A perturbative QCD analysis of charged-particle distributions in hadronic and nuclear collisions

TL;DR

Using collinear factorization with modern PDFs and fragmentation functions, the paper tests LO pQCD predictions for charged-hadron spectra at large $q_T$ in $pp$, $pA$, and $AA$ collisions. It introduces a constant $K(\sqrt s)$ factor and a $p_0$ cutoff to absorb higher-order and nonperturbative effects, finding that $K$ decreases with energy while $p_0$ increases, and applying EKS98 nuclear corrections to assess shadowing/antishadowing. The results show reasonable agreement with $pp$ data at high $q_T$, and reveal modest nuclear enhancements (up to ~15%) with central Au+Au data at RHIC showing deviations that point to medium-induced effects; PHENIX peripheral data align with expectations while central data indicate dynamics beyond the baseline. The work provides a practical perturbative-QCD reference for high-$q_T$ hadron production in nuclear collisions and highlights avenues for refinement, including NLO corrections and explicit medium effects.

Abstract

We compute the distributions of charged particles at large transverse momenta in $p\bar p(p)$, $pA$ and $AA$ collisions in the framework of perturbative QCD, by using collinear factorization and the modern PDFs and fragmentation functions. At the highest cms-energies the shape of the spectra measured in $p\bar p(p)$ collisions at large $q_T$ can be well explained. The difference between the data and the lowest-order computation is quantified in terms of a constant $K$-factor for each energy. The $K$-factor is found to systematically decrease with growing $\sqrt s$. Also a lower limit for the partonic transverse momentum, $p_0$, is extracted for each $\sqrt s$ based on the comparison with the measurements. A systematic increase of $p_0$ as a function of $\sqrt s$ is found. Nuclear effects in the charged-particle spectra in $pA$ and $AA$ collisions at RHIC and LHC are studied in the framework of collinear factorization by applying the EKS98 nuclear corrections to the parton distributions. The nuclear effects are shown to mostly enhance the computed spectra. A comparison with the recent PHENIX data from central and peripheral Au+Au collisions at RHIC is done.

Figures (13)

• Figure 1: Left: Inclusive cross section for charged-hadron production ($h\equiv h^+ + h^-$) in $p\bar{p}$ collisions at $\sqrt{s}= 630$ GeV averaged over $\vert\eta\vert<3.0$. The LO pQCD prediction with $K=2.19$ and scales $Q=p_T$, $\mu_F =q_T$ and $p_0=1.0, 1.9, 3.0$ GeV is shown by the curves. The data shown with the statistical error bars are from UA1 MIMI MIMI. Top right: The ratios data-to-data and data-to-theory as a function of transverse momentum for various $p_0$. Bottom right: The mimimized $\chi^2(N)/N$ (solid curve) and the resulting $K$-factor (with error bars) as a function of the smallest transverse momentum, $q_{TN}$, included in the fit. The $K$-factor is read off from the point where $\chi^2(N)/N=1$. The errors of the $K$-factor are computed from Eq. (\ref{['k-error']}).
• Figure 2: Left: An example of the dependence of the inclusive pQCD cross sections (as in Fig. \ref{['mitt630_1']}) on the choice of the fragmentation scale $\mu_F$. Based on the fit to the large-$q_T$ region of the UA1 MIMI data in Fig. \ref{['mitt630_1']}, we obtain $K=2.19\pm 0.11$ for $\mu_F=q_T$ and $K=1.76\pm 0.05$ for $\mu_F=q_T/2$. The scale $p_0$ has been fixed to 1.9 GeV and CTEQ5 PDF are used. Right: As in the top right panel of Fig. \ref{['mitt630_1']} but showing the dependence of the pQCD results on the PDF set. Three different sets are used, and the scales are fixed to $Q=p_T$ and $p_0=1.9$ GeV in both panels. For the sets CTQE5L, GRV98 and MRST(c-g), we obtain $K=2.19\pm0.11, 2.00\pm 0.10, 2.15\pm 0.10$ for $\mu_F=q_T$ (upper panel) and $K=1.76\pm 0.05, 1.53\pm 0.07, 1.65\pm 0.08$ for $\mu_F=q_T/2$ (lower panel).
• Figure 3: The LO pQCD prediction for the charged-particle spectra in $p\bar{p}$ collisions at $\sqrt s=630$ GeV with $K=2.19$ and $p_0=1.9$ GeV. The upper left panel corresponds to Fig. \ref{['mitt630_1']}, in the other panels the pseudorapidity interval $\vert\eta\vert <3.0$ has been divided into different subintervals. The data are from UA1 MIMI, Ref. MIMI.
• Figure 4: As Fig. \ref{['mitt630_1']} but for $h\equiv (h^++h^-)/2$, $\sqrt{s}=1800$ GeV and $\vert y\vert <1.0$. The data are from CDF CDF.
• Figure 5: As Fig. \ref{['mitt1800']} but for $\sqrt{s}=630$ GeV.