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March 7, 2007S. Manly, University of Rochester 1
Eccentric nuclear physicsEccentric nuclear physics
Steven ManlyUniv. of Rochester
University of RochesterMarch 7, 2007
[email protected]://hertz.pas.rochester.edu/smanly/
Full list of former/present UR PHOBOS Collaborators:
Frank Wolfs, Inkyu Park, Wojtek Skulski, Robert Pak, Josh
Hamblen, Pete Walters, Erik Johnson, Nazim Kahn, Adam
Harrington, Ian Spitzer, Clifford Cheung, Jennifer Ellsworth,
Alysse DeFranco, Garrett Mason, Yanting Wang
Other PHOBOS groups at BNL, Maryland, INP Krakow, U. Ill.
Chicago and MIT
Today’s results: among others … SM, Pete Walters (UR), Mark Baker (BNL), Burak Alver (MIT) and Constantin Loizides (MIT), Richard Bindel (Maryland), Barbara Wosiek (INP, Krakow), Peter Steinberg (BNL), Gunther Roland (MIT)
March 7, 2007S. Manly, University of Rochester 2
ec·cen·tric·i·ty ( k s n-tr s -t ) n. pl. ec·cen·tric·i·ties
The quality of being eccentric. Deviation from the normal, expected, or established.
An example or instance of eccentric behavior. Physics. The distance between the center of an eccentric and its axis. Mathematics. The ratio of the distance of any point on a conic section from a focus to its
distance from the corresponding directrix. This ratio is constant for any particular conic section.
From American Heritage Dictionary
Eccentric nuclear physicsEccentric nuclear physics
March 7, 2007S. Manly, University of Rochester 3
Strong color fieldEnergy grows with separation !!!E=mc2 !“white” proton
quark
quark-antiquark paircreated from vacuum
“white” proton(confined quarks)
“white” 0
(confined quarks)
Quantum Chromodynamics Quantum Chromodynamics QCDQCD
distance
energy density, temperature
rel
ativ
e st
ren
gth
asymptotic freedomSimilar to QED … Similar to QED … except the gauge field except the gauge field
carries the chargecarries the charge
Thanks to Mike Lisa (OSU) for parts of this animation
March 7, 2007S. Manly, University of Rochester 4
Generating a deconfined state
Nuclear Matter(confined)
Hadronic Matter(confined)
Quark Gluon Plasmadeconfined !
Present understanding of Quantum Chromodynamics (QCD)• heating• compression deconfined matter !
March 7, 2007S. Manly, University of Rochester 5
March 7, 2007S. Manly, University of Rochester 6
The soup wars
March 7, 2007S. Manly, University of Rochester 7
The phase diagram of QCDT
em
per
atu
re
baryon density
Neutron stars
Early universe
nucleinucleon gas
hadron gascolour
superconductor
quark-gluon plasmaTc
0
critical point ?
vacuum
CFL
March 7, 2007S. Manly, University of Rochester 8
Beamline
Terminology: angles
March 7, 2007S. Manly, University of Rochester 9
Beamline
Terminology: anglesPseudorapidity = = Lorentz invariant
angle with repect to the beampipe
0
+1
+2
+3
-1
-2
-3
March 7, 2007S. Manly, University of Rochester 10
Terminology: angles = azimuthal angle about the beampipe
Beamline
March 7, 2007S. Manly, University of Rochester 11
“Spectators”
Zero-degreeCalorimeter
“Spectators”
Paddle Counter
peripheral collisions central collisions
Nch
Npart
6%
Terminology: centrality
Thanks to P. Steinberg for parts of this slide
“Participants”
March 7, 2007S. Manly, University of Rochester 12
“Flow” = patterns in the energy, momentum, or particle density distributions that we use to ferret out clues as to the nature of the collision/matter
To what extent is the initial geometric
asymmetry mapped into the final state?
