Remark on Charm Quark Fragmentation to $D^{\ast \ast }$ Mesons

Abstract

The observed $D^{\ast \ast }$ mesons have $c\bar{q}$ flavor quantum numbers and spin-parity of the light degrees of freedom $s_{\ell }^{{\pi }_{\ell }}=3/2^{+}$. In the $m_c\to \infty$ limit the spin of the charm quark is conserved and the $c\to D^{\ast \ast }$ fragmentation process is characterized by the probability for the charm quark to fragment to a $D^{\ast \ast }$ meson with a given helicity for the light degrees of freedom. We consider the calculated $b\to B_c^{\ast \ast }$ fragmentation functions in the limit $m_c/m_b\to 0$ as a qualitative model for the $c\to D^{\ast \ast }$ fragmentation functions. We find that in this model charm quark fragmentation to $s_{\ell }^{{\pi }_{\ell }}=3/2^{+}$ light degrees of freedom with helicities $\pm 1/2$ is favored over fragmentation to $s_{\ell }^{{\pi }_{\ell }}=3/2^{+}$ light degrees of freedom with helicities $\pm 3/2$.

Comments: 6 pages, CALT-68-1928