Angular distributions and the physics of charmed-meson production at the 4.028-GeV resonance

A detailed study of angular distributions arising from $D\overline{D}$, $D^{*}\overline{D}$, ${\overline{D}}^{*}D$, and $D^{*}{\overline{D}}^{*}$ production at $\sqrt{s}=4.028\mathrm{}$ GeV is made, including the subsequent decays $D^{*}\to D\pi$ and $D^{*}\to D\gamma$. The production amplitudes are unique except for the $D^{*}{\overline{D}}^{*}$ case, where there are two $p$-wave amplitudes ($S=0, 2$) and one small $f$-wave amplitude ($S=2\mathrm{}$). It is shown that observations of the angular distributions and correlations of the ${\pi }^0\text{'}\mathrm{s}$ and $\gamma \text{'}\mathrm{s}$ from the $D^{*}\to D{\pi }^0$ and $D^{*}\to D\gamma$ decays provide an effective way of measuring the $p$-wave amplitudes. These amplitudes are a reflection of the underlying hadronic interactions among the charmed and uncharmed quarks.