View along beamline
(Initial geometry)(particle density)(time)(physics of interaction)
might reach hydro limit where given geometric asymmetry is converted into final state asymmetry as efficiently as possible
March 7, 2007S. Manly, University of Rochester 13
(reaction plane)
Flow quantifiedFlow quantified
dN/d(R ) = N0 (1 + 2V1cos (R) + 2V2cos (2(R) + ... )
View along beamline
Fourier decomposition of the azimuthal multiplicity distribution
Experimentally this is the azimuthal direction with the highest particle density, must
correct for imperfect resolution
March 7, 2007S. Manly, University of Rochester 14
(reaction plane)
dN/d(R ) = N0 (1 + 2V1cos (R) + 2V2cos (2(R) + ... )
Elliptic flow
Flow quantifiedFlow quantified
View along beamline
March 7, 2007S. Manly, University of Rochester 15
March 7, 2007S. Manly, University of Rochester 16
(PHOBOS : Normalized Paddle Signal)
Hydrodynamic limit
STAR: PRL86 (2001) 402
PHOBOS preliminary
Hydrodynamic limit
STAR: PRL86 (2001) 402
PHOBOS preliminary
Thanks to M. Kaneta
PRL 91 (2003) 182301
Non-viscous hydrodynamic models with QGP are successful in describing flow data at
mid-rapidity for central events at low pt.
March 7, 2007S. Manly, University of Rochester 17
S. Manly – U. Rochester March 7, 2007 18
Average Flow in PHOBOS
Ring counter
Octagon
Spectrometer arm
Paddle trigger
Vertex detector
S. Manly – U. Rochester March 7, 2007 19
Correlate reaction plane determined from azimuthal pattern of hits in one part of detector
Subevent A
Average Flow in PHOBOS
S. Manly – U. Rochester March 7, 2007 20
with azimuthal pattern of hits in another part of the detector
Average Flow in PHOBOS
Subevent B
S. Manly – U. Rochester March 7, 2007 21
Or with tracks identified in the spectrometer arms
Average Flow in PHOBOS
Tracks
S. Manly – U. Rochester March 7, 2007 22
PHOBOS has made differential measurements of the average flow:
CentralitypT
PseudorapidityEnergySpecies
Flow in PHOBOS
S. Manly – U. Rochester March 7, 2007 23
Au+Au, A=197
Cu+Cu, A=63
In the most central events, 0 but v2 does not for Cu+Cu!
Flow in PHOBOS
S. Manly – U. Rochester March 7, 2007 24
Bridging experiment and geometry
Since experiments cannot measure the underlying geometry directly, models remain a necessary evil.
multiplicity, etc. models
•centrality
•impact parameter
•number of participants
•eccentricity
Models are also needed to connect fundamental geometric parameters with each other
Experiment Geometry
S. Manly – U. Rochester March 7, 2007 25
Modeling Geometry Glauber’s formalism for the scattering of a particle
off of a nuclear potential.
Historically, this model involved integrating the nuclear
overlap function of two nuclei with densities given by the Woods-Saxon distribution.
•Nucleons proceed in a straight line, undeflected by collisions
•Irrespective of previous interactions, nucleons interact according to the inelastic cross section measured in pp collisions.
Glauber Assumptions
S. Manly – U. Rochester March 7, 2007 26
A different application of the Glauber formalism is a Monte Carlo technique, in which the average over many simulated
events takes the place of an integration.
Au+Au Collisions with the same Npart (64 participants)
(cross section, shape, impact parameter, number of participating nucleons, etc.)
This has been a very successful tool at RHIC in relatingvarious geometric properties
S. Manly – U. Rochester March 7, 2007 27
The nuclei are offset by an impact parameter generatedrandomly from a linear distribution (vanishing small at b=0)
Nucleons are treated as hard spheres. Their 2D projectionsare given an area of NN (taken from pp inelastic collisions)
The nuclei are “thrown” (their x-y projections are overlapped), and opposing nucleons that touch are marked as participants.
S. Manly – U. Rochester March 7, 2007 28
22
22
xy
xy
Standard eccentricity (standard)
x
System size and eccentricity
Expect the geometry, i.e., the eccentricity, of the collision to be important in comparing flow in the Au-Au and Cu-Cu systems
Centrality measure Npart
Paddle signal, ZDC, etc.
