Identifying the underlying physics of the ridge via 3-particle Δη−Δη correlations
aa r X i v : . [ nu c l - e x ] A p r Identifying the underlying physics of theridge via 3-particle ∆ η − ∆ η correlations Pawan Kumar Netrakanti (for the STAR Collaboration)
Purdue University, USA. e-mail: [email protected]
Abstract
We present the first results on 3-particle ∆ η -∆ η correlations in minimum bias d +Au, peripheral and central Au+Au collisions at √ s NN = 200 GeV measuredby the STAR experiment. The analysis technique is described in detail. Theridge particles, observed at large ∆ η in dihadron correlations in central Au+Aucollisions, appear to be uniformly distributed over the measured ∆ η -∆ η region in3-particle correlation. The results, together with theoretical models, should helpfurther our understanding of the underlying physics of the ridge. Dihadron correlations provide a powerful tool to study the properties of the mediumcreated in ultra-relativistic heavy-ion collisions. The observation of the near-side ridgein central Au+Au collisions [1, 2], where hadrons are correlated with a high transversemomentum ( p ⊥ ) trigger particle in the azimuthal angle (∆ φ ∼
0) but distributed ap-proximately uniformly in pseudorapidity (∆ η ), has generated great interest. The prop-erties of ridge particles, such as their p ⊥ spectral shape and particle compositions, aresimilar to those of inclusive particles, however the origin of the ridge is presently notunderstood. Various theoretical models have been proposed, including longitudinal flowpush [3], QCD bremsstrahlung radiation boosted by transverse flow [4, 5], recombinationbetween thermal and shower partons at intermediate p ⊥ [6], broadening of quenched jetsin turbulent color fields [7], and elastic collision between hard and medium partons (mo-mentum kick) [8]. Production of correlated particles in all these models can be broadlydivided into two categories: (1) particles from jet fragmentation in vacuum which gen-erate a jet-cone peak in dihadron correlation, and (2) particles from gluon radiationaffected by the medium and diffused broadly in ∆ η which generate the ridge. However,the qualitative features of dihadron correlations are all same from these models. On the1ther hand, because the physics mechanisms of gluon diffusion in ∆ η differs betweenmodels, the distribution of two ridge particles in coincidence with the trigger particlecan differ. Therefore, we analyze the 3-particle correlation in ∆ η -∆ η between two as-sociated particles and a trigger particle to potentially discriminate between the physicsmechanisms proposed in these models. Jet fragmentation in vacuum would give a peakaround (∆ η ,∆ η ) ∼ (0,0) in 3-particle ∆ η -∆ η correlations. Particles from ∆ η diffusionwould produce structures that depend on the physics mechanisms of diffusion and thuscan be used to discriminate models. Combinations of one particle from jet fragmentationin vacuum and the other from ∆ η gluon diffusion would generate horizontal or verticalstrips in 3-particle ∆ η -∆ η correlations. The data used in this analysis are from d +Au and Au+Au collisions at √ s NN = 200GeV and were taken by the STAR Time Projection Chamber (TPC) [9]. The Au+Aucollisions were recorded with the minimum bais trigger and central trigger from zerodegree calorimeters. The z -position of the constructed primary vertex (collision point)was restricted within ±
