$χ_{cJ}$ production associated with a $c\bar c$ pair at hadron colliders

$χ_{cJ}$ (J=0,1,2) production associated with a charm quark pair in hadron collisions is calculated in the framework of nonrelativistic QCD at the Tevatron and LHC. It is found that the color-singlet contribution is small and the color-octet contribution may be dominant in the large $p_T$ region. The differential cross section of $p\bar p\toχ_c+c\bar{c}$ is at least one order of magnitude smaller than the next-to-leading order result of $χ_{cJ}$ inclusive production $p\bar p\toχ_c+X$, therefore $χ_{cJ}$ production in $p\bar p\toχ_c+c\bar{c}$ may have negligible influence on the ratio $R_{χ_c}=\frac{σ_{χ_{c2}}}{σ_{χ_{c1}}}$ measured by CDF at the Tevatron. The feeddown contribution from $χ_{cJ}+c+\bar{c}$ to $J/ψ+c+\bar{c}$ is found to be large compared with $J/ψ$ direct production and may have important influence on the measurement of $J/ψ+c+\bar{c}$. The validity of fragmentation approximation for the process is also discussed.

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