Long-range collectivity in small collision-systems with two- and four-particle correlations @ STAR
NNuclear Physics A 00 (2020) 1–4
NuclearPhysics A / locate / procedia XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions(Quark Matter 2019)
Long-range collectivity in small collision-systems withtwo- and four-particle correlations @ STAR
Roy A. Lacey for the STAR Collaboration
Depts. of Chemistry & Physics, Stony Brook University, Stony Brook, NY, USA
Abstract
New STAR di ff erential and integral v , measurements that explicitly account for non-flow contributions, are reportedfor p / d / He + Au, collisions at √ s NN =
200 GeV. The measurements, which leverage the two-particle correlators for p / d / He + Au and minimum-bias p + p collisions in tandem with three well established methods of non-flow subtraction,are observed to be method-independent. For comparable multiplicities, they further indicate system-independent v { } and v { } values that are consistent with the critical role of both size (N ch ) and the subnucleonic-fluctuations-driveneccentricities ε , , but are inconsistent with the notion of shape engineering in p / d / He + Au collisions. The scalingfunction derived from the measurements, confirm the important role of final-state e ff ects across a broad spectrum ofcollision-system sizes and energies, and suggests an increase in η/ s ( T , µ B ) for small collision-systems. Keywords:
1. Introduction
Relativistic heavy-ion collisions can lead to high energy density strongly interacting matter with ananisotropic transverse energy density profile. This matter not only quenches jets, but also expands andhadronize to produce particles with an azimuthal anisotropy that reflects the viscous hydrodynamic re-sponse to the initial energy density profile [1]. The shape of this profile, ρ e ( r , ϕ ), can be characterizedby the complex eccentricity vectors [2, 3]: E n ≡ ε n e in Φ n ≡ − (cid:82) d r ⊥ r m e in ϕ ρ e ( r , ϕ ) / (cid:82) d r ⊥ r m ρ e ( r , ϕ ) , where ε n = (cid:68) |E n | (cid:69) / and Φ n denote the magnitude and azimuthal direction of the n th -order eccentricity vectorwhich fluctuates from event to event [2]. The eccentricity fluctuations are driven by both nucleonic andsubnucleonic fluctuations and can be estimated via a quark Glauber model. The quenched jets and theanisotropic flow which derives from the pressure gradients induced by ε n , result in an azimuthal anisotropyof the measured single-particle distribution, quantified by the complex anisotropy vectors [3]: V n ≡ v n e in Ψ n , ≡ { e in φ } , v n = (cid:68) | V n | (cid:69) / , where φ denotes the azimuthal angle around the beam direction, of a particle emit-ted in the collision, { . . . } denotes the average over all particles emitted in the event, and v n and Ψ n denotethe magnitude and azimuthal direction of the n th -order anisotropy vector which also fluctuates from event to a r X i v : . [ nu c l - e x ] M a y Roy A. Lacey for the STAR Collaboration / Nuclear Physics A 00 (2020) 1–4 event. Model comparisons to v n measurements continue to be an important avenue to estimate the transportcoe ffi cients for the partonic matter produced in large to moderate-sized collision systems [1, 3, 4].For the small collision-systems produced in p / d / He + Au and p + Pb collisions, collective flow might notdevelop due to the presence of large gradients that could excite non-hydrodynamic modes or render invalid,the hydrodynamic gradient expansion [5, 6] required to accurately characterize the viscous hydrodynamicresponse. Indeed, a most vexing question that pervades our field is whether an alternative initial-state-drivenmechanism [7] prevails over hydrodynamic expansion for these collision-systems. However, numericalsimulations in strongly interacting theories suggest that hydrodynamics remains applicable even when thesystem size (R) is of O (1 / T) – the inverse temperature [8]. Here, subnucleonic fluctuations become crucial.The current measurements for p / d / He + Au collisions, which supplement earlier measurements at bothRHIC [9] and the LHC [10] aim to address the respective influence of collision-system size, ε n and itsattendant subnucleonic fluctuations and viscous attenuation on the measured non-flow-mitigated v n .
2. Two particle correlators and v n extraction The measurements were obtained with the STAR detector, via the two-particle correlation method. Theper-trigger yields Y ( ∆ φ ) = / N Trig ∗ dN / d ∆ φ for 0 − p + Au, 0 − d + Au and 0 − He + Aucollisions are shown as a function of ∆ φ in Figs. 1 (a)-(c); for these correlators, the trigger (Trig − ) andthe associated (Assoc − ) particles are measured in the ranges 0 . < p T < . / c and | η | < .
