Elliptic flow and the high $p_T$ ridge in Au+Au collisions

In this paper we look for a correlations between intermediate $p_T$ particle pairs and the $v_2$ of the remaining low $p_T$ particles. We find that the shape of the flow vector distribution, which is calculated from all low $p_T$ tracks, depends in a non-trivial way on the angular separation between the high $p_T$ particle pairs in the event. Our analysis is based on 200 GeV Au+Au collision measured with the STAR detector.


Introduction
Dihadron correlations are used in heavy-ion collisions to study the effect of jet-quenching and other interactions of jets with the medium created in the collision overlap zone [1,2]. In non-central collisions, this overlap zone is not symmetric. The spatial asymmetry leads to large azimuthal anisotropies in momentum space resulting in high values of the second coefficient in the Fourier decomposition of the azimuthal distribution of produced particles with respect to reaction plane.(v 2 ) [3]. Dihadron measurements from STAR have revealed a correlation structure which is narrow in the azimuthal direction and broad in longitudinal direction (the narrow ∆φ, broad ∆η "ridge") [4,5,6]. This structure is unique to nucleus-nucleus collisions and its amplitude shows a non-monotonic rise with increase in collision centrality [7]. We search for evidence of jet-interactions with the medium by studying v 2 for events containing correlated dihadron pairs.

Method and discussion
Our analysis is based on 16 million Au+Au at 200GeV center of mass energy measured with the STAR detector [8]. We select events with at least two tracks having p T > 2.0 GeV and calculate the |q| for those events. The q("flow") vector can indicate if particles are produced in preferential direction. |q| is calculated from q x = Σ cos(2φ i ) and q y = Σ sin(2φ i ) [9], where the sums run over all tracks having p T < 2.0 GeV/c and φ i is azimuthal angle of track w.r.t reaction plane. The distribution of |q| (dN/d|q|) depends on the number of particles, v 2 , and other correlations not related to v 2 [10]. If there are more than two tracks with p T > 2.0 GeV/c, we select the leading and sub-leading tracks. This way we select one dihadron pair per event. This allows us to associate the |q| of an event with the angular seperation of a high momentum pair. In this way we can look for modifications to dN/d|q| for events with or without correlated high p T pairs. Fig. 1 (left) shows the distribution of the relative angle between leading and sub-leading dihadron pairs with p T > 2.0 GeV/c. If v 2 were the only source of correlations then dN/d∆φ should have the following shape: and v asso 2 are the v 2 values respectively, for the leading and subleading (trigger and associate) particles. Other physical processes leading to correlations are particle decays, fragmentation of partons (jets), and HBT. Jet correlations are expected to be prominent for high p T dihadron pairs so a twocomponent model is used to fit dN/d∆φ: a "jet" component on top of a v 2 modulated "background" [1,2,11]. Assuming the two components model is applicable, we can extract the fraction of correlated and uncorrelated pairs for each ∆φ bin. The next step of our analysis is to study dN/d|q| for the events with high p T pairs as a function of the angle ∆φ and ∆η of the high p T pairs. If jets are the source of the correlations (Signal) in Fig. 1 and they interact with the medium, they may modify the v 2 of the event. That modification would then change the shape of dN/d|q|. Or alternatively, if the correlations beyond the v 2 modulation in Fig. 1 is caused by the same space-momentum correlation that give rise to v 2 , then the correlation signal may result to large values of v 2 [12]. This would also cause dN/d|q| to depend on ∆φ and/or ∆η. Fig. 1 (right) shows average magnitude of flow vector ( |q| ) vs. ∆φ of the leading and subleading hadrons for either |∆η| > 0.7 or |∆η| < 0.7. We observe a non-trivial dependence on ∆φ. No prominent ∆η dependence is seen in this figure.
We also studied p T vs. ∆φ and find that within errors it is independent of the angle between the high p T tracks. The multiplicity distribution for the events with two tracks with p T > 2.0 GeV only deviates from the inclusive sample for peripheral events.  Having observed a non-trivial dependence of q on ∆φ, we next attempt to convert this into a v 2 for the events that had a correlated pair. We categorize the events in two parts depending on the highest p T particles (1) Ridge events : |(∆η)| > 0.7, (2) Ridge+jet events : |(∆η)| <0.7 and studied the dN/d|q| distributions.
We calculate the q-distributions for the signal and background by dividing the near-side into two bins (∆φ < 4π/20 and 4π/20 < ∆φ < 8π/20) and solving equations: is the number of events yielding a correlated pair in bin 1 or 2. B 1,2 is the number of events yielding an un-correlated pair in bin 1 or 2. dN 1 and dN 2 are the q-distributions for events in bin 1 and 2. dN S and dN B are the q-distributions for events giving correlated pairs (signal) and uncorrelated pairs (background). dN 1 and dN 2 are measured. S 1,2 and B 1,2 are extracted from the dN/d∆φ distributions by applying the two-component model. Then dN S and dN B can be determined from the two equations above. Elliptic flow is calculated by fitting the q-distributions (Fig. 2(left)) for signal for ridge and ridge+jet events. Two parameters can be extracted from the q-distribution : The term accounts for correlations that are not related to the reaction plane and σ v2 is the rms width of the v 2 distribution.
In Fig. 2(right), we report v 2 {2} for the event classes defined above. We use the ansatz that the near-side correlation contains a jet part (narrow in ∆φ and ∆η) and a ridge part (narrow in ∆φ but broad in ∆η) [6]. By calculating the signal v 2 for ridge and ridge+jet events we calculated v 2 for jet events by using equations Area jet = Area ridge+jet − Area ridge * Acceptancef actor (2) Acceptancef actor = Area ridge+jet(background)(∆η<0.7) Area ridge(background)(∆η>0.7)  This allows us to project the ridge from |∆η| > 0.7 to |∆η| < 0.7. The jet is the correlation that remains.
The selection of one unique pair per event, the application the two-component model, and the simple algebra above allows us to calculate v 2 {q} 2 = v 2 2 − σ 2 v2 and σ 2 q,dyn = δ 2 + 2σ 2 v2 for events giving rise to pairs of particles in the jet-cone region, in the ridge region, and in the background. The values of v 2 {q} vs. collision impact parameter b are presented in Fig. 2(right). v 2 {q} for the events that had a high p T pair contributing to the ridge-like correlation exhibit a slightly larger v 2 {q} for non-central and peripheral collisions than the corresponding events contributing a pair to the background. We also attempt to determine if the v 2 {q} values for events contributing pairs to the jet-like correlation are larger or smaller than those contributing to the background. Within the current estimates of the systematics uncertainties the values are consistent with v 2 from inclusive events.