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Gluon Fragmentation into P-wave Heavy Quarkonium

Eric Braaten·Tzu Chiang Yuan
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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 wavefunction 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 $χ_{c0}$, $χ_{c1}$, and $χ_{c2}$ are estimated to be $0.4 \times 10^{-4}$, $1.8 \times 10^{-4}$, and $2.4 \times 10^{-4}$, respectively. This fragmentation process may account for a significant fraction of the rate for the inclusive production of $χ_{cJ}$ at large transverse momentum in $p \bar p$ colliders.

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Eric Braaten, Tzu Chiang Yuan. 1994-03-30. Gluon Fragmentation into P-wave Heavy Quarkonium. https://doi.org/10.1103/physrevd.50.3176

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