>0.23 ± 0.10</td><td>10</td><td>5</td><td>WU</td><td>90 MRK2 E<sup>ee</sup><sub>cm</sub>=29 GeV</td></tr></table>

1 SHIMIZU 18A impose requirements on detected γ's corresponding to a τ-rest-frame energy cutoff $E_γ^*$ > 10 MeV.

2 LEES 15G impose requirements on detected γ's corresponding to a τ-rest-frame energy cutoff $E_γ^*$ > 10 MeV.

3 BERGFELD 00 impose requirements on detected γ's corresponding to a τ-rest-frame energy cutoff $E_γ^*$ > 10 MeV. For $E_γ^*$ > 20 MeV, they quote (3.04 ± 0.14 ± 0.30) × 10⁻³.

4 ALEXANDER 96s impose requirements on detected γ's corresponding to a τ-rest-frame energy cutoff $E_γ^*$ > 20 MeV.

5 WU 90 reports $\Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) / \Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) = 0.013 \pm 0.006$, which is converted to $\Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) / \Gamma_{\text{total}}$ using $\Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) / \Gamma_{\text{total}} = 17.35\%$. Requirements on detected γ's corresponding to a τ rest frame energy cutoff $E_γ^* > 37$ MeV.

$$ \Gamma(e^{-} \bar{\nu}_{e} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{5} / \Gamma $$

To minimize the effect of experiments with large systematic errors, we exclude experiments which together would contribute 0.2% of the weight in the average.

<table><thead><tr><th>VALUE (%)</th><th>EVENTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>17.82 ± 0.04 OUR FIT</strong> (Produced by HFLAV)</td></tr><tr><td colspan="5"><strong>17.82 ± 0.05 OUR AVERAGE</strong></td></tr><tr><td>17.837 ± 0.072 ± 0.036</td><td>56k</td><td>1</td><td>SCHAEL</td><td>05C ALEP 1991–1995 LEP runs</td></tr><tr><td>17.806 ± 0.104 ± 0.076</td><td>24.7k</td><td>2</td><td>ACCIARRI</td><td>01F L3 1991–1995 LEP runs</td></tr><tr><td>17.81 ± 0.09 ± 0.06</td><td>33.1k</td><td>3</td><td>ABBEDI</td><td>99H OPAL 1991–1995 LEP runs</td></tr><tr><td>17.877 ± 0.109 ± 0.110</td><td>23.3k</td><td>4</td><td>ABREU</td><td>99X DLPH 1991–1995 LEP runs</td></tr><tr><td>17.76 ± 0.06 ± 0.17</td><td></td><td>5</td><td>ANASTASSOV</td><td>97 CLEO E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

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

<table><tr><td>17.78 ± 0.10 ± 0.09</td><td>25.3k</td><td>ALEXANDER</td><td>96D OPAL</td><td>Repl. by ABBI-ENDI 99H</td></tr><tr><td>17.79 ± 0.12 ± 0.06</td><td>20.6k</td><td>BUSKULIC</td><td>96C ALEP</td><td>Repl. by SCHAEL 05c</td></tr><tr><td>17.51 ± 0.23 ± 0.31</td><td>5059</td><td>ABREU</td><td>95T DLPH</td><td>Repl. by ABREU 99x</td></tr><tr><td>17.9 ± 0.4 ± 0.4</td><td>2892</td><td>ADRIANI</td><td>93M L3</td><td>Repl. by ACCIARRI 01F</td></tr><tr><td>17.5 ± 0.3 ± 0.5</td><td></td><td>4</td><td>ALBRECHT</td><td>93G ARG E<sup>ee</sup><sub>cm</sub>=9.4–10.6 GeV</td></tr><tr><td>17.97 ± 0.14 ± 0.23</td><td>3970</td><td>AKERIB</td><td>92 CLEO</td><td>Repl. by ANAS-TASSOV 97</td></tr><tr><td>19.1 ± 0.4 ± 0.6</td><td>2960</td><td>5</td><td>AMMAR</td><td>92 CLEO E<sup>ee</sup><sub>cm</sub>=10.5–10.9 GeV</td></tr><tr><td>18.09 ± 0.45 ± 0.45</td><td></td><td>DECAMP</td><td>92C ALEP</td><td>Repl. by SCHAEL 05c</td></tr><tr><td>17.0 ± 0.5 ± 0.6</td><td>1.7k</td><td>ABACHI</td><td>90 HRS E<sup>ee</sup><sub>cm</sub>=29 GeV</td></tr><tr><td>18.4 ± 0.8 ± 0.4</td><td>644</td><td>BEHREND</td><td>90 CELL E<sup>ee</sup><sub>cm</sub>=35 GeV</td></tr><tr><td>16.3 ± 0.3 ± 3.2</td><td></td><td>JANSSEN</td><td>89 CBAL E<sup>ee</sup><sub>cm</sub>=9.4–10.6 GeV</td></tr><tr><td>18.4 ± 1.2 ± 1.0</td><td></td><td>AIHARA</td><td>87B TPC E<sup>ee</sup><sub>cm</sub>=29 GeV</td></tr><tr><td>19.1 ± 0.8 ± 1.1</td><td></td><td>BURCHAT</td><td>87 MRK2 E<sup>ee</sup><sub>cm</sub>=29 GeV</td></tr><tr><td>16.8 ± 0.7 ± 0.9</td><td>515</td><td>5</td><td>BARTEL</td><td>86D JADE E<sup>ee</sup><sub>cm</sub>=34.6 GeV</td></tr><tr><td>20.4 ± 3.0 ± 1.4–0.9</td><td></td><td>ALTHOFF</td><td>85 TASS E<sup>ee</sup><sub>cm</sub>=45.5 GeV</td></tr><tr><td>17.8 ± 0.9 ± 0.6</td><td>390</td><td>5</td><td>ASH</td><td>85B MAC E<sup>ee</sup><sub>cm</sub>=29 GeV</td></tr><tr><td>18.2 ± 0.7 ± 0.5</td><td></td><td>6</td><td>BALTRUSAIT</td><td>85 MRK3 E<sup>ee</sup><sub>cm</sub>=3.77 GeV</td></tr><tr><td>13.0 ± 1.9 ± 2.9</td><td></td><td>BERGER</td><td>85 PLUT E<sup>ee</sup><sub>cm</sub>=34.6 GeV</td></tr><tr><td>18.3 ± 2.4 ± 1.9</td><td>60</td><td>BEHREND</td><td>83C CELL E<sup>ee</sup><sub>cm</sub>=34 GeV</td></tr><tr><td>16.0 ± 1.3</td><td>459</td><td>7</td><td>BACINO</td><td>78B DLCO E<sup>ee</sup><sub>cm</sub>=3.1–7.4 GeV</td></tr></table>

1 Correlation matrix for SCHAEL 05c branching fractions, in percent:

(1) $\Gamma(\tau^- \to e^- \bar{\nu}_e \nu_\tau) / \Gamma_{\text{total}}$

(2) $\Gamma(\tau^- \to \mu^- \bar{\nu}_\mu \nu_\tau) / \Gamma_{\text{total}}$

(3) $\Gamma(\tau^- \to \pi^- \nu_\tau) / \Gamma_{\text{total}}$

(4) $\Gamma(\tau^- \to \pi^- \pi^0 \nu_\tau) / \Gamma_{\text{total}}$

(5) $\Gamma(\tau^- \to \pi^- 2\pi^0 \nu_\tau (\text{ex.}K^0)) / \Gamma_{\text{total}}$

(6) $\Gamma(\tau^- \to \pi^- 3\pi^0 \nu_\tau (\text{ex.}K^0)) / \Gamma_{\text{total}}$

(7) $\Gamma(\tau^- \to h^- 4\pi^0 \nu_\tau (\text{ex.}K^0, \eta)) / \Gamma_{\text{total}}$

(8) $\Gamma(\tau^- \to \pi^- \pi^- + \pi^- \nu_\tau (\text{ex.}K^0, \omega)) / \Gamma_{\text{total}}$

(9) $\Gamma(\tau^- \to \pi^- \pi^- + \pi^- \pi^0 \nu_\tau (\text{ex.}K^0)) / \Gamma_{\text{total}}$

(10) $\Gamma(\tau^- \to h^- h^- h^+ 2\pi^0 \nu_\tau (\text{ex.}K^0)) / \Gamma_{\text{total}}$

(11) $\Gamma(\tau^- \to h^- h^- h^+ 3\pi^0 \nu_\tau) / \Gamma_{\text{total}}$

(12) $\Gamma(\tau^- \to 3h^- 2h^+ \nu_\tau (\text{ex.}K^0)) / \Gamma_{\text{total}}$

(13) $\Gamma(\tau^- \to 3h^- 2h^+ \pi^0 \nu_\tau (\text{ex.}K^0)) / \Gamma_{\text{total}}$

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

(2) -20

(3) -9

(4) -16 -12 2

(5) -5 -5 -17 -37

(6) 0 -4 -15 2 -27

(7) -2 -4 -24 -15 20 -47

(8) -14 -9 15 -5 -17 -14 -8

<table><tr><td>(9)</td><td>-13</td><td>-12</td><td>-25</td><td>-30</td><td>4</td><td>-2</td><td>16</td><td>-15</td></tr><tr><td>(10)</td><td>0</td><td>-2</td><td>-23</td><td>-14</td><td>4</td><td>10</td><td>13</td><td>-6</td><td>-17</td></tr><tr><td>(11)</td><td>1</td><td>0</td><td>-5</td><td>1</td><td>4</td><td>6</td><td>0</td><td>-9</td><td>-2</td><td>-11</td></tr><tr><td>(12)</td><td>0</td><td>1</td><td>9</td><td>4</td><td>-8</td><td>-4</td><td>-6</td><td>9</td><td>-5</td><td>-4</td><td>-2</td></tr><tr><td>(13)</td><td>1</td><td>-4</td><td>-3</td><td>-5</td><td>3</td><td>2</td><td>-4</td><td>-3</td><td>-1</td><td>4</td><td>1 -24</td></tr></table>

2 The correlation coefficient between this measurement and the ACCIARRI 01F measurement of $B(\tau^- \to \mu^- \bar{\nu}_\mu \nu_\tau)$ is 0.08.

3 The correlation coefficients between this measurement and the ANASTASSOV 97 measurements of $B(\mu^- \bar{\nu}_\mu \nu_\tau)$, $B(\mu^- \bar{\nu}_\mu \nu_\tau) / B(e^- \bar{\nu}_e \nu_\tau)$, $B(h^- \nu_\tau)$, and $B(h^- \nu_\tau) / B(e^- \bar{\nu}_e \nu_\tau)$ are 0.50, -0.42, 0.48, and -0.39 respectively.

4 Not independent of ALBRECHT 92D $\Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) / \Gamma(e^- \bar{\nu}_e \nu_\tau)$ and ALBRECHT 93G $\Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) \times \Gamma(e^- \bar{\nu}_e \nu_\tau) / \Gamma_{\text{total}}^2$ values.

5 Modified using $B(e^- \bar{\nu}_e \nu_\tau) / B(\text{1 prong})$ and $B(\text{1 prong})$, $= 0.855$.

6 Error correlated with BALTRUSAITIS 85 $\Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) / \Gamma_{\text{total}}$.

7 BACINO 78B value comes from fit to events with $e^\pm$ and one other nonelectron charged prong.

$$ \Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) / \Gamma(e^- \bar{\nu}_e \nu_\tau) \quad \Gamma_3 / \Gamma_5 $$

Standard Model prediction including mass effects is 0.9726.

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVENTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>97.62 ± 0.28 OUR FIT</strong> (Produced by HFLAV)</td></tr><tr><td colspan="5"><strong>97.9 ± 0.4 OUR AVERAGE</strong></td></tr></tbody></table>

<table><tr><td>97.96 ± 0.16 ± 0.36</td><td>731k</td><td>1</td><td>AUBERT</td><td>10F BABR 467 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>97.77 ± 0.63 ± 0.87</td><td></td><td>2</td><td>ANASTASSOV</td><td>97 CLEO E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>99.7 ± 3.5 ± 4.0</td><td></td><td>3</td><td>ALBRECHT</td><td>92D ARG E<sup>ee</sup><sub>cm</sub>=9.4–10.6 GeV</td></tr></table>

1 Correlation matrix for AUBERT 10F branching fractions:

(1) $\Gamma(\tau^- \to \mu^- \bar{\nu}_\mu \nu_\tau) / \Gamma(\tau^- \to e^- \bar{\nu}_e \nu_\tau)$

(2) $\Gamma(\tau^- \to \pi^- \nu_\tau) / \Gamma(\tau^- \to e^- \bar{\nu}_e \nu_\tau)$

(3) $\Gamma(\tau^- \to K^- \nu_\tau) / \Gamma(\tau^- \to e^- \bar{\nu}_e \nu_\tau)$

(1) (2)

(2) 0.25

(3) 0.12 0.33

2 The correlation coefficients between this measurement and the ANASTASSOV 97 measurements of $B(\mu^- \bar{\nu}_\mu \nu_\tau)$, $B(e^- \bar{\nu}_e \nu_\tau)$, $B(h^- \nu_\tau)$, and $B(h^- \nu_\tau) / B(e^- \bar{\nu}_e \nu_\tau)$ are 0.58, -0.42, 0.07, and 0.45 respectively.

$$ \Gamma(e^{-} \bar{\nu}_{e} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{6} / \Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVENTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>1.83 ± 0.05 OUR AVERAGE</strong></td></tr><tr><td>1.79 ± 0.02 ± 0.10</td><td>12k</td><td>1</td><td>SHIMIZU</td><td>18A BELL 711 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>1.847 ± 0.015 ± 0.052</td><td>18k</td><td>2</td><td>LEES</td><td>15G BABR 431 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>1.75 ± 0.06 ± 0.17</td><td></td><td>3</td><td>BERGFELD</td><td>00 CLEO E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

1 SHIMIZU 18A impose requirements on detected γ's corresponding to a τ-rest-frame energy cutoff $E_γ^*$ > 10 MeV.

2 LEES 15G impose requirements on detected γ's corresponding to a τ-rest-frame energy cutoff $E_γ^*$ > 10 MeV.

3 BERGFELD 00 impose requirements on detected γ's corresponding to a τ-rest-frame energy cutoff $E_γ^*$ > 10 MeV.

$$ \Gamma(h^{-} \geq K^{0}_{L} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{7} / \Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVENTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>12.03 ± 0.05 OUR FIT</strong> (Produced by HFLAV)</td></tr><tr><td colspan="5"><strong>12.2 ± 0.4 OUR AVERAGE</strong></td></tr></tbody></table>

<table><tr><td>12.47 ± 0.26 ± 0.43</td><td>2967</td><td>1</td><td>ACCIARRI</td><td>95 L3 1992 LEP run</td></tr><tr><td>12.4 ± 0.7 ± 0.7</td><td>283</td><td>2</td><td>ABREU</td><td>92N DLPH 1990 LEP run</td></tr><tr><td>12.1 ± 0.7 ± 0.5</td><td>309</td><td>3</td><td>ALEXANDER</td><td>91D OPAL 1990 LEP run</td></tr></table>

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

<table><tr><td>11.3 ± 0.5 ± 0.8</td><td>798</td><td>3</td><td>FORD</td><td>87 MAC E<sup>ee</sup><sub>cm</sub>=29 GeV</td></tr></table>

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

<table><tr><td>12.44 ± 0.11 ± 0.11</td><td>15k</td><td>4</td><td>BUSKULIC</td><td>96 ALEP Repl. by SCHAEL 05C</td></tr><tr><td>11.7 ± 0.6 ± 0.8</td><td></td><td>5</td><td>ALBRECHT</td><td>92D ARG E<sup>ee</sup><sub>cm</sub>=9.4–10.6 GeV</td></tr><tr><td>12.98 ± 0.44 ± 0.33</td><td></td><td>6</td><td>DECAMP</td><td>92C ALEP Repl. by SCHAEL 05C</td></tr><tr><td>12.3 ± 0.9 ± 0.5</td><td>1338</td><td>7</td><td>BEHREND</td><td>90 CELL E<sup>ee</sup><sub>cm</sub>=35 GeV</td></tr><tr><td>11.1 ± 1.1 ± 1.4</td><td></td><td>8</td><td>BURCHAT</td><td>87 MRK2 E<sup>ee</sup><sub>cm</sub>=29 GeV</td></tr><tr><td>12.3 ± 0.6 ± 1.1</td><td>328</td><td>8</td><td>BARTEL</td><td>86D JADE E<sup>ee</sup><sub>cm</sub>=34.6 GeV</td></tr><tr><td>13.0 ± 2.0 ± 4.0</td><td></td><td>85</td><td>BERGER</td><td>85 PLUT E<sup>ee</sup><sub>cm</sub>=34.6 GeV</td></tr><tr><td>11.2 ± 1.7 ± 1.2</td><td>34</td><td>9</td><td>BEHREND</td><td>83C CELL E<sup>ee</sup><sub>cm</sub>=34 GeV</td></tr></table>

1 ACCIARRI 95 with 0.65% added to remove their correction for $\pi^- K^0_L$ backgrounds.

2 ABREU 92N with 0.5% added to remove their correction for $K^* (892)^-$ backgrounds.

3 FORD 87 result for $B(\pi^- \nu_\tau)$ with 0.67% added to remove their $K^-$ correction and adjusted for 1992 B(“1 prong”).

4 BUSKULIC 96 quote 11.78 ± 0.11 ± 0.13 We add 0.66 to undo their correction for unseen $K^0_S$ and modify the systematic error accordingly.

5 Not independent of ALBRECHT 92D $\Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) / \Gamma(e^- \bar{\nu}_e \nu_\tau)$, $\Gamma(\mu^- \bar{\nu}_\mu \nu_\tau) \times \Gamma(e^- \bar{\nu}_e \nu_\tau)$, and $\Gamma(h^- \nu_\tau)$, and $\Gamma(h^- \nu_\tau) / \Gamma(e^- \bar{\nu}_e \nu_\tau)$ values.

6 DECAMP 92C quote $B(h^- \geq K^0_L \geq 0 (K^0_S \to \pi^+ \pi^-) \nu_\tau) = 13.32 \pm 0.44 \pm 0.33$. We subtract 0.35 to correct for their inclusion of the $K^0_S$ decays.
⁷ BURCHAT 87 with 1.1% added to remove their correction for K⁻ and K*(892)⁻ backgrounds.

⁸ BARTEL 86D result for B(π⁻ντ) with 0.59% added to remove their K⁻ correction and adjusted for 1992 B("1 prong").

⁹ BEHREND 83C quote B(π⁻ντ) = 9.9 ± 1.7 ± 1.3 after subtracting 1.3 ± 0.5 to correct for B(K⁻ντ).

$$\Gamma(h^{-} \nu_{\tau}) / \Gamma_{\text{total}}$$

VALUE (%)

EVT$S

DOCUMENT ID

TECN

COMMENT

11.51 ±0.05 OUR FIT (Produced by HFLAV)

11.63 ±0.12 OUR AVERAGE Error includes scale factor of 1.4. See the ideogram below.
11.571 ±0.120 ±0.114 19k 1 ABDALLAH 06A DLPH 1992-1995 LEP runs
11.98 ±0.13 ±0.16 ACKERSTAFF 98M OPAL 1991-1995 LEP runs

¹ Correlation matrix for ABDALLAH 06A branching fractions, in percent:

(1) $\Gamma(\tau^{-} \rightarrow h^{-} \nu_{\tau}) / \Gamma_{\text{total}}$

(2) $\Gamma(\tau^{-} \rightarrow h^{-} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}}$

(3) $\Gamma(\tau^{-} \rightarrow h^{-} \ge 1 \pi^{0} \nu_{\tau} (\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(4) $\Gamma(\tau^{-} \rightarrow h^{-} 2 \pi^{0} \nu_{\tau} (\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(5) $\Gamma(\tau^{-} \rightarrow h^{-} \ge 3 \pi^{0} \nu_{\tau} (\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(6) $\Gamma(\tau^{-} \rightarrow h^{-} h^{-} h^{+} \nu_{\tau}^{+} (\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(7) $\Gamma(\tau^{-} \rightarrow h^{-} h^{-} h^{+} \pi^{0} \nu_{\tau}^{+} (\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(8) $\Gamma(\tau^{-} \rightarrow h^{-} h^{-} h^{+} \ge 1 \pi^{0} \nu_{\tau}^{+} (\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(9) $\Gamma(\tau^{-} \rightarrow h^{-} h^{-} h^{+} \ge 2 \pi^{0} \nu_{\tau}^{+} (\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(10) $\Gamma(\tau^{-} \rightarrow 3h^{-} 2h^{+} \nu_{\tau}^{+} (\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(11) $\Gamma(\tau^{-} \rightarrow 3h^{-} 2h^{+} \pi^{0} \nu_{\tau}^{+} (\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

(2) -34

(3) -47 56

(4) 6 -66 15

(5) -6 38 11 -86

(6) -7 -8 15 0 -2

(7) -2 -1 -5 -3 3 -53

(8) -4 -4 -13 -4 -2 -56 75

(9) -1 -1 -4 3 -6 26 -78 -16

(10) -1 -1 1 0 0 0 -2 -3 -1 3

(11) 0 0 0 0 0 1 0 -5 5 -57

² The correlation coefficients between this measurement and the ANASTASSOV 97 measurements of B(μνμντ), B(eνeντ), B(μνμντ)/B(eνeντ), and B(h⁻ντ)/B(eνeντ) are 0.50, 0.48, 0.07, and 0.63 respectively.

WEIGHTED AVERAGE

11.63±0.12 (Error scaled by 1.4)

<figure><img src="image_410.png" /></figure>

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

$$\Gamma(h^{-} \nu_{\tau}) / \Gamma(e^{-} \nu_{e} \nu_{\tau})$$

VALUE (units 10⁻²)

EVT$S

DOCUMENT ID

TECN

COMMENT

$$\Gamma_8 / \Gamma_5 = (\Gamma_9 + \Gamma_{10}) / \Gamma_5$$

64.61 ±0.33 OUR FIT (Produced by HFLAV)

64.0 ±0.7 OUR AVERAGE Error includes scale factor of 1.6.

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

63.33 ±0.14 ±0.61

394k

1 AUBERT 10F BABR 467 fb⁻¹ $E_{\text{cm}}^{\text{ee}} = 10.6$ GeV

64.84 ±0.41 ±0.60

2 ANASTASSOV 97

CLEO $E_{\text{cm}}^{\text{ee}} = 10.6$ GeV

¹ Not independent of AUBERT 10F $\Gamma(\tau^{-} \rightarrow \pi^{-} \nu_{\tau}) / \Gamma(\tau^{-} \rightarrow e^{-} \nu_{e} \nu_{\tau})$ and $\Gamma(\tau^{-} \rightarrow K^{-} \nu_{\tau}) / \Gamma(\tau^{-} \rightarrow e^{-} \nu_{e} \nu_{\tau})$.

² The correlation coefficients between this measurement and the ANASTASSOV 97 measurements of B(μνμντ), B(eνeντ), B(μνμντ)/B(eνeντ), and B(h⁻ντ) are 0.08, -0.39, 0.45, and 0.63 respectively.

$$\Gamma(\pi^{-} \nu_{\tau}) / \Gamma_{\text{total}}$$

VALUE (%)

EVT$S

DOCUMENT ID

TECN

COMMENT

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

11.06 ±0.11 ±0.14

2 BUSKULIC 96

ALEP Repl. by SCHAEL 05C

11.7 ±0.4 ±1.8

BLOCKER 82D

MRK2 $E_{\text{cm}}^{\text{ee}} = 3.5-6.7$ GeV

¹ See footnote to SCHAEL 05C $\Gamma(\tau^{-} \rightarrow e^{-} \nu_{e} \nu_{\tau}) / \Gamma_{\text{total}}$ measurement for correlations with other measurements.

² Not independent of BUSKULIC 96 B(h⁻ντ) and B(K⁻ντ) values.

$$\Gamma(\pi^{-} \nu_{\tau}) / \Gamma(e^{-} \nu_{e} \nu_{\tau})$$

VALUE (units 10⁻²)

EVT$S

DOCUMENT ID

TECN

COMMENT

$$\Gamma_9 / \Gamma_5$$

60.71 ±0.32 OUR FIT (Produced by HFLAV)

59.45 ±0.14 ±0.61

1 AUBERT 10F BABR

467 fb⁻¹ $E_{\text{cm}}^{\text{ee}} = 10.6$ GeV

¹ See footnote to AUBERT 10F $\Gamma(\tau^{-} \rightarrow \mu^{-} \nu_{\mu} \nu_{\tau}) / \Gamma(\tau^{-} \rightarrow e^{-} \nu_{e} \nu_{\tau})$ for correlations with other measurements.

$$\Gamma(K^{-} \nu_{\tau}) / \Gamma_{\text{total}}$$

VALUE (%)

EVT$S

DOCUMENT ID

TECN

COMMENT

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

0.696 ±0.010 OUR FIT (Produced by HFLAV)

0.685 ±0.023 OUR AVERAGE

0.658 ±0.027 ±0.029

1 ABBIENDI 01J

OPAL 1990-1995 LEP runs

0.696 ±0.025 ±0.014

BARATE 99K

ALEP 1991-1995 LEP runs

0.85 ±0.18

ABREU 94K

DLPH LEP 1992 Z data

0.66 ±0.07 ±0.09

BATTLE 99K

CLEO $E_{\text{cm}}^{\text{ee}} \approx 10.6$ GeV

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

0.72 ±0.04 ±0.04

BUSKULIC 96

ALEP Repl. by BARATE 99K

0.59 ±0.18

MILLS 84

DLCO $E_{\text{cm}}^{\text{ee}} = 29$ GeV

1.3 ±0.5

BLOCKER 82B

MRK2 $E_{\text{cm}}^{\text{ee}} = 3.9-6.7$ GeV

¹ The correlation coefficient between this measurement and the ABBIENDI 01J B(τ⁻ → K⁻ ≥ 0π⁰ ≥ 0K⁰ ≥ 0γντ) is 0.60.

$$\Gamma(K^{-} \nu_{\tau}) / \Gamma(e^{-} \nu_{e} \nu_{\tau})$$

VALUE (units 10⁻²)

EVT$S

DOCUMENT ID

TECN

COMMENT

$$\Gamma_{10} / \Gamma_5$$

3.91 ±0.05 OUR FIT (Produced by HFLAV)

3.882 ±0.032 ±0.057

25k 1 AUBERT 10F BABR

467 fb⁻¹ $E_{\text{cm}}^{\text{ee}} = 10.6$ GeV

¹ See footnote to AUBERT 10F $\Gamma(\tau^{-} \rightarrow \mu^{-} \nu_{\mu} \nu_{\tau}) / \Gamma(\tau^{-} \rightarrow e^{-} \nu_{e} \nu_{\tau})$ for correlations with other measurements.

$$\Gamma(K^{-} \nu_{\tau}) / \Gamma(\pi^{-} \nu_{\tau})$$

VALUE (units 10⁻²)

EVT$S

DOCUMENT ID

TECN

COMMENT

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

6.44 ±0.09 OUR FIT (Produced by HFLAV)

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

6.531 ±0.056 ±0.093

1 AUBERT 10F BABR

467 fb⁻¹ $E_{\text{cm}}^{\text{ee}} = 10.6$ GeV

¹ Not independent of AUBERT 10F $\Gamma(\tau^{-} \rightarrow \pi^{-} \nu_{\tau}) / \Gamma(\tau^{-} \rightarrow e^{-} \nu_{e} \nu_{\tau})$ and $\Gamma(\tau^{-} \rightarrow K^{-} \nu_{\tau}) / \Gamma(\tau^{-} \rightarrow e^{-} \nu_{e} \nu_{\tau})$.

$$\Gamma(h^{-} \ge 1 \text{ neutrals } \nu_{\tau}) / \Gamma_{\text{total}}$$

$\Gamma_{11} / \Gamma = (\Gamma_{14} + \Gamma_{16} + \Gamma_{20} + \Gamma_{23} + \Gamma_{28} + \Gamma_{30} + 0.15344 \Gamma_{36} + 0.15344 \Gamma_{38} + 0.15344 \Gamma_{41} + 0.15344 \Gamma_{43} + 0.0942 \Gamma_{48} + 0.0942 \Gamma_{52} + 0.7196 \Gamma_{150} + 0.7196 \Gamma_{152} + 0.7196 \Gamma_{154} + 0.1107 \Gamma_{156} + 0.0835 \Gamma_{178} + 0.0835 \Gamma_{179} + 0.0835 \Gamma_{180}) / \Gamma$

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

36.14 ±0.33 ±0.58

1 AKERS 94E OPAL 1991-1992 LEP runs

38.4 ±1.2 ±1.0

2 BURCHAT 87

MRK2 $E_{\text{cm}}^{\text{ee}} = 29$ GeV

42.7 ±2.0 ±2.9

BERGER 85

PLUT $E_{\text{cm}}^{\text{ee}} = 34.6$ GeV

¹ Not independent of ACKERSTAFF 98M B(h⁻π⁰ντ) and B(h⁻ ≥ 2π⁰ντ) values.

