Peter SteinbergBrookhaven National Laboratory

for the PHOBOS Collaboration

Workshop on the “Ridge”, BNL, September 22-24, 2008

A Large Range ofCorrelation Measurements

with .

BNL

Ridge

RHIC has always had a Ridge nearby

PHOBOS CollaborationBurak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts,

Richard Bindel, Wit Busza (Spokesperson), Vasundhara Chetluru, Edmundo García,

Tomasz Gburek, Joshua Hamblen, Conor Henderson, David Hofman, Richard Hollis,

Roman Hołyński, Burt Holzman, Aneta Iordanova, Chia Ming Kuo, Wei Li, Willis Lin,

Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen,

Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Christof Roland,

Gunther Roland, Joe Sagerer, Peter Steinberg, George Stephans, Andrei Sukhanov,

Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier,

Gábor Veres, Peter Walters, Edward Wenger, Frank Wolfs, Barbara Wosiek,

Krzysztof Woźniak, Bolek Wysłouch

ARGONNE NATIONAL LABORATORY, BROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW, MASSACHUSETTS INSTITUTE OF TECHNOLOGY

NATIONAL CENTRAL UNIVERSITY, TAIWAN, UNIVERSITY OF ILLINOIS AT CHICAGOUNIVERSITY OF MARYLAND, UNIVERSITY OF ROCHESTER

Main references:QM2008 talks by Li & WengerRHIC/AGS 2008 talk by Wenger

TriggeredCorrelations

Motivation: Nuclear Modifications

Away side strongly modifiedin central Au+Au & Cu+Cuat all energies (the “cone”)

Near side correlationshighly extended in ηin Au+Au collisions

(the “ridge”)

  Phys. Rev. Lett. 98, 232302 (2007)STARPHENIX

Explanations of the Ridge

• Coupling of induced radiation to longitudinal flow

• Recombination of shower + thermal partons

• Anisotropic plasma

• Turbulent color fields

• Bremsstrahlung + transverse flow + jet-quenching

• Splashback from away-side shock

• Momentum kick imparted on medium partons

• Glasma Flux Tubes

Various hypotheses proposed to explain ridge phenomenon

The PHOBOS contribution: large acceptance for associated yield

Armesto et al., PRL 93, 242301

Hwa, arXiv:nucl-th/0609017v1

Shuryak, arXiv:0706.3531v1

Romatschke, PRC 75, 014901

Majumder, Muller, Bass, arXiv:hep-ph/0611135v2

Pantuev, arXiv:0710.1882v1

Wong, arXiv:0707.2385v2

Dumitru, Gelis, McLerran, Venugopalan, arXiv:0804.3858; Gavin, McLerran, Moscelli, arXiv:0806.4718

Triggered Correlations in PHOBOSPHOBOS uses its two main subsystems

Spectrometer

Octagon

While spectrometer has small ϕ acceptance, it has alarge (Δη~1.5) forward acceptance (<η>~0.8)

PHOBOS Multiplicity Acceptance

Pros: nearly-full azimuthal acceptance for associated particlesnearly-full pseudorapidity acceptance (|η|<5.4)

Cons: no momentum measurement, no particle ID

ϕ

-5.4 5.43-3

PHOBOS Acceptance

η

ϕ

-5.4 5.431-1-3

STARPHOBOS Octagon

PHOBOS (Octagon & Rings)

Not yet using full potential of PHOBOS, but smaller systematics

Constructing Correlation Function

= - · a [ ]

= { - a [ ] }

V = <v2trig><v2assoc>

Acceptance corrected mixed-event pairs (per trigger)

Signal/BackgroundDetector acceptance cancels in the ratio

Modulation from elliptic flow

+

Calculating the Background

• B(Δη) is the per trigger mixed-event pair distribution corrected for the pair acceptance

• In other words, it is the corrected single-particle distribution (dN/dη) convoluted with ηtrig

