pdgLive Home   >   CHARMED, STRANGE MESONS ($\mathit C$ = $\pm1$, $\mathit S$ = $\pm1$) (including possibly non-${\mathit {\mathit q}}$ ${\mathit {\overline{\mathit q}}}$ states)   >   ${{\mathit D}_{{{s}}}^{\pm}}$

CHARMED, STRANGE MESONS ($\mathit C$ = $\pm1$, $\mathit S$ = $\pm1$) (including possibly non-${\mathit {\mathit q}}$ ${\mathit {\overline{\mathit q}}}$ states) ${{\mathit D}_{{{s}}}^{+}}$ = ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit s}}}$, ${{\mathit D}_{{{s}}}^{-}}$ = ${\mathit {\overline{\mathit c}}}$ ${\mathit {\mathit s}}$, similarly for ${{\mathit D}_{{{s}}}^{*}}$'s

INSPIRE   JSON PDGID: S034

${{\mathit D}_{{{s}}}^{\pm}}$ $I(J^P)$ = $0(0^{-})$

The angular distributions of the decays of the ${{\mathit \phi}}$ and ${{\overline{\mathit K}}^{*}{(892)}^{0}}$ in the ${{\mathit \phi}}{{\mathit \pi}^{+}}$ and ${{\mathit K}^{+}}{{\overline{\mathit K}}^{*}{(892)}^{0}}$ modes strongly indicate that the spin is zero. The parity given is that expected of a ${{\mathit c}}{{\overline{\mathit s}}}$ ground state.

See related review:
Leptonic Decays of Charged Pseudoscalar Mesons

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${{\mathit D}_{{{s}}}^{\pm}}$ MASS $1968.35$ $\pm0.07$ MeV

${\mathit m}_{{{\mathit D}_{{{s}}}^{\pm}}}-{\mathit m}_{{{\mathit D}^{\pm}}}$ $98.69$ $\pm0.05$ MeV

${{\mathit D}_{{{s}}}^{\pm}}$ MEAN LIFE ($5.012$ $\pm0.022$) $ \times 10^{-13}$ s (S = 1.3)

▸  exp ${{\mathit D}_{{{s}}}^{\pm}}$ Amplitude analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}_{{{S}}}}{{\mathit \pi}^{0}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \eta}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \eta}^{\,'}}$ partial wave analyses.

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}$2 ${{\mathit \pi}^{0}}$ partial wave analyses.

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ 2 ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{+}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ partial wave analyses

${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ partial wave analyses

▸  exp ${{\mathit D}_{{{s}}}^{+}}−{{\mathit D}_{{{s}}}^{-}}$ $\mathit CP$-VIOLATING DECAY-RATE ASYMMETRIES

$\mathit A_{CP}({{\mathit \mu}^{\pm}}{{\mathit \nu}}$) in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}}$, ${{\mathit D}_{{{s}}}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\overline{\mathit \nu}}_{{{\mu}}}}$ $-0.002$ $\pm0.025$

$\mathit A_{CP}({{\mathit \tau}^{\pm}}{{\mathit \nu}}$) in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \nu}_{{{\tau}}}}$, ${{\mathit D}_{{{s}}}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{-}}{{\overline{\mathit \nu}}_{{{\tau}}}}$ $0.03$ $\pm0.05$

$\mathit A_{CP}({{\mathit K}^{\pm}}{{\mathit K}_S^0}$ ) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit K}_S^0}$ $0.0007$ $\pm0.0024$

$\mathit A_{CP}({{\mathit K}^{\pm}}{{\mathit K}_L^0}$ ) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit K}_L^0}$ $-0.011$ $\pm0.027$

$\mathit A_{CP}({{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{\pm}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{\pm}}$ $0.0035$ $\pm0.0034$

$\mathit A_{CP}({{\mathit \phi}}{{\mathit \pi}^{\pm}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}^{\pm}}$ $-0.0038$ $\pm0.0027$

$\mathit A_{CP}({{\mathit K}^{\pm}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}$ $-0.009$ $\pm0.019$

$\mathit A_{CP}$(2 ${{\mathit K}_S^0}$ ${{\mathit \pi}^{\pm}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ 2 ${{\mathit K}_S^0}$ ${{\mathit \pi}^{\pm}}$ $0.013$ $\pm0.016$

$\mathit A_{CP}({{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}$ $-0.006$ $\pm0.009$

$\mathit A_{CP}({{\mathit K}^{\pm}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $0.007$ $\pm0.029$  (S = 1.3)

$\mathit A_{CP}({{\mathit K}_S^0}$ ${{\mathit K}^{\mp}}$2 ${{\mathit \pi}^{\pm}}$) in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{\mp}}$2 ${{\mathit \pi}^{\pm}}$ $0.007$ $\pm0.018$  (S = 1.3)

$\mathit A_{CP}({{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{\pm}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{\pm}}$ $-0.009$ $\pm0.011$

$\mathit A_{CP}({{\mathit \pi}^{\pm}}{{\mathit \eta}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \eta}}$ $0.0024$ $\pm0.0029$

$\mathit A_{CP}({{\mathit \pi}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \eta}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \eta}}$ $0.024$ $\pm0.030$

$\mathit A_{CP}({{\mathit \pi}^{\pm}}{{\mathit \eta}^{\,'}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \eta}^{\,'}}$ $-0.0008$ $\pm0.0017$  (S = 1.2)

$\mathit A_{CP}({{\mathit \eta}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}$ $0.009$ $\pm0.015$

$\mathit A_{CP}({{\mathit \eta}^{\,'}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}$ $-0.015$ $\pm0.025$

$\mathit A_{CP}({{\mathit K}^{\pm}}{{\mathit \pi}^{0}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{0}}$ $0.02$ $\pm0.04$  (S = 1.2)

$\mathit A_{CP}({{\overline{\mathit K}}^{0}}$ ${{\mathit K}^{0}}{{\mathit \pi}^{\pm}}$) in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\overline{\mathit K}}^{0}}{{\mathit \pi}^{+}}$, ${{\mathit D}_{{{s}}}^{-}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit \pi}^{-}}$ $0.004$ $\pm0.005$

$\mathit A_{CP}({{\mathit K}_S^0}$ ${{\mathit \pi}^{\pm}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{\pm}}$ $0.0020$ $\pm0.0018$

$\mathit A_{CP}({{\mathit K}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $0.022$ $\pm0.019$

$\mathit A_{CP}({{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}$ $-0.02$ $\pm0.05$

$\mathit A_{CP}({{\mathit K}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.07$ $\pm0.05$

$\mathit A_{CP}({{\mathit K}^{\pm}}{{\mathit \eta}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit \eta}}$ $0.018$ $\pm0.019$

$\mathit A_{CP}({{\mathit K}^{\pm}}{{\mathit \eta}^{\,'}{(958)}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit \eta}^{\,'}{(958)}}$ $0.06$ $\pm0.19$

