Evidence for a QCD accelerator in relativistic heavy-ion collisions

We report measurements of forward jets produced in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV at the Relativistic Heavy Ion Collider. The jet-energy distributions extend to energies much larger than expected by Feynman scaling. This constitutes the first clear evidence for Feynman-scaling violations in heavy-ion collisions. Such high-energy particle production has been in models via QCD string interactions, but so far is untested by experiment. One such model calls this a hadronic accelerator. Studies with a particular heavy-ion event generator (hijing) show that photons and mesons exhibit such very high-energy production in a heavy-ion collision, so a QCD accelerator appropriately captures the physics associated with such QCD string interactions. All models other than hijing used for hadronic interactions in the study of extensive air showers from cosmic rays either do not include these QCD string interactions or have smaller effects from the QCD accelerator.

Figure 1

A schematic of a QCD accelerator. Color charge is separated from anticolor charge in a hadronic collision. A QCD string, represented in the schematic as a gluon, is stretched between the separated charges. The schematic shows that three nearby QCD strings fuse, as they can because the QCD fields carry color charge. The fused string can produce particles with longitudinal momentum component $>\sqrt{s_{NN}}/2$.

Figure 2

(a) Model predictions for the distribution of longitudinal momenta for positive pions produced in a hadronic collision normalized to the number of minimum-bias collisions. The $\mathrm{Cu}+\mathrm{Au}$ predictions are at $\sqrt{s_{NN}}=200$ GeV and the $p+p$ predictions are at the $\sqrt{s}$ noted in the key. (b) hijing [10] predictions for the dependence of the $p_L$ distributions on the impact parameter for $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV.

Figure 3

Left: Average reconstructed energy versus energy of the $p+p$ jet embedded into minimum-bias $\mathrm{Cu}+\mathrm{Au}$ data for events having $\mathrm{\Sigma }{Q}_{Y1}<\mathrm{\Sigma }{Q}_Y<\mathrm{\Sigma }{Q}_{Y2}$. The black points show the linear relationship between input and reconstructed jets. The slope of the line fitting those points is the same as found for jet production in $p+p$. The offset ($e_0$) represents the average effect of UE, which grows with $\mathrm{\Sigma }{Q}_{Y2}$ as shown in the inset. Right: The jet-energy scale is determined from the comparison of particle jets ($E_P$) to tower jets ($E_R$) from hijing/geant simulations of $\mathrm{Cu}+\mathrm{Au}$ collisions. Results for $\mathrm{\Sigma }{Q}_Y<1000$ are shown. The green band represents $\pm 3$% variation of the jet-energy scale. The inset shows a distribution of energy difference $\mathrm{\Delta }E=E_P-E_R$ from jet finding with $R_{\mathrm{jet}}=0.5$ in one bin of particle-jet energy with a fit by a Gaussian distribution. The blue points show the variation of Gaussian centroid ($\mu$) with the average tower-jet energy. Results for jets found with $R_{\mathrm{jet}}=0.5$ and $R_{\mathrm{jet}}=0.7$ are shown.

Figure 4

Jet resolution is determined from (a) embedding jets into $\mathrm{Cu}+\mathrm{Au}$ MB events selected to have $\mathrm{\Sigma }{Q}_Y<1000$. The energy difference, $\mathrm{\Delta }E$, between reconstructed and embedded jet is shown for one $E_J$ bin. (b) Detector resolution is determined from comparing particle jets to tower jets. The ratio $\sigma /\mu$ from Gaussian fits to energy difference distributions is shown versus tower-jet energy. (c) The product of the response matrix from embedding with the response matrix from detector resolution is shown. The matrix is normalized to give the probability a jet is reconstructed with energy $E_R$ when produced with energy $E_J$.

Figure 5

Comparison of results from embedding $p+p$ jets into minimum-bias $\mathrm{Cu}+\mathrm{Au}$ events [Fig. 4] to a four-parameter simulation model described in the text. This simulation model then has parameters adjusted to estimate the impact of UE fluctuations on the results.

Figure 6

Multiplicity of towers within jets found in $\mathrm{Cu}+\mathrm{Au}$ data, in hijing/geant simulations, and in $p+p$ collisions at $\sqrt{s}=510$ GeV.

Figure 7

Jet-energy distribution from $\mathrm{Cu}+\mathrm{Au}$ collisions with $\mathrm{\Sigma }{Q}_Y<1000$. Open points are raw data for jets found with $R_{\mathrm{jet}}=0.5$ (left) and $R_{\mathrm{jet}}=0.7$ (right). Solid points are from unfolding [36] the response matrix [Fig. 4] from the data. The unfolded points are fit by power-law functions whose endpoints ($E_0$) are $>100$ GeV. At fixed $E$, the width of the green band is predominantly from the uncertainty in the jet-energy scale. The power-law parameters are listed in Table 1.

Figure 8

Jet-energy distribution from $\mathrm{Cu}+\mathrm{Au}$ collisions as a function of the upper limit on $\mathrm{\Sigma }{Q}_Y$. Open points are raw data for jets found with $R_{\mathrm{jet}}=0.5$. Solid points are from unfolding [36] the response matrix [Fig. (4)] from the data. The inset shows the fitted endpoint ($E_0$) as a function of the upper limit on $\mathrm{\Sigma }{Q}_Y$. Uncertainties on $E_0$ are the quadrature sum of uncertainties from power-law fits and systematic effects from detector-based jet resolution.