Using two- and Three-particle correlations to probe strongly interacting partonic matter
UUsing Two- and Three-Particle Correlations to Probe StronglyInteracting Partonic Matter
Wolf G. Holzmann a for the PHENIX collaboration a Columbia University and Nevis Laboratories, New York, NY 10027, USA
Abstract
The latest two- and three-particle correlation measurements obtained by the PHENIX collab-oration are presented. Three-particle correlations are consistent with the presence of conicalemission patterns in the data. Two-particle correlations relative to the collision geometry revealstrong shape and yield modifications of the away-side jet, that depend on the orientation of thetrigger particle with respect to the event plane. A di ff erence in the geometry dependence of theper trigger yields in the regions around ∆ φ ≈ π and ∆ φ ≈ π ± . ff erentgeometry dependence of jet energy loss and the medium response to the deposited energy.
1. Introduction
One of the most exciting results to have emerged from the Relativistic Heavy Ion Collider(RHIC), is the large energy loss of high transverse momentum ( p T ) partons in the strongly inter-acting partonic matter created in heavy ion collisions [1]. The fraction of energy transferred fromthe parton to the medium is expected to depend on the gluon densities and the spacio-temporalextent of the interaction [2]. Therefore, jet energy loss is considered a promising tool to obtain atomographic image of the partonic medium. Equally important is the medium excitation result-ing from the energy transfer, since it may carry information on the transport properties of bulkQCD matter [3].Azimuthal angular correlation measurements at intermediate p T reveal two o ff -center away-side peaks at ∆ φ ≈ π ± . c S ) of strongly interacting partonic matter and are expected to be sensitiveto the ratio of shear viscosity to entropy density ( η s ). An important prerequisite to extractingmedium properties from the data, however, is a solid understanding of the mechanistic detailsinvolved. Despite much recent progress, such an understanding has not yet been achieved. Twoimportant outstanding questions are wether conical emission patterns do indeed exist in the dataand how the underlying flow field may influence the observed correlation structures.
2. Three-particle correlations
Three-particle correlation analyses provide added topological insights over and above the in-formation content carried by two particle correlations. The PHENIX collaboration has measuredthe correlation of two charged hadrons at 1 < p T , assoc < . / c associated with a trigger Preprint submitted to Nuclear Physics A November 20, 2018 a r X i v : . [ nu c l - e x ] O c t adron at 2 . < p T , trig < / c in Au + Au collisions at √ s NN =
200 GeV. To this end, acoordinate system is defined for which the trigger particle orientation denotes the z-axis [5]. Tothe degree that the trigger particle approximates the jet axis, this coordinate system is somewhatmore natural to the investigated problem than the laboratory frame. Figure 1 shows the result-ing azimuthal and radial projections of the two dimensional correlation function for a centralityselection corresponding to 20-30% of the geometric cross-section. The flow modulated back-ground and the contributions from two-particle correlations have been subtracted following themethod outlined in [5]. The data (filled triangles) is compared to toy Monte Carlo simulations ofcone jets (filled squares) and bent jets (filled circles). For the latter case, the away-side jets havebeen displaced in azimuth to reproduce the signal in the two-particle correlation data. The com-parison indicates, that the observed correlation structures are consistent with expectations fromconical emission patterns. An interplay of other contributions to the three-particle correlation,however, cannot be ruled out. It is important to note, that the cone angle inferred from the righthand panel of Fig. 1 ( θ cone ≈ ff -center peaks in thetwo-particle azimuthal correlation analyses. Figure 1: Three-particle correlation functions for two charged hadrons at 1 < p T , assoc < . / c and a trigger hadronat 2 . < p T , trig < / c in 20-30% Au + Au collisions at √ s NN =
200 GeV. Left: Azimuthal projection of twodimensional correlation function. Right: Radial projection of two dimensional correlation function.
The depicted three-particle correlation analysis integrates over the entire collision geometry.In order to study the path-length dependence of jet-medium interactions, an analysis relative tothe event-plane was carried out.
3. Two-particle correlations relative to the event-plane
Jet energy loss depends on the initial gluon densities and the distance travelled by the partonsin the medium [2]. Similarly, the medium response to the energy transfer is expected to dependon the amount of matter that can be excited and the direction of the parton with respect to theflow field. Therefore, angular correlations relative to the reaction geometry hold much promise todisentangle energy loss from medium excitation e ff ects. They can also serve to tightly constrainmedium modification models. To this end, we report relative azimuthal angle correlations ofcharged hadrons in the range 1.0 < p T < / c associated with a trigger hadron at 2.0 < T < / c, that has been oriented with respect to the event plane. The shape and yield ofjet-induced correlations for both the near- and away-side jets are then studied as a function of therelative azimuthal angle between the trigger particle and the event plane ( φ S = φ trig − Ψ ). Theanalysis follows the techniques outlined in Refs. [4, 6]. A newly installed reaction plane detectorallows for the reconstruction of the event plane with excellent resolution ( (cid:104) cos (2 ∆Ψ ) (cid:105) ≈ .
