Charmless Final States and S--D-wave mixing in the $\psi''$

Abstract

The $\ppp = \psi(3770)$ resonance is expected to be mainly $c \bar c(1^3D_1)$, but tensor forces and coupling to charmed particle pairs can mix it with $\pp(2^3S_1)$ and other states. Implications of this mixing for decays of $\ppp$ to non-charmed final states are discussed. (i) The ratio $\Gamma(\ppp \to \gamma + \chi_{c2})/ \Gamma(\ppp \to \gamma + \chi_{c0})$ is expected to be highly suppressed if $\ppp$ is a pure D-wave state, and is enchanced by mixing. (ii) The expected decay $\pp \to \rho \pi$ and other ``missing'' modes can appear as corresponding $\ppp$ 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 $\ppp$. (iii) Enhancements can appear in penguin amplitudes in B decays, $B \to K \eta'$ branching ratios, and direct CP-violating asymmetries in $B \to K \pi$ decays.