PHOBOS: arXiv:0709.4008 [nucl-ex]

!-5 0 5

!/d

chdN

0

100

200

300

400 19.6 GeV

!/d

chdN

0

200

400

600130 GeV

!/d

chdN

0

200

400

600

800200 GeV 0- 6%

6-15%15-25%

25-35%35-45%45-55%

Calculating the s/b Ratio

15-20% central3mm < vz < 4mm

averaged over -15cm < vz < 10cm

Flow Correction• Parameterize published PHOBOS measurements as

v2(Npart,pT,η ) = A(Npart) B(pT) C(η )

• Correct v2(Npart,<pTtrig>,η tr ig) for occupancy and v2(Npart,<pTassoc>,ηassoc) for secondaries

V = <v2trig><v2assoc>

+

ZYAM Normalization

- a [ ]+

The scale factor, a , is calculated such that the yield after flow subtraction is zero at its minimum (ZYAM)

Ajitanand et al. PRC 72, 011902(R) (2005)

a

(a(Δη) = 1.000-1.002 in central events)

Systematic Errors

• The dominant systematic error in this analysis is the uncertainty on the magnitude of v2

trig v2assoc

• ~14% error on v2trig v2

assoc (η=0)

• ~20% error on v2trig v2

assoc (η=3)

• In the most central collision -- where flow is small compared to the correlation -- the error on v2trig v2assoc can exceed 50%.

PHOBOS preliminary10-30% central-0.5 < Δη < 0.0

PHOBOS preliminary10-30% central-0.5 < Δη < 0.0

PHOBOS preliminary0-6% central

-0.5 < Δη < 0.0

Δϕ

Δϕ

p+p reference data

PHOBOS does not have sufficient statistics for p+p

We use PYTHIA, but confirm it describes STAR data ontriggered correlations

PHOBOS Data compared with p+p

pTtrig >2.5 GeV/c pTassoc ⪎ 20 MeV/c

PYTHIA p+p 200 GeV PHOBOS Au+Au 200 GeV

Large Δη extent of correlations on both near and away side

“ridge” “Mach cone”

PHOBOS Preliminary

Slices of 2D Cond. Yield in Δη

Short range(|Δη|<1)

Long range(-4<Δη<-2)

Nuclear modifications @ near (|Δϕ|<1) & away, short & long range

Near side Yield vs. Δη

Integrating over near side, find that the correlated yield does notgo to zero at large Δη → ridge appears to be “long-range”

Yield vs. Centrality and Δη

Short-range |Δη| <1

Long-range –4 < Δη <–2

0-10% 40-50%

Away side decreases slightly, but ridge disappears

Associated yield vs. Centrality

PHOBOS preliminary

Short-range |Δη| <1

Long-range –4< Δη <–2

Based on PYTHIA subtraction (at short range only), observe that ridge & “Mach cone” yield is the same at short and long range

One Model Comparison

|Δϕ|<1C.Y. Wong, private communication

Momentum kick

Trigger

C.Y. Wong, PRC 76, 054908 (2007)

σy = rapidity width of partons

q

Wong’s momentum kick modelsuggests ridge comes from

collision of jet with bulk in early stage

Conclusions: Triggered Correlations• PHOBOS is able to contribute to this discussion by

measuring inclusive correlated yield at large Δη

• Results shown for 0-50% centrality in 200 GeV Au+Au collisions

• “Ridge” yield extends out to Δη=4, essentially constant after subtracting jet contribution

Disappears at Npart~80

• Long range of the ridge is a non-trivial feature, since it requires large momentum transfers, or very short times

InclusiveCorrelations

Inclusive Two-Particle Correlations• What about correlations not associated with a high pT

trigger particle?

• Jets are not the only source of correlated particle production

• “Cluster hadronization” has been discussed for many years now, given the observation of strong 2-particle correlations in p+p collisions at all energies

Cluster Hadronization Scenario

Hadronization proceeds via

“clusters”, which decay isotropicallyin their rest frame

Multiparticle production:many clusters, whichdecay into hadrons

(which themselves decay!)

