Charmless final states andS−andD-wave mixing in theψ″

The ${\psi }^{″}=\psi \mathrm{}\left(3770\right)\mathrm{}$ resonance is expected to be mainly $c\overline{c}\left(1\mathrm{}{}^3{D}_1\right),$ but tensor forces and coupling to charmed particle pairs can mix it with ${\psi }^{\prime }{(2\mathrm{}}^3{S}_1)$ and other states. The implications of this mixing for decays of ${\psi }^{″}$ to noncharmed final states are discussed. (i) The ratio $\Gamma ({\psi }^{″}\to \gamma +{\chi }_{c2\mathrm{}})/\Gamma ({\psi }^{″}\to \gamma +{\chi }_{c0\mathrm{}})$ is expected to be highly suppressed if ${\psi }^{″}$ is a pure D-wave state, and is enchanced by mixing. (ii) The expected decay ${\psi }^{\prime }\to \rho \pi$ and other “missing” modes can appear as corresponding ${\psi }^{″}$ partial widths, enhanced by a factor depending on the mixing angle. General arguments then suggest a branching ratio of about $1\%,$ give or take a factor of 2, for charmless hadronic decays of ${\psi }^{″}.$ (iii) Enhancements can appear in penguin amplitudes in B decays, $\overrightarrow{B}K{\eta }^{\prime }$ branching ratios, and direct $\mathrm{CP}$-violating asymmetries in $\overrightarrow{B}K\pi$ decays.