Energy and system dependence of high-$p_T$ triggered two-particle near-side correlations

Previous studies have indicated that the near-side peak of high-$p_T$ triggered correlations can be decomposed into two parts, the \textit{Jet} and the \textit{Ridge}. We present data on the yield per trigger of the \textit{Jet} and the \textit{Ridge} from $d+Au$, $Cu+Cu$ and $Au+Au$ collisions at $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV and compare data on the \textit{Jet} to PYTHIA 8.1 simulations for $p+p$. PYTHIA describes the \textit{Jet} component up to a scaling factor, meaning that PYTHIA can provide a better understanding of the \textit{Ridge} by giving insight into the effects of the kinematic cuts. We present collision energy and system dependence of the \textit{Ridge} yield, which should help distinguish models for the production mechanism of the \textit{Ridge}.


Introduction
Previous studies in Au+Au collisions at √ s N N = 200 GeV demonstrated that the near-side peak in high-p T triggered correlations can be decomposed into two structures. The Jet is narrow in both azimuth (∆φ) and pseudorapidity (∆η), similar to what is observed in d + Au, while the Ridge is narrow in azimuth but broad in pseudorapidity. The Jet component is similar to that expected from vacuum fragmentation, whereas the Ridge has properties similar to the bulk [1,2]. Comparing data from Au + Au and Cu + Cu collisions at √ s N N = 62.4 GeV and √ s N N = 200 GeV tests whether these conclusions hold for other collision systems and energies.
Several mechanisms have been proposed for the production of the Ridge [3,4,5,6,7]. These models have yielded few calculations which can be directly compared to data, in part because of the large number of factors which must be considered when theoretically calculating the experimentally measured quantitites. The results presented here should provide a good test of models for the production of the Jet and Ridge because trends expected with changing collision energy and in nuclei collided in a given model should be easier to calculate theoretically. GeV were used for the comparison of collision systems and energies. Details of the STAR detector can be found in [8]. The primary detector used for these analyses was the STAR Time Projection Chamber (TPC.) A high transverse momentum (p T ) particle is selected and the distribution of other particles in the event relative to that trigger particle in azimuth (∆φ) and pseudorapidity (∆η) d 2 N d∆φd∆η was determined. The p T of the trigger and associated particles was restricted in order to reduce the soft background; unless otherwise mentioned 1.5 GeV/c < p associated T < p trigger T and 3.0 < p trigger T < 6.0 GeV/c. d 2 N d∆φd∆η is normalized by the number of trigger particles. This was corrected for the single particle efficiency and for detector acceptance, which is dependent on the collision system and energy, p T , ∆η, ∆φ, and collision multiplicity. Except for studies of N part dependence, the Cu + Cu data at both energies are for 0-60% centrality, Au + Au data at √ s N N = 62.4 GeV are for 0-80% centrality, and Au + Au data at √ s N N = 200 GeV are for 0-10% centrality. d + Au data are minimum bias.
The yield measured is the number of particles associated with the trigger particle within limits on p associated T and p trigger T . The Ridge was previously observed to be roughly independent of ∆η within the acceptance of the STAR TPC [2]. To extract the yield it is assumed that the Ridge is independent of ∆η. Previous studies have demonstrated that the Jet component extends to |∆η | = 0.75 in the p T range studied here and that limited detector acceptance limits studies to |∆η | <1.75 [1,2,9]. To determine the Jet yield Y Jet , the projection of the distribution of particles d 2 N d∆φd∆η is taken in two different ranges in pseudorapidity: d∆φd∆η d∆η where the former contains only the Ridge and the latter contains both the Jet and the Ridge. The jet-like yield on the near-side is the integral over −1 < ∆φ < 1: The factor in front of the second term is the ratio of the ∆η width in the region containing the Jet and the Ridge to the width of the region containing only the Ridge. With this method for subtracting the Ridge contribution to Y Jet , the systematic errors due to v 2 cancel out assuming that v 2 is roughly independent of ∆η, a reasonable assumption in the mid-rapidity range |η| < 1 based on the available data [11,12]. It is also assumed that the Ridge is independent of ∆η.
To determine Y Ridge the integration is done over the entire ∆η region to minimize the effects of statistical fluctuations in the determination of the background: The integration over ∆φ is done by fitting a Gaussian to the near-side. This partially compensates for a detector effect which causes lost tracks at ∆φ ≈ 0 and ∆η ≈ 0; this effect is less than 10% in the p T range studied here [10].
The raw signal has a background due to particles correlated indirectly with each other in azimuth due to their correlation with the reaction plane. This random background is given by where v 2 is the second order harmonic in a Fourier expansion of the momentum anisotropy relative to the reaction plane, and must be subtracted in order to study the component associated with the jet. Systematic errors come from the errors on B, v trigger 2 and v associated 2 . It is assumed that v 2 is the same for events with a trigger particle as for minimum bias events and that v 2 is roughly independent of ∆η. For each data set v 2 (p T ) was fit in centrality bins to determine v trigger 2 and v associated 2 . Details of the v 2 subtraction for Au + Au collisions at √ s N N = 200 GeV are given in [1] and for Cu + Cu collisions at √ s N N = 200 GeV in [9]. For Cu + Cu collisions at √ s N N = 62.4 GeV, the v 2 using the reaction plane as determined from tracks in the Forward Time Projection Chamber was used as the nominal value and the lower bound was determined from a multiplicity-dependent approximation as described for √ s N N = 200 GeV in [9]. For Au + Au collisions at √ s N N = 62.4 GeV, v 2 and its systematic errors were taken from [13]. B is fixed using the ZYAM method [14]. PYTHIA 8.1 was used to simulate p + p collisions for comparisons to Y Jet . A trigger particle was selected and the distribution of particles in azimuth was calculated, as in the experimental measurements. The yield was determined as the number of charged hadrons in the range −1 < ∆φ < 1. For comparisons to data identical limits on p associated T and p trigger T were applied. The minimump T is the parameter in PYTHIA for the transverse momentum in the hard subprocess [15]. A minimum value ofp T = 0.1 GeV/c was used and 10 8 events were simulated to ensure that the minimump T did not affect the yield and that the statistical error was negligible. It was not necessary to study the distribution of particles in pseudorapidity since there is no Ridge in PYTHIA. Fig. 1 compares the dependence of Y Jet on p trigger T for all systems and energies to the yield from PYTHIA 8.1 scaled by 2/3. An overall scaling factor of 2/3 was applied to the PYTHIA yields to match the data. The need for the scaling factor implies that PYTHIA assumes that too many particles are produced in hard processes, however, kinematic effects should still be reflected accurately in PYTHIA. The scaled PYTHIA yield describes the shape of the p trigger T dependence well, with a few deviations at lower p trigger T . PYTHIA describes the energy dependence of Y Jet well, indicating that the energy dependence can be explained as a pQCD effect. If Y Jet is dominated by pQCD effects, deviations from PYTHIA at lower p T would be expected. No system dependence is observed in the data, as would be expected for an effect dominated by pQCD.