Aside: Short vs. Long Range

particles are grouped into clusters that are randomly

distributed in rapidity. The decays of clusters are iso-

tropic which leads to an approximately Gaussian

shape with a dispersion of 0.77 in pseudorapidity. The

average cluster decay multiplicity, of about two

charged particles, is chosen to roughly fit the correla-

tion data, as we shall see below. These features of

the cluster algorithm are independent of energy.

2.3 Inclusive and semi-inclusive two-particle

pseudorapidity correlations

The inclusive correlation function C(t/~, t/z ) at fixed

?/2 = 0 for 200, 546 and 900 GeV, presented in Fig. 1 a,

shows a striking increase in height and width com-

pared to results obtained at lower energies (]/~

= 63 GeV) [-1, 8]. This is to be expected since DZ/<n)

and therefore the f2 moment have increased signifi-

cantly from lower energies [23]. The errors shown

are only statistical. They take into account the fact

that the single and two-particle rapidity distributions

are not statistically independent quantities.

Mixing events with different charged multiplici-

ties, which have different single-particle densities [-20]

can cause strong correlations. In analogy to the case

of two-component models [-10, 24] the inclusive corre-

lation function can be expressed in terms of the intrin-

sic correlations inside each component (events with

a given multiplicity n), Cs, and a cross term arising

193

from the mixing of components (events with different

multiplicities n), CL. The inclusive correlation func-

tion is related to the semi-inclusive function C, at

fixed charged multiplicity n as [10] :

C ( t / a , q 2 ) = C s ( q l , t / 2 ) - t- C L ( t / 1 , t / 2 ) , ( 2 . 7 )

where

Cs(th, r/z)= Z ~" C.(t/,, r/2) (2.8) o

/I

and

CL(rh, t / z )=E a;(pt(t/,)--pZ.(rh))(pZ(t/z)--pZ,(t/z) ). (2.9) n

Figure l b shows the contribution of CL(t/1, t/z) and

Fig. 1 c the contribution of Cs(t/1, t/z) t o the inclusive

correlation function.

The first term in (2.7) is the semi-inclusive correla-

tion function averaged over all multiplicities. As

shown in Fig. ! c it is sharply peaked with a full width

of about 2 units in pseudorapidity and is therefore

called "short-range" correlation. The second term in

(2.7) is present even in the absence of true dynamical

correlations. It broadens the correlation function and

is therefore somewhat misleadingly often called a

"long-range" correlation. The comparison of different

energies shown in Fig. i b illustrates how this term

is responsible for the apparent increase of the correla-

9 PSB 63 GeV 0 UA5 2 0 0 GeV [ ] UA5 5,46 GeV

I I I I

b) C~(O,~) r r i i

o) c(o,~)

0 , +

4 I r r r o

,r r r e~ r r r

+ o o ~ 0 0

2 - + O 0 oeeeeee O 9

r 9 9 o o

t o ~176

0, .~o_._

Z~ UA5 9 0 0 GeV

I I I " I I r

c) c,(o,~)

, q + + + d + - -

+ + + +

+ +

o * 0 % ~ ~

0 0 - - ,~ ,~ - -

r 0

* 0 ~'o l, r I, r ~' r o r r

o o o o

- -+o o / ' ' ' ' ' N o o + - -

9 o %e ~ o~ o 9 9 o

f o o 9 9 o o l 9 o o 9 9 o

9 o o j

9 o , ~ ~ "og - e q

I I I I I I I I I I

- 4 - 2 0 2 4 - 4 - 2 0 2

.

