# CONSTRAINED FIT INFORMATIONshow precise values?

 An overall fit to 85 branching ratios uses 169 measurements and one constraint to determine 46 parameters. The overall fit has a $\chi {}^{2}$ = 134.9 for 124 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 x117 100 x118 100 x124 100 x125 100 x148 100 x149 100 x150 100 x152 100 x154 100 x158 100 x168 100 x171 100 x176 100 x177 100 x178 100 x180 100 x183 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 x117 x118 x124 x125 x148 x149 x150 x152 x154 x158 x168 x171 x176 x177 x178 x180 x183

 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 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\overline{\mathit K}}^{0}}{{\mathit \nu}_{{\tau}}}$ $0.00840$ $\pm0.00014$ Γ38 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{0}}{{\mathit \nu}_{{\tau}}}$ $0.00148$ $\pm0.00005$ 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 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit \nu}_{{\tau}}}$ ($2.33$ $\pm0.07$) $\times 10^{-4}$ 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 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ ($6.1$ $\pm1.8$) $\times 10^{-5}$ Γ117 ${{\mathit \tau}^{-}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$, ${{\mathit \omega}}$, ${{\mathit f}_{{1}}{(1285)}}$) ($7.69$ $\pm0.30$) $\times 10^{-4}$ Γ118 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) ($6$ $\pm12$) $\times 10^{-7}$ Γ124 ${{\mathit \tau}^{-}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$, ${{\mathit \eta}}$, ${{\mathit \omega}}$, ${{\mathit f}_{{1}}{(1285)}}$) ($3.8$ $\pm0.9$) $\times 10^{-5}$ Γ125 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) ($1.1$ $\pm0.6$) $\times 10^{-6}$ Γ148 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ $0.00139$ $\pm0.00007$ Γ149 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ ($1.9$ $\pm0.4$) $\times 10^{-4}$ Γ150 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit K}^{-}}{{\mathit \nu}_{{\tau}}}$ ($1.55$ $\pm0.08$) $\times 10^{-4}$ Γ152 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit K}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ ($4.8$ $\pm1.2$) $\times 10^{-5}$ Γ154 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\overline{\mathit K}}^{0}}{{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$ ($9.4$ $\pm1.5$) $\times 10^{-5}$ Γ158 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) ($2.19$ $\pm0.13$) $\times 10^{-4}$ Γ168 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit K}^{-}}{{\mathit \nu}_{{\tau}}}$ ($4.4$ $\pm1.6$) $\times 10^{-5}$ Γ171 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit f}_{{1}}{(1285)}}{{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \nu}_{{\tau}}}$ ($5.2$ $\pm0.4$) $\times 10^{-5}$ Γ176 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \omega}}{{\mathit \nu}_{{\tau}}}$ $0.0195$ $\pm0.0006$ Γ177 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \omega}}{{\mathit \nu}_{{\tau}}}$ ($4.1$ $\pm0.9$) $\times 10^{-4}$ Γ178 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit h}^{-}}{{\mathit \omega}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ $0.0041$ $\pm0.0004$ Γ180 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \omega}}$2 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ ($7.1$ $\pm1.6$) $\times 10^{-5}$ Γ183 ${{\mathit \tau}^{-}}$ $\rightarrow$ 2 ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \omega}}{{\mathit \nu}_{{\tau}}}$ (ex.${{\mathit K}^{0}}$) ($8.4$ $\pm0.6$) $\times 10^{-5}$