MC simulations MC simulations
22y
22x
yyσ
xxσ
y
S. Manly – U. Rochester March 7, 2007 29
x2
Au-Au collision with Npart =64
y2
x2
y2
Au-Au collision with Npart =
78
x2
22
22
xy
xy
Eccentricity - a representation of geometrical overlap
S. Manly – U. Rochester March 7, 2007 30
Sample of Cu-Cu collisions
Cu-Cu collision with Npart = 33 Cu-Cu collision with Npart = 28
Yikes! This is a negative eccentricity!
y2
x2 y
2
x2
S. Manly – U. Rochester March 7, 2007 31
Cu-Cu collision with Npart = 33 Cu-Cu collision with Npart = 28
Principal axis transformation
Maximizes the eccentricity
Sample of Cu-Cu collisions
y2
x2
x2y
2
March 7, 2007S. Manly, University of Rochester 32
S. Manly – U. Rochester March 7, 2007 33
System size and eccentricity
Au-Au
Au-Au
Cu-Cu
Cu-Cu
PHOBOS-Glauber MC preliminary
PHOBOS-Glauber MC preliminary
PHOBOS-Glauber MC preliminary
PHOBOS-Glauber MC preliminary
Mean eccentricity shown in blackS. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031
S. Manly – U. Rochester March 7, 2007 34
Statistical errors onlyStandard Eccentricity
PHOBOS CollaborationPRL: nucl-ex/0610037
Au+Au200 GeV
Cu+Cu200 GeV
Statistical errors only
200 GeV
PRL: nucl-ex/0610037
Au+Au 200 GeV
Cu+Cu200 GeV
PRC C72, 051901R (2005)
Scaling out the geometry
S. Manly – U. Rochester March 7, 2007 35
Statistical errors onlyStandard Eccentricity
PHOBOS CollaborationPRL: nucl-ex/0610037
Au+Au200 GeV
Cu+Cu200 GeV
Statistical errors only
200 GeV
PRL: nucl-ex/0610037
Au+Au 200 GeV
Cu+Cu200 GeV
PRC C72, 051901R (2005)
Scaling out the geometry
Flow is huge in the smaller system! Particularly when the impact parameter goes to zero …
What’s the air fare to Stockholm these days??
S. Manly – U. Rochester March 7, 2007 36
Participant Eccentricity
PHOBOS CollaborationPRL: nucl-ex/0610037
Au+Au 200 GeVCu+Cu
200 GeV
Statistical errors only
PHOBOS CollaborationPRL: nucl-ex/0610037
Cu+Cu200 GeV
Au+Au 200 GeV
Scaling out the geometry
S. Manly – U. Rochester March 7, 2007 37
STAR, NA49 and E877 data taken from STAR Collaboration, Phys.Rev. C66 (2002) 034904 with no adjustments
Statistical errors only
Au+Au at 200, 130, 62.4 and 19.6 GeV :PHOBOS CollaborationPRL 97, 012301 (2006)
Cu+Cu at 200, 62.4 GeV:PHOBOS CollaborationPRL: nucl-ex/0610037
Cu+Cu at 22.4 GeV PHOBOS Preliminary
S. Manly – U. Rochester March 7, 2007 38
Au+Au vs. Cu+Cu at Au+Au vs. Cu+Cu at 200 GeV200 GeV Au+Au vs. Cu+Cu at Au+Au vs. Cu+Cu at 62.4 GeV62.4 GeV
Same area density (1/S)dN/dy Same area density (1/S)dN/dy and and Scaled by Scaled by partpart
Statistical errors only
Statistical errors only
Npart=80Npart=82
S. Manly – U. Rochester March 7, 2007 39
Data seems to indicate that it is the participant eccentricity rather than the standard eccentricity that characterizes the relevant
azimuthal asymmetry that drives elliptic flow
Hot zone formed by participating nucleons rather than some sea of low-x partons?
S. Manly – U. Rochester March 7, 2007 40
Fluctuating ellipse shape seems to reconcile data from different systems. Within a single system (i.e.,
Au+Au) does the elliptic flow signal fluctuate? If so, does the fluctuation signal agree with
expectations from the participant eccentricity fluctuations?
S. Manly – U. Rochester March 7, 2007 41
Elliptic flow develops event-by-event with respect to the participant ellipse
S. Manly – U. Rochester March 7, 2007 42
Expected fluctuations from the part model
Elliptic flow develops event-by-event with respect to the participant ellipse
S. Manly – U. Rochester March 7, 2007 43
A new event-by-event flow analysis from PHOBOS
(Cliff Note or Spark Note version)
Use full detector (need statistics for event-by-event sensitivity)
Full detector is complicated. So, use MC to create map for “input” v2 to “observed” v2.
Input different v2 distributions, convoluting them with the map and compare with data. Do max likelihood fit.