T*;i i ii ",1 - 4 - 2 0 2 4

Fig. l a -c . The inclusive charged correlation function C(th, q2) a plotted for fixed q l = 0 versus ~2 at 63 GeV [I] , 200, 546 and 900 GeV.

b shows the long-range and e the short-range contribution to C l q l , tl2) plotted in a

Long range: mixing events w/ different multiplicitiesShort range: average over two-particle correlation @ fixed n

particles are grouped into clusters that are randomly

distributed in rapidity. The decays of clusters are iso-

tropic which leads to an approximately Gaussian

shape with a dispersion of 0.77 in pseudorapidity. The

average cluster decay multiplicity, of about two

charged particles, is chosen to roughly fit the correla-

tion data, as we shall see below. These features of

the cluster algorithm are independent of energy.

2.3 Inclusive and semi-inclusive two-particle

pseudorapidity correlations

The inclusive correlation function C(t/~, t/z ) at fixed

?/2 = 0 for 200, 546 and 900 GeV, presented in Fig. 1 a,

shows a striking increase in height and width com-

pared to results obtained at lower energies (]/~

= 63 GeV) [-1, 8]. This is to be expected since DZ/<n)

and therefore the f2 moment have increased signifi-

cantly from lower energies [23]. The errors shown

are only statistical. They take into account the fact

that the single and two-particle rapidity distributions

are not statistically independent quantities.

Mixing events with different charged multiplici-

ties, which have different single-particle densities [-20]

can cause strong correlations. In analogy to the case

of two-component models [-10, 24] the inclusive corre-

lation function can be expressed in terms of the intrin-

sic correlations inside each component (events with

a given multiplicity n), Cs, and a cross term arising

193

from the mixing of components (events with different

multiplicities n), CL. The inclusive correlation func-

tion is related to the semi-inclusive function C, at

fixed charged multiplicity n as [10] :

C ( t / a , q 2 ) = C s ( q l , t / 2 ) - t- C L ( t / 1 , t / 2 ) , ( 2 . 7 )

where

Cs(th, r/z)= Z ~" C.(t/,, r/2) (2.8) o

/I

and

CL(rh, t / z )=E a;(pt(t/,)--pZ.(rh))(pZ(t/z)--pZ,(t/z) ). (2.9) n

Figure l b shows the contribution of CL(t/1, t/z) and

Fig. 1 c the contribution of Cs(t/1, t/z) t o the inclusive

correlation function.

The first term in (2.7) is the semi-inclusive correla-

tion function averaged over all multiplicities. As

shown in Fig. ! c it is sharply peaked with a full width

of about 2 units in pseudorapidity and is therefore

called "short-range" correlation. The second term in

(2.7) is present even in the absence of true dynamical

correlations. It broadens the correlation function and

is therefore somewhat misleadingly often called a

"long-range" correlation. The comparison of different

energies shown in Fig. i b illustrates how this term

is responsible for the apparent increase of the correla-

9 PSB 63 GeV 0 UA5 2 0 0 GeV [ ] UA5 5,46 GeV

I I I I

b) C~(O,~) r r i i

o) c(o,~)

0 , +

4 I r r r o

,r r r e~ r r r

+ o o ~ 0 0

2 - + O 0 oeeeeee O 9

r 9 9 o o

t o ~176

0, .~o_._

Z~ UA5 9 0 0 GeV

I I I " I I r

c) c,(o,~)

, q + + + d + - -

+ + + +

+ +

o * 0 % ~ ~

0 0 - - ,~ ,~ - -

r 0

* 0 ~'o l, r I, r ~' r o r r

o o o o

- -+o o / ' ' ' ' ' N o o + - -

9 o %e ~ o~ o 9 9 o

f o o 9 9 o o l 9 o o 9 9 o

9 o o j

9 o , ~~ " og - e q

I I I I I I I I I I

- 4 - 2 0 2 4 - 4 - 2 0 2

.