30 cm from the center of the TPC. To ensure that these trackscome from the collision, the distance of closest approach to the primary vertex of less than3.0 cm was used. The number of track points in the TPC was required to be greater than15. The trigger and associated particles are restricted to | η | < p ⊥ ranges are3 < p trig ⊥ <
10 GeV/c and 1 < p assoc ⊥ < p ⊥ -, φ -dependent reconstruction efficiency for associatedparticles and the φ -dependent efficiency for trigger particles, and are normalized percorrected trigger particle.Figure 1 (a) shows the 2-particle correlation signal in ∆ φ for 0-12% central Au+Aucollisions, Y(∆ φ ). Also shown is the background constructed from the event-mixingtechnique, mixing a trigger particle from a triggered event with an associated particlefrom another event from the inclusive data sample. The inclusive event is required tohave the same centrality, same magnetic field configuration and similar primary vertex z position ( | ∆ z | < B inc (∆ η, ∆ φ ). The mixed event background is then scaled by a constant a : B (∆ φ ) = a Z − B inc ( ∆ η, ∆ φ ) h + 2 v trig2 v assoc2 cos (2 ∆ φ ) + 2 v trig4 v assoc4 cos (4 ∆ φ ) i d ( ∆ η ) . (1)This normalization was performed in the 0.8 < ∆ φ < φ =1 radian (ZYA1). The v and v are the anisotropicflow coefficients, and are measured to be independent of η [10].Figure 1 (b) shows the ∆ η distribution within | ∆ φ | < a factor as obtained by2 ∆ -1 0 1 2 3 4 5 φ ∆ d N / d t r i g / N Raw SignalMixed EventsMixed Events (ZYA1)STAR Preliminary (a) η∆ -1.5 -1 -0.5 0 0.5 1 1.5 η ∆ d N / d t r i g / N STAR Preliminary (b)
Figure 1: Two-particle ∆ φ and ∆ η correlations in 0-12% central Au+Au collisionsare plotted in (a) and (b) respectively. The mixed event background (before and after a scaling) are also shown. Both the trigger and associated particles are restricted to | η | < p ⊥ ranges are 3 < p trig ⊥ <
10 GeV/c and 1 < p assoc ⊥ < η distributions are obtained for near-side associated particleswithin | ∆ φ | < η correlations are corrected for the 2-particle ∆ η acceptance.the 2-particle ZYA1 in ∆ φ : B (∆ η ) = a Z . − . B inc ( ∆ η, ∆ φ ) h + 2 v trig2 v assoc2 cos (2 ∆ φ ) + 2 v trig4 v assoc4 cos (4 ∆ φ ) i d ( ∆ φ ) . (2)The correlated 2-particle yield is given by:ˆ Y (∆ η ) = Y (∆ η ) − B (∆ η ) . (3)In Figure 1 (b), the additional 2-particle ∆ η acceptance, A (∆ η ), is applied on boththe signal, Y(∆ η )/ A (∆ η ), and the background, B(∆ η )/ A (∆ η ). The broad jet-like peakaround ∆ η ∼ η ) ⊗ Y(∆ η ), is obtained from all tripletsof one trigger particle and two associated particles from the same triggered event. Theassociated particles were constrained in azimuthal angle relative to the trigger particlewithin | ∆ φ | < .
7. The signal is binned in ∆ η and ∆ η , the pseudorapidity differencesbetween the associated particles and the trigger. The raw 3-particle correlation signalcan be formulated as: Y (∆ η ) ⊗ Y (∆ η ) = ˆ Y (∆ η ) ⊗ ˆ Y (∆ η ) + B (∆ η ) ⊗ B (∆ η )+ h ˆ Y (∆ η ) ⊗ B (∆ η ) + ˆ Y (∆ η ) ⊗ B (∆ η ) i (4)where ˆ Y (∆ η ) and B(∆ η ) represent the correlated and background particles, respectively.The two sources of background in the raw 3-particle correlation are: (1) one of the two3ssociated particles is correlated with