richard bindel, umddivision of nuclear physics, maui, 2005 system size and energy dependence of...
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Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
System Size and Energy Dependence of Elliptical Flow
Richard Bindel
University of Maryland
For the collaborationDivision of Nuclear Physics, Maui
September 19th, 2005
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2Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Collaboration (Aug 2005)
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3Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Motivation For Studying Flow
Reaction plane
x
z
y
M. Kaneta
• Flow probes the very early thermalization of the system
• Elliptic flow as a function of: • Energy
• Centrality
• Pseudorapidity
• Momentum
Can be used to constrain theory.
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4Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Two Flow Measurement Methods
Hit Based MethodTrack Based Method
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5Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Motivation for Comparing Species
Mid-central AuAucollision
Central CuCu collision
Two similarsystem sizes!
roughlysame numberof participants
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6Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Cu+CuPreliminary
3-6%, Npart = 100
Au+Au35-40%, Npart = 99
Some observablesscale with number
of participants
Similar dN/d
Motivation for Comparing Species
Mid-central AuAucollision
Central CuCu collision
Two similarsystem sizes!
200 GeV
roughlysame numberof participants
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7Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Cu+CuPreliminary
3-6%, Npart = 100
Au+Au35-40%, Npart = 99
200 GeV
Some observablesscale with number
of participants
Similar dN/d
Motivation for Comparing Species
Mid-central AuAucollision
Central CuCu collision
Two similarsystem sizes!
We expect flow to depend on geometry!
Two similarsystem sizes!
roughlysame numberof participants
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8Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Cu+CuPreliminary
3-6%, Npart = 100
Au+Au35-40%, Npart = 99
200 GeV
Some observablesscale with number
of participants
Similar dN/d
Motivation for Comparing Species
Mid-central AuAucollision
Central CuCu collision
Two similarsystem sizes!
We expect flow to depend on geometry!
Two similarsystem sizes!
roughlysame numberof participants
Elliptical Circular
Using two species lets us change the geometrywhile holding the number of participants constant
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9Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Eccentricity: A measure of “Geometry”
Mid-central AuAucollision
Central CuCu collision
Elliptical
Circular
We need a way to quantify the geometry of the participating nucleons
The shape is characterized
by the eccentricity ()
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10Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Eccentricity: A measure of “Geometry”
Nucleus A Nucleus B
Participant Nucleons
A model of aAuAu collision:
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11Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Eccentricity: A measure of “Geometry”
Nucleus A Nucleus B
Participant Nucleons
A model of aAuAu collision:
b
Using the impact parameter as the x-axis, we define the standard eccentricity using the widths of the distribution in the x and y directions
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12Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Eccentricity: A measure of “Geometry”
Nucleus A Nucleus B
Participant Nucleons
A model of aAuAu collision:
b
Using the impact parameter as the x-axis, we define the standard eccentricity using the widths of the distribution in the x and y directions
22
22
xy
xy
σσσσ
+
−=
σy2
σx2
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13Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Au+Au
19.6 GeV 62.4 GeV 130 GeV 200 GeV
Cu+Cu
0.05
0.05
Au+Au: PRL 94 122303 (2005)
preliminarypreliminary
PHOBOS
Sizable v2 for Cu+Cu
The Phobos Elliptic Flow Data Set
from0% to 40% centrality
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14Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
preliminary
PHOBOS 200 GeV h±
Statistical errors only
Cu+Cupreliminary
Au+Au
PHOBOS 200 GeV Hit Based Statistical errors only
The Data: Something’s Amiss…
Elliptic flow is high even for the most central bin in Cu+Cu
How does it relate to the eccentricity?
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15Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
preliminary
PHOBOS 200 GeV h±
Statistical errors only
Cu+Cupreliminary
Au+Au
PHOBOS 200 GeV Hit Based Statistical errors only
For CuCu, the eccentricity drops to zero by NPart of 100
The Data: Something’s Amiss…
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16Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
preliminary
PHOBOS 200 Gave h±
Statistical errors only
Cu+Cupreliminary
Au+Au
PHOBOS 200 GeV Statistical errors only
v2 near mid-rapidity
The Data: Something’s Amiss…
Cu+Cupreliminary
Au+Au
PHOBOS 200 GeV
Dividing by the eccentricity shows no connection between the two species.
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17Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
The Data: Something’s Amiss…
What went wrong?We reexamine our definition of eccentricity
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18Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Reexamining Eccentricity
Eccentricity is not directly measurable
We use a Glauber model to relate eccentricity to our NPart bins.
