Helicity Probabilities For Heavy Quark Fragmentation Into Excited Mesons

In the fragmentation of a heavy quark into a heavy meson whose light degrees of freedom have angular momentum $3\mathrm{/}2$, all the helicity probabilities are completely determined in the heavy quark limit up to a single probability $w_{3\mathrm{/}2}$. We point out that this probability depends on the longitudinal momentum fraction $z$ of the meson and on its transverse momentum $p_{\mathrm{\perp }}$ relative to the jet axis. We calculate $w_{3\mathrm{/}2}$ as a function of scaling variables corresponding to $z$ and $p_{\mathrm{\perp }}$ for the heavy quark limit of the perturbative QCD fragmentation functions for $b$ quark to fragment into $(b \bar c)$ mesons. In this model, the light degrees of freedom prefer to have their angular momentum aligned transverse to, rather than along, the jet axis. Implications for the production of excited heavy mesons, like $D^{\ast \ast }$ and $B^{\ast \ast }$, are discussed.