An overall fit to 87 branching ratios uses 170 measurements and one constraint to determine 46 parameters. The overall fit has a $\chi {}^{2}$ = 135.0 for 125 degrees of freedom.
The following off-diagonal array elements are the correlation coefficients <$\mathit \delta $x$_{i}$~$\delta $x$_{j}$> $/$ ($\mathit \delta $x$_{i}\cdot{}\delta $x$_{j}$), in percent, from the fit to parameters ${{\mathit p}_{{i}}}$, including the branching fractions, $\mathit x_{i}$ =$\Gamma _{i}$ $/$ $\Gamma _{total}$. The fit constrains the ${{\mathit x}_{{i}}}$ whose labels appear in this array to sum to one.
 x3  100
 x5   100
 x9    100
 x10     100
 x14      100
 x16       100
 x20        100
 x23         100
 x27          100
 x28           100
 x30            100
 x36             100
 x38              100
 x41               100
 x43                100
 x45                 100
 x48                  100
 x49                   100
 x52                    100
 x56                     100
 x61                      100
 x70                       100
 x78                        100
 x85                         100
 x89                          100
 x97                           100
 x103                            100
 x106                             100
 x107                              100
 x119                               100
 x120                                100
 x126                                 100
 x127                                  100
 x150                                   100
 x151                                    100
 x152                                     100
 x154                                      100
 x156                                       100
 x160                                        100
 x170                                         100
 x173                                          100
 x178                                           100
 x179                                            100
 x180                                             100
 x182                                              100
 x185                                               100
   x3  x5  x9  x10  x14  x16  x20  x23  x27  x28  x30  x36  x38  x41  x43  x45  x48  x49  x52  x56  x61  x70  x78  x85  x89  x97  x103  x106  x107  x119  x120  x126  x127  x150  x151  x152  x154  x156  x160  x170  x173  x178  x179  x180  x182  x185
  Mode Fraction (Γi / Γ)Scale factor

Γ3  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\overline{\mathit \nu}}_{{\mu}}}{{\mathit \nu}_{{\tau}}}$  $0.1739$ $\pm0.0004$ 
Γ5  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}{{\mathit \nu}_{{\tau}}}$  $0.1782$ $\pm0.0004$ 
Γ9  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$  $0.1082$ $\pm0.0005$ 
Γ10  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \nu}_{{\tau}}}$  $0.00696$ $\pm0.00010$ 
Γ14  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  $0.2549$ $\pm0.0009$ 
Γ16  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  $0.00433$ $\pm0.00015$ 
Γ20  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) $0.0926$ $\pm0.0010$ 
Γ23  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) ($6.5$ $\pm2.2$) $ \times 10^{-4}$ 
Γ27  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}$3 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) $0.0104$ $\pm0.0007$ 
Γ28  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}$3 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$, ${{\mathit \eta}}$) ($4.8$ $\pm2.1$) $ \times 10^{-4}$ 
Γ30  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit h}^{-}}$4 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}},{{\mathit \eta}}$) $0.0011$ $\pm0.0004$ 
Γ36  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\overline{\mathit K}}^{0}}{{\mathit \nu}_{{\tau}}}$  $0.00838$ $\pm0.00014$ 
Γ38  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{0}}{{\mathit \nu}_{{\tau}}}$  $0.001486$ $\pm0.000034$ 
Γ41  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\overline{\mathit K}}^{0}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  $0.00382$ $\pm0.00013$ 
Γ43  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{0}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  $0.00150$ $\pm0.00007$ 
Γ45  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\overline{\mathit K}}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) ($2.6$ $\pm2.3$) $ \times 10^{-4}$ 