74 inmid-central collisions). This permits for di ff erential studies relative to the collision geometry.Representative jet pair distribution per trigger particle are shown in Fig. 2 for 0-5% and 25-30% of the geometric cross section (left and right, repsectively). The cases where the triggerparticle is oriented in-plane [filled circles, | φ S | < ◦ ] and out-of-plane [filled triangles, 85 ◦ < | φ S | < ◦ ], are contrasted with a selection in between these two extremes [filled squares, 40 ◦ < | φ S | < ◦ ]. The distributions have been folded into | ∆ φ | = − π and | φ S | = − π/ Figure 2: Jet pair distributions for 1 < p T , assoc < < p T , trig < / c and 0-5% and 25-30% of the geometric crosssection (top and bottom, repsectively). Shown are azimuthal distributions where the trigger particle is oriented in-plane[filled circles, | φ S | < ◦ ] and out-of-plane [filled triangles, 85 ◦ < | φ S | < ◦ ], as well as a selection in between these twoextremes [filled squares, 40 ◦ < | φ S | < ◦ ]. For the central events (Fig. 2 left), the three jet pair distributions are essentially identicalwithin the stated uncertainties. This is to be expected, since central events do not result in strongreaction plane dependent path length changes. All three distributions show a broad away-sidepeak that exhibits a minimum at ∆ φ = π and a maximum at ∆ φ ≈ π − .
1, in accordance withearlier inclusive correlation measurements [4].For the mid-central selection (Fig. 2 right), the away-side peak for the in-plane trigger ori-entation and the out-of-plane trigger orientation both appear to have similar width. However, thehead region at ∆ φ ≈ π seems to be suppressed in the out-of-plane direction, while the distributionfor the in-plane trigger particle still shows a sizable yield at ∆ φ = π. This observation is in qual-itative agreement with expectations from jet suppression. For a di-jet system that is aligned withthe short axis of the overlap region (in-plane), very little jet quenching is expected. By contrast,a jet opposite a trigger particle pointing perpendicular to the event plane has a larger path lengththrough the medium and is thus more likely to be quenched.It is interesting to note, that the jet pair distribution for a trigger particle oriented at 40 ◦ < | φ S | < ◦ shows a much broader away-side than its in-plane and out-of-plane counterparts. Theyield is depleted at ∆ φ = π , but now shows an enhancement away from ∆ φ = π which peaks at ∆ φ ≈ π − .
3. At present, it is unclear whether this merely reflects a geometry dependent shift in3he away-side peaks or perhaps an additional contribution at ∆ φ ≈ π/ ◦ < | ∆ φ | < ◦ , which we will call the ”head” regionand a ”shoulder” region identified by 60 ◦ < | ∆ φ | < ◦ . It is instructive to investigate theper-trigger-yield integrated in these regions as a function of the trigger particle orientation withrespect to the event plane. The result is given in Fig. 3, with the head yields depicted on theleft and the shoulder yields on the right. The head yields show a gradual depletion from in-plane Figure 3: Per-trigger-yield integrated over the azimuthal pair separations 140 ◦ < | ∆ φ | < ◦ (left) and 60 ◦ < | ∆ φ | < ◦ (right) plotted as a function of trigger particle orientation relative to the event plane ( φ trig − Ψ ). to out-of-plane trigger particle orientations. This is in agreement with qualitative expectationsfrom jet-quenching models, since the path-length opposite the trigger particle increases in thesame direction. By contrast, the shoulder yields increase from in-plane to reach a maximumat about | φ trig − Ψ | ≈ ◦ . They fall again to reach a value for the out-of-plane yield that iscomparable to the in-plane case. The correlation structures in the head region have predominantlybeen attributed to jet energy loss and the correlation signals in the shoulder region are generallyinterpreted as arising mostly from the medium’s response to this energy loss. In such a picture,the di ff erent yield dependence can be understood by a di ff erence in geometry dependence of jetenergy loss and the medium response to the deposited energy. Acknowledgments
This work was supported by U.S. Department of Energy grant DE-FG02-86ER40281.
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