march 7, 2007s. manly, university of rochester1 eccentric nuclear physics steven manly univ. of...

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)


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


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


Generating a deconfined state

Nuclear Matter(confined)

Hadronic Matter(confined)

Quark Gluon Plasmadeconfined !

Present understanding of Quantum Chromodynamics (QCD)• heating• compression deconfined matter !

Mike Lisa

Would be very cool to “reverse” the animation on the heating/compression slide, showing cooling/decompression.The point would be that even if we went into a QGP, the system would rapidly rehadronize (a process we don’t understand, but must, if we are to understand the strong force) into a hadronic system– hadrons in / hadrons out we will not “see” the QGP, but must infer it from hadronic patterns in the final state


The soup wars


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


Beamline

Terminology: angles


Beamline

Terminology: anglesPseudorapidity = = Lorentz invariant

angle with repect to the beampipe

0

+1

+2

+3

-1

-2

-3


Terminology: angles = azimuthal angle about the beampipe

Beamline


“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”


“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


(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


(reaction plane)

dN/d(R ) = N0 (1 + 2V1cos (R) + 2V2cos (2(R) + ... )

Elliptic flow

Flow quantifiedFlow quantified

View along beamline


(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.

S. Manly – U. Rochester March 7, 2007 18

Average Flow in PHOBOS

Ring counter

Octagon

Spectrometer arm

Paddle trigger

Vertex detector


Correlate reaction plane determined from azimuthal pattern of hits in one part of detector

Subevent A



with azimuthal pattern of hits in another part of the detector


Subevent B


Or with tracks identified in the spectrometer arms


Tracks


PHOBOS has made differential measurements of the average flow:

CentralitypT

PseudorapidityEnergySpecies

Flow in PHOBOS


Au+Au, A=197

Cu+Cu, A=63

In the most central events, 0 but v2 does not for Cu+Cu!

Flow in PHOBOS


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


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


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


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.


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


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


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


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


System size and eccentricity

Au-Au

Au-Au

Cu-Cu

Cu-Cu

PHOBOS-Glauber MC preliminary




Mean eccentricity shown in blackS. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031


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


Statistical errors onlyStandard Eccentricity


Au+Au200 GeV

Cu+Cu200 GeV


200 GeV

PRL: nucl-ex/0610037

Au+Au 200 GeV

Cu+Cu200 GeV

PRC C72, 051901R (2005)


Flow is huge in the smaller system! Particularly when the impact parameter goes to zero …

What’s the air fare to Stockholm these days??


Participant Eccentricity


Au+Au 200 GeVCu+Cu

200 GeV



Cu+Cu200 GeV

Au+Au 200 GeV



STAR, NA49 and E877 data taken from STAR Collaboration, Phys.Rev. C66 (2002) 034904 with no adjustments


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


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



Npart=80Npart=82


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?


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?


Elliptic flow develops event-by-event with respect to the participant ellipse


Expected fluctuations from the part model

Elliptic flow develops event-by-event with respect to the participant ellipse


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.



Determine v2obs



Construct kernel



Determine dynamical fluctuations


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>)


Elliptic flow fluctuations: <v2> and σv2

Au+Au 200 GeV

⟨v2 ⟩


|η|<1 PHOBOS preliminary (90% C.L.)• <v2>

Au+Au 200 GeV

v 2


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



PHOBOS preliminary (90% C.L.)• σv2/<v2>

|η|<1 Au+Au 200 GeV

2

v

v2

Elliptic flow fluctuations: σv2/ <v2>









2

v

v2

MC with nofluctuations





2

v

v2

MC with nofluctuations

Participanteccentricitymodel prediction

part

part



Things to consider and naïve questionsHow seriously should we take this Glauber-

driven participant eccentricity model?


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





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.





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?


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.


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?


Of course, the international fashion industry is always way ahead of the rest of us.

Where there are strings, there are clothes …

march 7, 2007s. manly, university of rochester1 eccentric nuclear physics steven manly univ. of...

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animation slide

slide participants

beampipe beamline slide

vacuum cfl slide