The Jet
The dependence of Y Jet on p associated T is shown in Fig. 2. As in Fig. 1, the scaled PYTHIA yield describes the shape of the data well and there is no system dependence. The inverse slope parameters from exponential fits to the data and to PYTHIA shown in Tab. 1 likewise support independence on collision system. Slight deviations from the  scaled PYTHIA yield at lower p associated T in Fig. 2 for collisions at √ s N N = 62.4 GeV are reflected in the inverse slope parameter, which is higher than that of the data.
The N part dependence of Y Jet is shown in Fig. 3 and compared to the scaled PYTHIA yield. In contrast to measurements at higher p T ,g which show no N part depedence, a small increase with N part is observed. This may be caused by either slight modifications of the Jet which increase with system size or some of the Ridge being misidentified as part of the Jet . If the Ridge were not completely independent of ∆η, some of the particles in the Ridge could be associated with the Jet . Since the Ridge has roughly four times as many particles than the Jet in central Au + Au, this would give a smaller relative error to the Ridge than the Jet . However, the Jet has also been observed to be considerably broader in ∆η in A + A collisions than in p + p and d + Au collisions [2,10], which would imply modifications of the Jet in A + A collisions. At this point models for Jet and Ridge production cannot distinguish these mechanisms.
That PYTHIA describes the p trigger T and p associated T dependence of Y Jet fairly well implies that PYTHIA can be used to approximate the momentum fraction carried by the leading hadron, z T . Fig. 4 shows thep T distribution  Fig. 4(a) shows that for the same p trigger T and p associated T , the mean z T is higher in √ s N N = 62.4 GeV and therefore the mean jet energy is lower. Fig. 4(b) shows that this is caused by the steeper spectrum at √ s N N = 62.4 GeV. The lower Y Jet in collisions at √ s N N = 62.4 GeV results from the higher mean z T and is a kinematic effect.

The Ridge
The dependence of Y Ridge on N part is given in Fig. 5. In collisions at both √ s N N = 62.4 GeV and √ s N N = 200 GeV Y Ridge increases with N part . As seen in Fig. 3, the yield at √ s N N = 62.4 GeV is considerably smaller than at √ s N N = 200 GeV. Fig. 6 shows the ratio Y Ridge /Y Jet and shows that this ratio does not depend on GeV likely correspond to a lower jet energy, so this implies that Y Ridge decreases with energy just like Y Jet .
Few models have attempted to make quantitative predictions for Y Ridge . An exception is the momentum kick model, which is consistent with data on the energy dependence of Y Ridge [17]. The collision energy dependence of Y Ridge is potentially a sensitive test of models because the dominant factor in collision energy dependence should be different for various classes of models. Models which involve parton energy loss due to interaction with the medium such as the momentum kick model should have a smaller Ridge at lower energy, as observed in the data, because the initial parton energy was lower. The radial flow+trigger bias model should predict a dependence of Y Ridge on the amount of radial flow in the system. An analysis similar to [18] could yield predictions for the collision system and energy dependence. Plasma instability models should depend on whether plasma instabilities are more or less likely in small systems and at lower energies. When more detailed calculations are available, it is likely that the data could exclude some production mechanisms.

Conclusions
The data from d + Au, Cu + Cu, and Au + Au and √ s N N = 62.4 GeV and √ s N N = 200 GeV demonstrate that the Jet shows no system dependence. In addition, the collision energy dependence of Y Jet is described well by PYTHIA even at fairly low p T and the p trigger T and p associated T dependencies agree with PYTHIA up to a scaling factor, with a few deviations at lower p T . This implies that the dominant production mechanism of the Jet is fragmentation. Deviations from PYTHIA may imply modifications of the Jet in A+A collisions. It also implies that PYTHIA or other models can be used to determine the effect of the kinematic cuts on p trigger T on the z T and jet energy distribution, which could be very useful for the theoretical interpretation of the Ridge.
Y Ridge is smaller at lower collision energies and increases with system size indepent of collision system. There is no dependence on the collision system. Data on the collision energy and system dependence could provide a robust test of models, and comparisons of Y Jet to PYTHIA imply that the effects of the kinematic cuts on the distribution of jet energies can be inferred from PYTHIA.