▸  exp ${{\mathit D}_{{{s}}}^{\pm}}{{\mathit \chi}^{2}}$ TESTS OF $\mathit CP$-VIOLATION ($\mathit CPV$)

Local $\mathit CPV$ in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit K}^{\pm}}$

▸  exp $\mathit CP$ VIOLATING ASYMMETRIES OF $\mathit P$-ODD ($\mathit T$-ODD) MOMENTS

$\mathit A_{\mathit Tviol}({{\mathit K}_S^0}$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$) in ${{\mathit D}_{{{s}}}^{\pm}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ [1] $-0.008$ $\pm0.006$

▸  exp ${{\mathit D}_{{{s}}}^{+}}$ Semileptonic Form Factors and Decay Constants

$\mathit r_{2}{}\equiv\mathit A_{2}(0)/\mathit A_{1}$(0) in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{{\mathit \ell}}}}}}$ $0.83$ $\pm0.08$  (S = 1.8)

$\mathit r_{\mathit v}{}\equiv\mathit V(0)/\mathit A_{1}$(0) in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{{\mathit \ell}}}}}}$ $1.76$ $\pm0.07$  (S = 1.1)

$\Gamma _{\mathit L}/\Gamma _{\mathit T}$ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{{\mathit \ell}}}}}}$ $0.72$ $\pm0.18$

${{\mathit f}_{{{+}}}}$(0) $\vert {{\mathit V}_{{{cs}}}}\vert $ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $0.449$ $\pm0.009$

${{\mathit f}_{{{+}}}{(0)}}$ $\vert {{\mathit V}_{{{cs}}}}\vert $ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ $0.452$ $\pm0.012$

${{\mathit r}_{{{1}}}}{}\equiv$ ${{\mathit a}_{{{1}}}}/{{\mathit a}_{{{0}}}}$ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ $-2.9$ $\pm0.6$

$\langle \mathit A{}^{{{\mathit \eta}}}_{FB}\rangle $ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ $-0.059$ $\pm0.031$

${{\mathit f}_{{{+}}}}$(0) $\vert {{\mathit V}_{{{cs}}}}\vert $ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $0.527$ $\pm0.024$

${{\mathit r}_{{{1}}}}{}\equiv$ ${{\mathit a}_{{{1}}}}/{{\mathit a}_{{{0}}}}$ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ $-11$ $\pm5$

$\langle \mathit A{}^{{{\mathit \eta}^{\,'}}}_{FB}\rangle $ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ $-0.06$ $\pm0.08$

${{\mathit f}_{{{+}}}{(0)}}$ $\vert {{\mathit V}_{{{cs}}}}\vert $ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ $0.50$ $\pm0.04$

${{\mathit f}_{{{+}}}}$(0) $\vert {{\mathit V}_{{{cs}}}}\vert $ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit f}_{{{0}}}{(980)}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $0.50$ $\pm0.04$

${{\mathit f}_{{{+}}}{(0)}}\vert {{\mathit V}_{{{cd}}}}\vert $ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $0.145$ $\pm0.010$

${{\mathit r}_{{{v}}}}{}\equiv$ ${{\mathit V}{(0)}}/{{\mathit A}_{{{1}}}{(0)}}$ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{*}{(892)}^{0}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $1.7$ $\pm0.4$

${{\mathit r}_{{{2}}}}{}\equiv$ ${{\mathit A}_{{{2}}}{(0)}}/{{\mathit A}_{{{1}}}{(0)}}$ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{*}{(892)}^{0}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $0.77$ $\pm0.29$

$\mathit f_{{{\mathit D}_{{{s}}}^{+}}}$ $\vert \mathit V_{cs}\vert $ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ $242.7$ $\pm3.0$ MeV

$\mathit f_{{{\mathit D}_{{{s}}}^{+}}}$ $\vert \mathit V_{cs}\vert $ in ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \nu}_{{{\tau}}}}$ $247.5$ $\pm2.3$ MeV