the trigger particle besides flow correlation, and(2) neither of the two associated particles is correlated with the trigger particle besidesflow correlation.The first background, referred to as Hard-Soft (HS), cannot be readily obtainedfrom the folding of the background subtracted 2-particle correlation with the underlyingbackground because of the non-uniform 2-particle ∆ η acceptance. The folding wouldresult in the product of two averages, the average 2-particle correlation, ˆ Y (∆ η ), andthe average background, B(∆ η ). Since ˆ Y (∆ η ) and B(∆ η ) are correlated event-by-eventbecause of the ∆ η acceptance, the average of the product does not equal to the productof the averages. Instead we construct the HS by mixing trigger-associated pair from thetriggered event with a particle from a different and inclusive event. Namely, HS = ˆ Y (∆ η ) ⊗ B (∆ η ) + ˆ Y (∆ η ) ⊗ B (∆ η )= a h Y (∆ η ) B inc (∆ η ) i F (2) + a h Y (∆ η ) B inc (∆ η ) i F (1) − a h B inc (∆ η ) B inc (∆ η ) i F. (5)Here the last term is constructed by mixing two different inclusive events to take care ofthe uncorrelated part in the first two terms of the Eq. 5. The F (1) and F (2) are to takeinto account the flow correlation related to associated particle 1 and 2, respectively, andare given by: F (1) = h v trig2 v (1)2 cos(2∆ φ ) + 2 v (1)2 v (2)2 cos(2∆ φ − φ ) + 2 v trig4 v (1)4 cos(4∆ φ )+2 v (1)4 v (2)4 cos(4∆ φ − φ ) + 2 v trig2 v (1)2 v (2)4 cos(2∆ φ − φ )+2 v trig2 v (2)2 v (1)4 cos(4∆ φ − φ ) + 2 v (1)2 v (2)2 v trig4 cos(2∆ φ + 2∆ φ ) i (6)and an analogous equation for F (2) with 1 ↔
2. The F is to take into account the flowcorrelation among all the three particles in the event mixing, and is given by F = h v trig2 v (1)2 cos(2∆ φ ) + 2 v trig2 v (2)2 cos(2∆ φ ) + 2 v (1)2 v (2)2 cos(2∆ φ − φ )+2 v trig4 v (1)4 cos(4∆ φ ) + 2 v trig4 v (2)4 cos(4∆ φ ) + 2 v (1)4 v (2)4 cos(4∆ φ − φ )+2 v trig2 v (1)2 v (2)4 cos(2∆ φ − φ ) + 2 v trig2 v (2)2 v (1)4 cos(4∆ φ − φ )+2 v (1)2 v (2)2 v trig4 cos(2∆ φ + 2∆ φ ) i . (7)The averages in Eq. 6, 7 are taken within | ∆ φ , | < v and v for trigger particle and associated particles. We used a parameterization of v =1.15 v . Again, the flow contributions are constant in the measured η range.The second background, referred to as Sof-Soft (SS), is constructed by mixing atrigger particle with an associated particle pair from an inclusive event which preservesall correlations between the two associated particles: SS = B (∆ η ) ⊗ B (∆ η ) = a b h B inc (∆ η ) ⊗ B inc (∆ η ) i F ( t ) (8)4here a is the same factor as obtained from 2-particle ZYA1 in ∆ φ . The flow contributionbetween trigger particle and the background particles is not preserved in the eventmixing. This contribution, the so-called trigger flow, is added by hand: F ( t ) = h v trig2 v (1)2 cos(2∆ φ ) + 2 v trig2 v (2)2 cos(2∆ φ ) + 2 v trig4 v (1)4 cos(4∆ φ )+2 v trig4 v (2)2 cos(4∆ φ ) + 2 v trig2 v (1)2 v (2)4 cos(2∆ φ − φ )+2 v trig2 v (2)2 v ( i )4 cos(4∆ φ − φ ) + 2 v (1)2 v (2)2 v trig4 cos(2∆ φ + 2∆ φ ) i (9)where the average is taken within | ∆ φ , | < a b in Eq. 8 scales the number of associated pairs from the inclusive eventto that in the background underlying the triggered event: b = h h N assoc ( N assoc − i / h N assoc i i bkgd h h N assoc ( N assoc − i / h N assoc i i inc (10)where N assoc denotes