² BURCHAT 87 quote for B(π± ≥ 1 neutralντ) = 0.378 ± 0.012 ± 0.010. We add 0.006 to account for contribution from (K⁻ντ) which they fixed at BR = 0.013.

$$\Gamma(h^{-} \ge 1 \pi^{0} \nu_{\tau}^{+} (\text{ex. K}^{0})) / \Gamma_{\text{total}}$$

$\Gamma_{12} / \Gamma = (\Gamma_{14} + \Gamma_{16} + \Gamma_{20} + \Gamma_{23} + \Gamma_{27} + \Gamma_{28} + \Gamma_{30} + 0.3257 \Gamma_{150} + 0.3257 \Gamma_{152} + 0.3257 \Gamma_{154}) / \Gamma$

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

36.50 ±0.09 OUR FIT (Produced by HFLAV)

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

36.641 ±0.155 ±0.127

45k 1 ABDALLAH 06A DLPH 1992-1995 LEP runs

¹ See footnote to ABDALLAH 06A $\Gamma(\tau^{-} \rightarrow h^{-} \nu_{\tau}) / \Gamma_{\text{total}}$ measurement for correlations with other measurements.

$$\Gamma(h^{-} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}}$$

VALUE (%)

EVT$S

DOCUMENT ID

TECN

COMMENT

$$\Gamma_{13} / \Gamma = (\Gamma_{14} + \Gamma_{16}) / \Gamma$$

25.93 ±0.09 OUR FIT (Produced by HFLAV)

25.73 ±0.16 OUR AVERAGE

25.67 ±0.01 ±0.39

5.4M FUJIKAWA 08

BELL 72 fb⁻¹ $E_{\text{cm}}^{\text{ee}} = 10.6$ GeV

25.740 ±0.201 ±0.138

1 ABDALLAH 06A

DLPH 1992-1995 LEP runs

25.89 ±0.17 ±0.29

ACKERSTAFF 98M

OPAL 1991-1995 LEP runs

25.05 ±0.35 ±0.50

ACCIARRI 95

L3 1992 LEP run

25.87 ±0.12 ±0.42

2 ARTUSO 94

CLEO $E_{\text{cm}}^{\text{ee}} = 10.6$ GeV
• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>25.76</td><td>±0.15</td><td>±0.13</td><td>31k</td><td>BUSKULIC</td><td>96</td><td>ALEC</td><td>Repl. by SCHAEL 05c</td></tr><tr><td>25.98</td><td>±0.36</td><td>±0.52</td><td></td><td><sup>3</sup>AKERS</td><td>94E</td><td>OPAL</td><td>Repl. by ACKER-STAFF 98M</td></tr><tr><td>22.9</td><td>±0.8</td><td>±1.3</td><td>283</td><td>4 ABREU</td><td>92N</td><td>DLPH</td><td>E<sup>ee</sup><sub>cm</sub> = 88.2-94.2 GeV</td></tr><tr><td>23.1</td><td>±0.4</td><td>±0.9</td><td>1249</td><td>5 ALBRECHT</td><td>92Q</td><td>ARG</td><td>E<sup>ee</sup><sub>cm</sub> = 10 GeV</td></tr><tr><td>25.02</td><td>±0.64</td><td>±0.88</td><td>1849</td><td>DECAMP</td><td>92C</td><td>ALEC</td><td>1989-1990 LEP runs</td></tr><tr><td>22.0</td><td>±0.8</td><td>±1.9</td><td>779</td><td>ANTREASYAN</td><td>91</td><td>CBAL</td><td>E<sup>ee</sup><sub>cm</sub> = 9.4-10.6 GeV</td></tr><tr><td>22.6</td><td>±1.5</td><td>±0.7</td><td>1101</td><td>BEHREND</td><td>90</td><td>CELL</td><td>E<sup>ee</sup><sub>cm</sub> = 35 GeV</td></tr><tr><td>23.1</td><td>±1.9</td><td>±1.6</td><td></td><td>BEHREND</td><td>84</td><td>CELL</td><td>E<sup>ee</sup><sub>cm</sub> = 14.22 GeV</td></tr></tbody></table>

1. See footnote to ABDALLAH 06A $\Gamma(\tau^{-} \to h^{-} \nu_{\tau})/\Gamma_{\text{total}}$ measurement for correlations with other measurements.

2. ARTUSO 94 reports the combined result from three independent methods, one of which (23% of the $\tau^{-} \to h^{-} \pi^{0} \nu_{\tau}$) is normalized to the inclusive one-prong branching fraction, taken as 0.854 ± 0.004. Renormalization to the present value causes negligible change.

3. AKERS 94E quote (26.25 ± 0.36 ± 0.52) × 10⁻²; we subtract 0.27% from their number to correct for $\tau^{-} \to h^{-} K^{0} \nu_{\tau}$.

4. ABREU 92N with 0.5% added to remove their correction for $K^{*}(892)^{-}$ backgrounds.

5. ALBRECHT 92Q with 0.5% added to remove their correction for $\tau^{-} \to K^{*}(892)^{-} \nu_{\tau}$ background.

$$ \Gamma(\pi^{-} \pi^{0} \nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{14}/\Gamma $$

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

<table><tr><td><b>25.49</b></td><td><b>±0.09</b></td><td><b>OUR FIT</b></td><td>(Produced by HFLAV)</td></tr></table>

<table><tr><td><b>25.46</b></td><td><b>±0.12</b></td><td><b>OUR AVERAGE</b></td><td></td></tr></table>

<table><tr><td>25.471 ± 0.097 ± 0.085</td><td>81k</td><td>1 SCHAEEL</td><td>05C</td><td>ALEC</td><td>1991-1995 LEP runs</td></tr></table>

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

25.36 ± 0.44 2 ARTUSO 94 CLEO E<sup>ee</sup><sub>cm</sub> = 10.6 GeV

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

25.30 ± 0.15 ± 0.13 3 BUSKULIC 96 ALEC Repl. by SCHAEL 05C
21.5 ± 0.4 ± 1.9 4400 4,5 ALBRECHT 88L ARG E<sup>ee</sup><sub>cm</sub> = 10 GeV

23.0 ± 1.3 ± 1.7 582 ADLER 87B MRK3 E<sup>ee</sup><sub>cm</sub> = 3.77 GeV

25.8 ± 1.7 ± 2.5 6 BURCHAT 87 MRK2 E<sup>ee</sup><sub>cm</sub> = 29 GeV

22.3 ± 0.6 ± 1.4 629 5 YELTON 86 MRK2 E<sup>ee</sup><sub>cm</sub> = 29 GeV

1. See footnote to SCHAEL 05C $\Gamma(\tau^{-} \to e^{-} \nu_{e} \nu_{\tau})/\Gamma_{\text{total}}$ measurement for correlations with other measurements.

2. Not independent of ARTUSO 94 B($\Gamma(h^{-} \pi^{0} \nu_{\tau})$ and BATTLE 94 B($K^{-} \pi^{0} \nu_{\tau}$) values.

3. Not independent of BUSKULIC 96 B($\Gamma(h^{-} \pi^{0} \nu_{\tau})$ and B($K^{-} \pi^{0} \nu_{\tau}$) values.

4. The authors divide by $(\Gamma_{3} + \Gamma_{5} + \Gamma_{9} + \Gamma_{10})/\Gamma = 0.467$ to obtain this result.

5. Experiment had no hadron identification. Kaon corrections were made, but insufficient information is given to permit their removal.

6. BURCHAT 87 value is not independent of YELTON 86 value. Nonresonant decays included.

$$ \Gamma(\pi^{-} \pi^{0} \text{ non-}\rho(770) \nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{15}/\Gamma $$

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

<table><tr><td>0.3 ± 0.1 ± 0.3</td><td>1 BEHREND</td><td>84</td><td>CELL</td><td>E<sup>ee</sup><sub>cm</sub> = 14.22 GeV</td></tr></table>

1. BEHREND 84 assume a flat nonresonant mass distribution down to the $\rho(770)$ mass, using events with mass above 1300 to set the level.

$$ \Gamma(K^{-} \pi^{0} \nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{16}/\Gamma $$

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

<table><tr><td><b>0.433</b></td><td><b>±0.015</b></td><td><b>OUR FIT</b></td><td>(Produced by HFLAV)</td></tr></table>

<table><tr><td><b>0.426</b></td><td><b>±0.016</b></td><td><b>OUR AVERAGE</b></td><td></td></tr></table>

<table><tr><td>0.416 ± 0.003 ± 0.018</td><td>78k</td><td>AUBERT</td><td>07AP</td><td>BABR</td><td>230 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

<table><tr><td>0.471 ± 0.059 ± 0.023</td><td>360</td><td>ABBIENDI</td><td>04J</td><td>OPAL</td><td>1991-1995 LEP runs</td></tr></table>

<table><tr><td>0.444 ± 0.026 ± 0.024</td><td>923</td><td>BARATE</td><td>99k</td><td>ALEC</td><td>1991-1995 LEP runs</td></tr></table>

<table><tr><td>0.51 ± 0.10 ± 0.07</td><td>37</td><td>BATTLE</td><td>94</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV</td></tr></table>

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

0.52 ± 0.04 ± 0.05 395 BUSKULIC 96 ALEC Repl. by BARATE 99k

$$ \Gamma(h^{-} \ge 2\pi^{0} \nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{17}/\Gamma $$

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

<table><tr><td>10.81 ± 0.09</td><td>OUR FIT</td><td>(Produced by HFLAV)</td></tr></table>

<table><tr><td><b>9.91</b></td><td><b>±0.31</b></td><td><b>±0.27</b></td><td>ACKERSTAFF 98M</td><td>OPAL</td><td>1991-1995 LEP runs</td></tr></table>

<table><tr><td><b>9.89</b></td><td><b>±0.34</b></td><td><b>±0.55</b></td><td>1 AKERS</td><td>94E</td><td>OPAL</td><td>Repl. by ACKER-STAFF 98M</td></tr></table>

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

<table><tr><td>14.0 ± 1.2 ± 0.6</td><td>938</td><td>2 BEHREND</td><td>90</td><td>CELL</td><td>E<sup>ee</sup><sub>cm</sub> = 35 GeV</td></tr></table>

<table><tr><td>12.0 ± 1.4 ± 2.5</td><td>3 BURCHAT</td><td>87</td><td>MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></table>

<table><tr><td>13.9 ± 2.0 ± 1.9</td><td>4 AIHARA</td><td>86E</td><td>TPC</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></table>

1. AKERS 94E not independent of AKERS 94E B($\Gamma(h^{-} \ge 1\pi^{0} \nu_{\tau})$ and B($\Gamma(h^{-} \pi^{0} \nu_{\tau})$ measurements.

2. No independent of BEHREND 90 $\Gamma(h^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}))$ and $\Gamma(h^{-} \ge 3\pi^{0} \nu_{\tau})$.

3. Error correlated with BURCHAT 87 $\Gamma(\rho^{-} \nu_{e})/\Gamma(\text{total})$ value.

4. AIHARA 86E (TPC) quote B($2\pi^{0} \pi^{-} \nu_{\tau}$) + 1.6B($3\pi^{0} \pi^{-} \nu_{\tau}$) + 1.1B($\pi^{0} \eta \pi^{-} \nu_{\tau}$).

$$ \Gamma(h^{-} 2\pi^{0} \nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{18}/\Gamma $$

$$ \Gamma_{18}/\Gamma = (\Gamma_{20} + \Gamma_{23} + 0.15344\Gamma_{36} + 0.15344\Gamma_{38})/\Gamma $$

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

<table><tr><td><b>9.48 ± 0.10</b></td><td><b>OUR FIT</b></td><td>(Produced by HFLAV)</td></tr></table>

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

<table><tr><td>9.48 ± 0.13 ± 0.10</td><td>12k</td><td>1 BUSKULIC</td><td>96</td><td>ALEC</td><td>Repl. by SCHAEL 05C</td></tr></table>

1. BUSKULIC 96 quote 9.29 ± 0.13 ± 0.10. We add 0.19 to undo their correction for $\tau^{-} \to h^{-} K^{0} \nu_{\tau}$.

$$ \Gamma(h^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}))/\Gamma_{\text{total}} \quad \Gamma_{19}/\Gamma $$

$$ \Gamma_{19}/\Gamma = (\Gamma_{20} + \Gamma_{23})/\Gamma $$

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

<table><tr><td><b>9.32</b></td><td><b>±0.10</b></td><td><b>OUR FIT</b></td><td>(Produced by HFLAV)</td></tr></table>

<table><tr><td><b>9.17</b></td><td><b>±0.27</b></td><td><b>OUR AVERAGE</b></td><td></td></tr></table>

<table><tr><td>9.498 ± 0.320 ± 0.275</td><td>9.5k</td><td>1 ABDALLAH</td><td>06A</td><td>DLPH</td><td>1992-1995 LEP runs</td></tr></table>

<table><tr><td>8.88 ± 0.37 ± 0.42</td><td>1060</td><td>ACCIARRI</td><td>95</td><td>L3</td><td>1992 LEP run</td></tr></table>

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

8.96 ± 0.16 ± 0.44 2 PROCARIO 93 CLEO E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV

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

10.38 ± 0.66 ± 0.82 809 3 DECAMP 92C ALEC Repl. by SCHAEL 05C
5.7 ± 0.5 ± 1.7 133 4 ANTREASYAN 91 CBAL E<sup>ee</sup><sub>cm</sub> = 9.4-10.6 GeV

<table><tr><td>10.0 ± 1.5 ± 1.1</td><td>333</td><td>5 BEHREND</td><td>90</td><td>CELL</td><td>E<sup>ee</sup><sub>cm</sub> = 35 GeV</td></tr></table>

<table><tr><td>8.7 ± 0.4 ± 1.1</td><td>815</td><td>6 BAND</td><td>87</td><td>MAC</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></table>

<table><tr><td>6.2 ± 0.6 ± 1.2</td><td>87</td><td>7 GAN</td><td>87</td><td>MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></table>

<table><tr><td>6.0 ± 3.0 ± 1.8</td><td>84</td><td>BEHREND</td><td>84</td><td>CELL</td><td>E<sup>ee</sup><sub>cm</sub> = 14.22 GeV</td></tr></table>

1. See footnote to ABDALLAH 06A $\Gamma(\tau^{-} \to h^{-} \nu_{\tau})/\Gamma_{\text{total}}$ measurement for correlations with other measurements.

2. PROCARIO 93 entry is obtained from $B(h^{-} 2\pi^{0} \nu_{\tau})/B(h^{-} \pi^{0} \nu_{\tau})$ using ARTUSO 94 result for $B(h^{-} \pi^{0} \nu_{\tau})$.

3. We subtract 0.0015 to account for $\tau^{-} \to K^{*}(892)^{-} \nu_{\tau}$ contribution.

4. ANTREASYAN 91 subtract 0.001 to account for the $\tau^{-} \to K^{*}(892)^{-} \nu_{\tau}$ contribution.

5. BEHREND 90 subtract 0.002 to account for the $\tau^{-} \to K^{*}(892)^{-} \nu_{\tau}$ contribution.

6. BAND 87 assume $B(\pi^{-} 3\pi^{0} \nu_{\tau}) = 0.01$ and $B(\pi^{-} \pi^{0} \eta \nu_{\tau}) = 0.005$.

7. GAN 87 analysis use photon multiplicity distribution.

$$ \Gamma(h^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}))/\Gamma(h^{-} \pi^{0} \nu_{\tau}) \quad \Gamma_{19}/\Gamma_{13} $$

$$ \Gamma_{19}/\Gamma_{13} = (\Gamma_{20} + \Gamma_{23})/(\Gamma_{14} + \Gamma_{16}) $$

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

<table><tr><td><b>36.0 ± 0.4</b></td><td><b>OUR FIT</b></td><td>(Produced by HFLAV)</td></tr></table>

<table><tr><td><b>34.2 ± 0.6</b></td><td><b>± 1.6</b></td><td>1 PROCARIO</td><td>93</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV</td></tr></table>

1. PROCARIO 93 quote 0.345 ± 0.006 ± 0.016 after correction for 2 kaon backgrounds assuming $B(K^{*} \nu_{\tau}) = 1.42 \pm 0.18\%$ and $B(h^{-} K^{0} \pi^{0} \nu_{\tau}) = 0.48 \pm 0.48\%$. We multiply by 0.990 ± 0.010 to remove these corrections to $B(h^{-} \pi^{0} \nu_{\tau})$.

$$ \Gamma(\pi^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}))/\Gamma_{\text{total}} \quad \Gamma_{20}/\Gamma $$

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

<table><tr><td><b>9.26</b></td><td><b>±0.10</b></td><td><b>OUR FIT</b></td><td>(Produced by HFLAV)</td></tr></table>

<table><tr><td><b>9.239</b></td><td><b>±0.06</b></td><td><b>±0.090</b></td><td>31k</td><td>1 SCHAEEL</td><td>05C</td><td>ALEC</td><td>1991-1995 LEP runs</td></tr></table>

• • • We use the following data for averages, fits, limits, etc. • • •

9.21 ± 0.13 ± 0.11 2 BUSKULIC 96 ALEC Repl. by SCHAEL 05C

1. See footnote to SCHAEL 05C $\Gamma(\tau^{-} \to e^{-} \nu_{e} \nu_{\tau})/\Gamma_{\text{total}}$ measurement for correlations with other measurements.

2. Not independent of BUSKULIC 96 B($\Gamma(h^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}))$ and $B(K^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}))$ values.

$$ \Gamma(\pi^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}), \text{scalar})/\Gamma(\pi^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0})) \quad \Gamma_{21}/\Gamma_{20} $$

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

<table><tr><td><b>&lt;0.094</b></td><td>95</td><td>1 BROWDER</td><td>00</td><td>CLEO</td><td>4.7 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

1. Model-independent limit from structure function analysis on contribution to $B(\tau^{-} \to \pi^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}))$ from scalars.

$$ \Gamma(\pi^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}), \text{vector})/\Gamma(\pi^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0})) \quad \Gamma_{22}/\Gamma_{20} $$

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

<table><tr><td><b>&lt;0.073</b></td><td>95</td><td>1 BROWDER</td><td>00</td><td>CLEO</td><td>4.7 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

1. Model-independent limit from structure function analysis on contribution to $B(\tau^{-} \to \pi^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}))$ from vectors.

$$ \Gamma(K^{-} 2\pi^{0} \nu_{\tau} (\exp K^{0}))/\Gamma_{\text{total}} \quad \Gamma_{23}/\Gamma $$

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

<table><tr><td><b>6.5 ± 2.2</b></td><td><b>OUR FIT</b></td><td>(Produced by HFLAV)</td></tr></table>

<table><tr><td><b>5.8 ± 2.4</b></td><td><b>OUR AVERAGE</b></td><td></td></tr></table>

<table><tr><td>5.6 ± 2.0 ± 1.5</td><td>131</td><td>BARATE</td><td>99k</td><td>ALEC</td><td>1991-1995 LEP runs</td></tr></table>

<table><tr><td>9 ± 10 ± 3</td><td>3</td><td>1 BATTLE</td><td>94</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV</td></tr></table>

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

8 ± 2 ± 2 59 BUSKULIC 96 ALEC Repl. by BARATE 99k

1. BATTLE 94 quote (14 ± 10 ± 3) × 10⁻⁴ or < 30 × 10⁻⁴ at 90% CL. We subtract (5 ± 2) × 10⁻⁴ to account for $\tau^{-} \to K^{0} (K^{0} \to \pi^{0} \pi^{0}) \nu_{\tau}$ background.
$$
\begin{align*}
\Gamma(h^{-} \ge 3\pi^{0} \nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{24}/\Gamma \\
\Gamma_{24}/\Gamma ={}& (\Gamma_{27} + \Gamma_{28} + \Gamma_{30} + 0.15344\Gamma_{41} + 0.15344\Gamma_{43} + 0.0942\Gamma_{48} + 0.0942\Gamma_{52} \\
& \quad + 0.3257\Gamma_{150} + 0.3257\Gamma_{152} + 0.3257\Gamma_{154} + 0.0501\Gamma_{156})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (%)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>1.34&plusmn;0.07 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td>1.53&plusmn;0.40&plusmn;0.46</td>
      <td>186</td>
      <td>DECAMP</td>
      <td>92c</td>
      <td>ALEC by SCHHAEL 05c</td>
    </tr>
    <tr>
      <td>3.2&plusmn;1.0&plusmn;1.0</td>
      <td></td>
      <td>BEHREND</td>
      <td>90</td>
      <td>CELL E<sup>ee</sup><sub>cm</sub> = 35 GeV</td>
    </tr>
  </tbody>
</table>

$$
\begin{align*}
\Gamma(h^{-} \ge 3\pi^{0} \nu_{\tau} (\text{ex. } K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{25}/\Gamma \\
\Gamma_{25}/\Gamma ={}& (\Gamma_{27} + \Gamma_{28} + \Gamma_{30} + 0.3257\Gamma_{150} + 0.3257\Gamma_{152} + 0.3257\Gamma_{154})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (%)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>1.25 &plusmn; 0.07 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>1.403 &plusmn; 0.214 &plusmn; 0.224</strong></td>
      <td>1.1k</td>
      <td><sup>1</sup> ABDALLAH</td>
      <td>06A</td>
      <td>DLPH 1992-1995 LEP runs</td>
    </tr>
  </tbody>
</table>

$$
\begin{align*}
\Gamma(h^{-} 3\pi^{0} \nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{26}/\Gamma \\
\Gamma_{26}/\Gamma ={}& (\Gamma_{27} + \Gamma_{28} + 0.15344\Gamma_{41} + 0.15344\Gamma_{43} + 0.3257\Gamma_{152})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (%)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>1.18 &plusmn; 0.07 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>1.21 &plusmn; 0.17 OUR AVERAGE</strong></td>
      <td colspan="4">Error includes scale factor of 1.2.</td>
    </tr>
    <tr>
      <td>1.70 &plusmn; 0.24 &plusmn; 0.38</td>
      <td>293</td>
      <td>ACCIARRI</td>
      <td>95</td>
      <td>L3 1992 LEP run</td>
    </tr>
    <tr>
      <td>• • •</td>
      <td colspan="4">We use the following data for averages but not for fits. • • •</td>
    </tr>
    <tr>
      <td>1.15 &plusmn; 0.08 &plusmn; 0.13</td>
      <td></td>
      <td><sup>1</sup> PROCARIO</td>
      <td>93</td>
      <td>CLEO E<sup>ee</sup><sub>cm</sub> &asymp; 10.6 GeV</td>
    </tr>
    <tr>
      <td>• • •</td>
      <td colspan="4">We do not use the following data for averages, fits, limits, etc. • • •</td>
    </tr>
    <tr>
      <td>1.24 &plusmn; 0.09 &plusmn; 0.11</td>
      <td>2.3k</td>
      <td><sup>2</sup> BUSKULIC</td>
      <td>96</td>
      <td>ALEC Repl. by SCHHAEL 05c</td>
    </tr>
    <tr>
      <td>0.0 &plusmn; 1.4 &plusmn; 1.1</td>
      <td>-0.1</td>
      <td><sup>3</sup> GAN</td>
      <td>87</td>
      <td>MRK2 E<sup>ee</sup><sub>cm</sub> = 29 GeV</td>
    </tr>
  </tbody>
</table>

¹PROCARIO 93 entry is obtained from B(h⁻ 3π⁰ντ)/B(h⁻ π⁰ντ) using ARTUSO 94 result for B(h⁻ π⁰ντ).

²BUSKULIC 96 quote B(h⁻ 3π⁰ντ (ex. K⁰)) = 1.17 ± 0.09 ± 0.11. We add 0.07 to remove their correction for K⁰ backgrounds.

³Highly correlated with GAN 87 Γ(ηπ⁻ π⁰ντ)/Γ<sub>total</sub> value. Authors quote B(π⁺ 3π⁰ντ) + 0.67B(π⁺ ηπ⁰ντ) = 0.047 ± 0.010 ± 0.011.

$$
\begin{align*}
\Gamma(h^{-} 3\pi^{0} \nu_{\tau})/\Gamma(h^{-} \pi^{0} \nu_{\tau}) & \quad \Gamma_{26}/\Gamma_{13} \\
\Gamma_{26}/\Gamma_{13} ={}& (\Gamma_{27} + \Gamma_{28} + 0.15344\Gamma_{41} + 0.15344\Gamma_{43} + 0.3257\Gamma_{152})/(\Gamma_{14} + \Gamma_{16})
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (units 10<sup>-2</sup>)</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>4.54 &plusmn; 0.28 OUR FIT</strong></td>
      <td colspan="3">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>4.4 &plusmn; 0.3 &plusmn; 0.5</strong></td>
      <td><sup>1</sup> PROCARIO</td>
      <td>93</td>
      <td>CLEO E<sup>ee</sup><sub>cm</sub> &asymp; 10.6 GeV</td>
    </tr>
  </tbody>
</table>

¹PROCARIO 93 quote 0.041 ± 0.003 ± 0.005 after correction for 2 kaon backgrounds assuming B(K⁺⁻ντ) =1.42 ± 0.18% and B(h⁻ K⁰π⁰ντ) =0.42 ± 0.48%. We add 0.003 ± 0.003 and multiply the sum by 0.990 ± 0.010 to remove these corrections.

$$
\begin{align*}
\Gamma(\pi^{-} 3\pi^{0} \nu_{\tau} (\text{ex.} K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{27}/\Gamma \\
\Gamma_{27}/\Gamma ={}& (\Gamma_{27} + \Gamma_{28} + 0.15344\Gamma_{41} + 0.15344\Gamma_{43} + 0.3257\Gamma_{152})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (%)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>1.04 &plusmn; 0.07 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>0.977 &plusmn; 0.069 &plusmn; 0.058</strong></td>
      <td>6.1k</td>
      <td><sup>1</sup> SCHAEEL</td>
      <td>05c</td>
      <td>ALEC 1991-1995 LEP runs</td>
    </tr>
  </tbody>
</table>

¹See footnote to SCHHAEL 05c Γ(τ⁻ → e⁻π⁰e⁻ντ)/Γ<sub>total</sub> measurement for correlations with other measurements.

$$
\begin{align*}
\Gamma(K^{-} 3\pi^{0} \nu_{\tau} (\text{ex. } K^{0}, \eta))/\Gamma_{\text{total}} & \quad \Gamma_{28}/\Gamma \\
\Gamma_{28}/\Gamma ={}& (\Gamma_{28} + \Gamma_{29} + 0.3257\Gamma_{150} + 0.3257\Gamma_{154})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (units 10<sup>-4</sup>)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>4.8 &plusmn; 2.1 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>3.7 &plusmn; 2.1 &plusmn; 1.1</strong></td>
      <td>22</td>
      <td>BARATE</td>
      <td>99k</td>
      <td>ALEC 1991-1995 LEP runs</td>
    </tr>
    <tr>
      <td>• • •</td>
      <td colspan="4">We do not use the following data for averages, fits, limits, etc. • • •</td>
    </tr>
  </tbody>
</table>

5 ±13
¹BUSKULIC 94E ALEC Repl. by BARATE 99k
¹BUSKULIC 94E quote B(K⁻ ≥ π⁰ ≥ 0K⁰ντ) - [B(K⁻ντ) + B(K⁻π⁰ντ) + B(K⁻ K⁰ντ) + B(K⁻π⁰π⁰ντ) + B(K⁻ K⁰K⁰ντ)] = (5 ± 13) × 10⁻⁴ accounting for common systematic errors in BUSKULIC 94E and BUSKULIC 94F measurements of these modes. We assume B(K⁻ ≥ 2K⁰ντ) and B(K⁻ ≥ 4π⁰ντ) are negligible.

$$
\begin{align*}
\Gamma(h^{-} 4\pi^{0} \nu_{\tau} (\text{ex.} K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{29}/\Gamma \\
\Gamma_{29}/\Gamma ={}& (\Gamma_{29} + 0.3257\Gamma_{150} + 0.3257\Gamma_{154})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (%)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>0.16 &plusmn; 0.04 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>0.16 &plusmn; 0.05 &plusmn; 0.05</strong></td>
      <td>1 PROCARIO</td>
      <td>93</td>
      <td>CLEO E<sup>ee</sup><sub>cm</sub> &asymp; 10.6 GeV</td>
      <td></td>
    </tr>
  </tbody>
</table>

• • • We do not use the following data for averages, fits, limits, etc. • • •
0.16±0.04±0.09 232 ²BUSKULIC 96 ALEC Repl. by SCHHAEL 05c

¹PROCARIO 93 quotes B(h⁻ 4π⁰ντ)/B(h⁻ π⁰ντ) =0.006±0.002±0.002. We multiply by the ARTUSO 94 result for B(h⁻ π⁰ντ) to obtain B(h⁻ 4π⁰ντ). PROCARIO 93 assume B(h⁻ ≥ 5 π⁰ντ) is small and do not correct for it.