9. Therequirement | ∆ η | > . − particles was also imposed to suppress possiblenon-flow contributions from the near-side jet. Figures 1 (a)-(c) indicate a near-side “ridge” suggestive of aninfluence from flow-like contributions to the measured correlators for p / d / He + Au collisions. The absenceof this ridge for minimum-bias (MB) p + p collisions (c.f Fig. 1), further suggests that the p + p correlator canbe leveraged to obtain quantitative estimates of the non-flow contributions to the p / d / He + Au correlators. - fD fD x d N / d t r i g / N He+Au a)0-10% - fD fD x d N / d t r i g / N b)0-10% d+Au STAR Preliminary - fD fD x d N / d t r i g / N c)0-2% p+Au |>1.0 hD | <2.0 GeV/c trig,assoT trig,asso h | |<0.9 h TPC Centrality:| = 200 GeV NN S He+Au p/d/Template Fit+G pp FY (0) pp +FY ridge Y Fig. 1. Illustration of the template fitting procedure which employs the MB p + p correlator to estimate the non-flow contributions andto extract the v and v Fourier coe ffi cients. The p T and ∆ η selections for the correlation functions are as indicated. Three separate methods were utilized to estimate and subtract the non-flow contributions to the measureddi ff erential correlation functions Y ( ∆ φ, p T , cent) used to extract v , ( p T ) and v , (N chg ). One is based on thetemplate-fit method [11]. The other two are based on Fourier expansion fits to the measured correlators[12]. The template fitting procedure [11] is illustrated in Fig. 1. It assumes that the central p / d / He + Au Y ( ∆ φ ) distributions are a superposition of a scaled MB Y ( ∆ φ ) distribution for p + p collisions and a constantmodulated by the ridge (cid:80) n = c subn cos( n ∆ φ ) as: Y ( ∆ φ ) templ = FY ( ∆ φ ) pp + Y ( ∆ φ ) ridge , where Y ( ∆ φ ) ridge = G (cid:16) + (cid:80) n = c sub , sysn cos ( n ∆ φ ) (cid:17) , with free parameters F and c subn . The coe ffi cient G , which representsthe magnitude of the combinatoric component of Y ( ∆ φ ) ridge , is fixed by requiring that (cid:82) π d ∆ φ Y templ = (cid:82) π d ∆ φ Y HM . Fig. 1 shows that the template fit accounts for the data quite well.Methods two and three rely on Fourier fits to the measured two particle correlators; Y ( ∆ φ ) = c (1 + (cid:80) n = c n cos( n ∆ φ )) . Method two assumes that the non-flow contributions to p / d / He + Au is a superpositionof several proton-proton collisions. This leads to non-flow contributions that are equal to c pp , but dilutedby the pair-yield coe ffi cient ( c ) di ff erence between p + p and p / d / He + Au. The subtracted coe ffi cients c subn oy A. Lacey for the STAR Collaboration / Nuclear Physics A 00 (2020) 1–4 v He+Au a) 0-10% = 200 GeV NN S |<0.9 h TPC Cent.:| w/0 Sub. Sub. by c Sub. by cTemp. Fit b) 0-10% d+Au
STAR preliminary c) 0-2% p+Au (GeV/c) T p v He+Au d) 0-10% (GeV/c) T p e) 0-10% d+Au (GeV/c) T p f) 0-2% p+Au Nch v {2} v {2} v He+Au 200 GeV {4} v d+Au 200 GeV{4} v STAR preliminary
Fig. 2. Comparison of the v , ( p T ) values for p / d / He + Au collisions, before and after non-flow subtraction, for all three methods (leftpanel). The right panel compares representative p T -integrated results for v { } and v { } for 0-10% d / He + Au collisions. v He+Au a) STAR: sub. by c
STAR 0-10%PHENIX 0-5% b) d+Au
STAR 0-10%PHENIX 0-5% c) p+Au
STAR 0-2%PHENIX 0-5% T p0.51.01.5 / F i t v He+Au d) STAR preliminary T p e) d+Au T p f) p+Au v He+Au a) STAR 0-10%PHENIX 0-5% b) d+Au
STAR 0-10%PHENIX 0-5% c) p+Au
STAR 0-2%PHENIX 0-5% T p0.51.01.5 / F i t v He+Au d) STAR: sub. by cSTAR preliminary T p e) d+Au T p f) p+Au Fig. 3. Comparison of the v ( p T ) (left panel) and v ( p T ) (right panel) measurements obtained by STAR and PHENIX. The solid linesin the top panels represent a fit to the STAR data. The bottom panels show the ratio of the respective data to this fit. for p / d / He + Au are then obtained as: c subn = c n − c ppn × c pp c , where c n = v Trig n × v Assoc n – the product of theflow coe ffi cients v n for trigger- and associated-particles. Then v Trig n = c n / v Assoc n and v sub , Trig n = c subn / v sub , Assoc n .Method three assumes that c is dominated by the away-side jet. This leads to the estimate that the ratioof the non-flow between p + p and p / d / He + Au is proportional to the ratio of the c values for p + p and p / d / He + Au respectively. Thus, c subn can be obtained as: c subn = c n − c ppn × c c pp , and used to extract v sub n asdescribed for method two. It is noteworthy that closure tests were performed with simulated events from theAMPT model to aid validation of the e ffi cacy of the respective methods for non-flow mitigation.
