a large range of correlation measurements with .steinber/talks/steinberg_ridge2008_v2.pdfa large...
TRANSCRIPT
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