²BUSKULIC 96 quote result for τ⁻ → h⁻ ≥ 4π⁰ντ. We assume B(h⁻ ≥ 5π⁰ντ) is negligible.

$$
\begin{align*}
\Gamma(h^{-} 4\pi^{0} \nu_{\tau} (\text{ex.} K^{0}, \eta))/\Gamma_{\text{total}} & \quad \Gamma_{30}/\Gamma \\
\Gamma_{30}/\Gamma ={}& (\Gamma_{30} + 0.3257\Gamma_{150} + 0.3257\Gamma_{154})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (%)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>0.11 &plusmn; 0.04 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>0.112 &plusmn; 0.037 &plusmn; 0.035</strong></td>
      <td>957</td>
      <td><sup>1</sup> SCHAEEL</td>
      <td>05c</td>
      <td>ALEC 1991-1995 LEP runs</td>
    </tr>
  </tbody>
</table>

¹See footnote to SCHHAEL 05c Γ(τ⁻ → e⁻π⁰e⁻ντ)/Γ<sub>total</sub> measurement for correlations with other measurements.

$$
\begin{align*}
\Gamma(a_1(1260)\nu_{\tau} \rightarrow \pi^{-} \gamma \nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{31}/\Gamma = (0.0022\Gamma_{20} + 0.0022\Gamma_{70})/\Gamma \\
\text{In the fit, } \Gamma(\tau^{-} \rightarrow a_1(1260)\nu_{\tau} \rightarrow \pi^{-} \gamma \nu_{\tau})/\Gamma_{\text{total}} \text{ is set equal to } \Gamma(\tau^{-} \rightarrow \\
& \pi^{-} 2\pi^{0} \nu_{\tau} (\text{ex. } K^{0})) + \Gamma(\tau^{-} \rightarrow \pi^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex. } K^{0}, \gamma))/\Gamma_{\text{total}} \times B(a_1(1260) \rightarrow \\
& \pi^{0})/(1 - B(a_1(1260) \rightarrow \pi^{0})) \text{ and } B(a_1(1260) \rightarrow \pi^{0}) = \Gamma(a_1(1260) \rightarrow \\
& \pi^{0})/\Gamma_{a_1(1260)} \text{ is a nuisance fit variable with a } \chi^2 \text{ term corresponding to its esti-} \\
& \text{mate in reference SCHHAEL 05c.}
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (units 10<sup>-4</sup>)</th>
      <th>DOCUMENT ID</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>4.0 &plusmn; 1.5 OUR FIT</strong></td>
      <td colspan="2">(Produced by HFLAV)</td>
    </tr>
  </tbody>
</table>

$$
\begin{align*}
\Gamma(K^{-} \ge 0\pi^{0} \ge 0K^{0} \ge 0\gamma \nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{32}/\Gamma = (\Gamma_{10} + \Gamma_{16} + \Gamma_{23} + \Gamma_{28} + \Gamma_{38} + \Gamma_{43} + 0.7196\Gamma_{152} + 0.1049\Gamma_{170})/\Gamma \\
\Gamma_{32}/\Gamma ={}& (\Gamma_{10} + \Gamma_{16} + \Gamma_{23} + \Gamma_{28} + \Gamma_{38} + \Gamma_{43} + 0.7196\Gamma_{152} + 0.1049\Gamma_{170})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (%)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>1.552 &plusmn; 0.029 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>1.53 &plusmn; 0.04 OUR AVERAGE</strong></td>
      <td colspan="4"></td>
    </tr>
    <tr>
      <td>1.528 &plusmn; 0.039 &plusmn; 0.040</td>
      <td></td>
      <td><sup>1</sup> ABIENDI</td>
      <td>01J</td>
      <td>OPAL 1990-1995 LEP runs</td>
    </tr>
    <tr>
      <td>1.54 &plusmn; 0.24</td>
      <td></td>
      <td>ABREU</td>
      <td></td>
      <td>94k DLPH LEP 1992 Z data</td>
    </tr>
    <tr>
      <td>1.70 &plusmn; 0.12 &plusmn; 0.19</td>
      <td>202</td>
      <td><sup>2</sup> BATTLE</td>
      <td>94</td>
      <td>CLEO E<sup>ee</sup><sub>cm</sub> &asymp; 10.6 GeV</td>
    </tr>
  </tbody>
</table>

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

1.520 ± 0.040 ± 0.041 4006 ³BARATE 99k ALEC 1991-1995 LEP runs

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

1.70 ± 0.05 ± 0.06 1610 ⁴BUSKULIC 96 ALEC Repl. by BARATE 99k

1.6 ± 0.4 ± 0.2 35 AIHARA 87B TPC E<sup>ee</sup><sub>cm</sub> = 29 GeV

1.71 ± 0.29 53 MILLS 84 DLCO E<sup>ee</sup><sub>cm</sub> = 29 GeV

¹The correlation coefficient between this measurement and the ABIENDI 01J B(τ⁻ → K⁻ντ) is 0.60.

²BATTLE 94 quote 1.60 ± 0.12 ± 0.19. We add 0.10 ± 0.02 to correct for their rejection of K<sup>S</sup> → π⁺π⁻ decays.

³Not independent of BARATE 99k B(K⁻ντ), B(K⁻π⁰ντ), B(K⁻ 2π⁰ντ (ex. K⁰)), B(K⁻ 3π⁰ντ (ex. K⁰)), B(K⁻ K⁰ντ), and B(K⁻ K⁰π⁰ντ) values.

⁴Not independent of BUSKULIC 96 B(K⁻ντ), B(K⁻π⁰ντ), B(K⁻ 2π⁰ντ), B(K⁻ K⁰ντ), and B(K⁻ K⁰π⁰ντ) values.

$$
\begin{align*}
\Gamma(K^{-} \ge 1 (\pi^{0} \text{ or } K^{0} \text{ or } \gamma) \nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{33}/\Gamma = (\Gamma_{16} + \Gamma_{23} + \Gamma_{28} + \Gamma_{38} + \Gamma_{43} + 0.7196\Gamma_{152} + 0.7196\Gamma_{154} + 0.1049\Gamma_{170})/\Gamma \\
\Gamma_{33}/\Gamma ={}& (\Gamma_{16} + \Gamma_{23} + \Gamma_{28} + \Gamma_{38} + \Gamma_{43} + \Gamma_{45} + \Gamma_{48} + \Gamma_{49} + \Gamma_{52} + \Gamma_{56} + 0.3598\Gamma_{156} + \\
& \quad 0.339\Gamma_{170})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (%)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>0.859 &plusmn; 0.028 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>0.86 &plusmn; 0.05 OUR AVERAGE</strong></td>
      <td colspan="4"></td>
    </tr>
  </tbody>
</table>

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

0.869 ± 0.031 ± 0.034 1 ABIENDI 01J OPAL 1990-1995 LEP runs

0.69 ± 0.25 2 ABREU 94k DLPH LEP 1992 Z data

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

1.2 ± 0.5 ± 0.2
-0.4 9 AIHARA 87B TPC E<sup>ee</sup><sub>cm</sub> = 29 GeV

¹Not independent of ABIENDI 01J B(τ⁻ → K⁻ντ) and B(τ⁻ → K⁻ ≥ 0π⁰ ≥ 0K⁰ ≥ 0γντ) values.

²Not independent of ABREU 94k B(K⁻ντ) and B(K⁻ ≥ 0 neutralsντ) measurements.

$$
\begin{align*}
\Gamma(K^{S}(\text{particles}^{-})\nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{34}/\Gamma = (\Gamma_{36} + \Gamma_{38} + \Gamma_{42} + \Gamma_{43} + \Gamma_{45} + \Gamma_{48} + \Gamma_{49} + \Gamma_{52} + \Gamma_{56} + 0.3598\Gamma_{156} + \\
& \quad 0.339\Gamma_{170})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (%)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>0.943 &plusmn; 0.028 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>0.918 &plusmn; 0.015 OUR AVERAGE</strong></td>
      <td colspan="4"></td>
    </tr>
    <tr>
      <td>0.970 &plusmn; 0.058 &plusmn; 0.062</td>
      <td>929</td>
      <td>BARATE</td>
      <td>98E</td>
      <td>ALEC 1991-1995 LEP runs</td>
    </tr>
    <tr>
      <td>0.97 &plusmn; 0.09 &plusmn; 0.06</td>
      <td>141</td>
      <td>AKERS</td>
      <td>94G</td>
      <td>OPAL E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td>
    </tr>
  </tbody>
</table>

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

0.915 ± 0.001 ± 0.015 398k ¹RYU 14 BELL 669 fb⁻¹ E<sup>ee</sup><sub>cm</sub>=10.6 GeV
¹Not independent of RYU 14 measurements of B(τ⁻ → π⁻K⁰ντ), B(τ⁻ → K⁻K⁰ντ), B(τ⁻ → π⁻K⁰π⁰ντ), B(τ⁻ → K⁻K⁰π⁰ντ), B(τ⁻ → π⁻K⁰S K⁰Sπ⁰ντ), and B(τ⁻ → π⁻K⁰S K⁰Sπ⁰ντ).

$$
\begin{align*}
\Gamma(h^{-} \bar{K}^{0} \nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{35}/\Gamma = (\Gamma_{36} + \Gamma_{38})/\Gamma \\
\Gamma_{35}/\Gamma ={}& (\Gamma_{36} + \Gamma_{38})/\Gamma
\end{align*}
$$

<table>
  <thead>
    <tr>
      <th>VALUE (%)</th>
      <th>EVTS</th>
      <th>DOCUMENT ID</th>
      <th>TECN</th>
      <th>COMMENT</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td><strong>0.987 &plusmn; 0.014 OUR FIT</strong></td>
      <td colspan="4">(Produced by HFLAV)</td>
    </tr>
    <tr>
      <td><strong>0.90 &plusmn; 0.07 OUR AVERAGE</strong></td>
      <td colspan="4"></td>
    </tr>
    <tr>
      <td>0.855 &plusmn; 0.036 &plusmn; 0.073</td>
      <td>1242</td>
      <td>COAN</td>
      <td>96</td>
      <td>CLEO E<sup>ee</sup><sub>cm</sub> &asymp; 10.6 GeV</td>
    </tr>
  </tbody>
</table>

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

1.01 ± 0.11 ± 0.07 555 ¹BARATE 98E ALEC 1991-1995 LEP runs

¹Not independent of BARATE 98E B(τ⁻ → π⁻K⁰ντ) and B(τ⁻ → K⁻K⁰ντ) values.
$$ \Gamma(\pi^{-} \bar{K}^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{36} / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>8.38&plusmn;0.14 OUR FIT</strong></td><td colspan="4">(Produced by HFLAV)</td></tr></tbody></table>

**8.39&plusmn;0.22 OUR AVERAGE** Error includes scale factor of 1.5. See the ideogram below.

<table><tbody><tr><td>8.32&plusmn;0.02&plusmn;0.16</td><td>158k</td><td>1 RYU</td><td>14</td><td>BELL</td><td>669 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>9.33&plusmn;0.68&plusmn;0.49</td><td>377</td><td>ABBIENDI</td><td>00c</td><td>OPAL</td><td>1991-1995 LEP runs</td></tr><tr><td>9.28&plusmn;0.45&plusmn;0.34</td><td>937</td><td>2 BARATE</td><td>99k</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>9.5 &plusmn; 1.5 &plusmn; 0.6</td><td></td><td>3 ACCIARRI</td><td>95f</td><td>L3</td><td>1991-1993 LEP runs</td></tr></tbody></table>

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

<table><tbody><tr><td>8.55&plusmn;1.17&plusmn;0.66</td><td>509</td><td>4 BARATE</td><td>98E</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>7.04&plusmn;0.41&plusmn;0.72</td><td></td><td>5 COAN</td><td>96</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> &asymp; 10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>8.08&plusmn;0.04&plusmn;0.26</td><td>53k</td><td>EPIFANOV</td><td>07</td><td>BELL</td><td>Repl. by RYU 14</td></tr><tr><td>7.9 &plusmn; 1.0 &plusmn; 0.9</td><td>98</td><td>6 BUSKULIC</td><td>96</td><td>ALEP</td><td>Repl. by BARATE 99k</td></tr></tbody></table>

1 RYU 14 reconstruct $K^0$'s using $K^0_S \to \pi^+\pi^-$ decays.

2 BARATE 99k measure $K^0$'s by detecting $K^0_L$'s in their hadron calorimeter.

3 ACCIARRI 95f do not identify $\pi^-/K^-$ and assume $B(K^- K^0 \nu_\tau) = (0.29 \pm 0.12)\%$.

4 BARATE 98E reconstruct $K^0$'s using $K^0_S \to \pi^+\pi^-$ decays. Not independent of BARATE 98E $B(K^0 \text{particles}^- \nu_\tau)$ value.

5 Not independent of COAN 96 $B(h^- K^0 \nu_\tau)$ and $B(K^- K^0 \nu_\tau)$ measurements.

6 BUSKULIC 96 measure $K^0$'s by detecting $K^0_L$'s in their hadron calorimeter.

WEIGHTED AVERAGE
8.39&plusmn;0.22 (Error scaled by 1.5)

<figure><img src="image_411.png" /></figure>

$\Gamma(\pi^{-} \bar{K}^{0} \nu_{\tau}) / \Gamma_{\text{total}}$ (units 10<sup>-3</sup>)

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

$$ \Gamma(\pi^{-} \bar{K}^{0} (\text{non-K}^{*}(892)^{-}) \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{37} / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>5.4&plusmn;2.1</strong></td><td></td><td>1 EPIFANOV</td><td>07</td><td>BELL</td><td>351 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;17</td><td>95</td><td>ACCIARRI</td><td>95f</td><td>L3</td><td>1991-1993 LEP runs</td></tr></tbody></table>

1 EPIFANOV 07 quote $B(\tau^- \to K^*(892)^- \nu_\tau)$ $B(K^*(892)^- \to K^0_S \pi^-) / B(\tau^- \to K^0_S \pi^- \nu_\tau) = 0.933 \pm 0.027$. We multiply their $B(\tau^- \to K^0 \pi^- \nu_\tau)$ by $[1-(0.933 \pm 0.027)]$ to obtain this result.

$$ \Gamma(K^{-} \bar{K}^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{38} / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>14.86&plusmn;0.34 OUR FIT</strong></td><td colspan="4">(Produced by HFLAV)</td></tr><tr><td><strong>14.83&plusmn;0.35 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<table><tbody><tr><td>14.78&plusmn;0.22&plusmn;0.40</td><td>29k</td><td>1 LEES</td><td>18b</td><td>BABR</td><td>468 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>14.80&plusmn;0.14&plusmn;0.54</td><td>33k</td><td>2 RYU</td><td>14</td><td>BELL</td><td>669 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>16.2 &plusmn; 2.1 &plusmn; 1.1</td><td>150</td><td>3 BARATE</td><td>99k</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>15.8 &plusmn; 4.2 &plusmn; 1.7</td><td>46</td><td>4 BARATE</td><td>98E</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>15.1 &plusmn; 2.1 &plusmn; 2.2</td><td>111</td><td>COAN</td><td>96</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> &asymp; 10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>26 &plusmn; 9 &plusmn; 2</td><td>13</td><td>5 BUSKULIC</td><td>96</td><td>ALEP</td><td>Repl. by BARATE 99k</td></tr></tbody></table>

1 LEES 18b reconstructs $K^0_S$'s using $K^0_S \to \pi^+\pi^-$ decays.

2 RYU 14 reconstruct $K^0$'s using $K^0_S \to \pi^+\pi^-$ decays.

3 BARATE 99k measure $K^0$'s by detecting $K^0_L$'s in their hadron calorimeter.

4 BARATE 98E reconstruct $K^0$'s using $K^0_S \to \pi^+\pi^-$ decays.

5 BUSKULIC 96 measure $K^0$'s by detecting $K^0_L$'s in their hadron calorimeter.

$$ \Gamma(K^{-} \bar{K}^{0} \ge 0 \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{39} / \Gamma = (\Gamma_{38} + \Gamma_{43}) / \Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.299&plusmn;0.007 OUR FIT</strong></td><td colspan="4">(Produced by HFLAV)</td></tr><tr><td><strong>0.330&plusmn;0.055&plusmn;0.039</strong></td><td>124</td><td>ABBIENDI</td><td>00c</td><td>OPAL</td><td>1991-1995 LEP runs</td></tr></tbody></table>

$$ \Gamma(h^{-} \bar{K}^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{40} / \Gamma = (\Gamma_{41} + \Gamma_{43}) / \Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.532&plusmn;0.013 OUR FIT</strong></td><td colspan="4">(Produced by HFLAV)</td></tr></tbody></table>

**0.50 &plusmn; 0.06 OUR AVERAGE** Error includes scale factor of 1.2.

<table><tbody><tr><td>0.562&plusmn;0.050&plusmn;0.048</td><td>264</td><td>COAN</td><td>96</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> &asymp; 10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>0.446&plusmn;0.052&plusmn;0.046</td><td>157</td><td>1 BARATE</td><td>98E</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr></tbody></table>

1 Not independent of BARATE 98E $B(\tau^- \to \pi^- \bar{K}^0 \pi^0 \nu_\tau)$ and $B(\tau^- \to K^- K^0 \pi^0 \nu_\tau)$ values.

$$ \Gamma(\pi^{-} \bar{K}^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{41} / \Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.382&plusmn;0.013 OUR FIT</strong></td><td colspan="4">(Produced by HFLAV)</td></tr><tr><td><strong>0.383&plusmn;0.014 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<table><tbody><tr><td>0.386&plusmn;0.004&plusmn;0.014</td><td>27k</td><td>1 RYU</td><td>14</td><td>BELL</td><td>669 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>0.347&plusmn;0.053&plusmn;0.037</td><td>299</td><td>2 BARATE</td><td>99k</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>0.294&plusmn;0.073&plusmn;0.037</td><td>142</td><td>3 BARATE</td><td>98E</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>0.41 &plusmn; 0.12 &plusmn; 0.03</td><td></td><td>4 ACCIARRI</td><td>95F</td><td>L3</td><td>1991-1993 LEP runs</td></tr></tbody></table>

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

<table><tbody><tr><td>0.417&plusmn;0.058&plusmn;0.044</td><td>5 COAN</td><td>96</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> &asymp; 10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>0.32 &plusmn; 0.11 &plusmn; 0.05</td><td>23</td><td>6 BUSKULIC</td><td>96</td><td>ALEP</td><td>Repl. by BARATE 99k</td></tr></tbody></table>

1 RYU 14 reconstruct $K^0$'s using $K^0_S \to \pi^+\pi^-$ decays.

2 BARATE 99k measure $K^0$'s by detecting $K^0_L$'s in their hadron calorimeter.

3 BARATE 98E reconstruct $K^0$'s using $K^0_S \to \pi^+\pi^-$ decays.

4 ACCIARRI 95f do not identify $\pi^-/K^-$ and assume $B(K^- K^0 \pi^0 \nu_\tau) = (0.05 \pm 0.05)\%$.

5 Not independent of COAN 96 $B(h^- K^0 \pi^0 \nu_\tau)$ and $B(K^- K^0 \pi^0 \nu_\tau)$ measurements.

6 BUSKULIC 96 measure $K^0$'s by detecting $K^0_L$'s in their hadron calorimeter.

$$ \Gamma(\bar{K}^{0} \rho^{-} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{42} / \Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.22 &plusmn; 0.05 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<table><tbody><tr><td>0.250&plusmn;0.057&plusmn;0.044</td><td>1 BARATE</td><td>99k</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>0.188&plusmn;0.054&plusmn;0.038</td><td>2 BARATE</td><td>98E</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr></tbody></table>

1 BARATE 99k measure $K^0$'s by detecting $K^0_L$'s in hadron calorimeter. They determine the $\bar{K}^0 \rho^-$ fraction in $\tau^- \to \pi^- \bar{K}^0 \pi^0 \nu_\tau$ decays to be $(0.72 \pm 0.12 \pm 0.10)$ and multiply their $B(\pi^- \bar{K}^0 \pi^0 \nu_\tau)$ measurement by this fraction to obtain the quoted result.

2 BARATE 98E reconstruct $K^0$'s using $K^0_S \to \pi^+\pi^-$ decays. They determine the $\bar{K}^0 \rho^-$ fraction in $\tau^- \to \pi^- \bar{K}^0 \pi^0 \nu_\tau$ decays to be $(0.64 \pm 0.09 \pm 0.10)$ and multiply their $B(\pi^- \bar{K}^0 \pi^0 \nu_\tau)$ measurement by this fraction to obtain the quoted result.

$$ \Gamma(K^{-} \bar{K}^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{43} / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>15.0 &plusmn; 0.7 OUR FIT</strong></td><td colspan="4">(Produced by HFLAV)</td></tr><tr><td><strong>14.9 &plusmn; 0.7 OUR AVERAGE</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<table><tbody><tr><td>14.96&plusmn;0.20&plusmn;0.74</td><td>8.3k</td><td>1 RYU</td><td>14</td><td>BELL</td><td>669 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>14.3 &plusmn; 2.5 &plusmn; 1.5</td><td>78</td><td>2 BARATE</td><td>99k</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>15.2 &plusmn; 7.6 &plusmn; 2.1</td><td>15</td><td>3 BARATE</td><td>98E</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>14.5 &plusmn; 3.6 &plusmn; 2.0</td><td>32</td><td>COAN</td><td>96</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> &asymp; 10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>10 &plusmn; 5 &plusmn; 3</td><td>5</td><td>4 BUSKULIC</td><td>96</td><td>ALEP</td><td>Repl. by BARATE 99k</td></tr></tbody></table>

1 RYU 14 reconstruct $K^0$'s using $K^0_S \to \pi^+\pi^-$ decays.

2 BARATE 99k measure $K^0$'s by detecting $K^0_L$'s in their hadron calorimeter.

3 BARATE 98E reconstruct $K^0$'s using $K^0_S \to \pi^+\pi^-$ decays.

4 BUSKULIC 96 measure $K^0$'s by detecting $K^0_L$'s in their hadron calorimeter.

$$ \Gamma(\pi^{-} \bar{K}^{0} \ge 1 \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{44} / \Gamma = (\Gamma_{41} + \Gamma_{45}) / \Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.408&plusmn;0.025 OUR FIT</strong></td><td colspan="4">(Produced by HFLAV)</td></tr><tr><td><strong>0.324&plusmn;0.074&plusmn;0.066</strong></td><td>148</td><td>ABBIENDI</td><td>00c</td><td>OPAL</td><td>1991-1995 LEP runs</td></tr></tbody></table>

$$ \Gamma(\pi^{-} \bar{K}^{0} \pi^{0} \pi^{0} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}} \qquad \Gamma_{45} / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.26&plusmn;0.23 OUR FIT</strong></td><td colspan="4">(Produced by HFLAV)</td></tr><tr><td><strong>0.26&plusmn;0.24</strong></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<table><tbody><tr><td>&lt;0.66</td><td>95</td><td>2 BARATE</td><td>99k</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>0.58&plusmn;0.33&plusmn;0.14</td><td>5</td><td>3 BARATE</td><td>98E</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr></tbody></table>

1 BARATE 99R combine the BARATE 98E and BARATE 99k measurements to obtain this value.

2 BARATE 99k measure $K^0$'s by detecting $K^0_L$'s in their hadron calorimeter.

3 BARATE 98E reconstruct $K^0$'s using $K^0_S \to \pi^+\pi^-$ decays.

$$ \Gamma(K^{-} \bar{K}^{0} \pi^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{46} / \Gamma $$

<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;0.16 &times; 10<sup>-3</sup></td><td>95</td><td>1 BARATE</td><td>99R</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;0.18 &times; 10<sup>-3</sup></td><td>95</td><td>2 BARATE</td><td>99k</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>&lt;0.39 &times; 10<sup>-3</sup></td><td>95</td><td>3 BARATE</td><td>98E</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr></tbody></table>

1 BARATE 99R combine the BARATE 98E and BARATE 99k bounds to obtain this value.

2 BARATE 99k measure $K^0$'s by detecting $K^0_L$'s in hadron calorimeter.

3 BARATE 98E reconstruct $K^0$'s by using $K^0_S \to \pi^+\pi^-$ decays.
$$
\begin{array}{l}
\Gamma(\pi^{-} K^{0} K^{0} \nu_{\tau}) / \Gamma_{\text{total}} \\
\text{VALUE (\%)} \\
\text{0.155} \pm 0.024 \text{ OUR FIT} \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \quad \text{\Gamma47/}\Gamma = (\Gamma_{48}+\Gamma_{49}+\Gamma_{50})/\Gamma \\
\text{(Produced by HFLAV)}
\end{array}
$$

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

$$
\begin{array}{l}
0.153 \pm 0.030 \pm 0.016 & 74 & 1 \text{ BARATE} & 98\text{E} & \text{ALEP} & 1991-1995 \text{ LEP runs} \\
\text{• • •} & & & & &
\end{array}
$$

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

$$
0.31 \pm 0.12 \pm 0.04 \quad 2 \text{ ACCIARRI} \quad 95\text{F} \quad \text{L3} \quad 1991-1993 \text{ LEP runs}
$$

¹BARATE 98E obtain this value by adding twice their B(π⁻ K⁰S K⁰S ντ) value to their B(π⁻ K⁰S K⁰L ντ) value.