T*;i i ii ",1 - 4 - 2 0 2 4

Fig. l a -c . The inclusive charged correlation function C(th, q2) a plotted for fixed q l = 0 versus ~2 at 63 GeV [I] , 200, 546 and 900 GeV.

b shows the long-range and e the short-range contribution to C l q l , tl2) plotted in a

Long range correlations have been in the literature for years,but short range correlations ~constant w/ energy

Constructing Correlation Function

Foreground: Fn(Δη,Δφ) (correlated + uncorrelated pairs):

Background: Bn(Δη,Δφ) (uncorrelated pairs):

(n-1) weighting makesCF multiplicity independent

Peak at Δϕ,Δη=0 dominated by deltarays and conversions

(this bin always removed)

MC-based corrections forsecondaries & acceptance gaps

First tried on RHIC p+p data

Δη=η1-η2

Δφ=φ1-φ2

PHOBOS p+p@200GeV

Phys. Rev. C75(2007)054913

PHOBOS200 GeV p+p

2D correlation function Integrated over Δϕ(first F, then B → R)

Cluster Model Fit

€

R(Δη) =αΓ(Δη)B(Δη)

−1

€

Γ(Δη)∝exp − (Δη)2

4δ 2

€

Keff =α +1=< k(k −1) >

< k >+1=< k > +

σ k2

< k >

Effective cluster size Keff

related to correlation strength:convolution of mean & sigma

of multiplicity distribution per cluster

Effective cluster width δrelated to correlation width:

Gaussian shape is assumedδ=0.7 for isotropic decay

Short Range Correlations in p+p

Phys. Rev. C75(2007)054913

Keff-1

Keff = 2.44±0.08

δ = 0.66 ±0.03(90% C.L.)

We observe ~1.5 additional particles correlated with every charged particle over ±3 units in η

Energy Systematics in p+pe

ffK

1.5

2

2.5

3

PHOBOS p+p

ISR p+p

pSPS-UA5 p+PYTHIA p+p

HIJING p+p

(GeV)s

210

310

!

0.4

0.6

0.8

PHOBOS p+pISR p+p

pSPS-UA5 p+PYTHIA p+pHIJING p+p

Slow change in Keff

Slow change in δ

havmultEntries 9938847Mean 1.568RMS 0.8665

5 10 15 20 25 301

10

210

310

410

510

610

710

havmultEntries 9938847Mean 1.568RMS 0.8665

Multiplicity of daughters per particle

Therminator: Keff ~ 2

Data suggests much highercluster size than MCs,which are themselves

consistent with clusters as just resonance decays

(cf. Therminator)

A. Kisiel, private comm.

Phys. Rev. C75(2007)054913

2D Comparison with Cluster Model

Cluster model (an example given here, not fit to data)does not just give a 1D shape,

but helps understand features of 2D CF

Phys. Rev. C75(2007)054913

Can resonances make a near side peak? Nuclear Physics B86 (1975) 201-215 North-Holland Pubhshlng Company

ANGULAR CORRELATIONS BETWEEN THE

CHARGED PARTICLES PRODUCED IN pp COLLISIONS

AT ISR ENERGIES

K EGGERT, H FRENZEL and W THOME

111 Phvstkahsches lnstttut der Teehmschen Hochschule, Aachen, Germany

B B E T E V * , P D A R R I U L A T , P DITTMANN,

M H O L D E R , K T McDONALD, T MODIS and H G. PUGH **

CERN, Geneva, Swttzerland

K TITTEL

Instttut fur Hochenergtephystk, Hetclelberg, Germany

I. D E R A D O , V ECKARDT, H J G E B A U E R ,

R MEINKE, O R S A N D E R *** and P SEYBOTH

Max-Planck-lnstttut f~r Phystk und Astrophystk, Mumch, Germany

Received 11 November 1974

Abstract We present an analysis of rapidity and azimuthal correlations between the charged

products of pp colhslons at ISR energies The use of streamer chambers as detectors permlts

a study of the correlation mechanism at fixed multaphcltIes The analysis is restricted to the

central rapidity region to suppress dlffractwe production A strong short-range correlation

is observed, which can be described by independent emission of low-multlphcaty clusters,

suggestive of abundant resonance production

1 Introduction

The existence o f short-range rapidi ty correlat ion among the products o f pp colh-

slons at ISR energies is well estabhshed [1] However , many d i f ferent processes m a y

generate rapidi ty correlat ions, and care must be exercised m interpret ing the data

