Comparison of the color-evaporation model and the NRQCD factorization approach in charmonium production

TL;DR

The paper systematically compares the color-evaporation model (CEM) and NRQCD factorization for inclusive charmonium production, deriving NRQCD matrix-element relations implied by CEM and testing them against Tevatron data. It shows that CEM predictions clash with NRQCD expectations and generally fail to describe the $p_T$ spectra and state ratios, even when $k_T$ smearing is applied, whereas NRQCD factorization, including color-octet contributions and fragmentation, better describes the data for $J/\psi$ and $\psi(2S)$, with chi_c production offering stringent tests. The results indicate that multiple gluon radiation and a proper separation into short- and long-distance effects are essential to reproduce the observed cross sections and their $p_T$ dependence. The work underscores NRQCD factorization as the more viable framework for heavy-quarkonium production at high energy, while also pointing to areas—especially chi_c and polarization observables—where higher-order corrections and more fundamental treatments of soft radiation are needed.

Abstract

We compare the color-evaporation model (CEM) and nonrelativistic QCD (NRQCD) factorization predictions for inclusive quarkonium production. Using the NRQCD factorization formulas for quarkonium production and for perturbative QQ-bar production, we deduce relationships that are implied by the CEM between the nonperturbative NRQCD matrix elements that appear in the factorization formula for quarkonium production. These relationships are at odds with the phenomenological values of the matrix elements that have been extracted from the Tevatron data for charmonium production at large transverse momentum. A direct comparison of the CEM and NRQCD factorization predictions with the CDF charmonium production data reveals that the CEM fits to the data are generally unsatisfactory, while the NRQCD factorization fits are generally compatible with the data. The inclusion of k_T smearing improves the CEM fits substantially, but significant incompatibilities remain. The NRQCD factorization fits to the chi_c data indicate that multiple gluon radiation is an essential ingredient in obtaining the correct shape of the cross section as a function of p_T.

Figures (6)

• Figure 1: $J/\psi$ production: $({\rm data}-{\rm theory})/{\rm theory}$. The data are from the measurements of the CDF collaboration Abe:1997yz. The upper figures are for the CEM predictions and the lower figures are for the NRQCD factorization predictions. The theoretical predictions for the left-hand and right-hand figures are based on the MRST98 HO Martin:1998sq and the GRV98 HO Gluck:1998xa parton distributions, respectively.
• Figure 2: $J/\psi$ production: $({\rm data}-{\rm theory})/{\rm theory}$, with $k_T$ smearing of the theory, as described in the text. The data are from the measurements of the CDF collaboration Abe:1997yz. The upper figures are for the CEM predictions and the lower figures are for the NRQCD factorization predictions. The theoretical predictions for the left-hand and right-hand figures are based on the MRST98 HO Martin:1998sq and the GRV98 HO Gluck:1998xa parton distributions, respectively.
• Figure 3: $\psi(2S)$ production: $({\rm data}-{\rm theory})/{\rm theory}$. The plots are as in Fig. \ref{['fig:psi-unsmeared']}, but for $\psi(2S)$.
• Figure 4: $\psi(2S)$ production: $({\rm data}-{\rm theory})/{\rm theory}$, with $k_T$ smearing of the theory, as described in the text. The plots are as in Fig. \ref{['fig:psi-smeared']}, but for $\psi(2S)$.
• Figure 5: $\chi_c$ production: $({\rm data}-{\rm theory})/{\rm theory}$. The plots are as in Fig. \ref{['fig:psi-unsmeared']}, except that they are for $\chi_c$, the top row is for the CEM predictions, and the middle and bottom rows are for the 1-parameter and 2-parameter NRQCD factorization predictions, respectively.