# 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 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.${{\mathit K}^{0}}$) ($8.4$ $\pm0.6$) $\times 10^{-5}$