A wel l -known example is the coexis tence o f &ff rac t lon and p lomza t lon componen t s

In addi t ion to the genuine correlat ions characterist ic o f each mechamsm, the corre-

la t ion funct ion contains a cross te rm which mere ly reflects the twofold nature o f

* On leave from Institute of Nuclear Research, Sofia, Bulgaria

** On leave from Unaverslty of Maryland, College Park, Md , USA

*** Now at Lawrence Berkeley Laboratory, Berkeley, Cal, USA

K Eggert et al, Angular ¢orrelattons 211

/ / / - , w z ~* I IS ,~ /2

) . . . .v 0 ) . . . ~ ~0

0 1 2 3 4

A'q

20

14

//~12

.- / ,- w 0 /

0 1 2 3 4

"lib'f1 ~ 'E °

0 I 2 3 4 0 I 2 3 4

A~ A~

I 0

. . ~o ~ ,,® / / / - , , , 2 ~" 2 3 4 0 1 2 3 4

b a ~ K ~ r( ° 0 ° ~ ~I E

[lg 6 Calculated angular correlation functions, CII(zart, ziO), for p0 ~ tr+~ - , rt and co ~ rr+rr n 0

decays Invanant cross sections for meson production have the form exp (!y2) X exp (-BPT), ~here y and P]F are the rapidity and transverse momentum of the decaying meson B has the

value 6 GeV- m the case of the top curves. For the bottom cur~es, B was adlusted to yield an

invariant cross section of the form exp (-6PT) for the decay plons Density funcUons are nor-

mahzed in the square 1,11 < 25 as for the x/s = 53 GeV data Lines oI constant clI(a,7, Ag0 are

labelled in units ot 10 -3

~5 = 0 5 4 _ + 0 0 4 ( 0 4 9 _ + 0 0 2 ) for Aq~ < "~r,

~5 = 0 89 _+ 0 05 (0 86 _+ 0 04 ) for Zlq~>~Tr

It is ins t ruc t ive to c o m p a r e these da ta wath angular cor re la t ions genera ted b y m-

d e p e n d e n t emiss ion o f low-mass resonances For this we have calculated the ef fec t

o f three typical decays , p ~ ~r+Tr - , co -+ ~+Tr 7r0, and r/-+ rr+Tr-Tr 0 The results, dis-

p layed in fig 6, have the fol lowing p roper t i e s

(a) The p mesons induce rap id i ty cor re la t ions towards Aq~ = lr only , while r / a n d

co mesons do so over the full A4~ range A n y t w o - b o d y decay w i th a Q value large

m compar i son wi th the t ransverse m o m e n t u m of the pa ren t , would q u a h t a t w e l y

behave as p mesons

(b) The ranges o f the rap id i ty cor re la t ions vary h t t l e w i th A4~ They are o f the

o rde r o f 0 8, 0 6. and 0 5 for p, co, and r/, respectwely . The dafferences are due to

the d i f f e ren t average m v a n a n t masses o f the rr+n - pair m the three decays

(c) The s t r eng th o f the shor t - range pa r t o f the rap id i ty cor re la t ion vanes w i t h

A~ m a way t ha t depends on ly very l i t t le u p o n the rap id i ty d l s t n b u U o n b u t very

It is often said that resonances can’tgive a “near side” peak.

