QCD Corrections to $J/\psi$ and ${\rm Y}$ Production at Hadron Colliders

We calculate the cross section for hadroproduction of a pair of heavy quarks in a ${}^{3}S_1$ color-singlet state at next-to-leading order in QCD. This corresponds to the leading contribution in the nonrelativistic QCD expansion for $J/\psi$ and ${\rm Y}$ production. The higher-order corrections have a large impact on the $p_T$ distributions, enhancing the production at high $p_T$ at both the Fermilab Tevatron and the CERN Large Hadron Collider. The total decay rate of a ${}^{3}S_1$ into hadrons at next-to-leading order is also computed, confirming for the first time the result obtained by Mackenzie and Lepage in 1981.

Figure 1

Representative Feynman diagrams for ${}^{3}S_1^{[1]}$ hadroproduction at (a) LO, (b) virtual, and (c) real contributions at NLO. Amplitudes with a light quark line (not shown) also contribute to the real corrections.

Figure 2

Variation of the cross section for direct ${\rm Y}$ production at the Tevatron (lower curves) and the LHC (upper curves) at LO (dashed line) and NLO (solid line). Renormalization and factorization scales are set equal (${\mu }_F={\mu }_R$) and ${\mu }_0=\sqrt{(2m_b{)}^2+p_T^2}$.

Figure 3

Variation of the cross section for direct $J/\psi$ production at the Tevatron (lower curves) and the LHC (upper curves) at LO (dashed line) and NLO (solid line). Renormalization and factorization scales are set equal (${\mu }_F={\mu }_R$) and ${\mu }_0=\sqrt{(2m_c{)}^2+p_T^2}$.

Figure 4

Differential cross sections for direct ${\rm Y}$ production via a ${}^{3}S_1^{[1]}$ intermediate state, at the Tevatron (lower histograms) and LHC (upper histograms), at LO (dashed line) and NLO (solid line). $p_T^{{\rm Y}}>3\mathrm{GeV}$ and $|y^{{\rm Y}}|<3$. Details on the input parameters are given in the text.

Figure 5

Differential cross sections for direct $J/\psi$ production via a ${}^{3}S_1^{[1]}$ intermediate state, at the Tevatron (lower histograms) and LHC (upper histograms), at LO (dashed line) and NLO (solid line). $p_T^{J/\psi }>3\mathrm{GeV}$ and $|y^{J/\psi }|<3$. Details on the input parameters are given in the text.