An upper bound on $P$-wave charmonium production via the color-octet mechanism

Abstract

A factorization theorem for $P$-wave quarkonium production, recently derived by Bodwin, Braaten, Yuan and Lepage, is applied to $Υ\to χ_{cJ} + X$, where $χ_{cJ}$ labels the ${}^3 P_J$ charmonium states. The widths for $χ_{cJ}$ production through color-singlet $P$-wave and color-octet $S$-wave $c \bar c$ subprocesses are computed each to leading order in $α_s$. Experimental data on $Υ\to J / ψ+ X$ is used to obtain an upper bound on a nonperturbative parameter (related to the probability for color-octet $S$-wave $c \bar c$ hadronization into $P$-wave charmonium) that enters into the factorization theorem.