Relativistic Correction to Color Octet J/psi Production at Hadron Colliders

TL;DR

This paper calculates relativistic corrections to color-octet J/psi production at hadron colliders, showing they significantly reduce cross sections and impact polarization predictions, thus refining theoretical models in nonrelativistic QCD.

Contribution

It provides the first detailed calculation of relativistic corrections up to order v^2 for color-octet J/psi production at Tevatron and LHC, improving the accuracy of theoretical predictions.

Findings

Relativistic corrections reduce cross sections by 20-40% at large p_T.

Corrections alter J/psi polarization predictions by 20-50%.

Relativistic effects are significant and should be included in production models.

Abstract

The relativistic corrections to the color-octet $J/\psi$ hadroproduction at the Tevatron and LHC are calculated up to $\mathcal{O}(v^2)$ in nonrelativistic QCD factorization frame. The short distance coefficients are obtained by matching full QCD with NRQCD results for the partonic subprocess $g+g\to J/\psi ({}^1S_0^{[8]},{}^3S_1^{[8]}, {}^3P_J^{[8]})+g$, $q+\bar{q}\to J/\psi ({}^1S_0^{[8]},{}^3S_1^{[8]}, {}^3P_J^{[8]})+g$ and $g+q({\bar{q}})\to J/\psi ({}^1S_0^{[8]},{}^3S_1^{[8]}, {}^3P_J^{[8]})+q({\bar{q}})$. The short distance coefficient ratios of relativistic correction to leading order for color-octet states ${^1}S_{0}^{[8]}$, ${^3}S_{1}^{[8]}$, and ${^3}P_{J}^{[8]}$ at large $p_T$ are approximately -5/6, -11/6, and -31/30, respectively, for each subprocess, and it is 1/6 for color-singlet state ${^3}S_{1}^{[1]}$. If the higher order long distance matrix elements are estimated through velocity scaling rule with adopting $v^2=0.23$ and the lower order long distance matrix elements are fixed, the leading order cross sections of color-octet states are reduced by about a factor of $20\sim40%$ at large $p_T$ at both the Tevatron and the LHC. Comparing with QCD radiative corrections to color-octet states, relativistic correction is ignored along with $p_T$ increasing. Using long distance matrix elements extracted from the fit to $J/\psi$ production at the Tevatron, we can find the unpolarization cross sections of $J/\psi$ production at the LHC taking into account both QCD and relativistic corrections are changed by about $20\sim50%$ of that considering only QCD corrections. These results indicate that relativistic corrections may play an important role in $J/\psi$ production at the Tevatron and the LHC.