Color-Octet Fragmentation and theψ′Surplus at the Fermilab Tevatron

The production rate of prompt ${\psi }^{\prime }$'s at large transverse momentum at the Fermilab Tevatron is larger than theoretical expectations by about a factor of 30. As a solution to this puzzle, we suggest that the dominant ${\psi }^{\prime }$ production mechanism is the fragmentation of a gluon into a $c\overline{c}$ pair in a pointlike color-octet $S$-wave state, which subsequently evolves nonperturbatively into a ${\psi }^{\prime }$ plus light hadrons. This contribution to the fragmentation function is enhanced by a short-distance factor of $1/{\alpha }_s^2$, which may compensate for its suppression by $v^4$, where $v$ is the relative momentum of the charm quark in the ${\psi }^{\prime }$.