QCD radiative corrections to $χ_{cJ}$ production at hadron colliders

To clarify the outstanding problem in charmonium production that existing theories cannot explain the observed cross sections of $χ_{cJ}$ (J=0,1,2) and ratio $R_{χ_c}=σ_{χ_{c2}}/σ_{χ_{c1}}\approx 0.75$ (in contrast to the spin counting value 5/3) at the Tevatron, we study the complete next-to-leading order radiative corrections in nonrelativistic QCD, and find next-to-leading order contributions of $^3P_J^{[1]}$ are more important than leading order at high $p_T$, and $^3P_1^{[1]}$ decreases slower than $^3P_2^{[1]}$, implying a natural explanation for the $R_{χ_c}$ puzzle. By fitting $R_{χ_c}$, the predicted cross sections of $χ_{cJ}$ are found to agree with data. The result indicates color-octet contribution is crucially needed, thus providing a unique test for heavy quarkonium production mechanisms. Feed-down contributions of $χ_{cJ}$ to prompt $J/ψ$ production are estimated to be substantial, about $30-40$ at $p_T=20$ GeV. Production of $χ_{cJ}$ (J=0,1,2) at the LHC is also predicted.

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