${{\mathit D}_{{{s}}}^{+}}$ DECAY MODES
Unless otherwise noted, the branching fractions for modes with a resonance in the final state include all the decay modes of the resonance. ${{\mathit D}_{{{s}}}^{-}}$ modes are charge conjugates of the modes below.
Mode   Fraction ($\Gamma_i$ / $\Gamma$) Scale Factor/ Conf. Level P(MeV/c)   ▸  exp Inclusive modes $\Gamma_{1}$ ${{\mathit e}^{+}}$ semileptonic [2] ($6.33$ $\pm0.15$ ) $\%$     $\Gamma_{2}$ ${{\mathit \pi}^{+}}$ anything ($119.3$ $\pm1.4$ ) $\%$     $\Gamma_{3}$ ${{\mathit \pi}^{-}}$ anything ($43.2$ $\pm0.9$ ) $\%$     $\Gamma_{4}$ ${{\mathit \pi}^{0}}$ anything ($123$ $\pm7$ ) $\%$     $\Gamma_{5}$ ${{\mathit K}^{-}}$ anything ($18.7$ $\pm0.5$ ) $\%$     $\Gamma_{6}$ ${{\mathit K}^{+}}$ anything ($28.9$ $\pm0.7$ ) $\%$     $\Gamma_{7}$ ${{\mathit K}_S^0}$ anything ($19.0$ $\pm1.1$ ) $\%$     $\Gamma_{8}$ ${{\mathit \eta}}$ anything [3] ($29.9$ $\pm2.8$ ) $\%$     $\Gamma_{9}$ ${{\mathit \omega}}$ anything ($6.1$ $\pm1.4$ ) $\%$     $\Gamma_{10}$ ${{\mathit \eta}^{\,'}}$ anything [4] ($10.3$ $\pm1.4$ ) $\%$ S=1.1      $\Gamma_{11}$ ${{\mathit f}_{{{0}}}{(980)}}$ anything, ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ <1.3 $\%$ CL=90%     $\Gamma_{12}$ ${{\mathit \phi}}$ anything ($15.7$ $\pm1.0$ ) $\%$     $\Gamma_{13}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ anything ($15.8$ $\pm0.7$ ) $\%$     $\Gamma_{14}$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}$ anything ($5.8$ $\pm0.5$ ) $\%$     $\Gamma_{15}$ ${{\mathit K}_S^0}$ ${{\mathit K}^{-}}$ anything ($1.9$ $\pm0.4$ ) $\%$     $\Gamma_{16}$ 2 ${{\mathit K}_S^0}$ anything ($1.70$ $\pm0.32$ ) $\%$     $\Gamma_{17}$ 2 ${{\mathit K}^{+}}$ anything $<2.6$ $\times 10^{-3}$ CL=90%     $\Gamma_{18}$ 2 ${{\mathit K}^{-}}$ anything $<6$ $\times 10^{-4}$ CL=90%     $\Gamma_{19}$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ + anything ($32.8$ $\pm0.7$ ) $\%$     ▸  exp Leptonic and semileptonic modes $\Gamma_{20}$ ${{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $<8.3$ $\times 10^{-5}$ CL=90% 984   $\Gamma_{21}$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ ($5.37$ $\pm0.11$) $ \times 10^{-3}$ 981   $\Gamma_{22}$ ${{\mathit \tau}^{+}}{{\mathit \nu}_{{{\tau}}}}$ ($5.39$ $\pm0.09$ ) $\%$ 182   $\Gamma_{23}$ ${{\mathit \gamma}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $<1.3$ $\times 10^{-4}$ CL=90% 984   $\Gamma_{24}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ 851   $\Gamma_{25}$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $<3.8$ $\times 10^{-4}$ CL=90% 849   $\Gamma_{26}$ ${{\mathit \phi}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ [5] ($2.34$ $\pm0.12$ ) $\%$ S=1.2  720   $\Gamma_{27}$ ${{\mathit K}_{{{1}}}{(1270)}^{0}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $<4.1$ $\times 10^{-4}$ CL=90% 585   $\Gamma_{28}$ ${{\mathit b}_{{{1}}}{(1235)}^{0}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ , ${{\mathit b}_{{{1}}}^{0}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \pi}^{0}}$ $<6.4$ $\times 10^{-4}$ CL=90%     $\Gamma_{29}$ ${{\mathit \phi}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ ($2.24$ $\pm0.11$ ) $\%$ 715   $\Gamma_{30}$ ${{\mathit \eta}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ [5] ($2.27$ $\pm0.06$ ) $\%$ 908   $\Gamma_{31}$ ${{\mathit \eta}^{\,'}{(958)}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ [5] ($8.1$ $\pm0.4$) $ \times 10^{-3}$ 751   $\Gamma_{32}$ ${{\mathit \eta}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ ($2.24$ $\pm0.07$ ) $\%$ 905   $\Gamma_{33}$ ${{\mathit \eta}^{\,'}{(958)}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ ($8.0$ $\pm0.6$) $ \times 10^{-3}$ 747   $\Gamma_{34}$ ${{\mathit \omega}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ [6] $<2.0$ $\times 10^{-3}$ CL=90% 829   $\Gamma_{35}$ ${{\mathit K}^{0}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ ($2.88$ $\pm0.26$) $ \times 10^{-3}$ S=1.2  921   $\Gamma_{36}$ ${{\mathit K}^{*}{(892)}^{0}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ [5] ($2.05$ $\pm0.20$) $ \times 10^{-3}$ 782   $\Gamma_{37}$ ${{\mathit f}_{{{0}}}{(500)}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $<7.3$ $\times 10^{-4}$ CL=90%     $\Gamma_{38}$ ${{\mathit f}_{{{0}}}{(500)}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $<3.3$ $\times 10^{-4}$ CL=90%     $\Gamma_{39}$ ${{\mathit f}_{{{0}}}{(980)}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ ($7.9$ $\pm1.5$) $ \times 10^{-4}$     $\Gamma_{40}$ ${{\mathit f}_{{{0}}}{(980)}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($1.64$ $\pm0.13$) $ \times 10^{-3}$     $\Gamma_{41}$ ${{\mathit f}_{{{0}}}{(980)}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ $<5.45$ $\times 10^{-4}$ CL=90%     $\Gamma_{42}$ ${{\mathit a}_{{{0}}}{(980)}^{0}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ , ${{\mathit a}_{{{0}}}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \eta}}$ $<1.2$ $\times 10^{-4}$ CL=90%     $\Gamma_{43}$ ${{\mathit \pi}^{0}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $<6.4$ $\times 10^{-5}$ CL=90% 980   ▸  exp Hadronic modes with a ${{\mathit K}}{{\overline{\mathit K}}}$ pair $\Gamma_{44}$ ${{\mathit K}^{+}}{{\mathit K}_S^0}$ ($1.500$ $\pm0.014$ ) $\%$ 850   $\Gamma_{45}$ ${{\mathit K}^{+}}{{\mathit K}_L^0}$ ($1.49$ $\pm0.06$ ) $\%$ 850   $\Gamma_{46}$ ${{\mathit K}^{+}}{{\overline{\mathit K}}^{0}}$ ($2.95$ $\pm0.14$ ) $\%$ 850   $\Gamma_{47}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ [7] ($5.45$ $\pm0.08$ ) $\%$ S=1.3  805   $\Gamma_{48}$ ${{\mathit \phi}}{{\mathit \pi}^{+}}$ [8] [5] ($4.5$ $\pm0.4$ ) $\%$ 712   $\Gamma_{49}$ ${{\mathit \phi}}{{\mathit \pi}^{+}}$ , ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ [8] ($2.25$ $\pm0.05$ ) $\%$ 712   $\Gamma_{50}$ ${{\mathit K}^{+}}{{\overline{\mathit K}}^{*}{(892)}^{0}}$ ($12.7^{+4.0}_{-3.1}$ ) $\%$ 685   $\Gamma_{51}$ ${{\mathit K}^{+}}{{\overline{\mathit K}}^{*}{(892)}^{0}}$ , ${{\overline{\mathit K}}^{*0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ ($2.61$ $\pm0.05$ ) $\%$ 416   $\Gamma_{52}$ ${{\mathit K}^{+}}{{\overline{\mathit K}}^{*}{(892)}^{0}}$ , ${{\overline{\mathit K}}^{*0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}$ ($4.8$ $\pm0.4$) $ \times 10^{-3}$     $\Gamma_{53}$ ${{\mathit f}_{{{0}}}{(980)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ ($1.12$ $\pm0.19$ ) $\%$ 732   $\Gamma_{54}$ ${{\mathit f}_{{{0}}}{(1370)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ ($7.2$ $\pm3.0$) $ \times 10^{-4}$     $\Gamma_{55}$ ${{\mathit f}_{{{0}}}{(1710)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ ($6.8$ $\pm2.8$) $ \times 10^{-4}$ 198   $\Gamma_{56}$ ${{\mathit a}_{{{0}}}{(980)}^{+}}{{\mathit \pi}^{0}}$ , ${{\mathit a}_{{{0}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}_S^0}$ ($1.1$ $\pm0.4$) $ \times 10^{-3}$     $\Gamma_{57}$ ${{\mathit a}_{{{0}}}{(1710)}^{+}}{{\mathit \pi}^{0}}$ , ${{\mathit a}_{{{0}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}_S^0}$ ($3.5$ $\pm0.6$) $ \times 10^{-3}$     $\Gamma_{58}$ ${{\mathit K}^{+}}{{\overline{\mathit K}}_{{{0}}}^{*}{(1430)}^{0}}$ , ${{\overline{\mathit K}}_{{{0}}}^{*}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ ($1.79$ $\pm0.26$) $ \times 10^{-3}$ 218   $\Gamma_{59}$ ${{\mathit K}^{+}}{{\overline{\mathit K}}^{*}{(1410)}^{0}}$ , ${{\overline{\mathit K}}_{{{0}}}^{*}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}$ ($8.8$ $\pm2.8$) $ \times 10^{-4}$     $\Gamma_{60}$ ${{\mathit K}^{+}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}$ ($1.471$ $\pm0.028$ ) $\%$ 805   $\Gamma_{61}$ ${{\mathit K}^{*}{(892)}^{+}}{{\mathit K}_S^0}$ , ${{\mathit K}^{*+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{0}}$ ($2.04$ $\pm0.32$) $ \times 10^{-3}$     $\Gamma_{62}$ 2 ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}$ ($7.32$ $\pm0.14$) $ \times 10^{-3}$ 802   $\Gamma_{63}$ ${{\mathit f}_{{{0}}}{(980)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ $<1.8$ $\times 10^{-4}$ CL=90%     $\Gamma_{64}$ ${{\mathit f}_{{{0}}}{(1710)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ($3.39$ $\pm0.31$) $ \times 10^{-3}$     $\Gamma_{65}$ ${{\mathit K}^{*}{(892)}^{+}}{{\mathit K}_S^0}$ , ${{\mathit K}^{*+}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}$ ($3.19$ $\pm0.29$) $ \times 10^{-3}$ 683   $\Gamma_{66}$ ${{\mathit K}^{0}}{{\overline{\mathit K}}^{0}}{{\mathit \pi}^{+}}$ 802   $\Gamma_{67}$ ${{\mathit K}^{*}{(892)}^{+}}{{\overline{\mathit K}}^{0}}$ [5] ($5.4$ $\pm1.2$ ) $\%$ 683   $\Gamma_{68}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ ($5.53$ $\pm0.15$ ) $\%$ S=1.3  748   $\Gamma_{69}$ ${{\mathit \phi}}{{\mathit \rho}^{+}}$ [5] ($5.59$ $\pm0.34$ ) $\%$ 401   $\Gamma_{70}$ ${{\overline{\mathit K}}_{{{1}}}{(1270)}^{0}}{{\mathit K}^{+}}$ , ${{\overline{\mathit K}}_{{{1}}}{(1270)}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \rho}^{+}}$ ($5.7$ $\pm0.6$) $ \times 10^{-3}$     $\Gamma_{71}$ ${{\overline{\mathit K}}_{{{1}}}{(1270)}^{0}}{{\mathit K}^{+}}$ , ${{\overline{\mathit K}}_{{{1}}}{(1270)}^{0}}$ $\rightarrow$ ${{\mathit K}^{*}{(892)}}{{\mathit \pi}}$ ($1.31$ $\pm0.25$ ) $\%$     $\Gamma_{72}$ ${{\overline{\mathit K}}_{{{1}}}{(1400)}^{0}}{{\mathit K}^{+}}$ , ${{\overline{\mathit K}}_{{{1}}}{(1400)}^{0}}$ $\rightarrow$ ${{\mathit K}^{*}{(892)}}{{\mathit \pi}}$ ($2.0$ $\pm0.4$ ) $\%$     $\Gamma_{73}$ ${{\mathit a}_{{{0}}}{(980)}^{0}}{{\mathit \rho}^{+}}$ , ${{\mathit a}_{{{0}}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ ($1.9$ $\pm0.4$) $ \times 10^{-3}$     $\Gamma_{74}$ ${{\mathit f}_{{{1}}}{(1420)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{1}}}{(1420)}^{0}}$ $\rightarrow$ ${{\mathit K}^{*}{(892)}^{\mp}}{{\mathit K}^{\pm}}$ ($3.9$ $\pm0.7$) $ \times 10^{-3}$     $\Gamma_{75}$ ${{\mathit f}_{{{1}}}{(1420)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{1}}}^{0}}$ $\rightarrow$ ${{\mathit a}_{{{0}}}{(980)}^{0}}{{\mathit \pi}^{0}}$ , ${{\mathit a}_{{{0}}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ ($4.0$ $\pm1.4$) $ \times 10^{-4}$     $\Gamma_{76}$ ${{\mathit \eta}{(1475)}}{{\mathit \pi}^{+}}$ , ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit a}_{{{0}}}{(980)}^{0}}{{\mathit \pi}^{0}}$ , ${{\mathit a}_{{{0}}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ ($7.0$ $\pm2.8$) $ \times 10^{-4}$     $\Gamma_{77}$ ${{\mathit K}_S^0}$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{+}}$ ($1.569$ $\pm0.028$ ) $\%$ 744   $\Gamma_{78}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}$ ($1.27$ $\pm0.15$) $ \times 10^{-4}$ 527   $\Gamma_{79}$ ${{\mathit K}^{*}{(892)}^{+}}{{\overline{\mathit K}}^{*}{(892)}^{0}}$ [5] ($5.64$ $\pm0.35$ ) $\%$ 417   $\Gamma_{80}$ ${{\mathit \eta}{(1475)}}{{\mathit K}_S^0}$ , ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit K}^{*}{(892)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{*0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ ($3.5$ $\pm1.0$) $ \times 10^{-4}$     $\Gamma_{81}$ ${{\mathit \eta}{(1475)}}{{\mathit \pi}^{+}}$ , ${{\mathit \eta}}$ $\rightarrow$ ${{\overline{\mathit K}}^{*}{(892)}^{+}}{{\mathit K}^{-}}$ , ${{\overline{\mathit K}}^{*+}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}$ ($3.5$ $\pm1.0$) $ \times 10^{-4}$     $\Gamma_{82}$ ${{\mathit \eta}{(1475)}}{{\mathit \pi}^{+}}$ , ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit a}_{{{0}}}{(980)}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit a}_{{{0}}}^{-}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{-}}$ ($1.7$ $\pm0.9$) $ \times 10^{-3}$     $\Gamma_{83}$ ${{\mathit f}_{{{1}}}{(1285)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{1}}}}$ $\rightarrow$ ${{\mathit a}_{{{0}}}{(980)}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit a}_{{{0}}}^{-}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{-}}$ ($3.5$ $\pm0.8$) $ \times 10^{-4}$     $\Gamma_{84}$ ${{\mathit K}^{+}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($9.34$ $\pm0.22$) $ \times 10^{-3}$ 744   $\Gamma_{85}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($6.6$ $\pm0.6$) $ \times 10^{-3}$ 673   $\Gamma_{86}$ ${{\mathit \phi}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ [5] ($1.21$ $\pm0.16$ ) $\%$ 640   $\Gamma_{87}$ ${{\mathit \phi}}{{\mathit \rho}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ ($4.9$ $\pm0.7$) $ \times 10^{-3}$ 181   $\Gamma_{88}$ ${{\mathit \phi}}{{\mathit a}_{{{1}}}{(1260)}^{+}}$ , ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ , ${{\mathit a}_{{{1}}}^{+}}$ $\rightarrow$ ${{\mathit \rho}^{0}}{{\mathit \pi}^{+}}$ ($7.5$ $\pm1.2$) $ \times 10^{-3}$ -1   $\Gamma_{89}$ ${{\mathit \phi}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ non- ${{\mathit \rho}}$ , ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ ($1.4$ $\pm0.5$) $ \times 10^{-3}$     $\Gamma_{90}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \rho}^{0}}{{\mathit \pi}^{+}}$ non-${{\mathit \phi}}$ $<2.0$ $\times 10^{-4}$ CL=90% 249   $\Gamma_{91}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ nonresonant ($1.0$ $\pm0.4$) $ \times 10^{-3}$ 673   $\Gamma_{92}$ 2 ${{\mathit K}_S^0}$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($8.0$ $\pm3.3$) $ \times 10^{-4}$ 669   ▸  exp Hadronic modes without ${{\mathit K}}$'s $\Gamma_{93}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ $<1.2$ $\times 10^{-4}$ CL=90% 975   $\Gamma_{94}$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($1.090$ $\pm0.014$ ) $\%$ 959   $\Gamma_{95}$ ${{\mathit \rho}^{0}}{{\mathit \pi}^{+}}$ ($1.14$ $\pm0.16$) $ \times 10^{-4}$ 825   $\Gamma_{96}$ ${{\mathit \omega}}{{\mathit \pi}^{+}}$ , ${{\mathit \omega}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($3.9$ $\pm0.4$) $ \times 10^{-5}$     $\Gamma_{97}$ ${{\mathit \pi}^{+}}$( ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$) $_{\mathit S-{\mathrm {wave}}}$ [9] ($9.23$ $\pm0.13$) $ \times 10^{-3}$ 959   $\Gamma_{98}$ ${{\mathit f}_{{{0}}}{(980)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ 732   $\Gamma_{99}$ ${{\mathit f}_{{{0}}}{(1370)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ 493   $\Gamma_{100}$ ${{\mathit f}_{{{0}}}{(1500)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ 388   $\Gamma_{101}$ ${{\mathit f}_{{{2}}}{(1270)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{2}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($1.42$ $\pm0.10$) $ \times 10^{-3}$ 559   $\Gamma_{102}$ ${{\mathit f}_{{{2}}}^{\,'}{(1525)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{2}}}^{\,'}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($5.8$ $\pm2.0$) $ \times 10^{-6}$     $\Gamma_{103}$ ${{\mathit \rho}{(1450)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit \rho}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($1.8$ $\pm0.6$) $ \times 10^{-4}$ 421   $\Gamma_{104}$ ${{\mathit \rho}{(1700)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit \rho}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($4$ $\pm4$) $ \times 10^{-5}$     $\Gamma_{105}$ ${{\mathit \pi}^{+}}$2 ${{\mathit \pi}^{0}}$ ($5.2$ $\pm0.5$) $ \times 10^{-3}$ S=1.1  961   $\Gamma_{106}$ ${{\mathit f}_{{{0}}}{(980)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ ($2.9$ $\pm0.6$) $ \times 10^{-3}$     $\Gamma_{107}$ ${{\mathit f}_{{{0}}}{(1370)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ ($1.3$ $\pm0.6$) $ \times 10^{-3}$     $\Gamma_{108}$ ${{\mathit f}_{{{2}}}{(1270)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{2}}}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ ($5.0$ $\pm3.5$) $ \times 10^{-4}$     $\Gamma_{109}$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ 935   $\Gamma_{110}$ ${{\mathit \omega}}{{\mathit \pi}^{+}}$ [5] ($1.93$ $\pm0.30$) $ \times 10^{-3}$ 822   $\Gamma_{111}$ ${{\mathit \eta}}{{\mathit \pi}^{+}}$ [5] ($1.686$ $\pm0.027$ ) $\%$ 902   $\Gamma_{112}$ (2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$) $_{{\mathrm {non}}-{{\mathit \eta}}}$ ($2.04$ $\pm0.09$ ) $\%$     $\Gamma_{113}$ ${{\mathit f}_{{{0}}}{(1370)}}{{\mathit \rho}^{+}}$ , ${{\mathit f}_{{{0}}}}{{\mathit \rho}^{+}}$ $\rightarrow$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($5.1$ $\pm0.9$) $ \times 10^{-3}$     $\Gamma_{114}$ ${{\mathit f}_{{{0}}}{(980)}^{0}}{{\mathit \rho}^{+}}$ , ${{\mathit f}_{{{0}}}^{0}}{{\mathit \rho}^{+}}$ $\rightarrow$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($2.6$ $\pm0.5$) $ \times 10^{-3}$     $\Gamma_{115}$ ${{\mathit f}_{{{2}}}{(1270)}^{0}}{{\mathit \rho}^{+}}$ , ${{\mathit f}_{{{2}}}{(1270)}^{0}}{{\mathit \rho}^{+}}$ $\rightarrow$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($1.9$ $\pm0.4$) $ \times 10^{-3}$     $\Gamma_{116}$ ( ${{\mathit \rho}^{+}}{{\mathit \rho}^{0}}$) $_{{\mathit S}{\mathrm -wave}}$ $\rightarrow$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($7.1$ $\pm2.8$) $ \times 10^{-4}$     $\Gamma_{117}$ ( ${{\mathit \rho}{(1450)}^{+}}{{\mathit \rho}^{0}}$) $_{{\mathit S}{\mathrm -wave}}$ $\rightarrow$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($9.4$ $\pm3.1$) $ \times 10^{-4}$     $\Gamma_{118}$ ( ${{\mathit \rho}^{+}}{{\mathit \rho}{(1450)}^{0}}$) $_{{\mathit P}{\mathrm -wave}}$ $\rightarrow$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($1.75$ $\pm0.29$) $ \times 10^{-3}$     $\Gamma_{119}$ ${{\mathit \phi}}{{\mathit \pi}^{+}}$ , ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \rho}}{{\mathit \pi}}$ ($5.08$ $\pm0.35$) $ \times 10^{-3}$     $\Gamma_{120}$ ${{\mathit \omega}}{{\mathit \pi}^{+}}$ , ${{\mathit \omega}}$ $\rightarrow$ ${{\mathit \rho}}{{\mathit \pi}}$ ($1.41$ $\pm0.19$) $ \times 10^{-3}$     $\Gamma_{121}$ ${{\mathit a}_{{{1}}}{(1260)}^{+}}{{\mathit \pi}^{0}}$ , ${{\mathit a}_{{{1}}}^{+}}$ $\rightarrow$ ( ${{\mathit \rho}^{0}}{{\mathit \pi}^{+}}$) $_{{\mathit S}{\mathrm -wave}}$ ($2.6$ $\pm0.4$) $ \times 10^{-3}$     $\Gamma_{122}$ ${{\mathit a}_{{{1}}}{(1260)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit a}_{{{1}}}^{0}}$ $\rightarrow$ ( ${{\mathit \rho}}{{\mathit \pi}}$) $_{{\mathit S}{\mathrm -wave}}$ ($1.3$ $\pm0.5$) $ \times 10^{-3}$     $\Gamma_{123}$ ${{\mathit \pi}{(1300)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit \pi}^{0}}$ $\rightarrow$ ( ${{\mathit \rho}}{{\mathit \pi}}$) $_{{\mathit P}{\mathrm -wave}}$ ($2.4$ $\pm0.7$) $ \times 10^{-3}$     $\Gamma_{124}$ 3 ${{\mathit \pi}^{+}}$2 ${{\mathit \pi}^{-}}$ ($8.0$ $\pm0.8$) $ \times 10^{-3}$ 899   $\Gamma_{125}$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{0}}$ 902   $\Gamma_{126}$ ${{\mathit \eta}}{{\mathit \rho}^{+}}$ [5] ($8.9$ $\pm0.8$ ) $\%$ 724   $\Gamma_{127}$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ ($9.10$ $\pm0.17$ ) $\%$ 885   $\Gamma_{128}$ ${{\mathit \eta}}$( ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$) $_{{\mathit P}{\mathrm -wave}}$ ($4.9$ $\pm3.0$) $ \times 10^{-3}$ 885   $\Gamma_{129}$ ${{\mathit a}_{{{0}}}{(980)}}{}^{+0}$ ${{\mathit \pi}}{}^{0+}$ , ${{\mathit a}_{{{0}}}{(980)}}{}^{+0}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}}{}^{+0}$ ($2.1$ $\pm0.4$ ) $\%$     $\Gamma_{130}$ ${{\mathit \omega}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ [5] ($2.8$ $\pm0.7$ ) $\%$ 802   $\Gamma_{131}$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \eta}}$ ($3.08$ $\pm0.08$ ) $\%$ 855   $\Gamma_{132}$ ${{\mathit a}_{{{1}}}{(1260)}^{+}}{{\mathit \eta}}$ , ${{\mathit a}_{{{1}}}^{+}}$ $\rightarrow$ ${{\mathit \rho}{(770)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit \rho}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($1.71$ $\pm0.14$ ) $\%$     $\Gamma_{133}$ ${{\mathit a}_{{{1}}}{(1260)}^{+}}{{\mathit \eta}}$ , ${{\mathit a}_{{{1}}}^{+}}$ $\rightarrow$ ${{\mathit f}_{{{0}}}{(500)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($2.5$ $\pm0.9$) $ \times 10^{-3}$     $\Gamma_{134}$ ${{\mathit a}_{{{0}}}{(980)}^{+}}{{\mathit \rho}{(770)}^{0}}$ , ${{\mathit a}_{{{0}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}$ ($2.1$ $\pm0.9$) $ \times 10^{-3}$     $\Gamma_{135}$ ${{\mathit \eta}{(1405)}}{{\mathit \pi}^{+}}$ , ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit a}_{{{0}}}{(980)}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit a}_{{{0}}}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{-}}$ ($2.2$ $\pm0.7$) $ \times 10^{-4}$     $\Gamma_{136}$ ${{\mathit \eta}{(1405)}}{{\mathit \pi}^{+}}$ , ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit a}_{{{0}}}{(980)}^{+}}{{\mathit \pi}^{-}}$ , ${{\mathit a}_{{{0}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}$ ($2.2$ $\pm0.7$) $ \times 10^{-4}$     $\Gamma_{137}$ ${{\mathit f}_{{{1}}}{(1420)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{1}}}}$ $\rightarrow$ ${{\mathit a}_{{{0}}}{(980)}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit a}_{{{0}}}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{-}}$ ($5.9$ $\pm1.8$) $ \times 10^{-4}$     $\Gamma_{138}$ ${{\mathit f}_{{{1}}}{(1420)}}{{\mathit \pi}^{+}}$ , ${{\mathit f}_{{{1}}}}$ $\rightarrow$ ${{\mathit a}_{{{0}}}{(980)}^{+}}{{\mathit \pi}^{-}}$ , ${{\mathit a}_{{{0}}}^{+}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}$ ($5.2$ $\pm1.8$) $ \times 10^{-4}$     $\Gamma_{139}$ 3 ${{\mathit \pi}^{+}}$2 ${{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($4.9$ $\pm3.2$ ) $\%$ 856   $\Gamma_{140}$ ${{\mathit \omega}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ [5] ($1.6$ $\pm0.5$ ) $\%$ 766   $\Gamma_{141}$ ${{\mathit \eta}^{\,'}{(958)}}{{\mathit \pi}^{+}}$ [5] [4] ($3.95$ $\pm0.08$ ) $\%$ 743   $\Gamma_{142}$ 3 ${{\mathit \pi}^{+}}$2 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{0}}$ 803   $\Gamma_{143}$ ${{\mathit \omega}}{{\mathit \eta}}{{\mathit \pi}^{+}}$ [5] ($5.4$ $\pm1.3$) $ \times 10^{-3}$ 654   $\Gamma_{144}$ ${{\mathit \eta}^{\,'}{(958)}}{{\mathit \rho}^{+}}$ [5] [4] ($5.8$ $\pm1.5$ ) $\%$ 465   $\Gamma_{145}$ ${{\mathit \eta}^{\,'}{(958)}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ ($6.14$ $\pm0.18$ ) $\%$ 720   $\Gamma_{146}$ ${{\mathit \eta}^{\,'}{(958)}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ nonresonant <5.1 $\%$ CL=90% 720   ▸  exp Modes with one or three ${{\mathit K}}$'s $\Gamma_{147}$ ${{\mathit K}^{+}}{{\mathit \pi}^{0}}$ ($7.5$ $\pm0.5$) $ \times 10^{-4}$ 917   $\Gamma_{148}$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}$ ($1.22$ $\pm0.04$) $ \times 10^{-3}$ 916   $\Gamma_{149}$ ${{\mathit K}^{+}}{{\mathit \eta}}$ [5] ($1.76$ $\pm0.08$) $ \times 10^{-3}$ 835   $\Gamma_{150}$ ${{\mathit K}^{+}}{{\mathit \omega}}$ [5] ($9.9$ $\pm1.5$) $ \times 10^{-4}$ 741   $\Gamma_{151}$ ${{\mathit K}^{+}}{{\mathit \eta}^{\,'}{(958)}}$ [5] ($2.68$ $\pm0.24$) $ \times 10^{-3}$ 646   $\Gamma_{152}$ ${{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($6.23$ $\pm0.10$) $ \times 10^{-3}$ 900   $\Gamma_{153}$ ${{\mathit K}^{+}}{{\mathit \rho}^{0}}$ ($2.18$ $\pm0.25$) $ \times 10^{-3}$ 745   $\Gamma_{154}$ ${{\mathit K}^{+}}{{\mathit \rho}{(1450)}^{0}}$ , ${{\mathit \rho}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($7.3$ $\pm1.7$) $ \times 10^{-4}$     $\Gamma_{155}$ ${{\mathit K}^{+}}{{\mathit f}_{{{0}}}{(500)}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($4.5$ $\pm3.0$) $ \times 10^{-4}$     $\Gamma_{156}$ ${{\mathit K}^{+}}{{\mathit f}_{{{0}}}{(980)}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($2.8$ $\pm1.1$) $ \times 10^{-4}$     $\Gamma_{157}$ ${{\mathit K}^{+}}{{\mathit f}_{{{0}}}{(1370)}}$ , ${{\mathit f}_{{{0}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($1.2$ $\pm0.6$) $ \times 10^{-3}$     $\Gamma_{158}$ ${{\mathit K}^{*}{(892)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{*0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ ($1.68$ $\pm0.26$) $ \times 10^{-3}$ 775   $\Gamma_{159}$ ${{\mathit K}^{*}{(1410)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{*0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ ($6$ $\pm4$) $ \times 10^{-4}$     $\Gamma_{160}$ ${{\mathit K}^{*}{(1430)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{*0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ ($9.4$ $\pm3.2$) $ \times 10^{-4}$     $\Gamma_{161}$ ${{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ nonresonant ($9.9$ $\pm3.2$) $ \times 10^{-4}$ 900   $\Gamma_{162}$ ${{\mathit K}^{0}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ 899   $\Gamma_{163}$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ ($5.09$ $\pm0.22$) $ \times 10^{-3}$ 899   $\Gamma_{164}$ ${{\mathit K}_S^0}$ ${{\mathit \rho}{(770)}^{+}}$ , ${{\mathit \rho}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ ($2.6$ $\pm0.4$) $ \times 10^{-3}$     $\Gamma_{165}$ ${{\mathit K}_S^0}$ ${{\mathit \rho}{(1450)}^{+}}$ , ${{\mathit \rho}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ ($1.04$ $\pm0.32$) $ \times 10^{-3}$     $\Gamma_{166}$ ${{\mathit K}^{*}{(892)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{*0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}$ ($4.3$ $\pm1.2$) $ \times 10^{-4}$     $\Gamma_{167}$ ${{\mathit K}^{*}{(892)}^{+}}{{\mathit \pi}^{0}}$ , ${{\mathit K}^{*+}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}$ ($2.3$ $\pm0.7$) $ \times 10^{-4}$     $\Gamma_{168}$ ${{\mathit