²ACCIARRI 95F assume B(π⁻ K⁰S K⁰S ν) = B(π⁻ K⁰S K⁰L ν) = 1/2B(π⁻ K⁰S K⁰L ν).

$$
\begin{array}{l}
\Gamma(\pi^{-} K_{S}^{0} K_{S}^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \text{\Gamma48/}\Gamma \\
\text{Bose-Einstein correlations might make the mixing fraction different than 1/4.}
\end{array}
$$

$$
\begin{array}{l}
\text{VALUE (units 10}^{-4}\text{)} \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{2.35} \pm 0.06 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
\end{array}
$$

$$
\textbf{2.32} \pm 0.06 \text{ OUR AVERAGE}
$$

$$
2.33 \pm 0.03 \pm 0.09 \quad 6.7\text{k} \quad \text{RYU} \quad 14 \quad \text{BELL} \quad 669 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV}
$$

$$
2.31 \pm 0.04 \pm 0.08 \quad 5.0\text{k} \quad 1 \text{ LEES} \quad 12\text{Y} \quad \text{BABR} \quad 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV}
$$

$$
2.6 \pm 1.0 \pm 0.5 \quad 6 \quad \text{BARATE} \quad 98\text{E} \quad \text{ALEP} \quad 1991-1995 \text{ LEP runs}
$$

$$
2.3 \pm 0.5 \pm 0.3 \quad 42 \quad \text{COAN} \quad 96 \quad \text{CLEO} \quad E_{\text{cm}}^{\text{ee}} \approx 10.6 \text{ GeV}
$$

¹The correlation coefficient between this measurement and the LEES 12Y Γ(τ⁻ → π⁻ K⁰S K⁰S π⁰ντ) / Γtotal one is 0.0828.

$$
\begin{array}{l}
\Gamma(\pi^{-} K_{S}^{0} K_{L}^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \text{\Gamma49/}\Gamma \\
\text{VALUE (units 10}^{-4}\text{)} \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{10.8} \pm 2.4 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
\end{array}
$$

$$
\begin{array}{l}
10.1 \pm 2.3 \pm 1.3 \quad 68 \quad \text{BARATE} \quad 98\text{E} \quad \text{ALEP} \quad 1991-1995 \text{ LEP runs}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(\pi^{-} K_{L}^{0} K_{L}^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{50}/\Gamma = \Gamma_{48}/\Gamma \\
\text{VALUE (units 10}^{-4}\text{)} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{2.35} \pm 0.06 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(\pi^{-} K^{0} K^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{51}/\Gamma = (\Gamma_{52}+\Gamma_{56}+\Gamma_{57})/\Gamma \\
\text{VALUE (units 10}^{-4}\text{)} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{3.6} \pm 1.2 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(\pi^{-} K_{S}^{0} K_{S}^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{52}/\Gamma \\
\text{VALUE (units 10}^{-5}\text{)} \quad \text{CL\% EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{1.82} \pm 0.21 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
\end{array}
$$

$$
\begin{array}{l}
1.80 \pm 0.21 \text{ OUR FIT} \quad \text{(Produced by HFLAV)} \\
\text{1.80} \pm 0.20 \pm 0.22 \quad 303 \quad \text{RYU} \quad 14 \quad \text{BELL} \quad 669 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV}
\end{array}
$$

$$
1.60 \pm 0.20 \pm 0.22 \quad 409 \quad 1 \text{ LEES} \quad 12\text{Y} \quad \text{BABR} \quad 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV}
$$

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

$$
\begin{array}{l}
<20 \quad 95 \quad \text{BARATE} \quad 98\text{E} \quad \text{ALEP} \quad 1991-1995 \text{ LEP runs} \\
\text{1} \text{ The correlation coefficient between this measurement and the LEES 12Y } \Gamma(\tau^{-} \rightarrow \pi^{-} K_{S}^{0} K_{S}^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \text{ one is 0.0828.}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(\kappa^{*} - \kappa^{0} \pi^{0} \nu_{\tau} \rightarrow \pi^{-} \kappa_{S}^{0} \kappa_{S}^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{53}/\Gamma \\
\text{VALUE (units 10}^{-6}\text{)} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{10.8} \pm 1.4 \pm 1.5 \quad \text{RYU} \quad 14 \quad \text{BELL} \quad 669 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(\bar{f}_1(1285)\pi^{-} \nu_{\tau} \rightarrow \pi^{-} K_S^0 K_S^0 \pi^0 \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{54}/\Gamma \\
\text{VALUE (units 10}^{-6}\text{)} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{6.8} \pm 1.3 \pm 0.7 \quad \text{RYU} \quad 14 \quad \text{BELL} \quad 669 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(\bar{f}_1(1420)\pi^{-} \nu_{\tau} \rightarrow \pi^{-} K_S^0 K_S^0 \pi^0 \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{55}/\Gamma \\
\text{VALUE (units 10}^{-6}\text{)} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{2.4} \pm 0.5 \pm 0.6 \quad \text{RYU} \quad 14 \quad \text{BELL} \quad 669 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(\pi^{-} K_{S}^{0} K_{L}^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{56}/\Gamma \\
\text{VALUE (units 10}^{-4}\text{)} \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{3.2} \pm 1.2 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
\end{array}
$$

$$
\begin{array}{l}
3.1 \pm 1.1 \pm 0.5 \quad 11 \quad \text{BARATE} \quad 98\text{E} \quad \text{ALEP} \quad 1991-1995 \text{ LEP runs}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(\pi^{-} K_{L}^{0} K_{L}^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{57}/\Gamma = \Gamma_{52}/\Gamma \\
\text{VALUE (units 10}^{-5}\text{)} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{1.82} \pm 0.21 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(\kappa^{-} K_{S}^{0} K_{S}^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{58}/\Gamma \\
\text{VALUE (\%)} \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{<6.3} \times 10^{-7} \quad 90 \quad \text{LEES} \quad 12\text{Y} \quad \text{BABR} \quad 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(\kappa^{-} K_{S}^{0} K_{S}^{0} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{59}/\Gamma \\
\text{VALUE (\%)} \quad \text{CL\%} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{<4.0} \times 10^{-7} \quad 90 \quad \text{LEES} \quad 12\text{Y} \quad \text{BABR} \quad 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV}
\end{array}
$$

$$
\begin{array}{l}
\Gamma(K^{0} h^{+} h^{-} \geq 0 \text{ neutrals } \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{60}/\Gamma \\
\text{VALUE (\%)} \quad \text{CL\%} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{<0.17} \quad 95 \quad \text{TSHIRHART} \quad 88 \quad \text{HRS} \quad E_{\text{cm}}^{\text{ee}} = 29 \text{ GeV}
\end{array}
$$

• • • We do not use the following data for averages, fits, limits, etc. • • •
<0.27 90 BELTRAMI 85 HRS E<sub>cm</sub><sup>ee</sup> = 29 GeV

$$
\begin{array}{l}
\Gamma(K^{0} h^{+} h^{-} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{61}/\Gamma \\
\text{VALUE (units 10}^{-4}\text{)} \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{2.5} \pm 2.0 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
\end{array}
$$

$$
2.3 \pm 1.9 \pm 0.7 \quad 6 \quad 1 \text{ BARATE} \quad 98\text{E} \quad \text{ALEP} \quad 1991-1995 \text{ LEP runs}
$$

¹BARATE 98E reconstruct K⁰'s using K⁰S → π⁺π⁻ decays.

$$
\begin{array}{l}
\Gamma(h^{-} h^{+} h^{+} \geq 0 \text{ neutrals} \geq 0 K_{S}^{0} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{62}/\Gamma \\
\Gamma_{62}/\Gamma = (0.34598f_{36}+0.34598f_{38}+0.34598f_{41}+0.34598f_{43}+0.42474f_{48}+ \\
0.6920f_{49}+0.42474f_{52}+0.6920f_{56}+0.6534f_{61}+\Gamma_{70}+\Gamma_{78}+\Gamma_{85}+\Gamma_{86}+\Gamma_{97}+\Gamma_{103}+ \\
\Gamma_{106}+\Gamma_{107}+0.2804f_{150}+0.2804f_{152}+0.2804f_{154}+0.2628f_{156}+0.7259f_{170}+ \\
0.9078f_{178}+0.9078f_{179}+0.9078f_{180})/\Gamma
\end{array}
$$

$$
\begin{array}{l}
\text{VALUE (\%)} \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \\
\textbf{15.20} \pm 0.06 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
\end{array}
$$

$$
14.4 \pm 0.6 \pm 0.3 \quad \text{ADEVA} \quad 91\text{F} \quad \text{L3} \quad E_{\text{cm}}^{\text{ee}} = 88.3-94.3 \text{ GeV}
$$

$$
15.0 \pm 0.4 \pm 0.3 \quad \text{BEHREND} \quad 89\text{B} \quad \text{CELL} \quad E_{\text{cm}}^{\text{ee}} = 14-47 \text{ GeV}
$$

$$
15.1 \pm 0.8 \pm 0.6 \quad \text{AIHARA} \quad 87\text{B} \quad \text{TPC} \quad E_{\text{cm}}^{\text{ee}} = 29 \text{ GeV}
$$

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

$$
13.5 \pm 0.3 \pm 0.3 \quad \text{ABACHI} \quad 89\text{B} \quad \text{HRS} \quad E_{\text{cm}}^{\text{ee}} = 29 \text{ GeV}
$$

$$
12.8 \pm 1.0 \pm 0.7 \quad \text{1 BURCHAT} \quad 87 \quad \text{MRK2} \quad E_{\text{cm}}^{\text{ee}} = 29 \text{ GeV}
$$

$$
12.1 \pm 0.5 \pm 1.2 \quad \text{RUCKSTUHL} \quad 86 \quad \text{DLCO} \quad E_{\text{cm}}^{\text{ee}} = 29 \text{ GeV}
$$

$$
12.8 \pm 0.5 \pm 0.8 \quad 1420 \quad \text{SCHMIDKE} \quad 86 \quad \text{MRK2} \quad E_{\text{cm}}^{\text{ee}} = 29 \text{ GeV}
$$

$$
15.3 \pm 1.1 \pm \frac{1+1.3}{-1.6} \quad 367 \quad \text{ALTHOFF} \quad 85 \quad \text{TASS} \quad E_{\text{cm}}^{\text{ee}} = 34.5 \text{ GeV}
$$

$$
13.6 \pm 0.5 \pm 0.8 \quad \text{BARTEL} \quad 85\text{F} \quad \text{JADE} \quad E_{\text{cm}}^{\text{ee}} = 34.6 \text{ GeV}
$$

$$
12.2 \pm 1.3 \pm 3.9 \quad \text{2 BERGER} \quad 85 \quad \text{PLUT} \quad E_{\text{cm}}^{\text{ee}} = 34.6 \text{ GeV}
$$

$$
13.3 \pm 0.3 \pm 0.6 \quad \text{FERNANDEZ} \quad 85 \quad \text{MAC} \quad E_{\text{cm}}^{\text{ee}} = 29 \text{ GeV}
$$

$$
24 \pm 6 \quad 35 \quad \text{BRANDELIK} \quad 80 \quad \text{TASS} \quad E_{\text{cm}}^{\text{ee}} = 30 \text{ GeV}
$$

$$
32 \pm 5 \quad 692 \quad \text{3 BACINO} \quad 78\text{B} \quad \text{DLCO} \quad E_{\text{cm}}^{\text{ee}} = 3.1-7.4 \text{ GeV}
$$

$$
35 \pm 11 \quad \text{3 BRANDELIK} \quad 78 \quad \text{DASP} \quad \text{Assumes V-A decay} \quad E_{\text{cm}}^{\text{ee}} = 3.1-7.4 \text{ GeV}
$$

$$
18 \pm 6.5 \quad 33 \quad \text{3 JAROS} \quad 78 \quad \text{LGW} \quad E_{\text{cm}}^{\text{ee}} > 6 \text{ GeV}
$$

¹BURCHAT 87 value is not independent of SCHMIDKE 86 value.

²Not independent of BERGER 85 Γ(μ⁻νµ⁺ντ) / Γtotal, Γ(e⁻νeντ) / Γtotal, Γ(h⁻ ≥ 1 neutralsντ) / Γtotal, and Γ(h⁻ ≥ 0 K⁰Lντ) / Γtotal, and therefore not used in the fit.

³Low energy experiments are not in average or fit because the systematic errors in background subtraction are judged to be large.

$$
\begin{array}{l}
\Gamma(h^{-} h^{+} h^{+} \geq 0 \text{ neutrals } \nu_{\tau} \text{ (ex. } K_{S}^{0} \rightarrow \pi^{+} \pi^{-}) ("3/2 h^{+} h^{+} h^{+}) / \Gamma_{\text{total}} \\
\Gamma_{63}/\Gamma = (\Gamma_{70}+\Gamma_{78}+\Gamma_{85}+\Gamma_{97}+\Gamma_{103}+\Gamma_{106}+\Gamma_{107}+0.2804f_{150}+ \\
0.2804f_{152}+0.2804f_{154}+0.491f_{170}+0.9078f_{178}+0.9078f_{179}+0.9078f_{180})/\Gamma
\end{array}
$$

$$
\text{VALUE (\%)} \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT} \quad \text{\Gamma63/}\Gamma
$$

$$
\textbf{14.55} \pm 0.06 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
$$

$$
\textbf{14.61} \pm 0.06 \text{ OUR AVERAGE}
$$

$$
14.55 \pm 0.105 \pm 0.076 \quad 1 \text{ ACHARD} \quad 01\text{D} \quad \text{L3} \quad 1992-1995 \text{ LEP runs}
$$

$$
14.96 \pm 0.09 \pm 0.22 \quad 10.4\text{k} \quad \text{AKERS} \quad 95\text{Y} \quad \text{OPAL} \quad 1991-1994 \text{ LEP runs}
$$

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

$$
14.652 \pm 0.067 \pm 0.086 \quad \text{SCHAEL} \quad 05\text{C} \quad \text{ALEP} \quad 1991-1995 \text{ LEP runs}
$$

$$
14.569 \pm 0.093 \pm 0.048 \quad 23\text{k} \quad \text{ABREU} \quad 01\text{M} \quad \text{DLPH} \quad 1992-1995 \text{ LEP runs}
$$

$$
14.22 \pm 0.10 \pm 0.37 \quad \text{3 BALEST} \quad 95\text{C} \quad \text{CLEO} \quad E_{\text{cm}}^{\text{ee}} \approx 10.6 \text{ GeV}
$$

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

$$
15.26 \pm 0.26 \pm 0.22 \quad \text{ACTON} \quad 92\text{H} \quad \text{OPAL} \quad \text{Repl. by AKERS 95Y}
$$

$$
13.3 \pm 0.3 \pm 0.8 \quad 4 \text{ ALBRECHT} \quad 92\text{D} \quad \text{ARG} \quad E_{\text{cm}}^{\text{ee}} = 9.4-10.6 \text{ GeV}
$$

$$
14.35 \pm \frac{+0.40}{-0.45} \pm 0.24 \quad \text{DECAMP} \quad 92\text{C} \quad \text{ALEP} \quad 1989-1990 \text{ LEP runs}
$$

¹The correlation coefficients between this measurement and the ACHARD 01D measurements of B(τ → “1-prong”) and B(τ → “5-prong”) are -0.978 and -0.19 respectively.

²The correlation coefficients between this measurement and the ABREU 01M measurements of B(τ → 1-prong) and B(τ → 5-prong) are -0.98 and -0.08 respectively.

³Not independent of BALEST 95C B(h⁻h⁺h⁺ντ) and B(h⁻h⁺h⁺π⁰ντ) values, and BORTOLETTO 93 B(h⁻h⁺h⁺2π⁰ντ)/B(h⁻h⁺h⁺ ≥ 0 neutrals ντ) value.

⁴This ALBRECHT 92D value is not independent of their Γ(μ⁻νµ⁺ντ)Γ(e⁻νeντ) / Γtotal value.

$$
\begin{array}{l}
\Gamma(h^{-} h^{+} h^{+} \nu_{\tau}) / \Gamma_{\text{total}} \qquad \Gamma_{64}/\Gamma \\
\Gamma_{64}/\Gamma = (0.34598f_{36}+0.34598f_{38}+\Gamma_{70}+\Gamma_{97}+\Gamma_{106}+0.491f_{170}+0.0153f_{179})/\Gamma
\end{array}
$$

$$
\text{VALUE (\%)} \quad \text{EVTS} \quad \text{DOCUMENT ID} \quad \text{TECN} \quad \text{COMMENT}
$$

$$
\textbf{9.80} \pm 0.05 \text{ OUR FIT} \quad \text{(Produced by HFLAV)}
$$

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

$$
7.6 \pm 0.1 \pm 0.5 \quad 7.5\text{k} \quad 1 \text{ ALBRECHT} \quad 96\text{E} \quad \text{ARG} \quad E_{\text{cm}}^{\text{ee}} = 9.4-10.6 \text{ GeV}
$$
• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>9.92 ± 0.10 ± 0.09</td><td>11.2k</td><td>2 BUSKULIC</td><td>96 ALEC</td><td>Repl. by SCHAEL 05C</td></tr><tr><td>9.49 ± 0.36 ± 0.63</td><td></td><td>DECAMP</td><td>92c ALEC</td><td>Repl. by SCHAEL 05C</td></tr><tr><td>8.7 ± 0.7 ± 0.3</td><td>694</td><td>3 BEHREND</td><td>90 CELL</td><td>E<sup>ee</sup><sub>cm</sub> = 35 GeV</td></tr><tr><td>7.0 ± 0.3 ± 0.7</td><td>1566</td><td>4 BAND</td><td>87 MAC</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>6.7 ± 0.8 ± 0.9</td><td></td><td>5 BURCHAT</td><td>87 MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>6.4 ± 0.4 ± 0.9</td><td></td><td>6 RUCKSTUHL</td><td>86 DLCO</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>7.8 ± 0.5 ± 0.8</td><td>890</td><td>SCHMIDKE</td><td>86 MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>8.4 ± 0.4 ± 0.7</td><td>1255</td><td>6 FERNANDEZ</td><td>85 MAC</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>9.7 ± 2.0 ± 1.3</td><td></td><td>BEHREND</td><td>84 CELL</td><td>E<sup>ee</sup><sub>cm</sub> = 14,22 GeV</td></tr></tbody></table>

1. ALBRECHT 96c not independent of ALBRECHT 93c $\Gamma(h^{-}h^{+}h^{+}\nu_{\tau}(\text{ex. K}^{0}) \times \Gamma(\text{particle}^{-} \ge 0 \text{ neutrals} \ge 0 K^{0} L_{\tau})/\Gamma_{\text{total}}^{2}$ value.

2. BUSKULIC 96 quote $B(h^{-}h^{-}h^{+}\nu_{\tau}(\text{ex. K}^{0})) = 9.50 \pm 0.10 \pm 0.11$. We add 0.42 to remove their $K^{0}$ correction and reduce the systematic error accordingly.

3. BEHREND 90 subtract 0.3% to account for the $\tau^{-} \to K^{+}(892)^{-}\nu_{\tau}$ contribution to measured events.

4. BAND 87 subtract for charged kaon modes; not independent of FERNANDEZ 85 value.

5. BURCHAT 87 value is not independent of SCHMIDKE 86 value.

6. Value obtained by multiplying paper's $R = B(h^{-}h^{-}h^{+}\nu_{\tau})/B(3\text{-(prong)})$ by B(3-prong) = 0.143 and subtracting 0.3% for $K^{+}(892)$ background.

$$ \Gamma(h^{-}h^{-}h^{+}\nu_{\tau}(\text{ex. K}^{0})) / \Gamma_{\text{total}} \quad \Gamma_{65}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>9.46 ± 0.05</b></td><td><b>OUR FIT</b></td><td><b>(Produced by HFLAV)</b></td><td></td><td></td></tr><tr><td><b>9.44 ± 0.14</b></td><td><b>OUR AVERAGE</b></td><td><b>Error includes scale factor of 1.4. See the ideogram below.</b></td><td></td><td></td></tr><tr><td>9.317 ± 0.090 ± 0.082</td><td>12.2k</td><td>1 ABDALLAH</td><td>06A DLPH</td><td>1992-1995 LEP runs</td></tr><tr><td>9.51 ± 0.07 ± 0.20</td><td>37.7k</td><td>BALEST</td><td>95C CLEO</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV</td></tr></tbody></table>

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

9.87 ± 0.10 ± 0.24 2 AKERS 95Y OPAL 1991-1994 LEP runs

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

9.50 ± 0.10 ± 0.11 11.2k 3 BUSKULIC 96 ALEC Repl. by SCHAEL 05C

1. See footnote to ABDALLAH 06A $\Gamma(\tau^{-} \to h^{-}\nu_{\tau})/\Gamma_{\text{total}}$ measurement for correlations with other measurements.

2. Not independent of AKERS 95Y $B(h^{-}h^{-}h^{+} \ge 0 \text{ neutrals} \nu_{\tau}(\text{ex. K}^{0} S \to \pi^{+}\pi^{-}))$ and $B(h^{-}h^{-}h^{+}\nu_{\tau}(\text{ex. K}^{0})) / B(h^{-}h^{-}h^{+} \ge 0 \text{ neutrals} \nu_{\tau}(\text{ex. K}^{0} S \to \pi^{+}\pi^{-}))$ values.

3. Not independent of BUSKULIC 96 $B(h^{-}h^{-}h^{+}\nu_{\tau})$ value.

WEIGHTED AVERAGE
9.44±0.14 (Error scaled by 1.4)

<figure><img src="image_412.png" /></figure>

$$ \Gamma(h^{-}h^{-}h^{+}\nu_{\tau}(\text{ex. K}^{0})) / \Gamma(h^{-}h^{-}h^{+} \ge 0 \text{ neutrals } \nu_{\tau}(\text{ex. K}^{0} S \to \pi^{+}\pi^{-}) \quad \Gamma_{65}/\Gamma_{63} $$

$$ \Gamma_{65}/\Gamma_{63} = (\Gamma_{70} + \Gamma_{97} + \Gamma_{106} + 0.491\Gamma_{170} + 0.0153\Gamma_{178} + 0.0153\Gamma_{179}) / (0.4247\Gamma_{52} + \Gamma_{70} + \Gamma_{78} + \Gamma_{85} + \Gamma_{89} + \Gamma_{97} + \Gamma_{103} + \Gamma_{106} + \Gamma_{107} + 0.2804\Gamma_{150} + 0.2302\Gamma_{151} + 0.2804\Gamma_{152} + 0.2804\Gamma_{154} + 0.1131\Gamma_{156} + 0.3257\Gamma_{160} + 0.491\Gamma_{170} + 0.9078\Gamma_{178} + 0.9078\Gamma_{179} + 0.9078\Gamma_{180} + 0.892\Gamma_{182}) $$

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>64.98 ± 0.31</b></td><td><b>OUR FIT</b></td><td><b>(Produced by HFLAV)</b></td><td></td></tr><tr><td><b>66.0 ± 0.4</b></td><td><b>± 1.4</b></td><td><b>AKERS</b></td><td><b>95Y OPAL</b></td><td><b>1991-1994 LEP runs</b></td></tr></tbody></table>

$$ \Gamma(h^{-}h^{-}h^{+}\nu_{\tau}(\text{ex. K}^{0}, \omega)) / \Gamma_{\text{total}} \quad \Gamma_{66}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>9.43 ± 0.05</b></td><td><b>OUR FIT</b></td><td><b>(Produced by HFLAV)</b></td><td></td></tr></tbody></table>

$$ \Gamma(\pi^{-} \pi^{+} \pi^{-} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{67}/\Gamma = (0.34598\Gamma_{36} + \Gamma_{70} + 0.0153\Gamma_{178}) / \Gamma $$

$$ \Gamma(\pi^{-} \pi^{+} \pi^{-} \nu_{\tau}(\text{ex. K}^{0})) / \Gamma_{\text{total}} \quad \Gamma_{68}/\Gamma = (\Gamma_{70} + 0.0153\Gamma_{178}) / \Gamma $$

9.02±0.05 OUR FIT (Produced by HFLAV)

8.77±0.13 OUR AVERAGE Error includes scale factor of 1.1.

<table><tbody><tr><td>8.42±0.00<sup>+0.26</sup><sub>-0.25</sub></td><td>8.9M</td><td>1 LEE</td><td>10 BELL</td><td>666 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr><tr><td>8.83±0.01±0.13</td><td>1.6M</td><td>2 AUBERT</td><td>08 BABR</td><td>342 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr><tr><td>9.13±0.05±0.46</td><td>43k</td><td>3 BRIERE</td><td>03 CLE3</td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

1. Quoted statistical error is 0.003%. Correlation matrix for LEE 10 branching fractions:

(1) $\Gamma(\tau^{-} \to \pi^{-}\pi^{+}\pi^{-}\nu_{\tau}(\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(2) $\Gamma(\tau^{-} \to K^{-}\pi^{+}\pi^{-}\nu_{\tau}(\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(3) $\Gamma(\tau^{-} \to K^{-}K^{+}\pi^{-}\nu_{\tau}) / \Gamma_{\text{total}}$

(4) $\Gamma(\tau^{-} \to K^{-}K^{+}K^{-}\nu_{\tau}) / \Gamma_{\text{total}}$

(1) (2) (3)

(2) 0.175

(3) 0.049 0.080

(4) -0.053 0.035 -0.008

2. Correlation matrix for AUBERT 08 branching fractions:

(1) $\Gamma(\tau^{-} \to \pi^{-}\pi^{+}\pi^{-}\nu_{\tau}(\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(2) $\Gamma(\tau^{-} \to K^{-}\pi^{+}\pi^{-}\nu_{\tau}(\text{ex. K}^{0})) / \Gamma_{\text{total}}$

(3) $\Gamma(\tau^{-} \to K^{-}K^{+}\pi^{-}\nu_{\tau}) / \Gamma_{\text{total}}$

(4) $\Gamma(\tau^{-} \to K^{-}K^{+}K^{-}\nu_{\tau}) / \Gamma_{\text{total}}$

(1) (2) (3)

(2) 0.544

(3) 0.390 0.177

(4) 0.031 0.093 0.087

3. 47% correlated with BRIERE 03 $\tau^{-} \to K^{-}\pi^{+}\pi^{-}\nu_{\tau}$ and 71% correlated with $\tau^{-} \to K^{-}K^{+}\pi^{-}\nu_{\tau}$ because of a common 5% normalization error.

$$ \Gamma(\pi^{-} \pi^{+} \pi^{-} \nu_{\tau}(\text{ex. K}^{0}), \text{non-axial vector}) / \Gamma(\pi^{-} \pi^{+} \pi^{-} \nu_{\tau}(\text{ex. K}^{0})) \quad \Gamma_{69}/\Gamma_{68} $$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>&lt;0.261</b></td><td>95</td><td>1 ACKERSTAFF</td><td>97R</td><td>OPAL 1992-1994 LEP runs</td></tr></tbody></table>

1. Model-independent limit from structure function analysis on contribution to $B(\tau^{-} \to \pi^{-}\pi^{+}\pi^{-}\nu_{\tau}(\text{ex. K}^{0}))$ from non-axial vectors.

$$ \Gamma(\pi^{-} \pi^{+} \pi^{-} \nu_{\tau}(\text{ex. K}^{0}, \omega)) / \Gamma_{\text{total}} \quad \Gamma_{70}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>8.99 ± 0.05</b></td><td><b>OUR FIT</b></td><td><b>(Produced by HFLAV)</b></td><td></td><td></td></tr><tr><td><b>9.041 ± 0.060 ± 0.076</b></td><td>29k</td><td>1 SCHAEL</td><td>05C ALEP</td><td>1991-1995 LEP runs</td></tr></tbody></table>

1. See footnote to SCHAEL 05C $\Gamma(\tau^{-} \to e^{-}\nu_{e}\nu_{\tau}) / \Gamma_{\text{total}}$ measurement for correlations with other measurements.

$$ \Gamma(h^{-}h^{-}h^{+} \ge 1 \text{ neutrals } \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{71}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><b>5.29 ± 0.05</b></td><td><b>OUR FIT</b></td><td><b>(Produced by HFLAV)</b></td><td></td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>5.6 ± 0.7 ± 0.3</td><td>352</td><td>1 BEHREND</td><td>90 CELL</td><td>E<sup>ee</sup><sub>cm</sub> = 35 GeV</td></tr><tr><td>4.2 ± 0.5 ± 0.9</td><td>203</td><td>2 ALBRECHT</td><td>87L ARG</td><td>E<sup>ee</sup><sub>cm</sub> = 10 GeV</td></tr><tr><td>6.1 ± 0.8 ± 0.9</td><td></td><td>3 BURCHAT</td><td>87 MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>7.6 ± 0.4 ± 0.9</td><td></td><td>4,5 RUCKSTUHL</td><td>86 DLCO</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>4.7 ± 0.5 ± 0.8</td><td>530</td><td>6 SCHMIDKE</td><td>86 MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>5.6 ± 0.4 ± 0.7</td><td></td><td>5 FERNANDEZ</td><td>85 MAC</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>6.2 ± 2.3 ± 1.7</td><td></td><td>BEHREND</td><td>84 CELL</td><td>E<sup>ee</sup><sub>cm</sub> = 14,22 GeV</td></tr></tbody></table>

1. BEHREND 90 value is not independent of BEHREND 90 $B(3h\nu_{\tau} \ge 1 \text{ neutrals}) + B(5\text{prong})$.

2. ALBRECHT 87L measure the product of branching ratios $B(3\pi^{+} \pi^{-} \nu_{\tau})$ ($B(e^{+}\pi^{0} \nu_{\tau} \text{ or } K \text{ or } \rho)\nu_{\tau}) = 0.029$ and use the PDG 86 values for the second branching ratio which sum to 0.69 ± 0.03 to get the quoted value.

