On the Application of Gluon to Heavy Quarkonium Fragmentation Functions

Abstract

We analyze the uncertainties induced by different definitions of the momentum fraction $z$ in the application of gluon to heavy quarkonium fragmentation function. We numerically calculate the initial $g\to J/\psi$ fragmentation functions by using the non-covariant definitions of $z$ with finite gluon momentum and find that these fragmentation functions have strong dependence on the gluon momentum $\vec{k}$. As $|\vec{k}|\to \infty$, these fragmentation functions approach to the fragmentation function in the light-cone definition. Our numerical results show that large uncertainties remains while the non-covariant definitions of $z$ are employed in the application of the fragmentation functions. We present for the first time the polarized gluon to $J/\psi$ fragmentation functions, which are fitted by the scheme exploited in this work.

11 pages, 7 figures;added reference for sec. 1

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Cited by in corpus (6)

• Heavy quark fragmentation functions at next-to-leading perturbative QCD
• Fragmentation functions of $g\to {\eta }_c{(}^1{S}_0)$ and $g\to J/\psi {(}^3{S}_1)$ considering the role of heavy quarkonium spin
• Spin-dependent fragmentation functions of Gluon splitting into heavy quarkonia considering three different scenarios
• Analytical calculation for the gluon fragmentation into spin-triplet S-wave quarkonium
• Comments on "Study of $J/\psi$ production in jets"
• Relativistic effect of $J/\psi$ hadroproduction in large $p_T$ region