the associated particle multiplicity. If the associated particle mul-tiplicity in the inclusive event and in the background underlying the triggered eventare both Poissonian or deviate from Poissonian equally, then b =1. In our analysis, weobtain b in the following way. We scale the 2-particle ∆ η distribution such that theridge contribution in 1.0 < | ∆ η | < a . We repeat ouranalysis with this new a , and obtain b by requiring the average 3-particle ∆ η -∆ η signalin 1.0 < | (∆ η , ∆ η ) | < b in our analysis withthe default a to obtain the final 3-particle correlation. The assumption in this is: h h N assoc ( N assoc − i / h N assoc i i bkgd = h h N assoc ( N assoc − i / h N assoc i i bkgd+ridge . (11)The 3-particle ∆ η -∆ η correlation, ˆ Y (∆ η ) ⊗ ˆ Y (∆ η ), is obtained by subtracting theHS ans SS backgrounds from the raw signal. The obtained correlation is corrected for3-particle ∆ η acceptance. The acceptance is obtained from event-mixing of a triggerparticle with associated particles from two different inclusive events, as was done for thelast term in Eq. 5, namely A (∆ η , ∆ η ) = B inc (∆ η ) B inc (∆ η ) B inc (0) B inc (0) . (12)The main sources of systematic uncertainty in our 3-particle correlation results arefrom the normalization factors a , b and the flow measurements. The v used in ouranalysis is the average v from the modified reaction plane method and the 4-particlecummulant method [1]. We assign a ±
10% systematic uncertainty on v . The systematicuncertainty on a is estimated by using the normalization range of 0.9 < ∆ φ < < ∆ φ < b is estimated by using the normalizationrange in ∆ η of − < | ∆ η | < − − < | ∆ η | < − Results and Discussion
Figure 2 (a), (b) and (c) show the background subtracted 3-particle ∆ η -∆ η correla-tion for d +Au, 40-80% Au+Au and 0-12% Au+Au at √ s NN = 200 GeV, respectively.The prominent jet structure is observed in d +Au and 40-80% Au+Au collisions around η∆ -1.5 -1 -0.5 0 0.5 1 1.5 η ∆ -1.5-1-0.500.511.5 -0.2-0.100.10.20.30.40.5 d+Au (a) STAR Preliminary η∆ -1.5 -1 -0.5 0 0.5 1 1.5 η ∆ -1.5-1-0.500.511.5 -0.2-0.100.10.20.30.40.5 (b) STAR Preliminary η∆ -1.5 -1 -0.5 0 0.5 1 1.5 η ∆ -1.5-1-0.500.511.5 η ∆ d η ∆ N / d d -0.2-0.100.10.20.30.40.5 (c) STAR Preliminary
Figure 2: Background subtracted 3-particle ∆ η -∆ η correlation in (a) d +Au, (b)40-80%Au+Au and (c) central 0-12% for Au+Au collisions. The trigger and associated particles p ⊥ ranges are 3 < p trig ⊥ <
10 GeV/c and 1 < p assoc ⊥ < η -∆ η correlations are obtained for near-side associated particles within | ∆ φ | < η acceptance.(∆ η ,∆ η ) ∼ (0,0). The peak is also observed in 0-12% central Au+Au collisions, but thepeak is atop of an overall pedestal. This pedestal is caused by the ridge particles, anddoes not seem to have other structures in (∆ η , ∆ η ). The ridge particles seem to bedistributed approximately uniformly over the measured ∆ η -∆ η region.To study the ∆ η -∆ η correlation in more detail, Figure 3 (a) and (b) show the projec-tions of the 3-particle ∆ η -∆ η correlation along the on-diagonal Σ = (∆ η + ∆ η ) / η − ∆ η ) /
2. These projections are performed within | ∆ | < | Σ | < R = p (∆ η ) + (∆ η ) projection.All projections are normalized by the projected area, therefore they are the averagecorrelation signal per radian . The average signals peak at Σ ∼ ∼