3. BURCHAT 87 value is not independent of SCHMIDKE 86 value.

4. Contributions from kaons and from $>1\pi^{0}$ are subtracted. Not independent of (3-prong + $0\pi^{0}$) and (3-prong + $\ge 0\pi^{0}$) values.

5. Value obtained using paper's $R = B(h^{-}h^{-}h^{+}\nu_{\tau}) / B(3\text{-(prong)})$ and current $B(3\text{-(prong)}) = 0.143$.

6. Not independent of SCHMIDKE 86 $h^{-}h^{-}h^{+}\nu_{\tau}$ and $h^{-}h^{-}h^{+}(\ge 0\pi^{0})\nu_{\tau}$ values.

$$ \Gamma(h^{-}h^{-}h^{+} \ge 1 \pi^{0} \nu_{\tau}(\text{ex. K}^{0})) / \Gamma_{\text{total}} \quad \Gamma_{72}/\Gamma $$

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

5.09 ± 0.05 OUR FIT (Produced by HFLAV)

5.10 ± 0.12 OUR AVERAGE

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

<table><tbody><tr><td>5.106 ± 0.083 ± 0.103</td><td>10.1k</td><td>1 ABDALLAH</td><td>06A DLPH</td><td>1992-1995 LEP runs</td></tr><tr><td>5.09 ± 0.10 ± 0.23</td><td></td><td>2 AKERS</td><td>95Y OPAL</td><td>1991-1994 LEP runs</td></tr></tbody></table>
• • • We do not use the following data for averages, fits, limits, etc. • • •

4.95 ± 0.29 ± 0.65 570 DECAMP 92C ALEP Repl. by SCHAEL 05C
1. See footnote to ABDALLAH 06A $\Gamma(\tau^{-} \rightarrow h^{-} \nu_{\tau})/\Gamma_{\text{total}}$ measurement for correlations with other measurements.

2. Not independent of AKERS 95Y B($h^{-}h^{-}h^{+} \ge 0$ neutrals$\nu_{\tau}$ (ex. $K^{0}_{S} \rightarrow \pi^{+}\pi^{-}$)) and B($h^{-}h^{-}h^{+} \ge 0$ neutrals$\nu_{\tau}$ (ex. $K^{0}$)) / B($h^{-}h^{-}h^{+} \ge 0$ neutrals$\nu_{\tau}$ (ex. $K^{0}_{S} \rightarrow \pi^{+}\pi^{-}$)) values.

$$
\begin{aligned}
\Gamma(h^{-}h^{-}h^{+}\pi^{0}\nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{73}/\Gamma = (0.34598\Gamma_{41}+0.34598\Gamma_{43}+\Gamma_{78}+\Gamma_{103}+\Gamma_{107}+0.2302\Gamma_{152}+0.892\Gamma_{178}+ \\
& \quad 0.892\Gamma_{179}+0.0153\Gamma_{180})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>4.76 ± 0.05</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

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

4.45 ± 0.09 ± 0.07 6.1k 1 BUSKULIC 96 ALEP Repl. by SCHAEL 05C

1. BUSKULIC 96 quote B($h^{-}h^{-}h^{+}\pi^{0}\nu_{\tau}$ (ex. $K^{0}$)) = 4.30 ± 0.09 ± 0.09. We add 0.15 to remove their $K^{0}$ correction and reduce the systematic error accordingly.

$$
\begin{aligned}
\Gamma(h^{-}h^{-}h^{+}\pi^{0}\nu_{\tau}(\text{ex.} K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{74}/\Gamma = (\Gamma_{78}+\Gamma_{103}+\Gamma_{107}+0.2302\Gamma_{152}+0.892\Gamma_{178}+0.892\Gamma_{179}+0.0153\Gamma_{180})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>4.57 ± 0.05</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

4.45 ± 0.14 OUR AVERAGE Error includes scale factor of 1.2.

4.545 ± 0.106 ± 0.103 8.9k 1 ABDALLAH 06A DLPH 1992-1995 LEP runs

4.23 ± 0.06 ± 0.22 7.2k BALEST 95C CLEO $E_{\text{cm}}^{ee} \approx 10.6$ GeV

1. See footnote to ABDALLAH 06A $\Gamma(\tau^{-} \rightarrow h^{-} \nu_{\tau})/\Gamma_{\text{total}}$ measurement for correlations with other measurements.

$$
\begin{aligned}
\Gamma(h^{-}h^{-}h^{+}\pi^{0}\nu_{\tau}(\text{ex. } K^{0}, \omega))/\Gamma_{\text{total}} & \quad \Gamma_{75}/\Gamma = (\Gamma_{78}+\Gamma_{103}+\Gamma_{107}+0.2302\Gamma_{152})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2.79 ± 0.07</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(\pi^{-}\pi^{+}\pi^{-}\pi^{0}\nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{76}/\Gamma = (0.34598\Gamma_{41}+\Gamma_{78}+0.892\Gamma_{178}+0.0153\Gamma_{180})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>4.62 ± 0.05</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(\pi^{-}\pi^{+}\pi^{-}\pi^{0}\nu_{\tau}(\text{ex.} K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{77}/\Gamma = (\Gamma_{78}+0.892\Gamma_{178}+0.0153\Gamma_{180})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>4.49 ± 0.05</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

4.45 ± 0.13 OUR AVERAGE Error includes scale factor of 1.6.

4.598 ± 0.057 ± 0.064 16k 1 SCHAEEL 05C ALEP 1991-1995 LEP runs

4.19 ± 0.10 ± 0.21 2 EDWARDS 00A CLEO 4.7 fb⁻¹ $E_{\text{cm}}^{ee} = 10.6$ GeV

1. SCHAEEL 05C quote (4.590 ± 0.057 ± 0.064)%. We add 0.008% to remove their correction for $\tau^{-} \rightarrow \pi^{-}\pi^{0}\omega\nu_{\tau} \rightarrow \pi^{-}\pi^{0}\pi^{+}\pi^{-}\nu_{\tau}$ decays. See footnote to SCHAEL 05C $\Gamma(\tau^{-} \rightarrow e^{-}\pi^{0}\nu_{\tau})/\Gamma_{\text{total}}$ measurement for correlations with other measurements.

2. EDWARDS 00A quote (4.19 ± 0.10) × 10⁻² with a 5% systematic error.

$$
\begin{aligned}
\Gamma(\pi^{-}\pi^{+}\pi^{-}\pi^{0}\nu_{\tau}(\text{ex.} K^{0}, \omega))/\Gamma_{\text{total}} & \quad \Gamma_{78}/\Gamma = (\Gamma_{78}+0.892\Gamma_{178}+0.0153\Gamma_{180})/\Gamma
\end{aligned}
$$

2.74 ± 0.07 OUR FIT (Produced by HFLAV)

$$
\begin{aligned}
\Gamma(h^{-}\rho\pi^{0}\nu_{\tau})/\Gamma(h^{-}h^{-}h^{+}\pi^{0}\nu_{\tau}) & \quad \Gamma_{79}/\Gamma_{73} \\
\Gamma(\rho^{-}h^{-}\nu_{\tau})/\Gamma(h^{-}h^{-}h^{+}\pi^{0}\nu_{\tau}) & \quad \Gamma_{80}/\Gamma_{73}
\end{aligned}
$$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>• • • We do not use the following data for averages, fits, limits, etc. • • •</td><td></td><td></td><td></td><td></td></tr><tr><td>0.30 ± 0.04 ± 0.02</td><td>393</td><td>ALBRECHT</td><td>91D</td><td>ARG $E_{\text{cm}}^{ee} = 9.4-10.6$ GeV</td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(h^{-}\rho^{+}h^{-}\nu_{\tau})/\Gamma(h^{-}h^{-}h^{+}\pi^{0}\nu_{\tau}) & \quad \Gamma_{80}/\Gamma_{73} \\
\Gamma(\rho^{-}h^{-}\nu_{\tau})/\Gamma(h^{-}h^{-}h^{+}\pi^{0}\nu_{\tau}) & \quad \Gamma_{81}/\Gamma_{73}
\end{aligned}
$$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>• • • We do not use the following data for averages, fits, limits, etc. • • •</td><td></td><td></td><td></td><td></td></tr><tr><td>0.10 ± 0.03 ± 0.04</td><td>142</td><td>ALBRECHT</td><td>91D</td><td>ARG $E_{\text{cm}}^{ee} = 9.4-10.6$ GeV</td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(h^{-}\rho^{-}h^{+}\nu_{\tau})/\Gamma(h^{-}h^{-}h^{+}\pi^{0}\nu_{\tau}) & \quad \Gamma_{81}/\Gamma_{73} \\
\Gamma(\rho^{-}h^{-}\nu_{\tau})/\Gamma(h^{-}h^{-}h^{+}\pi^{0}\nu_{\tau}) & \quad \Gamma_{82}/\Gamma_{73}
\end{aligned}
$$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>• • • We do not use the following data for averages, fits, limits, etc. • • •</td><td></td><td></td><td></td><td></td></tr><tr><td>0.26 ± 0.05 ± 0.01</td><td>370</td><td>ALBRECHT</td><td>91D</td><td>ARG $E_{\text{cm}}^{ee} = 9.4-10.6$ GeV</td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(h^{-}h^{-}h^{+} \ge 2\pi^{0}\nu_{\tau}(\text{ex. } K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{82}/\Gamma = (\Gamma_{85}+\Gamma_{86}+0.2302\Gamma_{150}+0.2302\Gamma_{154}+0.892\Gamma_{180})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.517 ± 0.031</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

0.561 ± 0.068 ± 0.095 1.3k 1 ABDALLAH 06A DLPH 1992-1995 LEP runs

1. See footnote to ABDALLAH 06A $\Gamma(\tau^{-} \rightarrow h^{-} \nu_{\tau})/\Gamma_{\text{total}}$ measurement for correlations with other measurements.

$$
\begin{aligned}
\Gamma(h^{-}h^{-}h^{+}2\pi^{0}\nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{83}/\Gamma = (0.4247\Gamma_{48}+\Gamma_{85}+0.2302\Gamma_{150}+0.2302\Gamma_{154}+0.892\Gamma_{180})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.505 ± 0.031</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(h^{-}h^{-}h^{+}2\pi^{0}\nu_{\tau}(\text{ex.} K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{84}/\Gamma = (\Gamma_{85}+0.2302\Gamma_{150}+0.2302\Gamma_{154}+0.892\Gamma_{180})/\Gamma \\
\Gamma_{84}/\Gamma_{62} & \quad (\Gamma_{85}+0.2302\Gamma_{150}+0.2302\Gamma_{154}+0.892\Gamma_{180})/(0.34598\Gamma_{36}+ \\
& \quad 0.34598\Gamma_{38}+0.34598\Gamma_{41}+0.34598\Gamma_{43}+0.4247\Gamma_{48}+0.6920\Gamma_{49}+0.8494\Gamma_{52}+ \\
& \quad 0.6920\Gamma_{56}+0.6534\Gamma_{61}+\Gamma_{70}+\Gamma_{78}+\Gamma_{85}+\Gamma_{89}+\Gamma_{97}+\Gamma_{103}+\Gamma_{106}+\Gamma_{107}+ \\
& \quad 0.2804\Gamma_{150}+0.2302\Gamma_{151}+0.2804\Gamma_{152}+0.2804\Gamma_{154}+0.3759\Gamma_{156}+0.3257\Gamma_{160}+ \\
& \quad 0.7259\Gamma_{170}+0.9078\Gamma_{178}+0.9078\Gamma_{179}+0.9078\Gamma_{180}+0.892\Gamma_{182})
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.495 ± 0.031</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

<table><thead><tr><th>0.435 ± 0.030 ± 0.035</th><th>2.6k</th><th>1 SCHAEEL</th><th>05C ALEP</th><th>1991-1995 LEP runs</th></tr></thead><tbody><tr><td>• • • We do not use the following data for averages, fits, limits, etc. • • •</td><td></td><td></td><td></td><td></td></tr></tbody></table>

0.50 ± 0.07 ± 0.07 1.8k BUSKULIC 96 ALEP Repl. by SCHAEL 05C

1. SCHAEEL 05C quote (0.392 ± 0.030 ± 0.035)%. We add 0.043% to remove their correction for $\tau^{-} \rightarrow \pi^{-}\eta\pi^{0}\nu_{\tau} \rightarrow \pi^{-}\pi^{+}\pi^{-}\pi^{0}\nu_{\tau}$ and $\tau^{-} \rightarrow K^{*}(892)\eta\nu_{\tau} \rightarrow K^{-}\pi^{+}\pi^{-}2\pi^{0}\nu_{\tau}$ decays. See footnote to SCHAEL 05C $\Gamma(\tau^{-} \rightarrow e^{-}\pi^{0}\nu_{\tau})/\Gamma_{\text{total}}$ measurement for correlations with other measurements.

$$
\begin{aligned}
\Gamma(h^{-}h^{-}h^{+}2\pi^{0}\nu_{\tau}(\text{ex.} K^{0}))/\Gamma(h^{-}h^{-}h^{+} \ge 0 \text{ neutrals} \ge 0 K^{0}\nu_{\tau}) & \quad \Gamma_{84}/\Gamma_{62} \\
\Gamma_{84}/\Gamma_{62} & \quad (\Gamma_{85}+0.2302\Gamma_{150}+0.2302\Gamma_{154}+0.892\Gamma_{180})/(0.34598\Gamma_{36}+ \\
& \quad 0.34598\Gamma_{38}+0.34598\Gamma_{41}+0.34598\Gamma_{43}+0.4247\Gamma_{48}+0.6920\Gamma_{49}+0.8494\Gamma_{52}+ \\
& \quad 0.6920\Gamma_{56}+0.6534\Gamma_{61}+\Gamma_{70}+\Gamma_{78}+\Gamma_{85}+\Gamma_{89}+\Gamma_{97}+\Gamma_{103}+\Gamma_{106}+\Gamma_{107}+ \\
& \quad 0.2804\Gamma_{150}+0.2302\Gamma_{151}+0.2804\Gamma_{152}+0.2804\Gamma_{154}+0.3759\Gamma_{156}+0.3257\Gamma_{160}+ \\
& \quad 0.7259\Gamma_{170}+0.9078\Gamma_{178}+0.9078\Gamma_{179}+0.9078\Gamma_{180}+0.892\Gamma_{182})
\end{aligned}
$$

<table><thead><tr><th>VALUE (units 10⁻²)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>3.26 ± 0.20</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

<table><thead><tr><th>3.4 ± 0.2 ± 0.3</th><th>668</th><th>BORTOLETTO93</th><th>CLEO</th><th>$E_{\text{cm}}^{ee} \approx 10.6$ GeV</th></tr></thead><tbody><tr><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(h^{-}h^{-}h^{+}2\pi^{0}\nu_{\tau}(\text{ex.} K^{0}, \omega, \eta))/\Gamma_{\text{total}} & \quad \Gamma_{85}/\Gamma = \\
\Gamma_{85}/\Gamma_{62} & \quad (\Gamma_{85}+0.2302\Gamma_{150}+0.2302\Gamma_{154}+0.892\Gamma_{180})/(0.34598\Gamma_{36}+ \\
& \quad 0.34598\Gamma_{38}+0.34598\Gamma_{41}+0.34598\Gamma_{43}+0.4247\Gamma_{48}+0.6920\Gamma_{49}+0.8494\Gamma_{52}+ \\
& \quad 0.6920\Gamma_{56}+0.6534\Gamma_{61}+\Gamma_{70}+\Gamma_{78}+\Gamma_{85}+\Gamma_{89}+\Gamma_{97}+\Gamma_{103}+\Gamma_{106}+\Gamma_{107}+ \\
& \quad 0.2804\Gamma_{150}+0.2302\Gamma_{151}+0.2804\Gamma_{152}+0.2804\Gamma_{154}+0.3759\Gamma_{156}+0.3257\Gamma_{160}+ \\
& \quad 0.7259\Gamma_{170}+0.9078\Gamma_{178}+0.9078\Gamma_{179}+0.9078\Gamma_{180}+0.892\Gamma_{182})
\end{aligned}
$$

$$
\begin{aligned}
\Gamma(h^{-}h^{-}h^{+}3\pi^{0}\nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{86}/\Gamma = (0.4247\Gamma_{52}+\Gamma_{87}+0.1131\Gamma_{156})/\Gamma \\
\Gamma_{86}/\Gamma_{62} & \quad (\Gamma_{85}+0.2302\Gamma_{150}+0.2302\Gamma_{154}+0.892\Gamma_{180})/(0.34598\Gamma_{36}+ \\
& \quad 0.34598\Gamma_{38}+0.34598\Gamma_{41}+0.34598\Gamma_{43}+0.4247\Gamma_{48}+0.6920\Gamma_{49}+0.8494\Gamma_{52}+ \\
& \quad 0.6920\Gamma_{56}+0.6534\Gamma_{61}+\Gamma_{70}+\Gamma_{78}+\Gamma_{85}+\Gamma_{89}+\Gamma_{97}+\Gamma_{103}+\Gamma_{106}+\Gamma_{107}+ \\
& \quad 0.2804\Gamma_{150}+0.2302\Gamma_{151}+0.2804\Gamma_{152}+0.2804\Gamma_{154}+0.3759\Gamma_{156}+0.3257\Gamma_{160}+ \\
& \quad 0.7259\Gamma_{170}+0.9078\Gamma_{178}+0.9078\Gamma_{179}+0.9078\Gamma_{180}+0.892\Gamma_{182})
\end{aligned}
$$

<table><thead><tr><th>2.13 ± 0.30</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></thead><tbody><tr><td>2.2 ± 0.3 ± 0.4</td><td>139</td><td>ANASTASSOV 01</td><td>CLEO</td><td>$E_{\text{cm}}^{ee} \approx 10.6$ GeV</td></tr></tbody></table>

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

<table><thead><tr><th>4.9</th><th>95</th><th>SCHAEL</th><th>05C ALEP</th><th>1991-1995 LEP runs</th></tr></thead><tbody><tr><td>2.85 ± 0.56 ± 0.51</td><td>57</td><td>ANDERSON</td><td>97</td><td>CLEO Repl. by ANASTASSOV 01</td></tr></tbody></table>

<table><thead><tr><th>11 ± 4 ± 5</th><th>440</th><th>1 BUSKULIC</th><th>96 ALEP</th><th>Repl. by SCHAEL 05C</th></tr></thead><tbody><tr><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

1. BUSKULIC 96 state their measurement is for B($h^{-}h^{-}h^{+} \ge 3\pi^{0}\nu_{\tau}$). We assume that B($h^{-}h^{-}h^{+} \ge 4\pi^{0}\nu_{\tau}$) is very small.

$$
\begin{aligned}
\Gamma(2\pi^{-}\pi^{+}3\pi^{0}\nu_{\tau}(\text{ex.} K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{87}/\Gamma = (\Gamma_{89}+0.2302\Gamma_{151}+0.3257\Gamma_{160}+0.892\Gamma_{182})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (units 10⁻⁴)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.94 ± 0.30</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

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

2.07 ± 0.18 ± 0.37 1 LEES 12x BABR 468 fb⁻¹ $E_{\text{cm}}^{ee} = 10.6$ GeV

1. Not independent of LEES 12x $\Gamma(\tau^{-} \rightarrow \eta\pi^{-}\pi^{+}\pi^{-}\nu_{\tau}(\text{ex.} K^{0}))/\Gamma$, $\Gamma(\tau^{-} \rightarrow \eta\pi^{-}\pi^{0}\pi^{0}\nu_{\tau})/\Gamma$, $\Gamma(\tau^{-} \rightarrow \pi^{-}\omega2\pi^{0}\nu_{\tau})/\Gamma$, and $\Gamma(\tau^{-} \rightarrow f_{1}(1285)\pi^{-}\nu_{\tau} \rightarrow \eta\pi^{-}\pi^{+}\pi^{-}\nu_{\tau})/\Gamma$ values.

$$
\begin{aligned}
\Gamma(2\pi^{-}\pi^{+}3\pi^{0}\nu_{\tau}(\text{ex.} K^{0}, \eta, f_{1}(1285)))/\Gamma_{\text{total}} & \quad \Gamma_{88}/\Gamma = (\Gamma_{89}+0.2302\Gamma_{151}+0.3257\Gamma_{160}+0.892\Gamma_{182})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (units 10⁻⁴)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.69 ± 0.08 ± 0.43</td><td>LEES</td><td>12x</td><td>BABR</td><td>468 fb⁻¹ $E_{\text{cm}}^{ee} = 10.6$ GeV</td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(2\pi^{-}\pi^{+}3\pi^{0}\nu_{\tau}(\text{ex.} K^{0}, \eta, \omega, f_{1}(1285)))/\Gamma_{\text{total}} & \quad \Gamma_{89}/\Gamma = (\Gamma_{91}/\Gamma = (\Gamma_{97}+\Gamma_{106}+0.0153\Gamma_{179})/\Gamma \\
\Gamma_{91}/\Gamma_{68} & \quad (\Gamma_{97}+\Gamma_{106}+0.0153\Gamma_{179})/(\Gamma_{70}+0.0153\Gamma_{178})
\end{aligned}
$$

<table><thead><tr><th>VALUE (units 10⁻⁵)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.4 ± 2.7</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

<table><thead><tr><th>1.0 ± 0.8 ± 3.0</th><th>1 LEES</th><th>12x BABR</th><th>468 fb⁻¹ $E_{\text{cm}}^{ee} = 10.6$ GeV</th><th></th></tr></thead><tbody><tr><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

1. LEES 12x measurement corresponds to the lower limit of < 5.8 × 10⁻⁵ at 90% CL.

$$
\begin{aligned}
\Gamma(K^{-}h^{+}h^{-} \ge 0 \text{ neutrals } \nu_{\tau})/\Gamma_{\text{total}} & \quad \Gamma_{90}/\Gamma = (0.34598\Gamma_{38}+0.34598\Gamma_{43}+\Gamma_{97}+\Gamma_{103}+\Gamma_{106}+\Gamma_{107}+0.2804\Gamma_{152}+ \\
& \quad 0.491\Gamma_{170}+0.9078\Gamma_{179})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.629 ± 0.014</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr><tr><td>&lt;0.6</td><td>90</td><td>AIHARA</td><td>84c</td><td>TPC $E_{\text{cm}}^{ee} = 29$ GeV</td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(K^{-}h^{-}\pi^{-}\nu_{\tau}(\text{ex.} K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{91}/\Gamma = (\Gamma_{97}+\Gamma_{106}+0.0153\Gamma_{179})/\Gamma \\
\Gamma_{91}/\Gamma_{68} & \quad (\Gamma_{97}+\Gamma_{106}+0.0153\Gamma_{179})/(\Gamma_{70}+0.0153\Gamma_{178})
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.437 ± 0.007</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(K^{-}h^{+}\pi^{-}\nu_{\tau}(\text{ex.} K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{91}/\Gamma = (\Gamma_{97}+\Gamma_{106}+0.0153\Gamma_{179})/(\Gamma_{70}+0.0153\Gamma_{178}) \\
\Gamma_{91}/\Gamma_{68} & \quad (\Gamma_{97}+\Gamma_{106}+0.0153\Gamma_{179})/(\Gamma_{70}+0.0153\Gamma_{178})
\end{aligned}
$$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>4.84 ± 0.08</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

<table><thead><tr><th>5.44 ± 0.21 ± 0.53</th><th>7.9k</th><th>RICHICHI</th><th>99 CLEO</th><th>$E_{\text{cm}}^{ee} = 10.6$ GeV</th></tr></thead><tbody><tr><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

$$
\begin{aligned}
\Gamma(K^{-}h^{+}\pi^{-}\nu_{\tau}(\text{ex.} K^{0}))/\Gamma_{\text{total}} & \quad \Gamma_{92}/\Gamma = (\Gamma_{103}+\Gamma_{107}+0.2302\Gamma_{152}+0.892\Gamma_{179})/\Gamma \\
\Gamma_{92}/\Gamma & \quad (\Gamma_{103}+\Gamma_{107}+0.2302\Gamma_{152}+0.892\Gamma_{179})/\Gamma
\end{aligned}
$$

<table><thead><tr><th>VALUE (units 10⁻⁴)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>8.6 ± 1.2</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>
$$ \Gamma(K^{-}h^{+} \pi^{-} \pi^{0} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma(\pi^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) \quad \Gamma_{92} / \Gamma_{77} \\ \Gamma_{92} / \Gamma_{77} = (\Gamma_{103} + \Gamma_{107} + 0.2302 \Gamma_{152} + 0.892 \Gamma_{179}) / (\Gamma_{78} + 0.892 \Gamma_{178} + 0.0153 \Gamma_{180}) $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.91 ± 0.26</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr><tr><td>2.61 ± 0.45 ± 0.42</td><td></td><td>719</td><td>RICCHI</td><td>99 CLEO E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \geq 0 \text{ neutrals } \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{93} / \Gamma \quad (\Gamma_{93} = (0.34598 \Gamma_{38} + 0.34598 \Gamma_{43} + \Gamma_{97} + \Gamma_{103} + 0.2804 \Gamma_{152} + 0.9078 \Gamma_{179}) / \Gamma_{\text{total}}) $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.477 ± 0.014</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr><tr><td>0.58 <sup>+0.15</sup><sub>-0.13</sub> ± 0.12</td><td></td><td>20</td><td>1 BAUER</td><td>94 TPC E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></tbody></table>

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

<table><tr><td>0.22 <sup>+0.16</sup><sub>-0.13</sub> ± 0.05</td><td>9</td><td>2</td><td>MILLS</td><td>85 DLCO E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></table>

1. We multiply 0.58% by 0.20, the relative systematic error quoted by BAUER 94, to obtain the systematic error.

2. Error correlated with MILLS 85 (K$\pi\pi\nu$) value. We multiply 0.22% by 0.23, the relative systematic error quoted by MILLS 85, to obtain the systematic error.

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \geq 0 \pi^{0} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}} \quad \Gamma_{94} / \Gamma \quad (\Gamma_{94} = (\Gamma_{97} + \Gamma_{103} + 0.2302 \Gamma_{152} + 0.9078 \Gamma_{179}) / \Gamma_{\text{total}}) $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.373 ± 0.013</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

### 0.30 ± 0.05 OUR AVERAGE

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

<table><tr><td>0.343 ± 0.073 ± 0.031</td><td>ABBENDI</td><td>00D</td><td>OPAL</td><td>1990-1995 LEP runs</td></tr></table>

<table><tr><td>0.275 ± 0.064</td><td>1</td><td>BARATE</td><td>98</td><td>ALEC</td><td>1991-1995 LEP runs</td></tr></table>

1. Not independent of BARATE 98 $\Gamma(\tau^{-} \rightarrow K^{-} \pi^{+} \pi^{-} \nu_{\tau}) / \Gamma_{\text{total}}$ and $\Gamma(\tau^{-} \rightarrow K^{-} \pi^{+} \pi^{-} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}}$ values.