K}^{*}{(1410)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{*0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}$ ($1.7$ $\pm0.9$) $ \times 10^{-4}$     $\Gamma_{169}$ ${{\mathit K}_S^0}$ 2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ($2.8$ $\pm1.0$) $ \times 10^{-3}$ 870   $\Gamma_{170}$ ${{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($9.7$ $\pm0.6$) $ \times 10^{-3}$ 873   $\Gamma_{171}$ ${{\mathit K}^{*}{(892)}^{0}}{{\mathit \rho}^{+}}$ , ${{\mathit K}^{*0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ ($3.9$ $\pm0.4$) $ \times 10^{-3}$     $\Gamma_{172}$ ${{\mathit K}^{*}{(892)}^{+}}{{\mathit \rho}^{0}}$ , ${{\mathit K}^{*+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{0}}$ ($4.2$ $\pm1.2$) $ \times 10^{-4}$     $\Gamma_{173}$ ${{\mathit K}_{{{1}}}{(1270)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit K}_{{{1}}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \rho}^{-}}$ ($3.9$ $\pm1.3$) $ \times 10^{-4}$ -1   $\Gamma_{174}$ ${{\mathit K}_{{{1}}}{(1400)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit K}_{{{1}}}^{0}}$ $\rightarrow$ ${{\mathit K}^{*}{(890)}^{+}}{{\mathit \pi}^{-}}$ , ${{\mathit K}^{*+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{0}}$ ($5.4$ $\pm0.9$) $ \times 10^{-4}$     $\Gamma_{175}$ ${{\mathit K}_{{{1}}}{(1400)}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit K}_{{{1}}}^{0}}$ $\rightarrow$ ${{\mathit K}^{*}{(890)}^{0}}{{\mathit \pi}^{0}}$ , ${{\mathit K}^{*0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ ($5.9$ $\pm1.0$) $ \times 10^{-4}$     $\Gamma_{176}$ ${{\mathit K}^{+}}{{\mathit a}_{{{1}}}{(1260)}^{0}}$ , ${{\mathit a}_{{{1}}}}$ $\rightarrow$ ${{\mathit \rho}^{+}}{{\mathit \pi}^{-}}$ ($1.8$ $\pm1.1$) $ \times 10^{-4}$     $\Gamma_{177}$ ${{\mathit K}^{+}}{{\mathit a}_{{{1}}}{(1260)}^{0}}$ , ${{\mathit a}_{{{1}}}}$ $\rightarrow$ ${{\mathit \rho}^{-}}{{\mathit \pi}^{+}}$ ($1.8$ $\pm1.1$) $ \times 10^{-4}$     $\Gamma_{178}$ ${{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ nonresonant ($9.2$ $\pm2.4$) $ \times 10^{-4}$ 873   $\Gamma_{179}$ ( ${{\mathit K}^{+}}{{\mathit \pi}^{0}}$) $_{{\mathit P}{\mathrm -wave}}$ ${{\mathit \rho}^{0}}$ ($1.01$ $\pm0.21$) $ \times 10^{-3}$ 688   $\Gamma_{180}$ ${{\mathit K}^{+}}{{\mathit \omega}}{{\mathit \pi}^{0}}$ [5] $<8.2$ $\times 10^{-3}$ CL=90% 684   $\Gamma_{181}$ ${{\mathit K}^{+}}{{\mathit \omega}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ [5] $<5.4$ $\times 10^{-3}$ CL=90% 603   $\Gamma_{182}$ ${{\mathit K}^{+}}{{\mathit \omega}}{{\mathit \eta}}$ [5] $<7.9$ $\times 10^{-3}$ CL=90% 366   $\Gamma_{183}$ 2 ${{\mathit K}^{+}}{{\mathit K}^{-}}$ ($2.18$ $\pm0.20$) $ \times 10^{-4}$ 628   $\Gamma_{184}$ ${{\mathit \phi}}{{\mathit K}^{+}}$ , ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ ($8.9$ $\pm2.0$) $ \times 10^{-5}$     ▸  exp Radiative decays $\Gamma_{185}$ ${{\mathit \rho}{(770)}^{+}}{{\mathit \gamma}}$ $<6.1$ $\times 10^{-4}$ CL=90%     ▸  exp Doubly Cabibbo-suppressed modes $\Gamma_{186}$ 2 ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ ($1.293$ $\pm0.027$) $ \times 10^{-4}$ S=1.1  805   $\Gamma_{187}$ ${{\mathit K}^{+}}{{\mathit K}^{*}{(892)}^{0}}$ , ${{\mathit K}^{*0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ ($6.1$ $\pm3.4$) $ \times 10^{-5}$     $\Gamma_{188}$ 2 ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $<1.7$ $\times 10^{-4}$ CL=90% 748   ▸  exp Baryon-antibaryon mode $\Gamma_{189}$ ${{\mathit p}}{{\overline{\mathit n}}}$ ($1.22$ $\pm0.11$) $ \times 10^{-3}$ 295   $\Gamma_{190}$ ${{\mathit p}}{{\overline{\mathit p}}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ $<2.0$ $\times 10^{-4}$ CL=90% 296   ▸  exp $\Delta \mathit C$ = 1 weak neutral current ($\mathit C1$) modes, Lepton family number ($\mathit LF$), or Lepton number ($\mathit L$) violating modes $\Gamma_{191}$ ${{\mathit \pi}^{+}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ [10] $<5.5$ $\times 10^{-6}$ CL=90% 979   $\Gamma_{192}$ ${{\mathit \pi}^{+}}{{\mathit \phi}}$ , ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ [11] ($1.17$ $\pm0.22$) $ \times 10^{-5}$     $\Gamma_{193}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $<7.0$ $\times 10^{-5}$ CL=90% 974   $\Gamma_{194}$ ${{\mathit \rho}^{+}}{{\mathit \phi}}$ , ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ($2.4$ $\pm0.7$) $ \times 10^{-5}$     $\Gamma_{195}$ ${{\mathit \pi}^{+}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ [10] $<1.8$ $\times 10^{-7}$ CL=90% 968   $\Gamma_{196}$ ${{\mathit K}^{+}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ C1 $<3.7$ $\times 10^{-6}$ CL=90% 922   $\Gamma_{197}$ ${{\mathit K}^{+}}{{\mathit \pi}^{0}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $<7.1$ $\times 10^{-5}$ CL=90% 917   $\Gamma_{198}$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $<8.1$ $\times 10^{-5}$ CL=90% 916   $\Gamma_{199}$ ${{\mathit K}^{+}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ C1 $<1.4$ $\times 10^{-7}$ CL=90% 909   $\Gamma_{200}$ ${{\mathit K}^{*}{(892)}^{+}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ C1 $<1.4$ $\times 10^{-3}$ CL=90% 765   $\Gamma_{201}$ ${{\mathit \pi}^{+}}{{\mathit e}^{+}}{{\mathit \mu}^{-}}$ LF $<1.1$ $\times 10^{-6}$ CL=90% 976   $\Gamma_{202}$ ${{\mathit \pi}^{+}}{{\mathit e}^{-}}{{\mathit \mu}^{+}}$ LF $<9.4$ $\times 10^{-7}$ CL=90% 976   $\Gamma_{203}$ ${{\mathit K}^{+}}{{\mathit e}^{+}}{{\mathit \mu}^{-}}$ LF $<7.9$ $\times 10^{-7}$ CL=90% 919   $\Gamma_{204}$ ${{\mathit K}^{+}}{{\mathit e}^{-}}{{\mathit \mu}^{+}}$ LF $<5.6$ $\times 10^{-7}$ CL=90% 919   $\Gamma_{205}$ ${{\mathit \pi}^{-}}$2 ${{\mathit e}^{+}}$ L $<1.4$ $\times 10^{-6}$ CL=90% 979   $\Gamma_{206}$ ${{\mathit \pi}^{-}}$2 ${{\mathit \mu}^{+}}$ L $<8.6$ $\times 10^{-8}$ CL=90% 968   $\Gamma_{207}$ ${{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit \mu}^{+}}$ L $<6.3$ $\times 10^{-7}$ CL=90% 976   $\Gamma_{208}$ ${{\mathit K}^{-}}$2 ${{\mathit e}^{+}}$ L $<7.7$ $\times 10^{-7}$ CL=90% 922   $\Gamma_{209}$ ${{\mathit K}^{-}}$2 ${{\mathit \mu}^{+}}$ L $<2.6$ $\times 10^{-8}$ CL=90% 909   $\Gamma_{210}$ ${{\mathit K}^{-}}{{\mathit e}^{+}}{{\mathit \mu}^{+}}$ L $<2.6$ $\times 10^{-7}$ CL=90% 919   $\Gamma_{211}$ ${{\mathit K}^{*}{(892)}^{-}}$2 ${{\mathit \mu}^{+}}$ L $<1.4$ $\times 10^{-3}$ CL=90% 765