What goes into making this plot…?
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19Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
•Glauber collisions are modeled over a range of impact parameters and are sorted by the number of participants.
Reexamining Eccentricity
•An eccentricity distribution is built up for each NPart
•The black line shows the average eccentricity
AuAu
AuAu collisions with same NPart
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20Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Reexamining Eccentricity
Au-Au Cu-Cu
•When we examine the eccentricity distribution for CuCu, it looks much broader than AuAu
•Also, notice that there are many more events with negative eccentricity.
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21Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Meaning of Negative Eccentricity
b22
22
xy
xy
σσσσ
+
−=
σy2
σx2
Here we revisit the standard definition of eccentricity applied to aGluaber model.
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22Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Meaning of Negative Eccentricity
b22
22
xy
xy
σσσσ
+
−=
σy2
σx2
Here we revisit the standard definition of eccentricity applied to aGluaber model.
Negative eccentricity results when σx
2 > σy2, apparently due to fluctuations
in the positions of the nucleons.
Because of its smaller size, CuCu is more susceptible to fluctuations
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23Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Redefining Eccentricity
Nucleus 1
Nucleus 2
Participant Region
x
yb
One reasonable method is to realign the coordinate systemto maximize the ellipsoidal shape (a principal axis transformation)
“Participant” eccentricityOpposed to “standard” eccentricity
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24Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Standard and Participant Eccentricity
Au-Au
Au-Au
Cu-Cu
Cu-Cu
Mean eccentricity shown in black
Sta
ndar
d E
c cen
tri c
i tyP
artic
ipan
t E
ccen
tric
ity
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25Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Fluctuations in eccentricity are important for the Cu-Cu system.
Must use care in doing Au-Au to Cu-Cu flow comparisons. Eccentricity scaling depends on definition of eccentricity.
Impact of Eccentricity Fluctuations
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26Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Elliptic Flow Puzzle Solved?Standard Eccentricity
Cu+Cupreliminary
Au+Au
PHOBOS 200 GeV
“Participant Eccentricity” allows v2 scaling from
Cu+Cu to Au+Au
Participant Eccentricity PHOBOS 200 GeV
Au+AuCu+Cupreliminary
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27Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Participant Eccentricity
Cu+Cu
Au+Au
Standard Eccentricity
Cu+Cu
Au+Au
<dN/dy> / <S> scaling:STAR, PRC 66 034904 (2002)Voloshin, Poskanzer, PLB 474 27 (2000)Heiselberg, Levy, PRC 59 2716, (1999)
<dN/dy> / <S> scaling
Overlap Area
Caveat: dNch/d corrected to dNch/dy
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28Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Conclusions
• Phobos has continued to expand its extensive flow data set using two techniques
• Studying CuCu compared to AuAu allows us to vary the geometry while holding Npart constant
• The expectation that elliptic flow scales with eccentricity continues to seem reasonable
• Careful consideration is needed when using eccentricity
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Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Back-up Slides
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30Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Limiting Fragmentation (Au+Au)19.6 GeV 62.4 GeV 130 GeV 200 GeV
PHOBOS preliminary
preliminary preliminary preliminary preliminary
“Extended Longitudinal Scaling” of all longitudinal distributions
- ybeam
preliminary
PHOBOSAu+Au0-6%
Au+Au0-40%
Au+Au0-40%
200GeV130GeV62.4 GeV (prel)19.6 GeV
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31Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Limiting Fragmentation (Cu+Cu)
preliminarypreliminary
preliminary preliminaryPHOBOS
62.4 GeV 200 GeV
‘Extended Longitudinal Scaling’ also seen in Cu+CuPersists from p+p to Au+Au over large range in ′
preliminary
preliminary
PHOBOS
- ybeam
Cu+Cu0-6%
200GeV
62.4GeV
Cu+Cu0-40%
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32Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
Cu-Cu more like Hydro than JAM hadron string cascade modelHere JAM uses a 1 fm/c formation time. Hydro (160) has kinetic freezeout temperature at 160 MeV
preliminary 200 GeV Cu-Cu
preliminary 200 GeV
15-25% Cu-Cu
Statistical errors only
Compared to JAM Model
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33Richard Bindel, UMDDivision of Nuclear Physics, Maui, 2005
PHOBOS preliminary Cu-Cu, h±
Hit based 62.4 GeV PHOBOS preliminary Cu-Cu, h±
Hit based 200 GeV
Track based 200 GeV
Two Flow Measurement Methods
Good agreementbetween methods
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