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{95} / \Gamma = (0.34598 \Gamma_{38} + \Gamma_{97} + 0.0153 \Gamma_{179}) / \Gamma \quad (\Gamma_{95} = (0.34598 \Gamma_{38} + \Gamma_{97} + 0.0153 \Gamma_{179}) / \Gamma_{\text{total}}) $$

### 0.345 ± 0.007 OUR FIT

(Produced by HFLAV)

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}} \quad \Gamma_{96} / \Gamma = (\Gamma_{97} + 0.0153 \Gamma_{179}) / \Gamma \quad (\Gamma_{96} = (\Gamma_{97} + 0.0153 \Gamma_{179}) / \Gamma_{\text{total}}) $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.293 ± 0.007</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

<table><tr><td>0.330 ± 0.001 <sup>+0.016</sup><sub>-0.017</sub></td><td>794k</td><td>1</td><td>LEE</td><td>10 BELL 666 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

<table><tr><td>0.273 ± 0.002 ± 0.009</td><td>70k</td><td>2</td><td>AUBERT</td><td>08 BABR 342 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

<table><tr><td>0.415 ± 0.053 ± 0.040</td><td>269</td><td>ABBENDI</td><td>04J</td><td>OPAL 1991-1995 LEP runs</td></tr></table>

<table><tr><td>0.384 ± 0.014 ± 0.038</td><td>3.5k</td><td>3</td><td>BRIERE</td><td>03 CLE3 E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

<table><tr><td>0.214 ± 0.037 ± 0.029</td><td>BARATE</td><td>98</td><td>ALEC</td><td>1991-1995 LEP runs</td></tr></table>

<table><tr><td>0.346 ± 0.023 ± 0.056</td><td>158</td><td>4</td><td>RICCHI</td><td>99 CLEO E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

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

<table><tr><td>0.360 ± 0.082 ± 0.048</td><td>ABBENDI</td><td>00D</td><td>OPAL</td><td>1990-1995 LEP runs</td></tr></table>

1. See footnote to LEE 10 $\Gamma(\tau^{-} \rightarrow \pi^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}}$ measurement for correlations with other measurements. Not independent of LEE 10 $\Gamma(\tau^{-} \rightarrow K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma(\tau^{-} \rightarrow \pi^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0}))$ value.

2. See footnote to AUBERT 08 $\Gamma(\tau^{-} \rightarrow \pi^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}}$ measurement for correlations with other measurements.

3. 47% correlated with BRIERE 03 $\tau^{-} \rightarrow \pi^{-} \pi^{+} \pi^{-} \nu_{\tau}$ and 34% correlated with $\tau^{-} \rightarrow K^{-} K^{+} \pi^{-} \nu_{\tau}$ because of a common 5% normalization error.

4. Not independent of RICCHI 99 $\Gamma(\tau^{-} \rightarrow K^{-} h^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma(\tau^{-} \rightarrow K^{-} K^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}}$ measurement for correlations with other measurements. Not independent of RICCHI 99 $\Gamma(\tau^{-} \rightarrow K^{-} h^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma(\tau^{-} \rightarrow K^{-} K^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}}$ and BALEST 95C $\Gamma(\tau^{-} \rightarrow h^{-} h^{-} h^{+} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}}$ values.

WEIGHTED AVERAGE
0.290 ± 0.018 (Error scaled by 2.4)

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

<figure><img src="image_413.png" /></figure>

$\Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}}$ (%)

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma(\pi^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) \quad \Gamma_{96} / \Gamma_{68} \quad (\Gamma_{96} = (\Gamma_{97} + 0.0153 \Gamma_{179}) / (\Gamma_{70} + 0.0153 \Gamma_{178})) $$

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>3.25 ± 0.07</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

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

$$ 3.92 ± 0.02 <sup>+0.15</sup><sub>-0.16</sub> \quad 794k \quad 1 LEE \quad 10 BELL \quad 666 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV $$

1. Not independent of LEE 10 $\Gamma(\tau^{-} \rightarrow K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}}$ and $\Gamma(\tau^{-} \rightarrow \pi^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}}$ values.

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0}, \omega)) / \Gamma_{\text{total}} \quad \Gamma_{97} / \Gamma \quad (\Gamma_{97} = (K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0}, \omega)) / \Gamma_{\text{total}}) $$

### 2.93 ± 0.07 OUR FIT

(Produced by HFLAV)

$$ \Gamma(K^{-} \rho^{0} \nu_{\tau} \rightarrow K^{-} \pi^{+} \pi^{-} \nu_{\tau}) / \Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) \quad \Gamma_{98} / \Gamma_{96} \quad (\Gamma_{98} = (K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}}) $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.48 ± 0.14 ± 0.10</td><td>1</td><td>ASNER</td><td>00B</td><td>CLEO E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

<table><tr><td>0.39 ± 0.14</td><td>2</td><td>BARATE</td><td>99R</td><td>ALEC 1991-1995 LEP runs</td></tr></table>

1. ASNER 00B assume $\tau^{-} \rightarrow K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})$ decays proceeded only through $K\rho$ and $K^{*}\pi$ intermediate states. They assume the resonance structure of $\tau^{-} \rightarrow K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})$ decays is dominated by $K_{1}(1270)^{-}$ and $K_{1}(1400)^{-}$ resonances, and assume $B(K_{1}(1270) \rightarrow K^{*}(892)\pi) = (16 \pm 5)\%$, $B(K_{1}(1270) \rightarrow K\rho) = (42 \pm 6)\%$, and $B(K_{1}(1400) \rightarrow K\rho) = 0$.

2. BARATE 99R assume $\tau^{-} \rightarrow K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})$ decays proceeded only through $K\rho$ and $K^{*}\pi$ intermediate states. The quoted error is statistical only.

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{99} / \Gamma = (0.34598 \Gamma_{43} + \Gamma_{103} + 0.2302 \Gamma_{152} + 0.892 \Gamma_{179}) / \Gamma \quad (\Gamma_{99} = (0.34598 \Gamma_{43} + \Gamma_{103} + 0.2302 \Gamma_{152} + 0.892 \Gamma_{179}) / \Gamma_{\text{total}}) $$

<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><tbody><tr><td>13.1 ± 1.2</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau}^{0} (\text{ex.} K^{0})) / \Gamma_{\text{total}} \quad \Gamma_{100} / \Gamma = (\Gamma_{103} + 0.2302 \Gamma_{152} + 0.892 \Gamma_{179}) / \Gamma \quad (\Gamma_{100} = (\Gamma_{103} + 0.2302 \Gamma_{152} + 0.892 \Gamma_{179}) / \Gamma_{\text{total}}) $$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>7.9 ± 1.2</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

$$ \Gamma_{\text{7.3 ± 1.2 OUR AVERAGE}} \quad 7.4 ± 0.8 ± 1.1 \quad 1 \quad \text{ARMS} \quad 05 \quad \text{CLE3} \quad 7.6 \text{ fb}^{-1}, \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} \\ \text{BARATE} \quad 98 \quad \text{ALEP} \quad 1991-1995 \text{ LEP runs} $$

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

<table><tr><td>7.5 ± 2.6 ± 1.8</td><td>2</td><td>RICCHI</td><td>99</td><td>CLEO E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

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

<table><tr><td>&lt;17</td><td>95</td><td>ABBENDI</td><td>00D</td><td>OPAL 1990-1995 LEP runs</td></tr></table>

1. Not independent of ARMS 05 $\Gamma(\tau^{-} \rightarrow K^{-} \pi^{+} \pi^{-} \pi^{0} \nu_{\tau} (\text{ex.} K^{0}, \omega)) / \Gamma_{\text{total}}$ and $\Gamma(\tau^{-} \rightarrow K^{-} \omega \nu_{\tau}) / \Gamma_{\text{total}}$ values.

2. Not independent of RICCHI 99 $\Gamma(\tau^{-} \rightarrow K^{-} h^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma(\tau^{-} \rightarrow \pi^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0}))$, $\Gamma(\tau^{-} \rightarrow K^{-} K^{+} \pi^{-} \nu_{\tau}) / \Gamma(\tau^{-} \rightarrow \pi^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0}))$ and BALEST 95C $\Gamma(\tau^{-} \rightarrow h^{-} h^{-} h^{+} \nu_{\tau} (\text{ex.} K^{0})) / \Gamma_{\text{total}}$ values.

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau} (\text{ex.} K^{0}, \eta)) / \Gamma_{\text{total}} \quad \Gamma_{101} / \Gamma = (\Gamma_{103} + 0.892 \Gamma_{179}) / \Gamma \quad (\Gamma_{101} = (\Gamma_{103} + 0.892 \Gamma_{179}) / \Gamma_{\text{total}}) $$

<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><tbody><tr><td>7.6 ± 1.2</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau}^{0} (\text{ex.} K^{0}, \omega)) / \Gamma_{\text{total}} \quad \Gamma_{102} / \Gamma \quad (\Gamma_{102} = (K^{-} \pi^{+} \pi^{-} \nu_{\tau}^{0} (\text{ex.} K^{0}, \omega)) / \Gamma_{\text{total}}) $$

<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><tbody><tr><td>3.7 ± 0.5 ± 0.8</td><td>833</td><td>ARMS</td><td>05</td><td>CLE3 7.6 fb<sup>-1</sup>, E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

$$ \Gamma(K^{-} \pi^{+} \pi^{-} \nu_{\tau}^{0} (\text{ex.} K^{0}, \omega, \eta)) / \Gamma_{\text{total}} \quad \Gamma_{103} / \Gamma = (\Gamma_{103} + 0.892 \Gamma_{179}) / \Gamma \quad (\Gamma_{103} = (\Gamma_{103} + 0.892 \Gamma_{179}) / \Gamma_{\text{total}}) $$

<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><tbody><tr><td>3.9 ± 1.4</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

$$ \Gamma(K^{-} \pi^{+} K^{-} \geq 0 \text{ neu. } \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{104} / \Gamma \quad (\Gamma_{104} = (K^{-} \pi^{+} K^{-} \geq 0 \text{ neu. } \nu_{\tau}) / \Gamma_{\text{total}}) $$

$$ \Gamma(K^{-} K^{+} \pi^{-} \geq 0 \text{ neu. } \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{105} / \Gamma = (\Gamma_{106} + \Gamma_{107}) / \Gamma \quad (\Gamma_{106} = (\Gamma_{106} + \Gamma_{107}) / \Gamma_{\text{total}}) $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.1496 ± 0.0033</td><td>OUR FIT</td><td>(Produced by HFLAV)</td><td></td><td></td></tr></tbody></table>

### 0.203 ± 0.031 OUR AVERAGE

<table><tr><td>0.159 ± 0.053</td><td>± 0.020</td><td>ABBENDI</td><td>00D</td><td>OPAL 1990-1995 LEP runs</td></tr></table>

<table><tr><td>0.15 ± 0.09</td><td>± 0.03</td><td>4</td><td>1 BAUER</td><td>94 TPC E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></table>

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

<table><tr><td>0.238 ± 0.042</td><td>2</td><td>BARATE</td><td>98</td><td>ALEC 1991-1995 LEP runs</td></tr></table>

1. We multiply 0.15% by 0.20, the relative systematic error quoted by BAUER 94, to obtain the systematic error.

2. Not independent of BARATE 98 $\Gamma(\tau^{-} \rightarrow K^{-} K^{+} \pi^{-} \nu_{\tau}) / \Gamma_{\text{total}}$ and $\Gamma(\tau^{-} \rightarrow K^{-} K^{+} \pi^{-} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}}$ values.
$$ \Gamma(K^- K^+ \pi^- \nu_\tau) / \Gamma_{\text{total}} \qquad \Gamma_{106}/\Gamma $$

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

1.435 ±0.027 OUR FIT (Produced by HFLAV)

1.43 ±0.07 OUR AVERAGE Error includes scale factor of 2.4. See the ideogram below.

<table><tbody><tr><td>1.55 ±0.01</td><td>+0.06<br>-0.05</td><td>108k</td><td>1 LEE</td><td>10 BELL</td><td>666 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>1.346 ±0.010 ±0.036</td><td></td><td>18k</td><td>2 AUBERT</td><td>08 BABR</td><td>342 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>1.55 ±0.06 ±0.09</td><td>932</td><td></td><td>3 BRIERE</td><td>03 CLE3</td><td>E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>1.63 ±0.21 ±0.17</td><td></td><td></td><td>BARATE</td><td>98 ALEP</td><td>1991-1995 LEP runs</td></tr></tbody></table>

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

<table><tbody><tr><td>0.87 ±0.56 ±0.40</td><td></td><td>ABBIENDI</td><td>00d</td><td>OPAL</td><td>1990-1995 LEP runs</td></tr></tbody></table>

<table><tbody><tr><td>1.45 ±0.13 ±0.28</td><td>2.3k</td><td>4 RICCHI</td><td>99</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>2.2</td><td>+1.7<br>-1.1</td><td>±0.5</td><td>9</td><td>5 MILLS</td><td>85</td><td>DLCO</td><td>E<sup>ee</sup><sub>cm</sub>=29 GeV</td></tr></tbody></table>

¹See footnote to LEE 10 Γ(τ⁻ → π⁻π⁺π⁻ν_τ(ex.K⁰))/Γ<sub>total</sub> measurement for correlations with other measurements. Not independent of LEE 10 Γ(τ⁻ → K⁻K⁺π⁻ν_τ)/Γ(τ⁻ → π⁻π⁺π⁻ν_τ(ex.K⁰)) value.

²See footnote to AUBERT 08 Γ(τ⁻ → π⁻π⁺π⁻ν_τ(ex.K⁰))/Γ<sub>total</sub> measurement for correlations with other measurements.

³71% correlated with BRIERE 03 τ⁻ → π⁻π⁺π⁻ν_τ and 34% correlated with τ → K⁻π⁺π⁻ν_τ because of a common 5% normalization error.

⁴Not independent of RICCHI 99 Γ(τ⁻ → K⁻K⁺π⁻ν_τ)/Γ(τ⁻ → π⁻π⁺π⁻ν_τ(ex.K⁰)) and BALEST 95C Γ(τ⁻ → h⁻h⁻h⁺h⁺ν_τ(ex.K⁰))/Γ<sub>total</sub> values.

⁵Error correlated with MILLS 85 (Kπππ⁰ν) value. We multiply 0.22% by 0.23, the relative systematic error quoted by MILLS 85, to obtain the systematic error.

WEIGHTED AVERAGE
1.43±0.07 (Error scaled by 2.4)

<figure><img src="image_414.png" /></figure>

$$ \Gamma_{106}/\Gamma_{68} = \Gamma_{106}/(\Gamma_{70}+0.0153\Gamma_{178}) $$

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

$$ \Gamma(K^- K^+ \pi^- \nu_\tau) / \Gamma(\pi^- \pi^+ \pi^- \nu_\tau \text{ (ex. K}^0\text{)}) \qquad \Gamma_{106}/\Gamma_{68} $$

$$ \Gamma_{106}/\Gamma_{68} = \Gamma_{106}/(\Gamma_{70}+0.0153\Gamma_{178}) $$

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

1.592 ±0.030 OUR FIT (Produced by HFLAV)

1.83 ±0.05 OUR AVERAGE

<table><tbody><tr><td>1.60 ±0.15 ±0.30</td><td>2.3k</td><td>RICCHI</td><td>99</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>1.84 ±0.01 ±0.05</td><td>108k</td><td>1 LEE</td><td>10 BELL</td><td>666 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

¹Not independent of LEE 10 Γ(τ⁻ → K⁻K⁺π⁻ν_τ)/Γ<sub>total</sub> and Γ(τ⁻ → π⁻π⁺π⁻ν_τ(ex.K⁰))/Γ<sub>total</sub> values.

$$ \Gamma(K^- K^+ \pi^- \pi^0 \nu_\tau) / \Gamma_{\text{total}} \qquad \Gamma_{107}/\Gamma $$

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

0.61 ±0.18 OUR FIT (Produced by HFLAV)

0.60 ±0.18 OUR AVERAGE

<table><tbody><tr><td>0.55 ±0.14 ±0.12</td><td>48</td><td>ARMS</td><td>05 CLE3</td><td>7.6 fb<sup>-1</sup>, E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

<table><tbody><tr><td>7.5 ±2.9 ±1.5</td><td></td><td>BARATE</td><td>98 ALEP</td><td>1991-1995 LEP runs</td></tr></tbody></table>

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

<table><tbody><tr><td>3.3 ±1.8 ±0.7</td><td>158</td><td>1 RICCHI</td><td>99</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;27</td><td>95</td><td>ABBIENDI</td><td>00d</td><td>OPAL</td><td>1990-1995 LEP runs</td></tr></tbody></table>

¹Not independent of RICCHI 99

Γ(τ⁻ → K⁻K⁺π⁻ν_τ)/Γ(τ⁻ → π⁻π⁺π⁻ν_τ(ex.K⁰)) and BALEST 95C Γ(τ⁻ → h⁻h⁻h⁺h⁺ν_τ(ex.K⁰))/Γ<sub>total</sub> values.

$$ \Gamma(K^- K^+ \pi^- \pi^0 \nu_\tau) / \Gamma(\pi^- \pi^+ \pi^- \pi^0 \nu_\tau \text{ (ex. K}^0\text{)}) \qquad \Gamma_{107}/\Gamma_{77} $$

$$ \Gamma_{107}/\Gamma_{77} = \Gamma_{107}/(\Gamma_{78}+0.892\Gamma_{178}+0.0153\Gamma_{180}) $$

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

0.14 ±0.04 OUR FIT (Produced by HFLAV)

<table><tbody><tr><td>0.79 ±0.44 ±0.16</td><td>158</td><td>1 RICCHI</td><td>99</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

¹RICCHI 99 also quote a 95%CL upper limit of 0.0157 for this measurement.

$$ \Gamma(K^- K^+ \pi^- \nu_\tau) / \Gamma_{\text{total}} \qquad \Gamma_{108}/\Gamma = 0.491\Gamma_{170}/\Gamma $$

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

2.2 ±0.8 OUR FIT Error includes scale factor of 5.4. (Produced by HFLAV)

2.1 ±0.8 OUR AVERAGE Error includes scale factor of 5.4.

<table><tbody><tr><td>3.29 ±0.17</td><td>+0.19<br>-0.20</td><td>3.2k</td><td>1 LEE</td><td>10 BELL</td><td>666 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>1.58 ±0.13 ±0.12</td><td></td><td>275</td><td>2 AUBERT</td><td>08 BABR</td><td>342 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;3.7</td><td>90</td><td>BRIERE</td><td>03 CLE3</td><td>E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>&lt;19</td><td>90</td><td>BARATE</td><td>98 ALEP</td><td>1991-1995 LEP runs</td></tr></tbody></table>

¹See footnote to LEE 10 Γ(τ⁻ → π⁻π⁺π⁻ν_τ(ex.K⁰))/Γ<sub>total</sub> measurement for correlations with other measurements. Not independent of LEE 10 Γ(τ⁻ → K⁻K⁺K⁻ν_τ)/Γ(τ⁻ → π⁻π⁺π⁻ν_τ(ex.K⁰)) value.

²See footnote to AUBERT 08 Γ(τ⁻ → π⁻π⁺π⁻ν_τ(ex.K⁰))/Γ<sub>total</sub> measurement for correlations with other measurements.

$$ \Gamma(K^- K^+ \pi^- \nu_\tau) / \Gamma(\pi^- \pi^+ \pi^- \nu_\tau \text{ (ex. K}^0\text{)}) \qquad \Gamma_{108}/\Gamma_{68} $$

<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>

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

<table><tbody><tr><td>3.90 ±0.02</td><td>+0.22<br>-0.23</td><td>3.2k</td><td>1 LEE</td><td>10 BELL</td><td>666 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

¹Not independent of LEE 10 Γ(τ⁻ → K⁻K⁺K⁻ν_τ)/Γ<sub>total</sub> and Γ(τ⁻ → π⁻π⁺π⁻ν_τ(ex.K⁰))/Γ<sub>total</sub> values.

$$ \Gamma(K^- K^+ \pi^- \nu_\tau) / \Gamma_{\text{total}} \qquad \Gamma_{109}/\Gamma $$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;2.5 × 10<sup>-6</sup></td><td>90</td><td>AUBERT</td><td>08 BABR</td><td>342 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

$$ \Gamma(K^- K^+ \pi^0 \nu_\tau) / \Gamma_{\text{total}} \qquad \Gamma_{110}/\Gamma $$

<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;4.8 × 10<sup>-6</sup></td><td>90</td><td>ARMS</td><td>05 CLE3</td><td>7.6 fb<sup>-1</sup>, E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

$$ \Gamma(\pi^- K^+ \pi^- \ge 0 \text{ neu. } \nu_\tau) / \Gamma_{\text{total}} \qquad \Gamma_{111}/\Gamma $$

<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;0.25</td><td>95</td><td>BAUER</td><td>94 TPC</td><td>E<sup>ee</sup><sub>cm</sub>=29 GeV</td></tr></tbody></table>

$$ \Gamma(e^- e^- + \bar{\nu}_e \nu_\tau) / \Gamma_{\text{total}} \qquad \Gamma_{112}/\Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2.8 ±1.4 ±0.4</td><td>5</td><td>ALAM</td><td>96 CLEO</td><td>E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

$$ \Gamma(\mu^- e^- + \bar{\nu}_\mu \nu_\tau) / \Gamma_{\text{total}} \qquad \Gamma_{113}/\Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;3.2</td><td>90</td><td>ALAM</td><td>96 CLEO</td><td>E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

$$ \Gamma(\pi^- e^- + \bar{\nu}_\tau) / \Gamma_{\text{total}} \qquad \Gamma_{114}/\Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-5</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>seen</td><td>400</td><td>1 JIN</td><td>19 BELL</td><td>562 fb<sup>-1</sup>, E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>1.46 ±0.13 ±0.21</td><td>400</td><td>1 JIN</td><td>19 BELL</td><td>axial-vector, 562 fb<sup>-1</sup>, E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

<table><tbody><tr><td>3.01 ±0.27 ±0.43</td><td>400</td><td>1 JIN</td><td>19 BELL</td><td>vector, 562 fb<sup>-1</sup>, E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

¹JIN 19 measures B(τ⁻ → π⁻e⁻e⁺ν_τ(m_π⁻e⁻e⁺ > 1.05GeV/c²)) = (5.90 ± 0.53 ± 0.86) × 10⁻⁶, which is only sensitive to the structure-dependent contribution, and assumes that the decay proceeds either with a pure axial-vector current or a pure vector current to obtain the two respective branching fraction measurements for this mode, which are 100% correlated.

$$ \Gamma(\pi^- \mu^- \mu^+ \nu_\tau) / \Gamma_{\text{total}} \qquad \Gamma_{115}/\Gamma $$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;1.14 × 10<sup>-5</sup></td><td>90</td><td>JIN</td><td>19 BELL</td><td>562 fb<sup>-1</sup>, E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

$$ \Gamma(3\hbar^2\hbar^+ \ge 0 \text{ neutrals } \nu_\tau \text{ (ex. } K_S^0 \to \pi^- \pi^+) \text{ ("5-prong"))} / \Gamma_{\text{total}} \qquad \Gamma_{116}/\Gamma $$

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

0.099 ±0.004 OUR FIT (Produced by HFLAV)

0.107 ±0.007 OUR AVERAGE Error includes scale factor of 1.1.

<table><tbody><tr><td>0.170 ±0.022 ±0.026</td><td></td><td>1 ACHARD</td><td>01D L3</td><td>1992-1995 LEP runs</td></tr><tr><td>0.097 ±0.005 ±0.011</td><td>419</td><td>GIBAUT</td><td>94B CLEO</td><td>E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr></tbody></table>

<table><tbody><tr><td>0.102 ±0.029</td><td>13</td><td>BYLSMA</td><td>87 HRS</td><td>E<sup>ee</sup><sub>cm</sub>=29 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>0.093 ±0.009 ±0.012</td><td></td><td>SCHAEL</td><td>05C ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>0.115 ±0.013 ±0.006</td><td>112</td><td>2 ABREU</td><td>01M DLPH</td><td>1992-1995 LEP runs</td></tr><tr><td>0.119 ±0.013 ±0.008</td><td>119</td><td>3 ACKERSTAFF</td><td>99E OPAL</td><td>1991-1995 LEP runs</td></tr></tbody></table>

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

<table><tbody><tr><td>0.15 ±0.05 ±0.012</td><td></td><td>SCHAEL</td><td>05C ALEP</td><td>1991-1995 LEP runs</td></tr></tbody></table>

<table><tbody><tr><td>0.115 ±0.013 ±0.006</td><td>112</td><td>ABREU</td><td>01M DLPH</td><td>1992-1995 LEP runs</td></tr></tbody></table>

<table><tbody><tr><td>0.119 ±0.013 ±0.008</td><td>119</td><td>ACKERSTAFF</td><td>99E OPAL</td><td>1991-1995 LEP runs</td></tr></tbody></table>

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

<table><tbody><tr><td>0.26 ±0.06 ±0.05</td><td></td><td>ACTON</td><td>92H OPAL</td><td>E<sup>ee</sup><sub>cm</sub>=88.2-94.2 GeV</td></tr></tbody></table>

<table><tbody><tr><td>0.10 ±0.05 ±0.04</td><td></td><td>DECAMP</td><td>92C ALEP</td><td>1989-1990 LEP runs</td></tr></tbody></table>

<table><tbody><tr><td>0.16 ±0.13 ±0.04</td><td></td><td>BEHREND</td><td>89B CELL</td><td>E<sup>ee</sup><sub>cm</sub>=14-47 GeV</td></tr></tbody></table>

<table><tbody><tr><td>0.3 ±0.1 ±0.2</td><td></td><td>BARTEL</td><td>85F JADE</td><td>E<sup>ee</sup><sub>cm</sub>=34.6 GeV</td></tr></tbody></table>

<table><tbody><tr><td>0.13 ±0.04</td><td>10</td><td>BELTRAMI</td><td>85 HRS</td><td>Repl. by BYLSMA 87</td></tr></tbody></table>
<table><tr><td>0.16</td><td>±0.08</td><td>±0.04</td><td>4</td><td>BURCHAT</td><td>85</td><td>MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>1.0</td><td>±0.4</td><td></td><td>10</td><td>BEHREND</td><td>82</td><td>CELL</td><td>Repl. by BEHREND 89B</td></tr></table>

¹The correlation coefficients between this measurement and the ACHARD 01D measurements of B(τ → “1-prong”) and B(τ → “3-prong”) are −0.082 and −0.19 respectively.

²The correlation coefficients between this measurement and the ABREU 01M measurements of B(τ → 1-prong) and B(τ → 3-prong) are −0.08 and −0.08 respectively.

³Not independent of ACKERSTAFF 99E B(τ⁻ → 3h⁻ 2h⁺ ν<sub>τ</sub> (ex. K⁰)) and B(τ⁻ → 3h⁻ 2h⁺ π⁰ ν<sub>τ</sub> (ex. K⁰)) measurements.

$$ \Gamma(3h^{-} 2h^{+} \nu_{\tau} (\text{ex. K}^{0})) / \Gamma_{\text{total}} \quad \Gamma_{117} / \Gamma = (\Gamma_{118} + \Gamma_{120} + 0.0153\Gamma_{185}) / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>8.29±0.31</strong> OUR FIT</td><td colspan="4">(Produced by HFLAV)</td></tr></tbody></table>

### 8.32±0.35 OUR AVERAGE

<table><tr><td>9.7</td><td>±1.5</td><td>±0.5</td><td>96</td><td>1 ABDALLAH</td><td>06A</td><td>DLPH</td><td>1992-1995 LEP runs</td></tr><tr><td>7.2</td><td>±0.9</td><td>±1.2</td><td>165</td><td>2 SCHAEL</td><td>05C</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>9.1</td><td>±1.4</td><td>±0.6</td><td>97</td><td>ACKERSTAFF</td><td>99E</td><td>OPAL</td><td>1991-1995 LEP runs</td></tr><tr><td>7.7</td><td>±0.5</td><td>±0.9</td><td>295</td><td>GIBAUT</td><td>94B</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr><tr><td>6.4</td><td>±2.3</td><td>±1.0</td><td>12</td><td>ALBRECHT</td><td>88B</td><td>ARG</td><td>E<sup>ee</sup><sub>cm</sub> = 10 GeV</td></tr><tr><td>5.1</td><td>±2.0</td><td></td><td>7</td><td>BYLSMA</td><td>87</td><td>HRS</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></table>

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

<table><tr><td>8.56±0.05</td><td>±0.42</td><td>34k</td><td>AUBERT,B</td><td>05W</td><td>BABR</td><td>232 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

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

<table><tr><td>8.0</td><td>±1.1</td><td>±1.3</td><td>58</td><td>BUSKULIC</td><td>96</td><td>ALEP</td><td>Repl. by SCHAEL 05C</td></tr><tr><td>6.7</td><td>±3.0</td><td></td><td>5</td><td>3 BELTRAMI</td><td>85</td><td>HRS</td><td>Repl. by BYLSMA 87</td></tr></table>

¹See footnote to ABDALLAH 06A Γ(τ⁻ → h⁻ ν<sub>τ</sub>)/Γ<sub>total</sub> measurement for correlations with other measurements.