3-body decays (ω,η) do give such a peak,while 2-body decays (e.g. ρ) do not.

pT distribution of resonances tuned to describe final state pions dNπ/dpT~ pTexp(-6pT)

From p+p to Cu+Cu & Au+Au

PHOBOS has extended study of 2D CF to Cu+Cu and Au+Auas a function of centrality

Nontrivial due to larger occupancies, but effects under control(fits to dE/dx, not counting hits)

Phys. Rev. C75(2007)054913

Centrality Dependence in Cu & Au

The observed long structure in Δη is not a ridge.Rather, it is the v2 component, which scales as <2(N-1)v22>

(where Cu+Cu and Au+Au overlap in N, v2 is different!)

Cu+

Cu

Au+

Au

One-Dimensional CF in Cu & Au

€

R(Δη)

€

R(Δη)

€

Δη

€

Δη-5 -55

Two-particle Δη correlation function • Cu+Cu@200GeV• Au+Au@200GeV

€

Δη

€

Δη

€

Δη5 -5 5 -5 5 -5 5

40%-50% 30%-40% 20%-30% 10%-20% 0%-10%

PHOBOS preliminary

(scale errors are shown as grey bands)

Integrating over ΔΦ automatically integrates out v2

Immediately see that correlation strength decreases with centrality

PHOBOS Preliminary

One-Dimensional CF in Cu & Au

€

R(Δη)

€

R(Δη)

€

Δη

€

Δη-5 -55

Two-particle Δη correlation function • Cu+Cu@200GeV• Au+Au@200GeV

€

Δη

€

Δη

€

Δη5 -5 5 -5 5 -5 5

40%-50% 30%-40% 20%-30% 10%-20% 0%-10%

PHOBOS preliminary

(scale errors are shown as grey bands)

Cluster fits have been performed for all binsto quantify parameters vs. centrality

PHOBOS Preliminary

Centrality Dependence of Cluster Parameters

The first big surprises in Cu+Cu & Au+Au1. Peripheral events have Keff much higher than p+p (a jump?)2. Central events are only a bit lower than p+p3. The peripheral events are “elongated” in Δη (large δ)

“Geometric Scaling” in A+A

The next big surprise: Cu+Cu & Au+Au have the samecentrality dependence vs. fraction of total cross section

Kef

f

Comparison to AMPT

Comparisons to standard AMPT: width and Keff

Magnitude somewhat lower, but trend is the same

“Fraction of the total Cross Section”d!

/dN

ch (

arb

itra

ry u

nit

s)

Nch

!b (fm)"

!Npart"

!/!tot

(%)

|"| < 1

10–1

10–2

10–3

10–40

50

50 70 90 9580

100 150 200 250 300 350

400 800 1200 1600 2000

1

Central

Semicentral

Semiperipheral

Peripheral

024681012

0%–5%

5%–10%

10%–20%

20%–30%

30%–50%

SteinbergFig08.pdf 4/5/07 3:00:53 PM

Matching systemsat the same

fraction of cross sectionis like choosing same

b

2R

Npart

2A

So similar geometry(both transverse& longitudinal)

“Geometric Scaling”

-4 -2 0 2

b)

/2Apart N

Cu+Cu Au+Au

0-3% 0-10%

200 GeV 0.84 0.83 62.4 GeV 0.81 0.80 22.4 GeV 0.81 0.80

’!’ !-4 -2 0 2

"/2

part

N#’/!/d

ch d

N

0

1

2

3

4central

0-6%

a)

200 GeV Cu+Cu62.4 GeV Cu+Cu22.4 GeV Cu+Cu

200 GeV Au+Au62.4 GeV Au+Au22.4 GeVscaled Au+Au

’!

dN/dη shapes coincideat the same centrality(not the same Npart)

!-4 -2 0 2 4

!/d

ch

dN

0

50

100

c) 22.4 GeV

Cu+Cu: 3-6%

= 95"part

Cu-CuN #

22.4 GeV, scaled Au+Au: 35-40%

19.6 GeV, Au+Au: 35-40%

= 95 "part

Au-AuN #

!

