Spin property of heavy hadron in heavy-quark fragmentation: A simple model

A simple model is presented to predict the branching ratio into heavy-flavored ${}_{}{}^3{}_{}{}^{}\mathrm{S}_1^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$ mesons in heavy-quark fragmentation. The ratio depends on the light-quark-to-heavy-quark mass ratio and varies as a function of the variable z (=$E_{\mathrm{hadron}/E_{\mathrm{beam})}}$. The theoretical predictions will be most decisively tested in the z dependence of the ${}_{}{}^3{}_{}{}^{}\mathrm{S}_1^{}{}_{}{}^{}$ ${/\mathrm{}}^1$ ${\mathrm{S}}_0$ ratio and the z dependence of the $D^{\mathrm{*}}$→Dπ decay-angular distribution dΓ/dΩ∝1+α(z) ${\cos }^2$theta in the $D^{\mathrm{*}}$ rest frame, where theta is measured from the $D^{\mathrm{*}}$ laboratory momentum.