# CONSTRAINED FIT INFORMATIONshow precise values?

 An overall fit to 66 branching ratios uses 128 measurements and one constraint to determine 33 parameters. The overall fit has a $\chi {}^{2}$ = 143.7 for 96 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.

 x6 100 x19 100 x20 100 x21 100 x30 100 x31 100 x36 100 x37 100 x39 100 x54 100 x71 100 x82 100 x86 100 x93 100 x107 100 x108 100 x109 100 x124 100 x131 100 x132 100 x133 100 x151 100 x179 100 x189 100 x191 100 x194 100 x195 100 x196 100 x197 100 x208 100 x267 100 x271 100 x336 100 x6 x19 x20 x21 x30 x31 x36 x37 x39 x54 x71 x82 x86 x93 x107 x108 x109 x124 x131 x132 x133 x151 x179 x189 x191 x194 x195 x196 x197 x208 x267 x271 x336

 Mode Fraction (Γi / Γ) Scale factor Γ6 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}$ anything $0.068$ $\pm0.006$ Γ19 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit e}^{+}}{{\mathit \nu}_{{e}}}$ $0.03541$ $\pm0.00034$ 1.3 Γ20 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{\mu}}}$ $0.0341$ $\pm0.0004$ 1.0 Γ21 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{*}{(892)}^{-}}{{\mathit e}^{+}}{{\mathit \nu}_{{e}}}$ $0.0215$ $\pm0.0016$ Γ30 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit \nu}_{{e}}}$ $0.00291$ $\pm0.00004$ 1.0 Γ31 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{\mu}}}$ $0.00267$ $\pm0.00012$ 1.3 Γ36 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ $0.03946$ $\pm0.00030$ 1.2 Γ37 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}$ $0.01239$ $\pm0.00022$ Γ39 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $0.0280$ $\pm0.0018$ 1.1 Γ54 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ $0.144$ $\pm0.005$ 2.0 Γ71 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $0.0822$ $\pm0.0014$ 1.1 Γ82 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.052$ $\pm0.006$ Γ86 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.043$ $\pm0.004$ Γ93 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \eta}}$ $0.0188$ $\pm0.0005$ 1.4 Γ107 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \eta}}$ $0.00508$ $\pm0.00013$ Γ108 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \omega}}$ $0.0111$ $\pm0.0006$ Γ109 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \eta}^{\,'}{(958)}}$ $0.00949$ $\pm0.00032$ Γ124 ${{\mathit D}^{0}}$ $\rightarrow$ 3 ${{\mathit K}_S^0}$ ($7.5$ $\pm0.7$) $\times 10^{-4}$ 1.4 Γ131 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $0.001453$ $\pm0.000024$ 1.4 Γ132 ${{\mathit D}^{0}}$ $\rightarrow$ 2 ${{\mathit \pi}^{0}}$ ($8.26$ $\pm0.25$) $\times 10^{-4}$ Γ133 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.0149$ $\pm0.0006$ 2.1 Γ151 ${{\mathit D}^{0}}$ $\rightarrow$ 2 ${{\mathit \pi}^{+}}$2 ${{\mathit \pi}^{-}}$ $0.00755$ $\pm0.00020$ Γ179 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}$ ($6.3$ $\pm0.6$) $\times 10^{-4}$ 1.1 Γ189 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}{(958)}}{{\mathit \pi}^{0}}$ ($9.2$ $\pm1.0$) $\times 10^{-4}$ Γ191 ${{\mathit D}^{0}}$ $\rightarrow$ 2 ${{\mathit \eta}}$ $0.00211$ $\pm0.00019$ 2.3 Γ194 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \eta}^{\,'}{(958)}}$ $0.00101$ $\pm0.00019$ Γ195 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ $0.00408$ $\pm0.00006$ 1.6 Γ196 ${{\mathit D}^{0}}$ $\rightarrow$ 2 ${{\mathit K}_S^0}$ ($1.41$ $\pm0.05$) $\times 10^{-4}$ 1.1 Γ197 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ $0.0033$ $\pm0.0005$ 1.1 Γ208 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ $0.00217$ $\pm0.00034$ 1.1 Γ267 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \gamma}}$ ($2.81$ $\pm0.19$) $\times 10^{-5}$ Γ271 ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ ($1.50$ $\pm0.07$) $\times 10^{-4}$ 3.0 Γ336 ${{\mathit D}^{0}}$ $\rightarrow$ Unaccounted decay modes $0.350$ $\pm0.012$ 1.1

 An overall fit to 3 branching ratios uses 3 measurements and one constraint to determine 4 parameters. The overall fit has a $\chi {}^{2}$ = 0.0 for 0 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.

 x1 100 x2 100 x3 100 x4 100 x1 x2 x3 x4

 Mode Fraction (Γi / Γ) Scale factor Γ1 ${{\mathit D}^{0}}$ $\rightarrow$ 0-prongs $0.15$ $\pm0.06$ Γ2 ${{\mathit D}^{0}}$ $\rightarrow$ 2-prongs $0.71$ $\pm0.06$ Γ3 ${{\mathit D}^{0}}$ $\rightarrow$ 4-prongs $0.146$ $\pm0.005$ Γ4 ${{\mathit D}^{0}}$ $\rightarrow$ 6-prongs ($6.5$ $\pm1.3$) $\times 10^{-4}$