Γ48  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit \nu}_{{\tau}}}$  ($2.35$ $\pm0.06$) $ \times 10^{-4}$ 
Γ49  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit K}_S^0}$ ${{\mathit K}_L^0}$ ${{\mathit \nu}_{{\tau}}}$  $0.00108$ $\pm0.00024$ 
Γ52  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  ($1.82$ $\pm0.21$) $ \times 10^{-5}$ 
Γ56  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit K}_S^0}$ ${{\mathit K}_L^0}$ ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  ($3.2$ $\pm1.2$) $ \times 10^{-4}$ 
Γ61  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit h}^{+}}{{\mathit h}^{-}}{{\mathit h}^{-}}{{\mathit \nu}_{{\tau}}}$  ($2.5$ $\pm2.0$) $ \times 10^{-4}$ 
Γ70  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}},{{\mathit \omega}}$) $0.0899$ $\pm0.0005$ 
Γ78  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}},{{\mathit \omega}}$) $0.0274$ $\pm0.0007$ 
Γ85  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit h}^{-}}{{\mathit h}^{-}}{{\mathit h}^{+}}$2 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}},{{\mathit \omega}},{{\mathit \eta}}$) $0.0010$ $\pm0.0004$ 
Γ89  ${{\mathit \tau}^{-}}$ $\rightarrow$ 2 ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$3 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$, ${{\mathit \eta}}$, ${{\mathit \omega}}$, ${{\mathit f}_{{1}}{(1285)}}$)  ($1.4$ $\pm2.7$) $ \times 10^{-5}$ 
Γ97  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}},{{\mathit \omega}}$) $0.00293$ $\pm0.00007$ 
Γ103  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}},{{\mathit \omega}},{{\mathit \eta}}$) ($3.9$ $\pm1.4$) $ \times 10^{-4}$ 
Γ106  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$  $0.001435$ $\pm0.000027$ 
Γ107  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  ($6.1$ $\pm1.8$) $ \times 10^{-5}$ 
Γ119  ${{\mathit \tau}^{-}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$, ${{\mathit \omega}}$, ${{\mathit f}_{{1}}{(1285)}}$) ($7.75$ $\pm0.30$) $ \times 10^{-4}$ 
Γ120  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) ($6$ $\pm12$) $ \times 10^{-7}$ 
Γ126  ${{\mathit \tau}^{-}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$, ${{\mathit \eta}}$, ${{\mathit \omega}}$, ${{\mathit f}_{{1}}{(1285)}}$) ($3.8$ $\pm0.9$) $ \times 10^{-5}$ 
Γ127  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) ($1.1$ $\pm0.6$) $ \times 10^{-6}$ 
Γ150  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  $0.00139$ $\pm0.00007$ 
Γ151  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  ($2.0$ $\pm0.4$) $ \times 10^{-4}$ 
Γ152  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit K}^{-}}{{\mathit \nu}_{{\tau}}}$  ($1.55$ $\pm0.08$) $ \times 10^{-4}$ 
Γ154  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit K}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  ($4.8$ $\pm1.2$) $ \times 10^{-5}$ 
Γ156  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\overline{\mathit K}}^{0}}{{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$  ($9.4$ $\pm1.5$) $ \times 10^{-5}$ 
Γ160  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) ($2.20$ $\pm0.13$) $ \times 10^{-4}$ 
Γ170  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit K}^{-}}{{\mathit \nu}_{{\tau}}}$  ($4.4$ $\pm1.6$) $ \times 10^{-5}$ 
Γ173  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit f}_{{1}}{(1285)}}{{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \nu}_{{\tau}}}$  ($5.2$ $\pm0.4$) $ \times 10^{-5}$ 
Γ178  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \omega}}{{\mathit \nu}_{{\tau}}}$  $0.0195$ $\pm0.0006$ 
Γ179  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \omega}}{{\mathit \nu}_{{\tau}}}$  ($4.1$ $\pm0.9$) $ \times 10^{-4}$ 
Γ180  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit h}^{-}}{{\mathit \omega}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  $0.0041$ $\pm0.0004$ 
Γ182  ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \omega}}$2 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$  ($7.2$ $\pm1.6$) $ \times 10^{-5}$ 
Γ185  ${{\mathit \tau}^{-}}$ $\rightarrow$ 2 ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \omega}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) ($8.4$ $\pm0.6$) $ \times 10^{-5}$