Gluon fragmentation into<i>P</i>-wave heavy quarkonium

Abstract

The fragmentation functions for gluons to split into P-wave heavy quarkonium states are calculated to leading order in the QCD coupling constant. Long-distance effects are factored into two nonperturbative parameters: the derivative of the radial wave function at the origin and a second parameter related to the probability for a heavy-quark--antiquark pair that is produced in a color-octet S-wave state to form a color-singlet P-wave bound state. The fragmentation probabilities for a high transverse momentum gluon to split into the P-wave charmonium states ${\mathrm{\ensuremath{\chi}}}_{\mathit{c}0}$, ${\mathrm{\ensuremath{\chi}}}_{\mathit{c}1}$, and ${\mathrm{\ensuremath{\chi}}}_{\mathit{c}2}$ are estimated to be 0.4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$, 1.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$, and 2.4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$, respectively. This fragmentation process may account for a significant fraction of the rate for the inclusive production of ${\mathrm{\ensuremath{\chi}}}_{\mathit{c}\mathit{J}}$ at large transverse momentum in pp\ifmmode\bar\else\textasciimacron\fi{} colliders.