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

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 $g+g\to J/\psi ({}^1{S}_0^{[8]},{}^3{S}_1^{[8]},{}^3{P}_J^{[8]})+g$, $q+\bar{q}\to J/\psi ({}^1{S}_0^{[8]},{}^3{S}_1^{[8]},{}^3{P}_J^{[8]})+g$ and $g+q(\bar{q})\to J/\psi ({}^1{S}_0^{[8]},{}^3{S}_1^{[8]},{}^3{P}_J^{[8]})+q(\bar{q})$. 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 $20\sim 40$ 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 $20\sim 50$ 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.

Published version. Figures and Equations are added

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