0, in d +Au and40-80% Au+Au collisions and rapidly fall off to zero at large Σ or ∆. For central 0-12%Au+Au collisions the signal also peaks at Σ ∼ ∼ R ∼ ξ = tan − (∆ η /∆ η ) in 0.7 < R < ξ shows no evidence forhorizontal or vertical strips in the ∆ η -∆ η correlation.Our results suggest that the ridge particles in the central 0-12% Au+Au collisions areuncorrelated in ∆ η between themselves. The ridge appears to be uniform event-by-event.We also observe the small ∆ η peak, suggesting contributions from jet fragmentation in6 /2 η∆ + η∆ = ( Σ -1.5 -1 -0.5 0 0.5 1 1.5 > η ∆ d η ∆ N / d < d -0.100.10.20.30.40.5 On-Diagonal (a)
STAR Preliminary |<0.2 ∆ | )/2 η∆ - η∆ = ( ∆ -1.5 -1 -0.5 0 0.5 1 1.5 > η ∆ d η ∆ N / d < d Off-Diagonal (b)
STAR Preliminary |<0.2 Σ | ) η∆ + η∆ ( √ R = 0 0.5 1 1.5 2 2.5 > η ∆ d η ∆ N / d < d Radial Projection
STAR Preliminary (c) ) η∆ / η∆ ( -1 = tan ξ -1.5 -1 -0.5 0 0.5 1 1.5 > η ∆ d η ∆ N / d < d dAuAuAu 40-80%AuAu 0-12% Angular Projection (d)
STAR Preliminary
Figure 3: Projections of the background subtracted 3-particle ∆ η -∆ η correlations in d +Au, 40-80% Au+Au and 0-12% central Au+Au collisions. Panels (a)-(d) show theon-diagonal, off-diagonal, radial and angular projections, respectively. The shaded boxrepresent the systematic uncertainty due to background normalization and the solid linesrepresents the systematic uncertainty due to flow subtraction.vacuum. However, the two contributions, one from jet fragmentation in vacuum, theother from the ridge, do not seem to co-exist in the same event because we do not ob-serve the horizontal and vertical strips in ∆ η -∆ η correlation. Since no plausible physicsexcludes the co-existence of these two effects, our results indicate that the probabilityof such a co-existence is small. We have presented the first results on 3-particle ∆ η -∆ η correlation for d +Au, 40-80%Au+Au and 0-12% Au+Au collisions at √ s NN = 200 GeV. A correlation peak at (∆ η ,∆ η ) ∼ (0,0) characteristic of jet fragmentation in vacuum, is observed in all systems.This peak sits atop of a pedestal in central 0-12% Au+Au collisions. This pedestal,composed of particle pairs from the ridge, is approximately uniform or broadly fallingwithin the measured ∆ η acceptance. No other significant structures, except that fromjet fragmentation in vacuum, were observed in the projection. The ridge particles areuncorrelated among themselves in ∆ η . The ridge is uniform event-by-event.To understand the physics mechanism(s) generating the ridge, quantitative modelcalculations are clearly needed. These results in comparison to theoretical models andhigh statistic data sets will help furhter our understanding of the underlying physics of7he ridge. References [1] J. Adams et al. , (STAR collaboration)
Phys. Rev. Lett. , 152301 (2005).[2] J. Putschke, (STAR collaboration) J. Phys. G , S679 (2007).[3] N. Armesto et al. , Phys. Rev. Lett. , 242301 (2004).[4] S. A. Voloshin, Phys. Lett. B , 490 (2006).[5] E. Shuryak,
Phys. Rev. C , 047901 (2007).[6] C. B. Chiu and R. Hwa, Phys. Rev. C , 034903 (2005).[7] A. Majumder et al. , Phys. Rev. Lett. , 042301 (2007).[8] C. Y. Wong, arXive:0712.3282 (2007).[9] K. H. Ackermann et al. , (STAR collaboration) Nucl. Phys. A 661 , 681, (1999).[10] J. Adams et al. , (STAR collaboration)
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