/dc

hd

N

50

100

150

b) 62.4 GeV

Cu+Cu: 0-6%

= 99"part

Cu-CuN #

Au+Au: 35-40%

= 98"part

Au-AuN #

!/d

ch

dN

50

100

150

200

a) 200 GeV

Cu+Cu: 0-6%

= 103"part

Cu-CuN #

Au+Au: 35-40%

= 103"part

Au-AuN #

“Geometric Scaling”

Directed flow in STAR also shows both limiting

fragmentation and scales with fraction of cross section

PHOBOS QM2006 R. Nouicerbeam - y!

-4 -2 0

(%

)1

v

-8

-7

-6

-5

-4

-3

-2

-1

0

30% - 60%

Data AMPT

= 0CM

y

200 GeV Au+Au

200 GeV Cu+Cu

62.4 GeV Au+Au

62.4 GeV Cu+Cu

This does not work for v2

Various longitudinal observablesscale with “fraction” of σin:how do correlations fit in?

0-40% central

Near vs. Away Side (vs. AMPT)

Near-side

Away-side

( )Ratio

€

AuAuCuCu

(Clu

ste

r si

ze)

Can split up correlation function into “near” (Δϕ<π/2) and “away”Separate fits: different centrality dependence,

might breaks geometric scaling in data (but not in AMPT...)

Near-side

Away-side

( )Ratio

€

AuAuCuCu

(Clu

ste

r si

ze)

A Problem?

STAR

PHOBOS

PHOBOS vs. STAR

transverse density2 4 6

Min

ijet P

eak

Ampl

itude

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 STAR PreliminaryBinary scaling200 GeV62 GeV

transverse density2 4 6

Wid

th!

Min

ijet P

eak

0

0.5

1

1.5

2

2.5STAR Preliminary

transverse density2 4 6

Min

ijet P

eak

Volu

me

0

1

2

3

4

5

6

7 STAR Preliminary

-2 -10 1 2

02

4

ref

! / !

"

-0.10

0.10.20.30.4

62 GeV 46-55% Data

"#"

$

STAR Preliminary

-2 -10 1 2

02

4

ref

! / !

"

-0.10

0.10.20.30.4

Model Fit

"#"

$-2 -1

0 1 20

24

ref

! / !

"

-0.10

0.10.20.30.4

Residual

"#"

$-2 -1

0 1 20

24

ref

! / !

"

-0.10

0.10.20.30.4

Same-side Peak

"#"

$

Smooth decrease

Suddenincrease

The near-side seems to behave quite differently!

Daugherity, Ray

Definitions of Correlation Function

PHOBOS

!!!

!ref=

F "B!B

STAR?

Are the two experiments using different definitions forthe correlation function that give different content?

PHOBOS/UA5 cluster fit specifically for UA5 definition.PHOBOS data is consistent with previous results

Same true for STAR? I can buy that sqrt(B)~n...€

R(Δη) =αΓ(Δη)B(Δη)

−1

Acceptance Matters

!"-5

0

5

(deg)

#"

0

100

200

)#"

, !"

R( -2

0

2

Independent Cluster Model

!"-5 0 5

)!

"R

(

-2

0

2

4

6<1!-1<

<3!-3<

Full acceptance

-3 < η < 3

Same cluster model: different maximum η acceptance

Acceptance can change correlation strength & width:However, centrality dependence should not be affected unless

width is a strong function of centrality.

Conclusions• PHOBOS has measured inclusive 2-particle correlations

in p+p, Cu+Cu, and Au+Au

• Interpretation in terms of cluster modelDecrease of cluster size with centrality

Geometric scaling between Cu+Cu an Au+Au

Central A+A is most like p+p, not semi-peripheral A+A (which is both larger and longer than p+p!)

• How do we understand the difference in centrality dependence between STAR & PHOBOS?

Definition of CF? Acceptance?

STAR could integrate over full acceptance and do centrality dependence!

Methodology

Two particle correlationfunction (UA5 definition)

This definition is often used in the literature.Ratio of F and B cancels detector/acceptance systematics