²See footnote to SCHAEL 05C Γ(τ⁻ → e⁻ ν<sub>e</sub> ν<sub>τ</sub>)/Γ<sub>total</sub> measurement for correlations with other measurements.

³The error quoted is statistical only.

$$ \Gamma(3\pi^{-} 2\pi^{+} \nu_{\tau} (\text{ex. K}^{0}, \omega)) / \Gamma_{\text{total}} \quad \Gamma_{118} / \Gamma = (\Gamma_{119} + \Gamma_{173}) / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>8.27±0.31</strong> OUR FIT</td><td colspan="4">(Produced by HFLAV)</td></tr></tbody></table>

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

<table><tr><td>8.33±0.04</td><td>±0.43</td><td>1 LEES</td><td>12x</td><td>BABR</td><td>468 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

¹Not independent of LEES 12x Γ(τ⁻ → f₁(1285)ν⁻ → 3π⁻ 2π⁺ ν<sub>τ</sub>)/Γ and Γ(τ⁻ → 3π⁻ 2π⁺ ν<sub>τ</sub> (ex. K⁰, ω, f₁(1285)))/Γ values.

$$ \Gamma(3\pi^{-} 2\pi^{+} \nu_{\tau} (\text{ex. K}^{0}, \omega, f_{1}(1285))) / \Gamma_{\text{total}} \quad \Gamma_{119} / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>7.75±0.30</strong> OUR FIT</td><td colspan="4">(Produced by HFLAV)</td></tr><tr><td><strong>7.68±0.04</strong></td><td>±0.40</td><td>69k</td><td>LEES</td><td>12x</td><td>BABR</td><td>468 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

$$ \Gamma(K^{-} 2\pi^{-} 2\pi^{+} \nu_{\tau} (\text{ex. K}^{0})) / \Gamma_{\text{total}} \quad \Gamma_{120} / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.6±1.2</strong> OUR FIT</td><td colspan="3">(Produced by HFLAV)</td></tr><tr><td><strong>0.6±0.5</strong></td><td>±1.1</td><td>1 LEES</td><td>12x</td><td>BABR</td><td>468 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

¹LEES 12x measurement corresponds to the lower limit of < 2.4 × 10⁻⁶ at 90% CL.

$$ \Gamma(K^{+} 3\pi^{-} \pi^{+} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{121} / \Gamma $$

<table><thead><tr><th>VALUE</th><th>CL<sup>+</sup></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;5.0</strong> × 10<sup>-6</sup></td><td>90</td><td>LEES</td><td>12x</td><td>BABR</td><td>468 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

$$ \Gamma(K^{+} K^{-} 2\pi^{-} \pi^{+} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{122} / \Gamma $$

<table><thead><tr><th>VALUE</th><th>CL<sup>+</sup></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;4.5</strong> × 10<sup>-7</sup></td><td>90</td><td>LEES</td><td>12x</td><td>BABR</td><td>468 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

$$ \Gamma(3h^{-} 2h^{+} \pi^{0} \nu_{\tau} (\text{ex. K}^{0})) / \Gamma_{\text{total}} \quad \Gamma_{123} / \Gamma = (\Gamma_{124} + \Gamma_{127}) / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>1.65±0.11</strong> OUR FIT</td><td colspan="4">(Produced by HFLAV)</td></tr></tbody></table>

### 1.74±0.27 OUR AVERAGE

<table><tr><td>1.6</td><td>±1.2</td><td>±0.6</td><td>13</td><td>1 ABDALLAH</td><td>06A</td><td>DLPH</td><td>1992-1995 LEP runs</td></tr><tr><td>2.1</td><td>±0.7</td><td>±0.9</td><td>95</td><td>2 SCHAEL</td><td>05C</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>1.7</td><td>±0.2</td><td>±0.2</td><td>231</td><td>ANASTASSOV</td><td>01</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr><tr><td>2.7</td><td>±1.8</td><td>±0.9</td><td>23</td><td>ACKERSTAFF</td><td>99E</td><td>OPAL</td><td>1991-1995 LEP runs</td></tr><tr><td>1.8</td><td>±0.7</td><td>±1.2</td><td>18</td><td>BUSKULIC</td><td>96</td><td>ALEP</td><td>Repl. by SCHAEL 05C</td></tr><tr><td>1.9</td><td>±0.4</td><td>±0.4</td><td>31</td><td>GIBAUT</td><td>94B</td><td>CLEO</td><td>Repl. by ANASTASSOV 01</td></tr><tr><td>5.1</td><td>±2.2</td><td></td><td>6</td><td>BYLSMA</td><td>87</td><td>HRS</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>6.7</td><td>±3.0</td><td></td><td>5</td><td>3 BELTRAMI</td><td>85</td><td>HRS</td><td>Repl. by BYLSMA 87</td></tr></table>

¹See footnote to ABDALLAH 06A Γ(τ⁻ → h⁻ ν<sub>τ</sub>)/Γ<sub>total</sub> measurement for correlations with other measurements.

²SCHAEL 05C quote (1.4 ± 0.7 ± 0.9) × 10⁻⁴. We add 0.7 × 10⁻⁴ to remove their correction for τ⁻ → ηπ⁻ π⁺ π⁻ ν<sub>τ</sub> → 3π⁻ 2π⁺ π⁰ ν<sub>τ</sub> and τ⁻ → K*(892)⁻ ην<sub>τ</sub> → 3π⁻ 2π⁺ π⁰ ν<sub>τ</sub> decays. See footnote to SCHAEL 05C Γ(τ⁻ → e⁻ ν<sub>e</sub> ν<sub>τ</sub>)/Γ<sub>total</sub> measurement for correlations with other measurements.

³The error quoted is statistical only.

$$ \Gamma(3\pi^{-} 2\pi^{+} \nu_{\tau} (\text{ex. K}^{0})) / \Gamma_{\text{total}} \quad \Gamma_{124} / \Gamma = (\Gamma_{126} + 0.2302\Gamma_{160} + 0.892\Gamma_{185}) / \Gamma $$

<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>1.64±0.11</strong> OUR FIT</td><td colspan="3">(Produced by HFLAV)</td></tr></tbody></table>

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

<table><tr><td><strong>1.65±0.05</strong>±0.09</td><td>1 LEES</td><td>12x</td><td>BABR</td><td>468 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

¹Not independent of LEES 12x measurements of Γ(τ⁻ → 2π⁻ π⁺ ων<sub>τ</sub> (ex. K⁰))/Γ, Γ(τ⁻ → ηπ⁻ π⁺ π⁻ ν<sub>τ</sub> (ex. K⁰))/Γ, and Γ(τ⁻ → 3π⁻ 2π⁺ π⁰ ν<sub>τ</sub> (ex. K⁰, η, ω, f₁(1285)))/Γ.

$$ \Gamma(3\pi^{-} 2\pi^{+} \nu_{\tau} (\text{ex. K}^{0}, \eta, f_{1}(1285))) / \Gamma_{\text{total}} \quad \Gamma_{125} / \Gamma $$

<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>1.11±0.04</strong>±0.09</td><td>1 LEES</td><td>12x</td><td>BABR</td><td>468 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

¹Not independent of LEES 12x Γ(τ⁻ → 2π⁻ π⁺ ων<sub>τ</sub> (ex. K⁰))/Γ and Γ(τ⁻ → 3π⁻ 2π⁺ π⁰ ν<sub>τ</sub> (ex. K⁰, η, ω, f₁(1285)))/Γ values.

$$ \Gamma(3\pi^{-} 2\pi^{+} \nu_{\tau} (\text{ex. K}^{0}, \eta, \omega, f_{1}(1285))) / \Gamma_{\text{total}} \quad \Gamma_{126} / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.38±0.09</strong> OUR FIT</td><td colspan="4">(Produced by HFLAV)</td></tr></tbody></table>

<table><tr><td><strong>0.36±0.03</strong>±0.09</td><td>7.3k</td><td>LEES</td><td>12x</td><td>BABR</td><td>468 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

$$ \Gamma(K^{-} 2\pi^{-} 2\pi^{+} \nu_{\tau} (\text{ex. K}^{0})) / \Gamma_{\text{total}} \quad \Gamma_{127} / \Gamma $$

<table><thead><tr><th>VALUE (units 10<sup>-6</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>1.1±0.6</strong> OUR FIT</td><td colspan="3">(Produced by HFLAV)</td></tr></tbody></table>

<table><tr><td><strong>1.1±0.4</strong>±0.4</td><td>1 LEES</td><td>12x</td><td>BABR</td><td>468 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

¹LEES 12x measurement corresponds to the lower limit of < 1.9 × 10⁻⁶ at 90% CL.

$$ \Gamma(K^{+} 3\pi^{-} \pi^{+} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{128} / \Gamma $$

<table><thead><tr><th>VALUE</th><th>CL<sup>+</sup></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;8</strong> × 10<sup>-7</sup></td><td>90</td><td>LEES</td><td>12x</td><td>BABR</td><td>468 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

$$ \Gamma(3h^{-} 2h^{+} 2\pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{129} / \Gamma $$

<table><thead><tr><th>VALUE</th><th>CL<sup>+</sup></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;3.4</strong> × 10<sup>-6</sup></td><td>90</td><td>AUBERT,B</td><td>06</td><td>BABR</td><td>232 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

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

<table><tr><td><strong>&lt;1.1</strong> × 10<sup>-4</sup></td><td>90</td><td>GIBAUT</td><td>94B</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

$$ \Gamma((5\pi^{-}) \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{130} / \Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.78±0.05</strong> OUR FIT</td><td colspan="3">(Produced by HFLAV)</td></tr></tbody></table>

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

<table><tr><td><strong>0.61±0.06</strong>±0.08</td><td>1 GIBAUT</td><td>94B</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></table>

¹Not independent of GIBAUT 94B B(3h⁻ 2h⁺ ν<sub>τ</sub>), PROCARIO 93 B(h⁻ 4π⁰ ν<sub>τ</sub>), and BORTOLETTO 93 B(2h⁻ h⁺ 2π⁰ ν<sub>τ</sub>)/B(“3prong”) measurements. Result is corrected for η contributions.

$$ \Gamma(4h^{-} 3h^{+} \ge 0 \text{ neutrals } \nu_{\tau} (“7-prong”)) / \Gamma_{\text{total}} \quad \Gamma_{131} / \Gamma $$

<table><thead><tr><th>VALUE</th><th>CL<sup>+</sup></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;3.0</strong> × 10<sup>-7</sup></td><td>90</td><td>AUBERT,B</td><td>05F</td><td>BABR</td><td>232 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

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

<table><tr><td><strong>&lt;1.8</strong> × 10<sup>-5</sup></td><td>95</td><td>ACKERSTAFF</td><td>97J</td><td>OPAL</td><td>1990-1995 LEP runs</td></tr><tr><td><strong>&lt;2.4</strong> × 10<sup>-6</sup></td><td>90</td><td>EDWARDS</td><td>97B</td><td>CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr><tr><td><strong>&lt;2.9</strong> × 10<sup>-4</sup></td><td>90</td><td>BYLSMA</td><td>87</td><td>HRS</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></table>

$$ \Gamma(4h^{-} 3h^{+} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{132} / \Gamma $$

<table><thead><tr><th>VALUE</th><th>CL<sup>+</sup></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;4.3</strong> × 10<sup>-7</sup></td><td>90</td><td>AUBERT,B</td><td>05F</td><td>BABR</td><td>232 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

$$ \Gamma(4h^{-} 3h^{+} \pi^{0} \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{133} / \Gamma $$

<table><thead><tr><th>VALUE</th><th>CL<sup>+</sup></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>&lt;2.5</strong> × 10<sup>-7</sup></td><td>90</td><td>AUBERT,B</td><td>05F</td><td>BABR</td><td>232 fb<sup>-1</sup></td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

$$ \Gamma(X^{-} (S=-1) \nu_{\tau}) / \Gamma_{\text{total}} \quad \Gamma_{134} / \Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>1.34±0.04</strong> OUR FIT</td><td colspan="3">(Produced by HFLAV)</td></tr></tbody></table>

<table><thead><tr><th>VALUE (%)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>2.92±0.04</strong> OUR FIT</td><td colspan="3">(Produced by HFLAV)</td></tr></tbody></table>

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

<table><tr><td><strong>2.87±0.12</strong></td><td>1 BARATE</td><td>99R</td><td>ALEP</td><td>1991-1995 LEP runs</td></tr></table>

¹BARATE 99R perform a combined analysis of all ALEPH LEP 1 data on τ branching fraction measurements for decay modes having total strangeness equal to −1.
$$ \Gamma(K^*(892)^- \ge 0 \text{ neutrals} \ge 0 K_S^0 \nu_\tau) / \Gamma_{\text{total}} \quad \Gamma_{135}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.42±0.18</td><td>OUR AVERAGE</td><td colspan="3">Error includes scale factor of 1.4. See the ideogram below.</td></tr></tbody></table>

<table><tbody><tr><td>1.19±0.15</td><td>+0.13</td><td>104</td><td>ALBRECHT</td><td>95H ARG</td><td>E<sup>ee</sup><sub>cm</sub> = 9.4-10.6 GeV</td></tr><tr><td>1.94±0.27</td><td>±0.15</td><td>74</td><td>1 AKERS</td><td>94G OPAL</td><td>E<sup>ee</sup><sub>cm</sub> = 88-94 GeV</td></tr><tr><td>1.43±0.11</td><td>±0.13</td><td>475</td><td>2 GOLDBERG</td><td>90 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 9.4-10.9 GeV</td></tr></tbody></table>

¹AKERS 94G reject events in which a $K_S^0$ accompanies the $K^*(892)^-$. We do not correct for them.

²GOLDBERG 90 estimates that 10% of observed $K^*(892)$ are accompanied by a $\pi^0$.

WEIGHTED AVERAGE
1.42±0.18 (Error scaled by 1.4)

<figure><img src="image_415.png" /></figure>

$$ \Gamma(K^*(892)^- \nu_\tau) / \Gamma_{\text{total}} \quad \Gamma_{136}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.20 ±0.07</td><td>OUR AVERAGE</td><td colspan="3">Error includes scale factor of 1.8. See the ideogram below.</td></tr></tbody></table>

<table><tbody><tr><td>1.131±0.006</td><td>±0.051</td><td>49k</td><td>1 EPIFANOV</td><td>07 BELL</td><td>351 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub>=10.6 GeV</td></tr><tr><td>1.326±0.063</td><td></td><td></td><td>BARATE</td><td>99R ALEP</td><td>1991-1995 LEP runs</td></tr><tr><td>1.11 ±0.12</td><td></td><td></td><td>2 COAN</td><td>96 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV</td></tr><tr><td>1.42 ±0.22</td><td>±0.09</td><td></td><td>3 ACCIARRI</td><td>95F L3</td><td>1991-1993 LEP runs</td></tr><tr><td colspan="6">• • We do not use the following data for averages, fits, limits, etc. • •</td></tr><tr><td>1.39 ±0.09</td><td>±0.10</td><td>4</td><td>BUSKULIC</td><td>96 ALEP</td><td>Repl. by BARATE 99R</td></tr><tr><td>1.45 ±0.13</td><td>±0.11</td><td>273</td><td>5 BUSKULIC</td><td>94F ALEP</td><td>Repl. by BUSKULIC 96</td></tr><tr><td>1.23 ±0.21</td><td>+0.11</td><td>54</td><td>6 ALBRECHT</td><td>88L ARG</td><td>E<sup>ee</sup><sub>cm</sub> = 10 GeV</td></tr><tr><td>1.9 ±0.3</td><td>±0.4</td><td>44</td><td>7 TSCHIRHART</td><td>88 HRS</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>1.5 ±0.4</td><td>±0.4</td><td>15</td><td>8 AIHARA</td><td>87C TPC</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>1.3 ±0.3</td><td>±0.3</td><td>31</td><td>YELTON</td><td>86 MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>1.7 ±0.7</td><td></td><td>11</td><td>DORFAN</td><td>81 MRK2</td><td>E<sup>ee</sup><sub>cm</sub> = 4.2-6.7 GeV</td></tr></tbody></table>

WEIGHTED AVERAGE
1.20±0.07 (Error scaled by 1.8)

<figure><img src="image_416.png" /></figure>

¹EPIFANOV 07 quote B($\tau^- \to K^*(892)^- \nu_\tau$) B($K^*(892)^- \to K_S^0 \pi^-$) = (3.77 ± 0.02(stat) ±0.12(syst) ±0.12 mod)) × 10⁻³. We add the systematic and model uncertainties in quadrature and divide by B($K^*(892)^- \to K_S^0 \pi^-$) = 0.3333.

²Not independent of COAN 96 B($\pi^- \bar{K}^0 \nu_\tau$) and BATTLE 94 B($K^- \pi^0 \nu_\tau$) measurements. $K\pi$ final states are consistent with and assumed to originate from $K^*(892)^-$ production.

³This result is obtained from their B($\pi^- \bar{K}^0 \nu_\tau$) assuming all those decays originate in $K^*(892)^-$ decays.

⁴Not independent of BUSKULIC 96 B($\pi^- \bar{K}^0 \nu_\tau$) and B($K^- \pi^0 \nu_\tau$) measurements.

⁵BUSKULIC 94f obtain this result from BUSKULIC 94f B($\bar{K}^0 \pi^- \nu_\tau$) and BUSKULIC 94f B($K^- \pi^0 \nu_\tau$) assuming all of those decays originate in $K^*(892)^-$ decays.

⁶The authors divide by $\Gamma_2/\Gamma = 0.865$ to obtain this result.

⁷Not independent of TSCHIRHART 88 $\Gamma(\tau^- \to h^- \bar{K}^0 \ge 0 \text{ neutrals} \ge 0 K_L^0 \nu_\tau) / \Gamma$.

⁸Decay $\pi^-$ identified in this experiment, is assumed in the others.

$$ \Gamma(K^*(892)^- \nu_\tau) / \Gamma(\pi^- \pi^0 \nu_\tau) \quad \Gamma_{136}/\Gamma_{14} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.075±0.027</td><td></td><td>1 ABREU</td><td>94K DLPH</td><td>LEP 1992 Z data</td></tr></tbody></table>

¹ABREU 94K quote B($\tau^- \to K^*(892)^- \nu_\tau$)B($K^*(892)^- \to K^- \pi^0$)/B($\tau^- \to \rho^- \nu_\tau$) = 0.025 ± 0.009. We divide by B($K^*(892)^- \to K^- \pi^0$) = 0.333 to obtain this result.

$$ \Gamma(K^*(892)^- \nu_\tau \to \pi^- \bar{K}^0 \nu_\tau) / \Gamma(\pi^- \bar{K}^0 \nu_\tau) \quad \Gamma_{137}/\Gamma_{36} $$

<table><thead><tr><th>VALUE</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.933±0.027</td><td>49k</td><td>EPIFANOV</td><td>07 BELL</td><td>351 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

$$ \Gamma(K^*(892)^0 \bar{K}^- \ge 0 \text{ neutrals} \nu_\tau) / \Gamma_{\text{total}} \quad \Gamma_{138}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.32±0.08</td><td>±0.12</td><td>119</td><td>GOLDBERG</td><td>90 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 9.4-10.9 GeV</td></tr></tbody></table>

$$ \Gamma(K^*(892)^0 \bar{K}^- \nu_\tau) / \Gamma_{\text{total}} \quad \Gamma_{139}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.21 ±0.04</td><td>OUR AVERAGE</td><td></td><td></td><td></td></tr></tbody></table>

¹BARATE 98 measure the $K^- (\rho^0 \to \pi^+ \pi^-)$ fraction in $\tau^- \to K^- \pi^+ \pi^- \nu_\tau$ decays to be (35 ± 11)% and derive this result from their measurement of $\Gamma(\tau^- \to K^- \pi^+ \pi^- \nu_\tau) / \Gamma_{\text{total}}$ assuming the intermediate states are all $K^- \rho$ and $K^- K^*(892)^0$.

$$ \Gamma(\bar{K}^*(892)^0 \pi^- \ge 0 \text{ neutrals} \nu_\tau) / \Gamma_{\text{total}} \quad \Gamma_{140}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.38±0.11</td><td>±0.13</td><td>105</td><td>GOLDBERG</td><td>90 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 9.4-10.9 GeV</td></tr></tbody></table>

$$ \Gamma(\bar{K}^*(892)^0 \pi^- \nu_\tau) / \Gamma_{\text{total}} \quad \Gamma_{141}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.22 ±0.05</td><td>OUR AVERAGE</td><td></td><td></td><td></td></tr></tbody></table>

¹BARATE 98 measure the $K^- K^*(892)^0$ fraction in $\tau^- \to K^- K^+ \pi^- \nu_\tau$ decays to be (87 ± 13)% and derive this result from their measurement of $\Gamma(\tau^- \to K^- K^+ \pi^- \nu_\tau) / \Gamma_{\text{total}}$.

$$ \Gamma((\bar{K}^*(892)^-) \nu_\tau \to \pi^- \bar{K}^0 \pi^0 \nu_\tau) / \Gamma_{\text{total}} \quad \Gamma_{142}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.10 ±0.04</td><td>OUR AVERAGE</td><td></td><td></td><td></td></tr></tbody></table>

¹BARATE 99K measure $K^0$'s by detecting $K^0$'s in their hadron calorimeter. They determine the $\bar{K}^0 \rho^-$ fraction in $\tau^- \to \pi^- \bar{K}^0 \pi^0 \nu_\tau$ decays to be (0.72 ± 0.12 ± 0.10) and multiply their B($\pi^- \bar{K}^0 \pi^0 \nu_\tau$) measurement by one minus this fraction to obtain the quoted result.

²BARATE 98E reconstruct $K^0$'s using $K_S^0 \to \pi^+ \pi^-$ decays. They determine the $\bar{K}^0 \rho^-$ fraction in $\tau^- \to \pi^- \bar{K}^0 \pi^0 \nu_\tau$ decays to be (0.64 ± 0.09 ± 0.10) and multiply their B($\pi^- \bar{K}^0 \pi^0 \nu_\tau$) measurement by one minus this fraction to obtain the quoted result.

$$ \Gamma(K_1(1270)^- \nu_\tau) / \Gamma_{\text{total}} \quad \Gamma_{143}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.47±0.11</td><td>OUR AVERAGE</td><td></td><td></td><td></td></tr></tbody></table>

¹BARATE 99R ALEP 1991-1995 LEP runs

²BARATE 98E ALEP 1991-1995 LEP runs

¹We multiply 0.41% by 0.25, the relative systematic error quoted by BAUER 94, to obtain the systematic error.

$$ \Gamma(K_1(1400)^- \nu_\tau) / \Gamma_{\text{total}} \quad \Gamma_{144}/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.17±0.26</td><td>OUR AVERAGE</td><td colspan="3">Error includes scale factor of 1.7.</td></tr></tbody></table>

¹BARATE 99R ALEP 1991-1995 LEP runs

²BARATE 98E ALEP 1991-1995 LEP runs

$$ \frac{[\Gamma(K_1(1270)^-) \nu_\tau) + \Gamma(K_1(1400)^-) \nu_\tau]}{\Gamma_{\text{total}}} \quad (\Gamma_{143} + \Gamma_{144})/\Gamma $$

<table><thead><tr><th>VALUE (%)</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.17±0.41</td><td>+0.37</td><td>16</td><td>1 BAUER</td><td>94 TPC</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></tbody></table>

¹We multiply 1.17% by 0.25, the relative systematic error quoted by BAUER 94, to obtain the systematic error.

²We multiply 0.76% by 0.25, the relative systematic error quoted by BAUER 94, to obtain the systematic error.
$$ \Gamma(\kappa_1(1270)^- \nu_\tau) / [\Gamma(\kappa_1(1270)^- \nu_\tau) + \Gamma(\kappa_1(1400)^- \nu_\tau)] \quad \Gamma_{143}/(\Gamma_{143} + \Gamma_{144}) $$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.69±0.15</td><td colspan="3">OUR AVERAGE</td></tr><tr><td>0.71±0.16±0.11</td><td>1</td><td>ABBIENDI</td><td>00D OPAL 1990-1995 LEP runs</td></tr><tr><td>0.66±0.19±0.13</td><td>2</td><td>ASNER</td><td>00B CLEO E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

¹ABBIENDI 00D assume the resonance structure of $\tau^- \to K^-\pi^+\pi^-\nu_\tau$ decays is dominated by the $K_1(1270)^-$ and $K_1(1400)^-$ resonances.

²ASNER 00B assume the resonance structure of $\tau^- \to K^-\pi^+\pi^-\nu_\tau$ (ex. $K^0$) decays is dominated by $K_1(1270)^-$ and $K_1(1400)^-$ resonances.

<table><thead><tr><th>Γ(K*(1410)−ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>145</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.5+1.4<br/>-1.0</td><td>BARATE</td><td>99R</td><td>ALEP 1991-1995 LEP runs</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>*</sup><sub>0</sub>(1430)−ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>146</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;0.5</td><td>95</td><td>BARATE</td><td>99R</td><td>ALEP 1991-1995 LEP runs</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>*</sup><sub>2</sub>(1430)−ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>147</sub>/Γ</th></tr><tr><th>VALUE (%)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;0.3</td><td>95</td><td></td><td>TSCHIRHART</td><td>88</td><td>HRS E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt;0.33</td><td>95</td><td>1</td><td>ACCIARRI</td><td>95F L3</td><td>1991-1993 LEP runs</td></tr><tr><td>&lt;0.9</td><td>95</td><td>0</td><td>DORFAN</td><td>81</td><td>MRK2 E<sup>ee</sup><sub>cm</sub> = 4.2-6.7 GeV</td></tr></tbody></table>

¹ACCIARRI 95F quote B($\tau^- \to K^*(1430)^- \to \pi^-\bar{K}^0\nu_\tau$) < 0.11%. We divide by B($K^*(1430)^- \to \pi^-\bar{K}^0$) = 0.33 to obtain the limit shown.

<table><thead><tr><th>Γ(a<sub>0</sub>(980)<sup>−</sup> ≥ 0 neutrals ν<sub>τ</sub>)/Γ<sub>total</sub> × B(a<sub>0</sub>(980) → K<sup>0</sup> K<sup>−</sup>)</th><th>Γ<sub>148</sub>/Γ × B</th></tr><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;2.8</td><td>90</td><td>GOLDBERG</td><td>90</td><td>CLEO E<sup>ee</sup><sub>cm</sub> = 9.4-10.9 GeV</td></tr></tbody></table>

<table><thead><tr><th>Γ(ηπ<sup>-</sup>ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>149</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt; 0.99</td><td>95</td><td></td><td>1 DEL-AMO-SA..11E</td><td>BABR</td><td>470 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>&lt; 6.2</td><td>95</td><td>BUSKULIC</td><td>97C ALEP</td><td>1991-1994 LEP runs</td></tr><tr><td>&lt; 1.4</td><td>95</td><td>0</td><td>BARTELT</td><td>96</td><td>CLEO E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV</td></tr><tr><td>&lt; 3.4</td><td>95</td><td>ARTUSO</td><td>92</td><td>CLEO E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV</td></tr><tr><td>&lt; 90</td><td>95</td><td>ALBRECHT</td><td>88M ARG</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10 GeV</td></tr><tr><td>&lt;140</td><td>90</td><td>BEHREND</td><td>88</td><td>CELL E<sup>ee</sup><sub>cm</sub> = 14-46.8 GeV</td></tr><tr><td>&lt;180</td><td>95</td><td>BARINGER</td><td>87</td><td>CLEO E<sup>ee</sup><sub>cm</sub> = 10.5 GeV</td></tr><tr><td>&lt;250</td><td>90</td><td>COFFMAN</td><td>87</td><td>MRK3 E<sup>ee</sup><sub>cm</sub> = 3.77 GeV</td></tr><tr><td>510 ±100±120</td><td>65</td><td>DERRICK</td><td>87</td><td>HRS E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr><tr><td>&lt;10</td><td>95</td><td>GAN</td><td>87B MRK2 E<sup>ee</sup><sub>cm</sub> = 29 GeV</td><td></td></tr></tbody></table>

¹DEL-AMO-SANCHEZ 11E also quote B($\tau^- \to \eta\pi^-\nu_\tau$) = (3.4 ± 3.4 ± 2.1) × 10⁻⁵.