S. Manly – U. Rochester March 7, 2007 44
A new event-by-event flow analysis from PHOBOS
S. Manly – U. Rochester March 7, 2007 45
A new event-by-event flow analysis from PHOBOS
Determine v2obs
S. Manly – U. Rochester March 7, 2007 46
A new event-by-event flow analysis from PHOBOS
Determine v2obs
S. Manly – U. Rochester March 7, 2007 47
A new event-by-event flow analysis from PHOBOS
Construct kernel
S. Manly – U. Rochester March 7, 2007 48
A new event-by-event flow analysis from PHOBOS
Determine dynamical fluctuations
S. Manly – U. Rochester March 7, 2007 49
Event-by-event mean v2 vs published results
|η|<1<v2>
PRC 72, 051901 (2005)
Number of participants
Very good agreement of the event-by-event measured mean v2 with the hit- and tracked-based, event averaged, published results
<v2>(|η|<1) = 0.5 x (11/12 <v2triangular> + <v2
trapezodial>)
S. Manly – U. Rochester March 7, 2007 50
Elliptic flow fluctuations: <v2> and σv2
Au+Au 200 GeV
⟨v2 ⟩
Number of participants
|η|<1 PHOBOS preliminary (90% C.L.)• <v2>
Au+Au 200 GeV
v 2
Number of participants
PHOBOS preliminary (90% C.L.)• σv2
|η|<1
“Scaling” errors cancel in the ratio:relative fluctuations, σv2/<v2>
Mean elliptic flow Dynamical flow fluctuations
Systematic errors: Variation in η-shape Variation of f(v2) MC response Vertex binning Ф0 binning
S. Manly – U. Rochester March 7, 2007 51
Number of participants
PHOBOS preliminary (90% C.L.)• σv2/<v2>
|η|<1 Au+Au 200 GeV
2
v
v2
Elliptic flow fluctuations: σv2/ <v2>
S. Manly – U. Rochester March 7, 2007 52
Elliptic flow fluctuations: σv2/ <v2>
Number of participants
PHOBOS preliminary (90% C.L.)• σv2/<v2>
|η|<1 Au+Au 200 GeV
Number of participants
PHOBOS preliminary (90% C.L.)• σv2/<v2>
|η|<1 Au+Au 200 GeV
2
v
v2
MC with nofluctuations
S. Manly – U. Rochester March 7, 2007 53
Number of participants
PHOBOS preliminary (90% C.L.)• σv2/<v2>
|η|<1 Au+Au 200 GeV
2
v
v2
MC with nofluctuations
Participanteccentricitymodel prediction
part
part
Elliptic flow fluctuations: σv2/ <v2>
March 7, 2007S. Manly, University of Rochester 54
Things to consider and naïve questionsHow seriously should we take this Glauber-
driven participant eccentricity model?
Number of participants
2
v
v2
Allows us to make sense of both the system size scaling and fluctuations in the data
Really need Cu-Cu fluctuations measurement where the eccentricity fluctuations will be larger … let’s hope the measurements can be made
March 7, 2007S. Manly, University of Rochester 55
Things to consider and naïve questionsHow seriously should we take this Glauber-
driven participant eccentricity model?
Number of participants
2
v
v2
There is a wonderful and complementary STAR measurement (P. Sorensen – QM2006) which provides a consistency check. Data-driven and independent. Agrees well.
March 7, 2007S. Manly, University of Rochester 56
Things to consider and naïve questionsHow seriously should we take this Glauber-
driven participant eccentricity model?
Number of participants
2
v
v2
Participant eccentricity model calculation has proven to be robust during studies that followed its introduction at QM2005
It seems we should take it seriously
Should we be bothered that we don’t have much room for other sources of fluctuations?
March 7, 2007S. Manly, University of Rochester 57
Things to consider and naïve questionsIf we take the participant eccentricity model
seriously, what do we learn?
Whatever the form of the matter in the early stage of the collision, it seems the relevant interactions that drive the flow signal are initially localized transversely in a way similar to the participant nucleons.
Inconsistent with any picture where the initial state is driven by a large number of low-x partons that fill the nuclear transverse area.
March 7, 2007S. Manly, University of Rochester 58
Things to consider and naïve questions
It seems we are seeing transversely localized matter production with a granularity not so different from the interacting nucleons! Something
like color strings? This contradicts the naïve view many of us might have had (well, me anyway) of a densely packed initial transverse distribution.
If we take the participant eccentricity model seriously, what do we learn?
March 7, 2007S. Manly, University of Rochester 59
Of course, the international fashion industry is always way ahead of the rest of us.
Where there are strings, there are clothes …