Charmless Final States and S--D-wave mixing in the ${\psi }^{\prime \prime }$

Abstract

The $\text{ppp}=\psi (3770)$ resonance is expected to be mainly $c\bar{c}(1^3{D}_1)$, but tensor forces and coupling to charmed particle pairs can mix it with $\text{pp}(2^3{S}_1)$ and other states. Implications of this mixing for decays of $\text{ppp}$ to non-charmed final states are discussed. (i) The ratio $\Gamma (\text{ppp}\to \gamma +{\chi }_{c2})/\Gamma (\text{ppp}\to \gamma +{\chi }_{c0})$ is expected to be highly suppressed if $\text{ppp}$ is a pure D-wave state, and is enchanced by mixing. (ii) The expected decay $\text{pp}\to \rho \pi$ and other ``missing'' modes can appear as corresponding $\text{ppp}$ 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 $\text{ppp}$. (iii) Enhancements can appear in penguin amplitudes in B decays, $B\to K{\eta }^{\prime }$ branching ratios, and direct CP-violating asymmetries in $B\to K\pi$ decays.

Comments: 11 pages, LaTeX, no figures, to be submitted to Phys. Rev. D. New discussions and references added