<table><thead><tr><th>Γ(ηπ<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>150</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-3</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.39 ± 0.07</td><td colspan="3">OUR FIT</td><td>(Produced by HFLAV)</td><td></td></tr><tr><td>1.38 ± 0.09</td><td colspan="3">OUR AVERAGE</td><td>Error includes scale factor of 1.2.</td><td></td></tr><tr><td>1.35 ± 0.03 ± 0.07</td><td>6.0k</td><td>INAMI</td><td>09 BELL</td><td>490 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td><td></td></tr><tr><td>1.8 ± 0.4 ± 0.2</td><td></td><td>BUSKULIC</td><td>97C ALEP</td><td>1991-1994 LEP runs</td><td></td></tr><tr><td>1.7 ± 0.2 ± 0.2</td><td>125</td><td>ARTUSO</td><td>92 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV</td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>1.38 ± 0.09</td><td colspan="3">OUR AVERAGE</td><td>Error includes scale factor of 1.2.</td><td></td></tr><tr><td>1.35 ± 0.03 ± 0.07</td><td>6.0k</td><td>INAMI</td><td>09 BELL</td><td>490 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td><td></td></tr><tr><td>1.8 ± 0.4 ± 0.2</td><td></td><td>BUSKULIC</td><td>97C ALEP</td><td>1991-1994 LEP runs</td><td></td></tr><tr><td>1.7 ± 0.2 ± 0.2</td><td>125</td><td>ARTUSO</td><td>92 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV</td><td></td></tr></tbody></table>

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

<table><tbody><tr><td>&lt; 11.0</td><td>95</td><td>ALBRECHT</td><td>88M ARG</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10 GeV</td><td></td></tr><tr><td>&lt; 21.0</td><td>95</td><td>BARINGER</td><td>87 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 10.5 GeV</td><td></td></tr><tr><td>42.0 + 7.0<br/>-12.0 ± 16.0</td><td>1</td><td>GAN</td><td>87 MRK2 E<sup>ee</sup><sub>cm</sub> = 29 GeV</td><td></td></tr></tbody></table>

¹Highly correlated with GAN 87 Γ($\pi^- 3\pi^0 \nu_\tau$)/Γ(total) value.

<table><thead><tr><th>Γ(ηπ<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>151</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.9 ± 0.4</td><td colspan="3">OUR FIT</td><td>(Produced by HFLAV)</td><td></td></tr><tr><td>1.81 ± 0.31</td><td colspan="3">OUR AVERAGE</td><td></td><td></td></tr></tbody></table>

<table><tbody><tr><td>2.01 ± 0.34 ± 0.22</td><td>381</td><td>LEES</td><td>12x BABR</td><td>468 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>1.5 ± 0.5</td><td>30</td><td>1</td><td>ANASTASSOV 01</td><td>CLEO E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

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

<table><tbody><tr><td>1.4 ± 0.6 ± 0.3</td><td>15</td><td>2</td><td>BERGFELD</td><td>97 CLEO</td><td>Repl. by ANASTASSOV 01</td></tr><tr><td>&lt; 4.3</td><td>95</td><td>ARTUSO</td><td>92 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV</td></tr><tr><td>&lt;120</td><td>95</td><td>ALBRECHT</td><td>88M ARG</td><td>E<sup>ee</sup><sub>cm</sub> ≈ 10 GeV</td></tr></tbody></table>

¹Weighted average of BERGFELD 97 and ANASTASSOV 01 value of (1.5 ± 0.6 ± 0.3) × 10⁻⁴ obtained using $\eta$'s reconstructed from $\eta \to \pi^+\pi^-\pi^0$ decays.

²BERGFELD 97 reconstruct $\eta$'s using $\eta \to \gamma\gamma$ decays.

<table><thead><tr><th>Γ(ηK<sup>-</sup>ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>152</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.55 ± 0.08</td><td colspan="3">OUR FIT</td><td>(Produced by HFLAV)</td><td></td></tr><tr><td>1.54 ± 0.08</td><td colspan="3">OUR AVERAGE</td><td></td><td></td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>*</sup>(892)<sup>-</sup>ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>153</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1.38 ± 0.15</td><td colspan="3">OUR AVERAGE</td><td></td><td></td></tr><tr><td>1.34 ± 0.12 ± 0.09</td><td>245</td><td>1</td><td>INAMI</td><td>09 BELL</td><td>490 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr><tr><td>2.90 ± 0.80 ± 0.42</td><td>25</td><td></td><td>BISHAI</td><td>99 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •
< 4.7 95 ARTUSO 92 CLEO E<sup>ee</sup><sub>cm</sub> ≈ 10.6 GeV

<table><thead><tr><th>Γ(K<sup>*</sup>(892)<sup>-</sup>ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>154</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.48 ± 0.12</td><td colspan="3">OUR FIT</td><td>(Produced by HFLAV)</td><td></td></tr><tr><td>0.48 ± 0.12</td><td colspan="3">OUR AVERAGE</td><td></td><td></td></tr></tbody></table>

<table><tbody><tr><td>0.46 ± 0.11 ± 0.04</td><td>270</td><td>INAMI</td><td>09 BELL</td><td>490 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr><tr><td>1.77 ± 0.56 ± 0.71</td><td>36</td><td>BISHAI</td><td>99 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

¹Not independent of INAMI 09 B($\tau^- \to \eta K^-\pi^0 \nu_\tau$) and B($\tau^- \to \eta \bar{K}^0 \nu_\tau$) values.

<table><thead><tr><th>Γ(K<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>155</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.94 ± 0.15</td><td colspan="3">OUR FIT</td><td>(Produced by HFLAV)</td><td></td></tr><tr><td>0.93 ± 0.15</td><td colspan="3">OUR AVERAGE</td><td></td><td></td></tr></tbody></table>

<table><tbody><tr><td>0.88 ± 0.14 ± 0.06</td><td>161</td><td>1</td><td>INAMI</td><td>09 BELL</td><td>490 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr><tr><td>2.20 ± 0.70 ± 0.22</td><td>15</td><td>2</td><td>BISHAI</td><td>99 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>-</sup>π<sup>0</sup> (non-K*(892))ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>155</sub>/Γ</th></tr><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;3.5 × 10<sup>-5</sup></td><td>90</td><td>INAMI</td><td>09 BELL</td><td>490 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

<table><thead><tr><th>Γ(K<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>156</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.94 ± 0.15</td><td colspan="3">OUR FIT</td><td>(Produced by HFLAV)</td><td></td></tr><tr><td>0.93 ± 0.15</td><td colspan="3">OUR AVERAGE</td><td></td><td></td></tr></tbody></table>

<table><tbody><tr><td>0.88 ± 0.14 ± 0.06</td><td>161</td><td>1</td><td>INAMI</td><td>09 BELL</td><td>490 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr><tr><td>2.20 ± 0.70 ± 0.22</td><td>15</td><td>2</td><td>BISHAI</td><td>99 CLEO</td><td>E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

¹We multiply the INAMI 09 measurement B($\tau^- \to \eta K^0 S \pi^- \nu_\tau$) = (0.44 ± 0.07 ± 0.03) × 10⁻⁴ by 2 to obtain the listed value.

²We multiply the BISHAI 99 measurement B($\tau^- \to \eta K^0 S \pi^- \nu_\tau$) = (1.10 ± 0.35 ± 0.11) × 10⁻⁴ by 2 to obtain the listed value.

<table><thead><tr><th>Γ(K<sup>-</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>157</sub>/Γ</th></tr><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;5.0 × 10<sup>-5</sup></td><td>90</td><td>1</td><td>INAMI</td><td>09 BELL</td><td>490 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

¹We multiply the INAMI 09 measurement B($\tau^- \to \eta K^0 S \pi^- \nu_\tau$) < 2.5 × 10⁻⁵ by 2 to obtain the listed value.

<table><thead><tr><th>Γ(K<sup>-</sup>K<sup>0</sup>ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>158</sub>/Γ</th></tr><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;9.0 × 10<sup>-6</sup></td><td>90</td><td>1</td><td>INAMI</td><td>09 BELL</td><td>490 fb<sup>-1</sup> E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr></tbody></table>

¹We multiply the INAMI 09 measurement B($\tau^- \to \eta K^- K^0 S \nu_\tau$) < 4.5 × 10⁻⁶ by 2 to obtain the listed value.

<table><thead><tr><th>Γ(ηπ<sup>+</sup>π<sup>-</sup> ≥ 0 neutrals ν<sub>τ</sub>)/Γ<sub>total</sub></th><th>Γ<sub>159</sub>/Γ</th></tr><tr><th>VALUE (%)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;0.3</td><td>90</td><td>ABACHI</td><td>87B HRS</td><td>E<sup>ee</sup><sub>cm</sub> = 29 GeV</td></tr></tbody></table>

<table><thead><tr><th>Γ(ηπ<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>))/Γ<sub>total</sub></th><th>Γ<sub>160</sub>/Γ</th></tr><tr><th>VALUE (units 10<sup>-4</sup>)</th><th>CL%</th><th>EVTS</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>2.20 ± 0.13</td><td colspan="3">OUR FIT</td><td>(Produced by HFLAV)</td><td></td></tr><tr><td>2.23 ± 0.12</td><td colspan="3">OUR AVERAGE</td><td></td><td></td></tr></tbody></table>

<table><tbody><tr><td>2.10 ± 0.09 ± 0.13</td><td>2.9k</td><td>1</td><td>LEES</td><td>12x BABR</td><td>η → γγ</td></tr><tr><td>2.37 ± 0.12 ± 0.18</td><td>1.4k</td><td>1</td><td>LEES</td><td>12x BABR</td><td>η → π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td></tr><tr><td>2.54 ± 0.27 ± 0.25</td><td>315</td><td>1</td><td>LEES</td><td>12x BABR</td><td>η → 3π<sup>0</sup></td></tr></tbody></table>

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

<table><tbody><tr><td>2.3 ± 0.5</td><td>170</td><td>2</td><td>ANASTASSOV 01</td><td>CLEO E<sup>ee</sup><sub>cm</sub> = 10.6 GeV</td></tr><tr><td>1.60 ± 0.05 ± 0.11</td><td>1.8 k</td><td>AUBERT</td><td>08AE BABR</td><td>Repl. by LEES 12x</td></tr><tr><td>3.4 +0.6<br/>-0.5 ± 0.6</td><td>89</td><td>3</td><td>BERGFELD</td><td>97 CLEO</td><td>Repl. by ANASTASSOV 01</td></tr></tbody></table>

¹LEES 12x uses 468 fb⁻¹ of data taken at $E_{cm}^{ee} = 10.6$ GeV. It gives the average of the three measurements listed here as (2.25 ± 0.07 ± 0.12) × 10⁻⁴.

²Weighted average of BERGFELD 97 and ANASTASSOV 01 measurements using $\eta$'s reconstructed from $\eta \to \pi^+\pi^-\pi^0$ and $\eta \to 3\pi^0$ decays.

³BERGFELD 97 reconstruct $\eta$'s using $\eta \to \gamma\gamma$ and $\eta \to 3\pi^0$ decays.
$$ \Gamma(\eta\pi^{-}\pi^{+}\pi^{-}\nu_{\tau}(\text{ex.}\mathbf{K}^{0}, f_{1}(1285)))/\Gamma_{\text{total}} \quad \Gamma_{161}/\Gamma $$

$\text{VALUE (units } 10^{-4})$

$$ 0.99\pm0.09\pm0.13 $$

$\text{DOCUMENT ID}$

$$ 1 \text{ LEES} $$

$\text{TECN}$

$$ 12\chi \text{ BABR} $$

$\text{COMMENT}$

$$ 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

¹LEES 12x obtain this result by subtracting their B(τ⁻ → f₁(1285)π⁻ντ⁻ → ηπ⁻π⁺π⁻ντ⁻) measurement from their B(τ⁻ → ηπ⁻π⁺π⁻ντ⁻(ex. K⁰)) measurement.

$$ \Gamma(\eta a_1(1260)^- \nu_{\tau} \rightarrow \eta \pi^- \rho^0 \nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{162}/\Gamma $$

$\text{VALUE}$

$$ <3.9 \times 10^{-4} $$

$\text{DOCUMENT ID}$

$$ 90 $$

$\text{TECN}$

$$ 97 $$

$\text{COMMENT}$

$$ E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

$$ \Gamma(\eta\eta\pi^-\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{163}/\Gamma $$

$\text{VALUE}$

$$ <7.4 \times 10^{-6} $$

$\text{DOCUMENT ID}$

$$ 90 $$

$\text{TECN}$

$$ 09 $$

$\text{COMMENT}$

$$ 490 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

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

$$ <1.1 \times 10^{-4} $$

$\text{ARTUSO}$

$$ 95 $$

$\text{CLEO}$

$$ 92 $$

$\text{CLEO}$

$$ E_{\text{cm}}^{\text{ee}} \approx 10.6 \text{ GeV} $$

$$ <8.3 \times 10^{-3} $$

$\text{ALBRECHT}$

$$ 95 $$

$\text{ARG}$

$$ 88\text{M} $$

$\text{ARG}$

$$ E_{\text{cm}}^{\text{ee}} \approx 10 \text{ GeV} $$

$$ \Gamma(\eta\eta\pi^-\pi^0\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{164}/\Gamma $$

$\text{VALUE (units } 10^{-4})$

$$ <2.0 $$

$\text{DOCUMENT ID}$

$$ 95 $$

$\text{TECN}$

$$ 92 $$

$\text{COMMENT}$

$$ E_{\text{cm}}^{\text{ee}} \approx 10.6 \text{ GeV} $$

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

$$ <90 $$

$\text{ALBRECHT}$

$$ 95 $$

$\text{ARG}$

$$ 88\text{M} $$

$\text{ARG}$

$$ E_{\text{cm}}^{\text{ee}} \approx 10 \text{ GeV} $$

$$ \Gamma(\eta\eta K^-\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{165}/\Gamma $$

$\text{VALUE}$

$$ <3.0 \times 10^{-6} $$

$\text{DOCUMENT ID}$

$$ 90 $$

$\text{TECN}$

$$ 09 $$

$\text{COMMENT}$

$$ 490 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

$$ \Gamma(\eta'(958)\pi^-\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{166}/\Gamma $$

$\text{VALUE}$

$$ <4.0 \times 10^{-6} $$

$\text{DOCUMENT ID}$

$$ 90 $$

$\text{TECN}$

$$ 12\chi \text{ BABR} $$

$\text{COMMENT}$

$$ 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

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

$$ <7.2 \times 10^{-6} $$

$\text{AUBERT}$

$$ 90 $$

$\text{CLEO}$

$$ 98\text{AE} $$

$\text{BABR}$

$$ 384 \text{ fb}^{-1}, \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

$$ <7.4 \times 10^{-5} $$

$\text{BERGFELD}$

$$ 90 $$

$\text{CLEO}$

$$ 97 $$

$\text{E}_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

$$ \Gamma(\eta'(958)\pi^-\pi^0\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{167}/\Gamma $$

$\text{VALUE}$

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

$\text{DOCUMENT ID}$

$$ 90 $$

$\text{TECN}$

$$ 12\chi \text{ BABR} $$

$\text{COMMENT}$

$$ 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

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

$$ <8.0 \times 10^{-5} $$

$\text{BERGFELD}$

$$ 90 $$

$\text{CLEO}$

$$ 97 $$

$\text{E}_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

$$ \Gamma(\eta'(958)K^-\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{168}/\Gamma $$

$\text{VALUE}$

$$ <2.4 \times 10^{-6} $$

$\text{DOCUMENT ID}$

$$ 90 $$

$\text{TECN}$

$$ 12\chi \text{ BABR} $$

$\text{COMMENT}$

$$ 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

$$ \Gamma(\phi\pi^-\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{169}/\Gamma $$

$\text{VALUE (units } 10^{-5})$

$$ 3.42\pm0.55\pm0.25 $$

$\text{CL%, EVTS}$

$$ 344 $$

$\text{DOCUMENT ID}$

$$ 08 $$

$\text{COMMENT}$

$$ 342 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

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

$$ <20 $$

$1 \text{ AVERY}$

$$ 90 $$

$\text{CLEO}$

$$ 97 $$

$\text{E}_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

$$ <35 $$

$\text{ALBRECHT}$

$$ 95\text{H} $$

$\text{ARG}$

$$ 94\text{.}5 \times 10.6 \text{ GeV} $$

$\text{ARG}$

$$ E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

¹AVERY 97 limit varies from (1.2–2.0) × 10⁻⁴ depending on decay model assumptions.

$$ \Gamma(\phi K^-\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{170}/\Gamma $$

$\text{VALUE (units } 10^{-5})$

$$ 4.4 \pm 1.6 \text{ OUR FIT} \quad \text{(Produced by HFLAV)} $$

$\text{EVTS}$

$$ 274 $$

$\text{DOCUMENT ID}$

$$ 08 $$

$\text{COMMENT}$

$$ 342 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

³⁷.⁰⁰±⁰.⁰³ OUR AVERAGE Error includes scale factor of 1.3.

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

$$ 3.39\pm0.20\pm0.28 $$

$\text{AUBERT}$

$$ 551 $$

$\text{INAMI}$

$$ 06 $$

$\text{BELL}$

$$ 401 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

$$ 4.05\pm0.25\pm0.26 $$

$\text{INAMI}$

$$ 551 $$

$\text{BELL}$

$$ 401 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

$$ <6.7 $$

$90$

¹ AVERY

$$ 97 $$

$\text{CLEO}$

$$ 94 \text{.}5 \times 10.6 \text{ GeV} $$

$\text{E}_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

¹AVERY 97 limit varies from (5.4–6.7) × 10⁻⁵ depending on decay model assumptions.

$$ \Gamma(f_1(1285)\pi^-\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{171}/\Gamma $$

$\text{VALUE (units } 10^{-4})$

$\text{3.9} \pm 0.5 \text{ OUR AVERAGE}$

$\text{DOCUMENT ID}$

$$ 1 \text{ LEES} $$

$\text{TECN}$

$$ 12\chi \text{ BABR} $$

$\text{COMMENT}$

$$ 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

Error includes scale factor of 1.9.

$$ 4.73\pm0.28\pm0.45 $$

$3.7k$

$1 \text{ LEES}$

$12\chi \text{ BABR}$

$468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

$\text{COMMENT}$

$$ 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

$$ 3.60\pm0.18\pm0.23 $$

$2\text{LEES}$

$12\chi \text{ BABR}$

$468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

$\text{COMMENT}$

$$ 468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

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

$$ 3.19\pm0.18\pm1.00 $$

$1.3 k$

$3 \text{ AUBERT}$

$4 \text{ AUBERT,B}$

$05\text{W} \text{ BABR}$

$1.4 k$

$4 \text{ AUBERT,B}$

$05\text{W} \text{ BABR}$

$\text{Repl. by LEES } 12\chi$

$\text{Repl. by LEES } 12\chi$

$$ 5.8 \pm 1.4 \quad \begin{array}{c} -1.3 \\ \text{+1.4} \end{array} $$

$54$

$5 \text{ BERGFELD}$

$97$

$\text{CLEO}$

$$ 94 \text{.}5 \times 10.6 \text{ GeV} $$

$\text{E}_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

¹LEES 12x obtain this value by dividing their B(τ⁻ → f₁(1285)π⁻ντ⁻ → 3π⁻2π⁺ντ⁺) measurement by the PDG 12 value of B(f₁(1285) → 2π⁺2π⁻) = 0.111±0.007

²LEES 12x obtain this value by dividing their B(τ⁻ → f₁(1285)π⁻ντ⁻ → ηπ⁻π⁺π⁻ντ⁻) measurement by 2/3 of the PDG 12 value of B(f₁(1285) → ηππ) = 0.524±0.019

³AUBERT 08AE obtain this value by dividing their B(τ⁻ → f₁(1285)π⁻ντ⁻ → ηπ⁻π⁺π⁻ντ⁻) measurement by the PDG 06 value of B(f₁(1285) → ηππ) = 0.35 ± 0.11. The quote (3.19 ± 0.18 ± 0.16 ± 0.99) × 10⁻⁴ where the final error is due to the uncertainty on B(f₁(1285) → ηππ). We combine the two systematic errors in quadrature.

⁴AUBERT,B 05W use the f₁(1285) → 2π⁺2π⁻ decay mode and the PDG 04 value of B(f₁(1285) → 2π⁺2π⁻) = 0.110±0.007

⁵ BERGFELD 97 use the f₁(1285) → ηπ⁺π⁻ decay mode.

$$ \Gamma(f_1(1285)\pi^-\nu_{\tau} \rightarrow \eta\pi^+\pi^+\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{172}/\Gamma $$

$\text{VALUE (units } 10^{-4})$

$1.18\pm0.07 \text{ OUR AVERAGE}$

Error includes scale factor of 1.3.

$$ 1.26\pm0.06\pm0.06 \quad 2.5k \quad \text{LEES} $$

$12\chi \text{ BABR}$

$468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

$$ 1.11\pm0.06\pm0.05 \quad 1.3 k \quad \text{AUBERT} $$

$08\text{AE BABR}$

$384 \text{ fb}^{-1}, \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

$$ \Gamma(f_1(1285)\pi^-\nu_{\tau} \rightarrow \eta\pi^+\pi^+\nu_{\tau})/\Gamma(\eta\pi^-\pi^+\pi^-\nu_{\tau}(\text{ex.}\mathbf{K}^0)) \quad \Gamma_{172}/\Gamma_{160} $$

$\text{VALUE}$

$$ 0.69\pm0.01\pm0.05 $$

$\text{DOCUMENT ID}$

$$ 1 \text{ AUBERT} $$

$\text{TECN}$

$$ 08\text{AE BABR} $$

$384 \text{ fb}^{-1}, \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

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

$$ 0.55\pm0.14 $$

$\text{BERGFELD}$

$$ 97 $$

$\text{CLEO}$

$$ 94 \text{.}5 \times 10.6 \text{ GeV} $$

¹Not independent of AUBERT 08AE B(τ⁻ → f₁(1285)π⁻ντ⁻ → ηπ⁻π⁺π⁻ντ⁻) and B(τ⁻ → ηπ⁻π⁺π⁻ντ⁻(ex. K⁰)) values.

$$ \Gamma(f_1(1285)\pi^-\nu_{\tau} \rightarrow 3\pi^-2\pi^+\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{173}/\Gamma $$

$\text{VALUE (units } 10^{-4})$

$0.52 \pm 0.04 \text{ OUR FIT}$

(Produced by HFLAV)

$$ 0.520\pm0.031\pm0.037 \quad 3.7k \quad \text{LEES} $$

$12\chi \text{ BABR}$

$468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

$$ \Gamma(\pi(1300)^-\nu_{\tau} \rightarrow (\rho\pi)^-\nu_{\tau} \rightarrow (3\pi)^-\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{174}/\Gamma $$

$\text{VALUE}$

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

$\text{CL%}$

$90$

$\text{ASNER}$

$00$

$468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

$\text{COMMENT}$

$$ E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

$$ \Gamma(\pi(1300)^-\nu_{\tau} \rightarrow ((\pi\pi)^S \text{ wave } \pi^-\nu_{\tau} \rightarrow (3\pi)^-\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{175}/\Gamma $$

$\text{VALUE}$

$$ <1.9 \times 10^{-4} $$

$\text{CL%}$

$90$

$\text{ASNER}$

$00$

$468 \text{ fb}^{-1} \quad E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $

$\text{COMMENT}$

$$ E_{\text{cm}}^{\text{ee}} = 10.6 \text{ GeV} $$

$$ \Gamma(\bar{h}^-\omega \ge 0 \text{ neutrals } \nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{176}/\Gamma $$

$\Gamma_{176}/\Gamma = (\Gamma_{178} + \Gamma_{179})/\Gamma$

$\text{VALUE ()}$

$2.40\pm0.08 \text{ OUR FIT}$

(Produced by HFLAV)

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

$$ 1.65\pm0.3 \pm 0.2 $$

$1513 \quad \text{ALBRECHT}$

$88\text{M ARG}$

$E_{\text{cm}}^{\text{ee}} \approx 10 \text{ GeV}$

$\text{COMMENT}$

$$ E_{\text{cm}}^{\text{ee}} \approx 10 \text{ GeV} $$

$$ \Gamma(\bar{h}^-\omega\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{177}/\Gamma = (\Gamma_{178}+\Gamma_{179})/\Gamma $$

$\text{VALUE ()}$

$1.99\pm0.06 \text{ OUR FIT}$

(Produced by HFLAV)

³.⁹²±⁰.⁰⁷ OUR AVERAGE

$$ 1.91\pm0.07\pm0.06 \quad 5803 $$

$\text{BUSKULIC}$

$97\text{C ALEP}$

$1991-1994 \text{ LEP runs}$

$$ 1.60\pm0.27\pm0.41 \quad 139 $$

$\text{BARINGER}$

$87 \text{ CLEO}$

$E_{\text{cm}}^{\text{ee}} = 10.5 \text{ GeV}$

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

$$ 1.95\pm0.07\pm0.11 $$

$2223 \quad 1 \text{ BALEST}$

$95\text{C CLEO}$

$E_{\text{cm}}^{\text{ee}} \approx 10.6 \text{ GeV}$

¹Not independent of BALEST 95C B(τ⁻ → h⁻h⁻h⁺π⁰ντ⁻)(B(τ⁻ → h⁻h⁻h⁺π⁰ντ⁻)) value.

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

$43.5\pm1.4 \text{ OUR FIT}$

(Produced by HFLAV)

⁴.⁵³±⁰.⁰⁹ OUR AVERAGE

$$ 43.1\pm3.3 \quad 2350 $$

$1 \text{ BUSKULIC}$

$96 \text{ ALEP}$

$1991-1993 \text{ data}$

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

$$ 37 \pm 5 \pm 2 $$

$458 \quad 3 \text{ BALECHT}$

$91\text{D ARG}$

$E_{\text{cm}}^{\text{ee}} = 9.4-10.6 \text{ GeV}$

$\text{COMMENT}$

$$ E_{\text{cm}}^{\text{ee}} \approx 9.4 \text{–} 10.6 \text{ GeV} $$

$\text{COMMENT}$

$$ E_{\text{cm}}^{\text{ee}} \approx 9.4 \text{–} 10.6 \text{ GeV} $$

¹BUSKULIC 96 quote the fraction of τ⁻ → h⁻h⁻h⁺π⁰ντ⁻ (ex. K⁰) decays which originate in a h⁻ω final state equals 0.383 ± 0.029. We divide this by the ω(782) → π⁺π⁻π⁰ branching fraction (0.888).

²BALEST 95C quote the fraction of τ⁻ → h⁻h⁻h⁺π⁰ντ⁻ (ex. K⁰) decays which originate in a h⁻ω final state equals 0.412 ± 0.014 ± 0.015. We divide this by the ω(782) → π⁺π⁻π⁰ branching fraction (0.888).

³ALBRECHT 91D quote the fraction of τ⁻ → h⁻h⁻h⁺π⁰ντ⁻ decays which originate in a π⁻ω final state equals 0.33 ± 0.04 ± 0.02. We divide this by the ω(782) → π⁺π⁻π⁰ branching fraction (0.888).

$$ \Gamma(\pi^-\omega\nu_{\tau})/\Gamma_{\text{total}} \quad \Gamma_{178}/\Gamma $$

$\text{VALUE ()}$

$1.95\pm0.06 \text{ OUR FIT}$

(Produced by HFLAV)

$\text{COMMENT}$

$$ E_{\text{cm}}^{\text{ee}} \approx 10 \text{ GeV} $$