[1] See the Particle Listings for the (complicated) definition of this quantity. [2] This is the purely ${{\mathit e}^{+}}$ semileptonic branching fraction: the ${{\mathit e}^{+}}$ fraction from ${{\mathit \tau}^{+}}$ decays has been subtracted off. The sum of our (non-${{\mathit \tau}}$) ${{\mathit e}^{+}}$ exclusive fractions $-$ an ${{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$ with an ${{\mathit \eta}}$, ${{\mathit \eta}^{\,'}}$, ${{\mathit \phi}}$, ${{\mathit K}^{0}}$, or ${{\mathit K}^{*0}}$ $-$ is $5.99$ $\pm0.31$ $\%$. [3] This fraction includes ${{\mathit \eta}}$ from ${{\mathit \eta}^{\,'}}$ decays. [4] The sum of our exclusive ${{\mathit \eta}^{\,'}}$ fractions $-$ ${{\mathit \eta}^{\,'}}{{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}$, ${{\mathit \eta}^{\,'}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}$, ${{\mathit \eta}^{\,'}}{{\mathit \pi}^{+}}$, ${{\mathit \eta}^{\,'}}{{\mathit \rho}^{+}}$, and ${{\mathit \eta}^{\,'}}{{\mathit K}^{+}}$ $-$ is $11.8$ $\pm1.6\%$. [5] This branching fraction includes all the decay modes of the final-state resonance. [6] A test for ${{\mathit u}{\overline{\mathit u}}}$ or ${{\mathit d}{\overline{\mathit d}}}$ content in the ${{\mathit D}_{{{s}}}^{+}}$. Neither Cabibbo-favored nor Cabibbo-suppressed decays can contribute, and ${{\mathit \omega}}−{{\mathit \phi}}$ mixing is an unlikely explanation for any fraction above about $2 \times 10^{-4}$. [7] The branching fraction for this mode may differ from the sum of the submodes that contribute to it, due to interference effects. See the relevant papers. [8] We decouple the ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}^{+}}$ branching fraction obtained from mass projections (and used to get some of the other branching fractions) from the ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}^{+}}$, ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ branching fraction obtained from the Dalitz-plot analysis of ${{\mathit D}_{{{s}}}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$. That is, the ratio of these two branching fractions is not exactly the ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ branching fraction 0.491. [9] This is the average of a model-independent and a $\mathit K$-matrix parametrization of the ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{\mathit S}{\mathrm -wave}$ and is a sum over several ${{\mathit f}_{{{0}}}}$ mesons. [10] This mode is not a useful test for a $\Delta \mathit C$=1 weak neutral current because both quarks must change flavor in this decay. [11] This is $\mathit not$ a test for the $\Delta \mathit C$=1 weak neutral current, but leads to the ${{\mathit \pi}^{+}}{{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ final state.

Constrained Fit information