Relativistic Correction to J/ψProduction at Hadron Colliders

TL;DR

This work evaluates relativistic corrections to color-singlet J/ψ hadroproduction within NRQCD up to O(v^2). Short-distance coefficients are obtained by matching full QCD to NRQCD for the gg→J/ψg subprocess, and long-distance matrix elements are extracted from J/ψ decay widths, with PDF convolutions used to compute hadronic cross sections. The results show that O(v^2) corrections contribute only about 1% to the differential cross section dσ/dp_t over a wide range of transverse momentum, indicating that relativistic effects cannot resolve the Tevatron discrepancy between leading-order predictions and data. Consequently, the study suggests that alternative mechanisms or higher-order QCD contributions must be explored to explain J/ψ production at hadron colliders.

Abstract

Relativistic corrections to the color-singlet J/ψhadroproduction at the Tevatron and LHC are calculated up to O(v^2) in nonrelativistic QCD (NRQCD). The short distance coefficients are obtained by matching full QCD with NRQCD results for the subprocess g+g\to J/ψ+g. The long distance matrix elements are extracted from observed J/ψhadronic and leptonic decay widths up to O}(v^2). Using the CTEQ6 parton distribution functions, we calculate the LO production cross sections and relativistic corrections for the process p+\bar{p}(p)\to J/ψ+X at the Tevatron and LHC. We find that the enhancement of O(v^2) relativistic corrections to the cross sections over a wide range of large transverse momentum p_t is negligible, only at a level of about 1 %. This tiny effect is due to the smallness of the correction to short distance coefficients and the suppression from long distance matrix elements. These results indicate that relativistic corrections can not help to resolve the large discrepancy between leading order prediction and experimental data for J/ψproduction at the Tevatron.

Figures (5)

• Figure 1: Typical Feynman diagram for ${}^3S_1^{[1]}$$c\bar{c}$ hadroproduction at LO.
• Figure 2: The $p_t$ distribution of $d\sigma(p+\bar{p}\rightarrow J/\psi+X)/dp_t$ at the Tevatron with $\sqrt{S}=1.96~TeV$. The $\mathcal{O}(v^0)$ and $\mathcal{O}(v^2)$ results are represented by the solid and dotted lines respectively.
• Figure 3: The $p_t$ distribution of $d\sigma(p+\bar{p}\rightarrow J/\psi+X)/dp_t$ (with enhanced matrix elements) at the Tevatron with $\sqrt{S}=1.96~TeV$. The $\mathcal{O}(v^0)$ and $\mathcal{O}(v^2)$ results are represented by the solid and dotted lines respectively.
• Figure 4: The $p_t$ distribution of $d\sigma(p+p\rightarrow J/\psi+X)/dp_t$ at the LHC with $\sqrt{S}=14~ TeV$. The $\mathcal{O}(v^0)$ and $\mathcal{O}(v^2)$ results are represented by the solid and dotted lines respectively.
• Figure 5: The $p_t$ distribution of $d\sigma(p+p\rightarrow J/\psi+X)/dp_t$ (with enhanced matrix elements) at the LHC with $\sqrt{S}=14~TeV$. The $\mathcal{O}(v^0)$ and $\mathcal{O}(v^2)$ results are represented by the solid and dotted lines respectively.