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

TL;DR

This paper calculates next-to-leading order QCD radiative corrections to $oldsymbol{ ext{chi}_cJ}$ production, explaining experimental cross sections and ratios at the Tevatron, and predicts $ ext{chi}_cJ$ production at the LHC, highlighting the importance of color-octet mechanisms.

Contribution

It provides the first complete NLO QCD correction analysis for $ ext{chi}_cJ$ production, resolving the $R_{ ext{chi}_c}$ puzzle and emphasizing the role of color-octet contributions.

Findings

NLO corrections are more significant than LO at high $p_T$.

The ratio $R_{ ext{chi}_c}$ is naturally explained by the different $p_T$ dependencies.

Predicted cross sections agree with Tevatron data and $ ext{chi}_cJ$ production at the LHC is forecasted.

Abstract

To clarify the outstanding problem in charmonium production that existing theories cannot explain the observed cross sections of $\chi_{cJ}$ (J=0,1,2) and ratio $R_{\chi_c}=\sigma_{\chi_{c2}}/\sigma_{\chi_{c1}}\approx 0.75$ (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 $R_{\chi_c}$ puzzle. By fitting $R_{\chi_c}$, the predicted cross sections of $\chi_{cJ}$ 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 $\chi_{cJ}$ to prompt $J/\psi$ production are estimated to be substantial, about $30-40%$ at $p_T=20$ GeV. Production of $\chi_{cJ}$ (J=0,1,2) at the LHC is also predicted.