3. Results
The v ( p T ) and v ( p T ) values for p / d / He + Au before and after non-flow subtraction, are compared for allthree methods in the left panel of Fig. 2. They indicate non-flow contributions that are system-dependent, butthe non-flow mitigated v ( p T ) (top panels) and v ( p T ) (bottom panels) are method-independent within theindicated uncertainties. Here, it is noteworthy that the un-subtracted v ( p T ) is a lower limit since non-flowsubtraction leads to higher v ( p T ) values. The uncertainties for v ( p T ) and v ( p T ) reflect statistical, as wellas systematic uncertainties linked to (i) track related backgrounds, (ii) pileup e ff ects and (iii) the methods ofnon-flow subtraction. The right panel of Fig. 2 indicates magnitudes and trends for the p T -integrated v { } and v { } for d + Au and He + Au, that are consistent with an important influence from both subnucleoniceccentricity fluctuations and size-driven (N ch ) viscous attenuation. Note that the statistics available for the p + Au data precluded a statistically significant measurement of c { } and hence, v { } .The v ( p T ) and v ( p T ) measurements for p / d / He + Au are compared to published PHENIX measure-ments [9] in Fig. 3. The comparisons for v ( p T ) (left panel) show that, within the indicated uncertainties, Roy A. Lacey for the STAR Collaboration / Nuclear Physics A 00 (2020) 1–4 the v ( p T ) data from both experiments are in reasonable agreement, albeit with modest p T -dependent dif-ferences for p T > / c ( d + Au) and p T < / c ( p + Au). The v ( p T ) data for He + Au (right panel)are also in reasonably good agreement. However, the v ( p T ) measurements for p + Au and d + Au are abouta factor of 3-4 larger than those reported by PHENIX, and lie well outside the statistical and systematicuncertainties of the current measurements. The STAR results indicate that the fluctuations-driven v ( p T ) issystem-independent which contrasts with the earlier report of a system-dependent v ( p T ) [9]. Fig. 4. Anisotropy scaling function for severalcollision-systems and beam energies.
The non-flow mitigated v n measurements shown in Fig. 2,can be checked for the respective influence of collision-system size (N ch ), ε n and its attendant subnucleonic fluctua-tions and viscous attenuation, via an anisotropy scaling function[13]. The scaling function S FS (v n /ε n , p T , N ch , η/ s , ˆq): v n /ε n = exp ( − n [ n β (cid:48) + κ p T ] RT ) √ p T ), which incorporates the physics ofjet suppression: R AA ( p T , L ) (cid:39) exp[ α s C F √ π L (cid:113) (cid:95) q (cid:61) p T ] , R AA (90 , p T ) R AA (0 , p T ) = − v ( p T )1 + v ( p T ) and hydrodynamic viscous attenuation: v n /ε n ∝ exp ( − n [ n β + κ p T ] RT ) , RT ∝ (cid:104) N chg (cid:105) / , confirms these dependen-cies via a collapse of diverse measurements of v n on to a singlecurve, for fully constrained scaling coe ffi cients. In turn, the co-e ffi cients give insight on the magnitude of the associated trans-port coe ffi cients. The scaling function shown in Fig. 4, indicatesthat the measurements are consistent with the final-state (FS) ef-fects which account for the broad spectrum of collision-systemsizes and energies summarized in the figure. Note the jet quench-ing(viscous attenuation) branch for p T > p T <
4) GeV / c .The resulting scaling coe ffi cients not only suggest an increase in the magnitude of the specific viscosity (cid:104) η/ s ( T , µ B ) (cid:105) , from RHIC to LHC energies, but also an increase for relatively small collision-systems.
4. Summary
New STAR di ff erential and integral v n measurements that explicitly account for non-flow contribu-tions, are reported for p / d / He + Au collisions at √ s NN =
200 GeV. The measurements which are comparedto published PHENIX results, indicate system-independent values of v and v for comparable chargedhadron multiplicity, that are consistent with the critical influence of both size (N ch ) and the subnucleonic-fluctuations-driven eccentricities, ε , . However, they are inconsistent with the notion of shape engineeringin p / d / He + Au collisions. The scaling function derived from the measurements, confirm the important roleof final-state e ff ects across a broad spectrum of collision-system sizes and energies, and suggests an in-crease in η/ s ( T , µ B ) for small collision-systems. Future supplemental measurements at RHIC and the LHC,for systems such as O + O, could provide additional constraints and insights.